*Article* **New Command Mechanism of Flaps and Wings of a Light Sport Aircraft**

**Ion-Marius Ghi¸tescu <sup>1</sup> , Maria Luminita Scutaru 1,\*, Marilena Ghi¸tescu <sup>1</sup> , Paul Nicolae Borza <sup>2</sup> and Marin Marin <sup>3</sup>**


**Abstract:** Commercial aircraft have well-designed and optimized systems, the result of a huge experience in the field, due to the large fleet of aircraft in operation. For light, utility, or sports aircraft, with a multitude of shapes, tasks, and construction types, there are different solutions that seek to best meet the requirements of the designed aircraft. In this sense, for a sport plane, an increased maneuverability is desired, and the system that controls flaps and wing must be properly designed. A new flap mechanism command solution is proposed and justified in the paper, for use in sports and recreational aviation, in order to achieve angles of braking greater than 40◦ , take-off and landing in a shorter time and over a shorter distance, as well as the gliding of the aircraft in critical flight conditions or when fuel economy is needed. A finite element model is used to verify the optimized command system for the flap and wing and to check if the strength structure of the aircraft is properly designed. The main result consists of the new design command system for flaps and wings and in verifying, by calculation, the acceptability of the new mechanism proposed from the point of view of the strength of the materials.

**Keywords:** Light Sport Aircraft; conceptual aircraft design; wing; flap; aileron; weight estimation; symmetric profile

#### **1. Introduction**

Aircraft engineering represents an intensive process full of evaluation and decisionmaking [1]. Much as 80% of the life cycle costs in aeronautical engineering are determined in the conceptual design phase [2]. In this, the phase will define the aircraft characteristics, such as type of being propulsion used; the purpose of aircraft—Light Sport Aircraft; technology of aircraft—materials, engine; occupant comfort requirements—fuselage cavity, pressurization; ergonomics of both crew and passenger; aircraft's aerodynamics and auxiliary lifting surfaces; certification basic of aircraft—Light Sport Aircraft FAR 23 [3]; ways of manufacturing the aircraft; aircraft's maintainability in the future; cost estimation [4].

Flight mechanics is a field studied in numerous works, and the results obtained are already classic [5,6]. The preliminary design phase is carried out after all characteristics presented in the conceptual phase had been made, and a rough aircraft sketch had been made. This phase is critical where normally it is a go situation where the negative outcome will result in a further continuation of the project until the aircraft is being manufactured [7].

In discussing the structural layout of an aircraft and its strength, it is important that we know about the material that is being used so that we can know the material load limit. There are several factors that influence the selection of materials that are being used in building the structure of an aircraft, mainly material fatigue, toughness, stiffness,

**Citation:** Ghi¸tescu, I.-M.; Scutaru, M.L.; Ghi¸tescu, M.; Borza, P.N.; Marin, M. New Command Mechanism of Flaps and Wings of a Light Sport Aircraft. *Symmetry* **2021**, *13*, 221. https://doi.org/sym13020221

Academic Editors: Victor A. Eremeyev and Sergei D. Odintsov Received: 30 December 2020 Accepted: 26 January 2021 Published: 29 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

and resistance to corrosion, but the overall lightness of the material is commonly looked upon by the structure and material engineer [8–11]. The main groups of materials that are usually selected to be the part of aircraft are duralumin or aluminum.

All aircraft in the world, including Light Structure Aircraft (LSA), are strictly regulated and bounded by certification based on the system of aircraft certification it possesses for each country. Several variants of light aircraft are presented below. The light aircraft Extra 300 LT, at which the force load of the direction reaches 90 Kg [12], is a one- or two-seater acrobat aircraft produced by German Extra Flugzeugproduktions- und Vertriebs-GmbH. The technical characteristics of some known aircraft are shown in Table 1.



In the last column, the characteristics of the sport I.-M.G. light aircraft LSA studied in the paper are presented. It is known as the Zlin 142 light aircraft, in which the load with forces reaches 200–250 N [13]. Zlin Z 142 is a single-engine aircraft with two seats for tourism and produced by Czechoslovak manufacturer Moravan Otrokovice (now ZLIN Aircraft Otrokovice, Czech Republic). The Festival R40 is a single-engine aircraft with two seats for tourism produced by SC. Aerostar Bacau S.A. [14]. The F2 light aircraft is produced by Flight Design Hoerselberg [15]. On the light aircrafts Extra 300 LT, Zlin 142, Festival R40, and F2, the flaps poach up to a maximum of 45◦ . Before a design layout can be started in order to obtain a new type of light aircraft with greater angles of braking, a number of parameters must be chosen. There is a light aircraft wing with a rectangular form and asymmetric profile, mounted at the top, which has been modeled in 3D in Solid Works and analyzed with the finite element method (FEM) in Abaqus CAE. The wing is made of aluminum and steel. The wing is loaded with distributed pressures, and the stress and strain fields in the wing structure are studied [16].

A light aircraft wing has been modeled as CAD in Solid Works and imported into ANSYS Workbench [17]. The aircraft wings are attached to both sides of the fuselage to produce lift force [18]. A fuselage wing is used in the light acrobatic aircraft, which has been subjected to the extended finite element method (XFEM) for determining stress intensity factors (FIS) [19]. The presence of a crack through the attachment opening is not allowed, as its growth due to high dynamic loads is usually rapid and can lead to catastrophic consequences. In order to demonstrate how dangerous the appearance of the crack could be, as well as to estimate the residual strength and life of fatigue of the cracked component, the analyses are carried out using the maximum load that may occur during the flight. The expected number of cycles to complete the failure is decreased, confirming that the fastening ears must be designed using the safety approach [20]. A reconfigurable active vibration control (AVC) system is known [21,22].

The S-LSA aircraft, for which the design methodology, design requirements, weight sizing, performance sizing, weight and balance, aerodynamics, and stability and control are

established, is presented in [23]. This aircraft is a tandem aircraft with sufficient visibility for both occupants. There are studies on the material from which an airplane wing is made. Tests are performed on a wing made of three types of materials: aluminum alloy, conventional carbon fiber reinforced composite, and towed carbon fiber reinforced composite. Significant performance is found in terms of the wing made of the conventional aluminum composite [24].

A high wing of an ultra-light aircraft is known, which is followed by the structural design and analysis of the wing. Wing design involves its initial considerations, such as planning shape selection, aircraft location, and structural design involves design calculations for air profile selection, wing area, wing load characteristics, and wing weight. The design is done according to the values calculated using the ANSYS FLUENT software design [25].

There is a study of the design and development of a new light aircraft, which meets the standards of the European regulations on ultra-light aircraft and the US regulations for light sports aircraft. The aircraft is a two-seater model [26]. To this end, the development of the wings, propeller, and fuselage is performed with extra caution to get the best possible results.

In connection with an aerodynamic profile used for an ultralight aircraft sailing at low speed, the invention relates to an aerodynamic profile for an ultralight aircraft, which maintains the aerodynamic performance of a main aerial profile made of plastic. Air wing pressure is reduced by bending a curved surface from a leading edge to the bottom surface and improves manufacturing comfort and structural strength by increasing the thickness of a leading-edge [27].

The invention relates to the weight-shift-controlled airplane that is characterized by a novel design of airplanes with closed passenger compartment and that combines the advantages of conventional aerodynamically controlled airplanes with those of weightshift-controlled ultra-light airplanes. The inventive weight-shift-controlled airplane comprises a passenger compartment with a fitted propeller as the pressure drive and a chassis, an airfoil 1, and an adjustable support system between the passenger compartment. The airfoil 1 allows that the airfoil is tilted for controlling the airplane [28,29].

The utility model discloses and provides a flap control mechanism of a Light Sport Aircraft. The flap control mechanism is simple in structure, reduces resistance, and allows each flap to be independently controlled and completely sealed in a flap structure. The flap control mechanism of the Light Sport Aircraft comprises flaps and a flap driving mechanism, wherein the flap driving mechanism is arranged in the flaps and is used for enabling each flap to be independently operated and unfolded; the utility model is applied to the technical field of airplane structures [30]. All these results give an image of the effort made to obtain optimized solutions for the control mechanisms of a light aircraft.

The presented literature summarizes the main researches performed for the study of some types of related airplanes, with constructive solutions close to the structure studied in the paper. There are two aspects that are studied in the paper: first, the proposed solution for the control mechanism, and then a study of the strength of the aircraft structure to see if the proposed solution for the mechanism is compatible with the requirements appearing in the aircraft structure. The mechanism introduced in the control system must not cause stresses that exceed the strength of the material.

The paper is in line with this research trend, proposing a new system optimized for the control of flaps and wings of I.-M.G. Light Sport Aircraft.

The new Light Sport Aircraft has a maximum take-off weight of 900 Kg, and the cruising speed is 470 km per hour, and the maximum flight ceiling is 5000 m. In the design of the aircraft, it has been considered that the parts of the aircraft must be simple to manufacture and install and accessible to repair.

In determining the aerodynamic shape and design dimensions of the light aircraft, the optimal design of the aircraft is considered, easily taking into account the parameters influencing the aerodynamic shape of the fuselage and the wing, as well as the systems

and mechanisms of the flap and aileron that are mounted in these areas. The technical characteristics of a new proposed I.-M.G. light aircraft are shown in Table 1 (column 5). In the new I.-M.G. light aircraft, the constructive solution of the flaps control mechanism allows the flaps to be braced up to a maximum of 55◦ . The fuselage is to accommodate the engine, people, fuel, and baggage. The two seats are arranged in a cote-a-cote configuration.

The new model of light aircraft proposed has a certain aerodynamic shape, symmetry geometry, and good stability being made up of middle wings of rectangular shape and having in section a symmetrical profile, from the fuselage with a certain aerodynamic shape, propeller helmet, ailerons, flaps, cockpit, vertical tail, horizontal tail, rudder with profiled shapes. The choice of the optimal solution, from an engineering and maneuverability point of view but also of the simplicity of the solution, is made following the analysis of some functional models, varying the parameters of the proposed model until obtaining an advantageous solution from several points of view.

The purpose of this article is to create the virtual model of the I.-M.G. light aircraft, the flap, and the wing that will be built and analyzed, optimizing the shape of these using CAD-CAE systems with CATIA V5R21 software. The subject of the paper is the proposal of a new flap and wing control mechanism. It is obvious that this mechanism is incorporated in a complex mechanical structure, with multiple functions and requirements, to which it must respond accordingly. Therefore, in order to see if this new type of mechanism satisfies the needs, a calculation of the strength of the structure of the entire plane is made in order to determine the deformations, strains, and stresses that appear in the components of the structure. The new type of mechanism changes the stresses that can occur in the elements of the aircraft structure, and it must be verified if, in these conditions, safety is ensured from the point of view of strength. To achieve this, the FEM is applied.

#### **2. A New Model of I.-M.G. Light Sport Aircraft**

The light aircraft and its flap control mechanism improve the dynamic behavior of the aircraft easily through the aircraft's constructive shape and the vole control mechanism that allows braking angles greater than 40◦ required for take-offs and landings over a short distance and in a shorter and greater load time, as well as the operation of the aircraft in critical flight conditions or when fuel economy is required, the airplane being able to hover in these situations, under conditions of reduced manufacturing costs. The proposed Light Sport Aircraft designed has as its areas of use sports and recreational aviation with a maximum capacity of two seats and having a certain aerodynamic shape and has on its wings mounted steering voles without a run-away, in order to achieve angles of braking greater than 40◦ , take-off and landing in a shorter time and over a shorter distance, as well as the gliding of the aircraft in critical flight conditions or when fuel economy is needed.

The main components of this light aircraft variant are the propeller helmet, propeller, cockpit, plane fuselage, a left wing with symmetrical profile, a right wing with symmetrical profile, ailerons (one on each wing) with symmetrical profile, flaps (one on each wing) with symmetrical profile, the depth on the horizontal tail, the left horizontal tail, the right horizontal tail, the direction on the vertical tail, the vertical tail. The newly designed light aircraft, named I.-M.G., shown in Figure 1, has a maximum take-off weight of 900 Kg, and the cruising speed is 470 km per hour, and the maximum flight ceiling is 5.000 m.

In determining the aerodynamic shape and design dimensions of the light aircraft, the optimal design of the aircraft is considered, easily taking into account the parameters influencing the aerodynamic shape of the fuselage and the wing, as well as the systems and mechanisms of the flap and aileron that are mounted in these areas (Figure 1).

ceiling is 5.000 m.

ceiling is 5.000 m.

aileron.

craft.

designed light aircraft, named I.-M.G., shown in Figure 1, has a maximum take-off weight of 900 Kg, and the cruising speed is 470 km per hour, and the maximum flight

designed light aircraft, named I.-M.G., shown in Figure 1, has a maximum take-off weight of 900 Kg, and the cruising speed is 470 km per hour, and the maximum flight

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 5 of 16

**Figure 1.** A mew model of I.-M.G. Light Sport Aircraft with a symmetric profile of wing–flaps– **Figure 1.** A mew model of I.-M.G. Light Sport Aircraft with a symmetric profile of wing–flaps–aileron. influencing the aerodynamic shape of the fuselage and the wing, as well as the systems and mechanisms of the flap and aileron that are mounted in these areas (Figure 1).

In determining the aerodynamic shape and design dimensions of the light aircraft, Figure 2 shows a wing with a symmetric profile equipped with a flap and an aileron with a symmetrical profile each. They can be made of duralumin or aluminum. Figure 2 shows a wing with a symmetric profile equipped with a flap and an aileron with a symmetrical profile each. They can be made of duralumin or aluminum.

the optimal design of the aircraft is considered, easily taking into account the parameters

Figure 3 presents the structure of the wing with a symmetrical profile unequipped Figure 3 presents the structure of the wing with a symmetrical profile unequipped with flap and aileron. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 6 of 16

The control mechanism of the voles of a light aircraft, shown in Figure 4, transmits

tuators 4, to the complex connecting bodies 5, which transmit the rotational motion, on the one hand, to the non-snake-board curvature flaps 6, and, on the other hand, the kinematic connecting elements 9 transmit the movement between the complex connect-

**Figure 3.** Wing with symmetrical profile unequipped with flap and aileron. **Figure 4.** Kinematic structural scheme of the flaps command mechanism. **Figure 3.** Wing with symmetrical profile unequipped with flap and aileron.

ing bodies 5 and the oscillating arms 10.

The control mechanism of the voles of a light aircraft, shown in Figure 4, transmits the rotational motion from a valve lever 1 (1—leading element being the input into the mechanism), to a torsion tube 2, to the kinematic drive elements 3, to the kinematic actuators 4, to the complex connecting bodies 5, which transmit the rotational motion, on the one hand, to the non-snake-board curvature flaps 6, and, on the other hand, the kinematic connecting elements 9 transmit the movement between the complex connecting bodies 5 and the oscillating arms 10. The control mechanism of the voles of a light aircraft, shown in Figure 4, transmits the rotational motion from a valve lever 1 (1—leading element being the input into the mechanism), to a torsion tube 2, to the kinematic drive elements 3, to the kinematic actuators 4, to the complex connecting bodies 5, which transmit the rotational motion, on the one hand, to the non-snake-board curvature flaps 6, and, on the other hand, the kinematic connecting elements 9 transmit the movement between the complex connecting bodies 5 and the oscillating arms 10.

**Figure 3.** Wing with symmetrical profile unequipped with flap and aileron.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 6 of 16

**Figure 4.** Kinematic structural scheme of the flaps command mechanism. **Figure 4.** Kinematic structural scheme of the flaps command mechanism.

Elements 7 finally transmit the movement from the oscillating arms 10 to the 6th of the frictionless curvature for the escape board, thus transmitting the rotational movement, amplifying the force, and transmitting the mechanical power from lever 1 to the nonsnake-board curvature flaps 6 (final driven elements set in motion with elements 1–10), with the aim of achieving larger gears corresponding to a high-performance flight regime characteristic of these aircraft and allowing take-off and landing over a short distance and in a short time.

The kinematic connecting elements (9, 8) are arranged at an angle with values between (0◦ . . . 90◦ ) to the complex connecting bodies 5 and the oscillating arms 10, respectively, to the non-snake-board curvature flaps 6 and the oscillating arms 10. When operating the 1 control valve, the rotational movement is transmitted to a torsion tube 2, in solidarity with the kinematic drive elements 3 articulated at the base by the rotational couplings of A and A1 (which is the base, A and A1) and further to the kinematic actuators 4 by the rotation couplings of B and B1.

From the kinematic actuators 4, 16, the movement is transmitted to the kinematic actuator 5 through the rotational couplings in E and E1, the kinematic actuator 5 elements being connected to the bases by the rotational couplings in C and C1. These five bodies have three links (rotation couplings E, F, G, E1, F1, G1, respectively) and bases C and C1,

respectively. The rotational couplings in F and F1 provide the connection between bodies 5 and bodies 9, and the rotation couplings in G and G1 provide the connection with the output bodies 6 (the endless curvature of the escape board, the asymmetric profile flap). 5 and bodies 9, and the rotation couplings in G and G1 provide the connection with the output bodies 6 (the endless curvature of the escape board, the asymmetric profile flap). From bodies 5 via rotational couplings F and F1, the rotational movement is trans-

Elements 7 finally transmit the movement from the oscillating arms 10 to the 6th of the frictionless curvature for the escape board, thus transmitting the rotational movement, amplifying the force, and transmitting the mechanical power from lever 1 to the non-snake-board curvature flaps 6 (final driven elements set in motion with elements 1– 10), with the aim of achieving larger gears corresponding to a high-performance flight regime characteristic of these aircraft and allowing take-off and landing over a short

The kinematic connecting elements (9, 8) are arranged at an angle with values between (0°... 90°) to the complex connecting bodies 5 and the oscillating arms 10, respectively, to the non-snake-board curvature flaps 6 and the oscillating arms 10. When operating the 1 control valve, the rotational movement is transmitted to a torsion tube 2, in solidarity with the kinematic drive elements 3 articulated at the base by the rotational couplings of A and A1 (which is the base, A and A1) and further to the kinematic actua-

From the kinematic actuators 4, 16, the movement is transmitted to the kinematic actuator 5 through the rotational couplings in E and E1, the kinematic actuator 5 elements being connected to the bases by the rotational couplings in C and C1. These five bodies have three links (rotation couplings E, F, G, E1, F1, G1, respectively) and bases C and C1, respectively. The rotational couplings in F and F1 provide the connection between bodies

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 7 of 16

distance and in a short time.

tors 4 by the rotation couplings of B and B1.

From bodies 5 via rotational couplings F and F1, the rotational movement is transmitted to bodies 10 and 20 by means of the rotational couplings J and J1, and from the 10 in rotational bodies of H and H1, the movement is transmitted to bodies 8, and then through the rotational couplings I and I1 to the non-snake-board curvature flaps 6 (6—output body = final driven element). Bodies 10 have a base connection through the rotational couplings in D and D1. This flap control mechanism of the new I.-M.G. light aircraft allows the volts to be braced up to a maximum of 55◦ . mitted to bodies 10 and 20 by means of the rotational couplings J and J1, and from the 10 in rotational bodies of H and H1, the movement is transmitted to bodies 8, and then through the rotational couplings I and I1 to the non-snake-board curvature flaps 6 (6—output body = final driven element). Bodies 10 have a base connection through the rotational couplings in D and D1. This flap control mechanism of the new I.-M.G. light aircraft allows the volts to be braced up to a maximum of 55°. In Figures 5 and 6, the proposed optimized solution for the command system and

In Figures 5 and 6, the proposed optimized solution for the command system and the kinematical model of the mechanism are presented. the kinematical model of the mechanism are presented.

**Figure 5.** The proposed optimized solution. **Figure 5.** The proposed optimized solution.

**Figure 6.** Kinematical model of the mechanism. **Figure 6.** Kinematical model of the mechanism.

#### **3. Significant Loads on I.-M.G. Aircraft 3. Significant Loads on I.-M.G. Aircraft**

by the propeller.

The fundamental factors to be taken into account in the design of this type of aircraft, class LSA, are the strength, weight, and reliability of the aircraft material. The aircraft housing shall be of low weight, but the strength shall make the total mass of the empty aircraft as small as possible and be able to support an additional load, crew, and fuel to be operated for as long as possible. The materials to be used in the manufacture of the aircraft must be reliable so as to minimize the likelihood of material failure and sudden failure during operation. In this section, we have tried to get more ideas on the The fundamental factors to be taken into account in the design of this type of aircraft, class LSA, are the strength, weight, and reliability of the aircraft material. The aircraft housing shall be of low weight, but the strength shall make the total mass of the empty aircraft as small as possible and be able to support an additional load, crew, and fuel to be operated for as long as possible. The materials to be used in the manufacture of the aircraft must be reliable so as to minimize the likelihood of material failure and sudden failure during operation. In this section, we have tried to get more ideas on the strength of the aircraft structure, as it is a part of the field of the research study.

strength of the aircraft structure, as it is a part of the field of the research study. Before going deeper into understanding the loads and stresses acting on an aircraft that will lead to the idea of aircraft strength, we first must recognize the major forces on Before going deeper into understanding the loads and stresses acting on an aircraft that will lead to the idea of aircraft strength, we first must recognize the major forces on

aircraft. This is illustrated in Figure 7, where these major forces occur when the aircraft is

aircraft during a flight are thrust, drag force, weight, and lift [31–33]. This is illustrated in Figure 7 in horizontal rectilinear and uniform flight. Thrust is the forward force produced

> For constant speed & altitude

Force

L = W; T = D.

equilibrium:

The total weight consists of the weight of the empty aircraft plus the weight of the two crew members plus the weight of the fuel plus the weight of the aircraft installations

The method of finite elements is used as a need to study the state of deformations and stresses in the structure of the light aircraft named I.-M.G. The wing structure is an-

alyzed using the CATIA computer-aided engineering (CAE) FEA software [34].

**Weight, W** 

**Lift, L** 

**Thrust, T Drag, D** 

**CG** 

**Figure 7.** Major equivalent forces acting on the aircraft during straight and level flight.

**4. Optimization, Using Finite Element Model, of Wing and Flap** 

plus the weight of the crew baggage.

kg/m3.

aircraft. This is illustrated in Figure 7, where these major forces occur when the aircraft is in steady unaccelerated flight or called straight and level flight. The forces acting on the aircraft during a flight are thrust, drag force, weight, and lift [31–33]. This is illustrated in Figure 7 in horizontal rectilinear and uniform flight. Thrust is the forward force produced by the propeller. aircraft. This is illustrated in Figure 7, where these major forces occur when the aircraft is in steady unaccelerated flight or called straight and level flight. The forces acting on the aircraft during a flight are thrust, drag force, weight, and lift [31–33]. This is illustrated in Figure 7 in horizontal rectilinear and uniform flight. Thrust is the forward force produced by the propeller.

The fundamental factors to be taken into account in the design of this type of aircraft, class LSA, are the strength, weight, and reliability of the aircraft material. The aircraft housing shall be of low weight, but the strength shall make the total mass of the empty aircraft as small as possible and be able to support an additional load, crew, and fuel to be operated for as long as possible. The materials to be used in the manufacture of the aircraft must be reliable so as to minimize the likelihood of material failure and sudden failure during operation. In this section, we have tried to get more ideas on the

Before going deeper into understanding the loads and stresses acting on an aircraft that will lead to the idea of aircraft strength, we first must recognize the major forces on

strength of the aircraft structure, as it is a part of the field of the research study.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 8 of 16

**Figure 6.** Kinematical model of the mechanism.

**3. Significant Loads on I.-M.G. Aircraft** 

**Figure 7.** Major equivalent forces acting on the aircraft during straight and level flight. **Figure 7.** Major equivalent forces acting on the aircraft during straight and level flight.

The total weight consists of the weight of the empty aircraft plus the weight of the two crew members plus the weight of the fuel plus the weight of the aircraft installations plus the weight of the crew baggage. The total weight consists of the weight of the empty aircraft plus the weight of the two crew members plus the weight of the fuel plus the weight of the aircraft installations plus the weight of the crew baggage. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 9 of 16

#### **4. Optimization, Using Finite Element Model, of Wing and Flap 4. Optimization, Using Finite Element Model, of Wing and Flap**

The method of finite elements is used as a need to study the state of deformations and stresses in the structure of the light aircraft named I.-M.G. The wing structure is an-The method of finite elements is used as a need to study the state of deformations and stresses in the structure of the light aircraft named I.-M.G. The wing structure is analyzed using the CATIA computer-aided engineering (CAE) FEA software [34]. The properties of the material are diversified according to the type of element and the type of problem to analyze. The mechanical characteristics of the material/materials used are defined. For the analysis of elastic structures, restrictions are necessary on the

alyzed using the CATIA computer-aided engineering (CAE) FEA software [34]. The properties of the material are diversified according to the type of element and the type of problem to analyze. The mechanical characteristics of the material/materials used are defined. For the analysis of elastic structures, restrictions are necessary on the movements of translation and rotation with known values. To analyze the elastic mechanical structures, the loading of the model is carried out by inserting concentrated forces in knots and/or normal pressures in the centers of the faces of the finished elements or moments. Figure 8 shows the 3D model of the wing with a symmetrical profile realized from duralumin. The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software, from which the metallic material from duralumin is chosen, with the following characteristics: Young's modulus = 7.31 <sup>×</sup> <sup>10</sup><sup>10</sup> N/m<sup>2</sup> , Poisson ratio = 0.33, density = 2790 kg/m<sup>3</sup> . movements of translation and rotation with known values. To analyze the elastic mechanical structures, the loading of the model is carried out by inserting concentrated forces in knots and/or normal pressures in the centers of the faces of the finished elements or moments. Figure 8 shows the 3D model of the wing with a symmetrical profile realized from duralumin. The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software, from which the metallic material from duralumin is chosen, with the following characteristics: Young's modulus = 7.31x1010 N/m2, Poisson ratio = 0.33, density = 2790

**Figure 8.** Boundary conditions and load with the force of wing with symmetrical profile from duralumin. **Figure 8.** Boundary conditions and load with the force of wing with symmetrical profile from duralumin.

**Figure 9.** The displacements in the wing with symmetric duralumin profile.

being 9.72 mm.

degrees of possible freedom associated with the lateral surface of the wing (Figure 9) [22].

To generate the model, the finite element method is performed, which involves the

The loading of the model is a uniform pressure after the Y-axis on the face of the wing. The model solution is offered by soft. The displacement field of the wing with a symmetrical profile from duralumin is presented in Figure 9, the maxim displacement

The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software, from which the metallic material from aluminum is chosen, with the following characteristics:

Young's modulus = 7.0 × 1010 N/m2, Poisson ratio = 0.346, and density = 2710 kg/m3.

kg/m3.

ralumin.

To generate the model, the finite element method is performed, which involves the static analysis of the structure under conditions of imposed constraints and independent time loads. The link with the base imposed on the model is defined by canceling the 6 degrees of possible freedom associated with the lateral surface of the wing (Figure 9) [22]. To generate the model, the finite element method is performed, which involves the static analysis of the structure under conditions of imposed constraints and independent time loads. The link with the base imposed on the model is defined by canceling the 6 degrees of possible freedom associated with the lateral surface of the wing (Figure 9) [22].

**Figure 8.** Boundary conditions and load with the force of wing with symmetrical profile from du-

The properties of the material are diversified according to the type of element and the type of problem to analyze. The mechanical characteristics of the material/materials used are defined. For the analysis of elastic structures, restrictions are necessary on the movements of translation and rotation with known values. To analyze the elastic mechanical structures, the loading of the model is carried out by inserting concentrated forces in knots and/or normal pressures in the centers of the faces of the finished elements or moments. Figure 8 shows the 3D model of the wing with a symmetrical profile realized from duralumin. The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software, from which the metallic material from duralumin is chosen, with the following characteristics: Young's modulus = 7.31x1010 N/m2, Poisson ratio = 0.33, density = 2790

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 9 of 16

**Figure 9.** The displacements in the wing with symmetric duralumin profile. **Figure 9.** The displacements in the wing with symmetric duralumin profile. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 10 of 16

The loading of the model is a uniform pressure after the Y-axis on the face of the wing. The model solution is offered by soft. The displacement field of the wing with a symmetrical profile from duralumin is presented in Figure 9, the maxim displacement being 9.72 mm. The loading of the model is a uniform pressure after the Y-axis on the face of the wing. The model solution is offered by soft. The displacement field of the wing with a symmetrical profile from duralumin is presented in Figure 9, the maxim displacement being 9.72 mm. The finite element method is performed to generate the model, involving the static analysis of the structure under conditions of imposed constraints and independent time loads. The liaisons with the base imposed on the model are defined by canceling the 6

The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software, from which the metallic material from aluminum is chosen, with the following characteristics: Young's modulus = 7.0 × 1010 N/m2, Poisson ratio = 0.346, and density = 2710 kg/m3. The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software, from which the metallic material from aluminum is chosen, with the following characteristics: Young's modulus = 7.0 <sup>×</sup> <sup>10</sup><sup>10</sup> N/m<sup>2</sup> , Poisson ratio = 0.346, and density = 2710 kg/m<sup>3</sup> . degrees of possible freedom associated with the lateral surface of the wing (Figure 10). For the flap, the material characteristics of duralumin and aluminum are defined, and the structure is analyzed with finite elements to obtain the Von Misses field of deformations and stresses. The aim is to see the influence of the material on the defor-

The finite element method is performed to generate the model, involving the static analysis of the structure under conditions of imposed constraints and independent time loads. The liaisons with the base imposed on the model are defined by canceling the 6 degrees of possible freedom associated with the lateral surface of the wing (Figure 10). mations appearing in the structure of the flap. The mechanical characteristics of aluminum and duralumin are presented in Table 2. It can be observed that the elasticity module for duralumin is higher than the elasticity module for aluminum, and the Poisson's coefficient for duralumin is lower than the Poisson's coefficient for aluminum.

**Figure 10.** Boundary conditions and load with the force of wing with symmetrical profile from aluminum. **Figure 10.** Boundary conditions and load with the force of wing with symmetrical profile from aluminum.

**Table 2.** Mechanical characteristics of aluminum and duralumin. **Mechanical Characteristics Material Duralumin Aluminum**  Young's elasticity modulus, For the flap, the material characteristics of duralumin and aluminum are defined, and the structure is analyzed with finite elements to obtain the Von Misses field of deformations and stresses. The aim is to see the influence of the material on the deformations appearing in the structure of the flap. The mechanical characteristics of aluminum and

E (N/m2) 7.31 × 1010 7 × 1010

Figure 11 shows the symmetric profile, which can be made by aluminum and which has relief holes that also have a functional role, through which the rods of the control mechanisms and the 3D model of the flap with symmetric profile from duralumin are passed. The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software. Boundary conditions are presented in Figure 12. To generate the model, the finite element method is performed, which involves the static analysis of the structure under conditions of imposed con-

ν

Poisson coefficient

ρ

straints and independent time loads.

Density,

duralumin are presented in Table 2. It can be observed that the elasticity module for duralumin is higher than the elasticity module for aluminum, and the Poisson's coefficient for duralumin is lower than the Poisson's coefficient for aluminum.


**Table 2.** Mechanical characteristics of aluminum and duralumin.

Figure 11 shows the symmetric profile, which can be made by aluminum and which has relief holes that also have a functional role, through which the rods of the control mechanisms and the 3D model of the flap with symmetric profile from duralumin are passed. The introduction of the values of the material characteristics necessary for the analysis with finite elements is done using the material library of the CATIA software. Boundary conditions are presented in Figure 12. To generate the model, the finite element method is performed, which involves the static analysis of the structure under conditions of imposed constraints and independent time loads. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 11 of 16 *Symmetry* **2021**, *13*, x FOR PEER REVIEW 11 of 16

**Figure 11.** The displacements in the wing with the symmetric aluminum profile. **Figure 11.** The displacements in the wing with the symmetric aluminum profile. **Figure 11.** The displacements in the wing with the symmetric aluminum profile.

**Figure 12.** Boundary conditions and load with the force of flap with symmetric profile from aluminum. **Figure 12.** Boundary conditions and load with the force of flap with symmetric profile from aluminum. **Figure 12.** Boundary conditions and load with the force of flap with symmetric profile from aluminum.

The displacement field is calculated, the maxim displacement being 0.106 mm. The

The displacement field is calculated, the maxim displacement being 0.106 mm. The results of Equivalent Von Misses stress is visualized in Figure 13, the maxim value being

2.63 × 106 N/m2.

The displacement field is calculated, the maxim displacement being 0.106 mm. The results of Equivalent Von Misses stress is visualized in Figure 13, the maxim value being 2.63 <sup>×</sup> <sup>10</sup><sup>6</sup> N/m<sup>2</sup> . *Symmetry* **2021**, *13*, x FOR PEER REVIEW 12 of 16 *Symmetry* **2021**, *13*, x FOR PEER REVIEW 12 of 16

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 12 of 16

**Figure 13.** Von Misses stress in the flap with symmetric duralumin profile. **Figure 13.** Von Misses stress in the flap with symmetric duralumin profile. possible freedom associated with the lateral surface of the flap (Figure 14). The loading of

The link with the base imposed by the model is defined by canceling the 6 degrees of possible freedom associated with the lateral surface of the flap (Figure 14). The loading of the model is a uniform pressure, after Y-direction, on the face of a wing made from aluminum. The displacement field in the flap with the symmetric aluminum profile is presented The link with the base imposed by the model is defined by canceling the 6 degrees of possible freedom associated with the lateral surface of the flap (Figure 14). The loading of the model is a uniform pressure, after Y-direction, on the face of a wing made from aluminum. minum. The displacement field in the flap with the symmetric aluminum profile is presented in Figure 15. The maxim displacement is 0.011 mm to the extremity free of the flap from aluminum. **Figure 13.** Von Misses stress in the flap with symmetric duralumin profile. The link with the base imposed by the model is defined by canceling the 6 degrees of possible freedom associated with the lateral surface of the flap (Figure 14). The loading of the model is a uniform pressure, after Y-direction, on the face of a wing made from alu-

the model is a uniform pressure, after Y-direction, on the face of a wing made from alu-

**Figure 14.** Boundary conditions and load with the force of flap. **Figure 14.** Boundary conditions and load with the force of flap.

**Figure 14.** Boundary conditions and load with the force of flap. The displacement field in the flap with the symmetric aluminum profile is presented in Figure 15. The maxim displacement is 0.011 mm to the extremity free of the flap from aluminum. **Figure 14.** Boundary conditions and load with the force of flap.

**Figure 15.** The displacements in the flap. **Figure 15.** The displacements in the flap.

profile.

Table 3 presents the results of finite element analysis for the wing with a symmetric profile. Table 4 shows the results of finite element analysis for the flap with a symmetric profile. Table 3 presents the results of finite element analysis for the wing with a symmetric profile. Table 4 shows the results of finite element analysis for the flap with a symmetric

**Table 3.** The results of finite element analysis for the wing with a symmetric profile. **Table 3.** The results of finite element analysis for the wing with a symmetric profile.


**Table 4.** The results of finite element analysis for the flap with a symmetric profile. **Table 4.** The results of finite element analysis for the flap with a symmetric profile.


Equivalent Von Misses stress in the flap with the symmetric aluminum profile is presented in Figure 16, the maxim value being 2.63 <sup>×</sup> <sup>10</sup><sup>6</sup> N/m<sup>2</sup> . Equivalent Von Misses stress in the flap with the symmetric aluminum profile is presented in Figure 16, the maxim value being 2.63 × 106 N/m2.

**Figure 16.** Von Misses stress that appears in the flap with the symmetric aluminum profile. **Figure 16.** Von Misses stress that appears in the flap with the symmetric aluminum profile.

#### **5. Discussions 5. Discussions**

The modern design process is a complex process that involves, among other things, the use of modeling methods and analysis based on the use of high-performance software. The finite element method offers solutions to the problems to identify the fields of variation in stresses and deformations. Field identification problems provide a spatial distribution of dependent variables, mathematical modeling of distributions, and dependencies being achieved by differential equations and expressions that contain integrals. CAD modeling of the I.-M.G. light aircraft and finite element analysis are done with the Catia V5 software using the Part Design module that allows the creation of the 3D model of pieces and the application of material characteristics specific to the material The modern design process is a complex process that involves, among other things, the use of modeling methods and analysis based on the use of high-performance software. The finite element method offers solutions to the problems to identify the fields of variation in stresses and deformations. Field identification problems provide a spatial distribution of dependent variables, mathematical modeling of distributions, and dependencies being achieved by differential equations and expressions that contain integrals. CAD modeling of the I.-M.G. light aircraft and finite element analysis are done with the Catia V5 software using the Part Design module that allows the creation of the 3D model of pieces and the application of material characteristics specific to the material chosen for the creation of

chosen for the creation of the pieces, features existing in the material library of the pro-

the pieces, features existing in the material library of the program or by introducing in the program the material characteristics specific to the material of the piece created.

After solid modeling in the CATIA Part Design module, the piece is considered to have a material (aluminum, duralumin), with physical properties, important during the analysis. These values are indicated by default by the CATIA program after selecting the piece in the specification tree and choosing the material "Aluminum/Duralumin" in the "Library" dialog window.

For the finite element analysis of the I.-M.G. light aircraft, the Catia V5 R21 software is used with the CATIA Generative Structural Analysis Module.

From the FEM analysis of the symmetrical profile wing of I.-M.G. aircraft loaded with a force, uniformly distributed and analyzed in two situations (duralumin, aluminum), it is apparent that the maximum deformation occurs in the duralumin wing. From the FEM analysis of the symmetrical profile wing and for the asymmetric profile wing loaded each with force, uniformly distributed, and analyzed in two situations (duralumin, aluminum), it is apparent that the deformation is minimal in the case of the asymmetric profile wing.

The advantages of this mechanism consist of a simple realization, easy maintenance, low-cost price but also the achievement of excellent performances for the studied plane. For this reason, it becomes important to study the compatibility of this type of mechanism with the structure of the studied aircraft. From all the results presented above, this compatibility, from the point of view of strength, is ensured.

#### **6. Conclusions**

The ever-increasing complexity of the products leads to some difficulties in design and manufacture. There are several solutions to this feature of modern production—the most used being the realization of new tools and technologies to support the approach of the project without significantly affecting the time of realization or the quality obtained.

Thus, improvements are imposed in the processes of design, calculation and optimization, simulation of manufacturing, or in the way of information management. Between all this, the assisted design presents a decisive link.

Reducing the duration of the product production cycle is possible when the design, manufacture, and finite element method are increasingly integrated.

CATIA allows the design of parts and assemblies directly in three dimensions, without first drawing the plates in representation (two-dimensional). Note that calculations can be made, which can be of great help to the engineer who wants to hold a single platform for CAD-CAE-CAM domains.

On the I.-M.G. light aircraft, a static analysis is carried out, with uniformly distributed forces, after the state of tensions and deformations in the analyzed parts is obtained. The I.-M.G. Light Sport Aircraft is designed with the median wing with a rectangular section, with a symmetrical profile. The wing is equipped with a flap and an aileron. The median wing is advantageous in terms of interaction with the fuselage. By increasing the length of the wings, the length of the flaps is also increased, which increases the lift during the take-off and landing of the aircraft slightly. The proposed I.-M.G. lightweight aircraft is designed by using original component elements like shape and size to improve the aerodynamics of the aircraft and its stability as follows: rectangular-shaped median wings and with an asymmetrical profile in its section so that the profile string forms an angle with the forward direction, of a range to a value greater than the fuselage length, L = (1.1...1.3) ∗ L<sup>f</sup> , and implicitly increasing the surface of the flaps, which may allow the airplane to glide in critical flight situations when the engine is no longer running or when needed for fuel economy, allowing the aircraft to behave easily and like a plane, the central plane of the fuselage, the propeller helmet, the previous fuselage (hoods), the propellers and the handles of curvature without a run-out board (one on each wing), the cabin in which the crew sits, the depth, drift, direction, rear fuselage, stabilizer, and the 2nd section of the central fuselage. By mounting the flaps on the wings, the landings are smooth, and the plane does not hit the ground. The designed constructive solution of the flaps

control mechanism for the new I.-M.G. light aircraft allows the steering to be braced up to a maximum of 55◦ , this value being superior to the classic solutions of mechanisms with flaps that poach up to a maximum of 45◦ . The finite element analysis of the flap and wing offers us a convenient solution with real maneuverability advantages.

A comparison of the stress and strain fields that occur in the aircraft structure when equipped with the new type of control mechanism, with the stress field that occurs when equipped with current mechanisms [35], shows that these fields are admissible from the point of view of strength. So the proposed mechanism is compatible with the structure analyzed in the paper, and the calculated stress is lower than the limit stress.

**Author Contributions:** Conceptualization, I.-M.G., M.L.S., M.M.; methodology, I.-M.G., M.G., M.L.S.; software, I.-M.G., M.G., M.M.; validation, I.-M.G., M.G., M.L.S.; formal analysis, I.-M.G., M.G., P.N.B.; investigation, I.-M.G.; resources, I.-M.G., M.L.S., M.M.; data curation, I.-M.G., M.G., P.N.B.; writing original draft preparation, M.G.; writing—review and editing, M.G., I.-M.G., M.L.S.; visualization, M.G., M.L.S.; supervision, I.-M.G., M.G., M.L.S., M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We want to thank the reviewers who have read the manuscript carefully and have proposed pertinent corrections that have led to an improvement in our manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Marilena Ghi¸tescu <sup>1</sup> , Ion-Marius Ghi¸tescu 1,\*, Paul Nicolae Borza <sup>2</sup> and Sorin Vlase 1,\***


**Abstract:** The paper presents a new constructive and functional solution of flexible coupling with bolts and nonmetallic intermediary elements. The bolts have a special shape in the sense that they have a milled area on a certain length equal to the width of the non-metallic element, a cylindrical area that reduces the stress concentrators at the diameter passages. The novelty of this coupling consists of the existence of one intermediary disk between two semi couplings (driver and driven semi couplings). This is fixed by the semi-coupling on the right side, the intermediary disc having milled four locations in which to mount the left, as the right has a metal plate with a special shape of eight metallic plates that are mounted with screws in the four milled places processed on the intermediate disc. The nonmetallic elements have various forms and can be made from different qualities of rubber mounted on the bolts. Eight milled bolts (four on each semi-coupling) allow the transmission of the torsion moment in both directions of rotation, in one direction becoming rigid and thus behaving like a safety coupling. Finite element method is used to obtain the mechanical response of this new type of coupling.

**Keywords:** flexible coupling; bolt; non-metallic element; finite element method; elastic characteristic

#### **1. Introduction**

Rotating machines in which the drive system and the working machine are different require an adapting element in order to transmit power between the two sides. For this, a drive shaft can be used with universal joints or a particular coupling system. Ideally, the two shafts should be properly connected by a rigid coupling so that the two shafts work as one. This offers advantages such as not allowing relative movement between the two shafts, the motor, and the conduced shaft. Vertically positioned applications, such as vertical pumps, use this solution. More used, however, are flexible couplings, which aim to transmit torque or rotary motion without slipping and to compensate for axial, parallel, or angular misalignment. Additionally, the non-linear flexibility of the couplings makes the dynamics of the rotary movement smoother and improves the dynamic response for both the electric motor and the work machine. Examples of such couplings can be pumps, air pumps, engine generator sets, conveyors, crushers, vibrating screens, etc. In practice, flexible coupling can be a major contributor to performance problems of the two machines [1–8], which is why an extensive study is required for each particular application.

Flexible couplings with bolts used in industrial application are presented in a wide variety of constructive solutions, in accordance with their functional role and the demands they must respond to. These demands differ not only by dimensions for each constructive solution but also by the shape of the elastic element. Two of these variants are standardized: variant N, normal, and variant B, with spacer bush [9]. In general, couplings are frequently used in the composition of mechanical transmissions. Flexible couplings with non-metallic elements are of great importance due to the numerous and very diverse fields of activity

**Citation:** Ghi¸tescu, M.; Ghi¸tescu, I.-M.; Borza, P.N.; Vlase, S. A New Optimized Solution for a Flexible Coupling with Bolts Used in the Mechanical Transmissions. *Symmetry* **2021**, *13*, 171. https://doi.org/ 10.3390/sym13020171

Received: 27 December 2020 Accepted: 20 January 2021 Published: 22 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of equipment and installations they equip (compressors, pumps, generators, pulleys, cranes, conveyors, mixers, piston motors, general industrial applications, as well as in the metallurgical industry, the mining industry, the paper industry, and the pulp industry). In applications, the couplings are made in a great diversity of constructive solutions, a unitary and generally accepted classification of them being difficult. Specific to flexible couplings with non-metallic elements is the fact that the transmission of rotational motion and torque is achieved through the non-metallic element, which dampens shocks and vibrations and can take axial, radial, angular, or combined deviations. The stress characteristic of nonmetallic coupling elements together with their size and shape of these elements represent a key design factor for mitigating the transmission of power between the sides of coupling.

Herein are presented some constructive coupling solutions for flexible coupling. These emphasize the advantages of the proposed solution, its applicability, and the way in which this solution meets the requirements of the industry. Known from literature [10], constructive solutions that include flexible bolt coupling consist of two identical semicouplings. In this case, the torsion moment is transmitted through the rubber sleeves mounted on the bolts, which are rigidly fixed in the other half of the coupling. The profiled sleeves mounted on the bolts are fixed at one end. This type of coupling transmits small and medium.

There are flexible couplings with rubber pins whose half-couplings are machined differently from each other. Thus, one has holes for pins, and the other has the holes machined so as to allow the mounting of rubber bushes. The holes are arranged in a circle on the circumference of each coupling half [11,12].

In [13,14] is presented flexible coupling with studs and washers or rubber bushes. The rubber elements are mounted in one coupling half on the studs, and on the other, the studs are fixed with flanges. Flexible coupling allows, within certain limits, the relative rotation of semi-couples and the variation of shafts alignment.

The Guardian Superflex coupling has two hubs: a super flexible rubber element and a bolts with self-locking nuts [15]. The Superflex Coupling has been used worldwide on a variety of applications, including light towers, air pumps, welding sets, and other machinery with large driven inertia. The coupling consists of two cast iron hubs, a super-elastic rubber element, and a locking hardware. In a rigid coupling, the torque is transmitted from one half of the coupling to the other through the bolts, and in this arrangement, shafts need to be aligned [16].

A flexible Rupex coupling consists of two semi-couplings, bolts and non-metallic rubber element. The non-metallic element is mounted on bolts fixed only on one side of the coupling [17,18]. This coupling absorbs shocks and cushions vibrations. The movement is transmitted from one half-coupling to the other through non-metallic elements fixed with bolts.

Flexible couplings with bolts and bushings are made up of two semi-coupled panels that are mounted on the shafts of the machine [19]. These pieces allow additional torsional flexibility compared to simple cylindrical pieces.

Bolt and barrel bushings couplings are widespread on engineering applications. A flange coupling and non-metallic barrel element is used to connect trees that have a small parallel misalignment, angular misalignment, or axial misalignment. This coupling works with coupling surge. In general, this is used to assemble electric machine with working machines [20–22].

A flexible coupling with elastic rubber bushings and pins consists of two semicouplings with different flanges having conical bore inside and elastic rubber bushings that are mounted on notched head pins [23]. The flexible coupling with elastic rubber bushings allows an increased load-bearing capacity and durability. The resulted stiffness characteristics are non-linear and asymmetrical. These couplings are used by the transport systems.

The rubber-cushioned sleeve bearing coupling is fast to replace, and this comprises a right half coupling body, a pin, a flexible sleeve, and a nut [24]. The flexible sleeve can be quickly replaced, and it does not need a coaxially correction after replacement. Due to this, an improved production efficiency is obtained.

It is well known that the flexible coupling consists of fixing screws, transition sleeves, elastic rubber rings, a connecting pressure disc, a brake wheel, and studs [25]. The multiple holes for screws and sleeves are evenly distributed alternately on the same circle in the left brake wheel. The connecting pressure disc and the brake wheel are fixedly connected by the fixed screws. The flexible coupling cannot be worn completely and has a long service life. The coupling can be easily removed.

In case of maritime couplings, it is known that these consist of two different halfcouplings, a tapered sleeve, screws, drive couplings, connecting pins, elastic rubber rings, nuts, transition sleeves, and connecting pressure plates [26]. Depending on the maritime coupling, the service life of the coupling can be extended by the transition sleeves and the rate of replacement of rubber spring rings, and the frequency of maintenance can be reduced, thus maintenance is convenient. The marine coupling especially shows its superiority when it is used in places where the maintenance is difficult.

A constructive solution of flexible coupling with bolts can be made up by two halfcouplings. These have distributed holes on their circumference on a certain circle diameter where cylindrical bolts are placed. These are threaded at one end, being alternately mounted on the two semi-couplings [27]. The movement is transmitted from one halfcoupling to another by bolts and non-metallic elements.

Another constructive solution for flexible coupling with bolts and non-metallic elements consists of a coupling part placed radially and having non-metallic elastic link elements. As these elements use materials with composite structures as armatures, the different shape and the used materials generate the desired anisotropy. Additionally, the deformation characteristics of link elements will be different. Thus, the coupling is able to be adapted for a wide set of applications without major changes. In mounting processes, different solutions can be adopted by usage of specific mounting pieces having different kinds of shape, size, and screws. By usage of anysotropic link elements in correlation with disc shape, bolt placement, spacer elements, and screws, all of these generate cheaper and simpler solutions for transfer of movement by coupling. Shape, size, and materials used for link elements represent key factors for adapting to application by the amount of energy that can be absorbed inside coupling. Additionally, the coupling's elements design influences the time response of the system at variation of torque from both sides: motor and load. Moreover, by using elastomer based link elements, these provide a lubrication effect that has beneficial effects for coupling lifespan and its usage [28].

The study of the specialized literature in the field of flexible couplings with nonmetallic elements revealed the existence of flexible couplings with non-metallic elements with relatively simple functional and constructive principles. These couplings are made in a wide range of types and sizes, being produced by specialized companies with international reputation. Because the literature in the field of flexible couplings with non-metallic elements is very poor, new research is welcome in the field.

Published articles are very rare, and the books (courses, monographs, etc. [1–8]) present general references regarding design and construction. In modern transmissions, the couplings are mounted immediately after the drive motor, which can be direct current motor with series or parallel excitation or with permanent magnets or could be asynchronous or synchronous motors. The motor or the load torque inherently vary in time function as a result of machine functioning and also as a result of functioning of the control system. The designer is able to design a coupling that smooth movement harmonics in time (speed angular acceleration in time). The dynamic response of the acting system can by optimized by the designed coupling for target work-torque, speed, and for the transient regimes. Thus, the designed coupling is able to perform oscillation dumping during transitory and stationary regimes.

plates.

count.

11—screws; 12—milled bolts.

The problems that appear with the couplings listed above would be related to the following: a technological achievement, generally difficult assembly of the component elements, and generally high loads on the coupling elements. The semi-couplings are approximately identical, the constructive differences consisting of the presence on the driven semi-coupling 2 at the level of diameter Ds, of four

Our paper proposes a coupling system that has several advantages: easy disassembly of non-metallic elements; easy disassembly of bolts; by mounting the non-metallic element between the plates and not in bores processed in semi-couplings, it allows the non-metallic element to relax, this being required besides crushing, shearing, and traction; transmits the torque in both directions, in a direction of rotation that becomes rigid and thus behaves like a safety coupling (which means that it fulfills a new function with this coupling compared to the classic solutions of bolt couplings and non-metallic elements); fulfills the function of limiting the load in order to avoid breaking the non-metallic elements. equidistant holes, three of them being threaded, for fixing by means of screws 8 the intermediate disk 7 of the driven semi-coupling 2, and of the fourth orifice for centering by means of the cylindrical pin 9 of the intermediate disc on the driven semi-coupling. The subassembly consists of the half-coupling (2), the milled bolts 12 fixed by the semi-coupling by means of the Grower washers 5 and the M8 nuts 6, the metal plates 10 fixed to the intermediate disc 7 by means of the screws 11 in the space between the plates and the non-metallic elements 3, which come into contact with the milled bolts that are fitted. The intermediate disk 7 is fixed to the semi-coupling driven 2 by means of the screws 8, the centering of the disk in relation to the intermediate disk being achieved by

#### **2. Description of the Proposed Flexible Coupling with Milled Bolts and Non-Metallic Elements** means of the cylindrical pin 9. In the coupling component, in the milled locations on the intermediate disc 7 are mounted four subassemblies plates 10, a non-metallic element 3,

In the literature, there is no flexible coupling solution with milled bolts and nonmetallic elements by type of coupling designed (Figure 1). The novelty of this coupling consists of the existence of one intermediary disk which has four processed holes, the intermediary disk being mounted between two semi couplings. The disk is and fixed to the right half-coupling with screws and centered with the semi-coupling with one cylindrical pin of eight metallic plates fixed with one left and one right to each processed hole on the intermediate disc (there are four disk stakes arranged at 90 degrees). The nonmetallic elements from different qualities of rubber are mounted with bolts and with eight milled bolts, four on each semi-coupling. By using the milled bolts, four mounted on each halfcoupling, the transmission of the movement and the torque in both directions are obtained. Each metal plate attaches to the intermediate disc by means of two screws. and screws 11, one in each milled location of the type shown in Figure 1. The non-metallic element has various shapes presented below in the form of the letter H. The foot of the letter H ensures fastening and centering in the places of the The non-metallic element 3 that is mounted between the plates is made of the same rubber quality. Non-metallic element 3 can be made of three rubber qualities (natural rubber, NR; butadiene rubber acrylonitrile, NBR; ethylene propylene diene rubber, EPDM. When designing the coupling, the influence of the shape of the non-metallic element and the quality of the rubber on the coupling performance were taken into ac-

**Figure 1.** The flexible coupling with milled bolts and non-metallic elements. 1—driver semi-coupling; 2—driven semi-coupling; 3—non-metallic elements; 4—milled bolts; 5—Grower washers; 6—M8 nuts 6; 7—intermediary disk; 8—screws; 9—cylindrical pin; 10—metal plates; **Figure 1.** The flexible coupling with milled bolts and non-metallic elements. 1—driver semi-coupling; 2—driven semicoupling; 3—non-metallic elements; 4—milled bolts; 5—Grower washers; 6—M8 nuts 6; 7—intermediary disk; 8—screws; 9—cylindrical pin; 10—metal plates; 11—screws; 12—milled bolts.

In existing locations between two plates (there are four locations), a non-metallic element is mounted. Non-metallic rubber elements of different qualities are mounted in the space between two plates, thus there are four non-metallic elements mounted. At the same time, the non-metallic element is mounted on the bolts.

This is a new flexible coupling with bolts that differs from the classic solutions of flexible couplings with milled bolts and non-metallic elements by the existence of the intermediate disc, the existence and the form of non-metallic plates and of non-metallic elements that have various constructive forms that can be changed, and by the existence of the eight milled bolts, which are mounted/fixed with four on each half-coupling (Figure 1). On each semi-coupling, four milled bolts are mounted, fixing each semi-coupling bolt by means of a nut and a Grower washer.

In this constructive variant, the bolts 4 and 12 are milled, and their number is eight, four on each semi-coupling. The contact between the milled faces of the bolts is about the length equal to the width of the non-metallic element 3 [9].

The number of bolts mounted on each semi-coupling is four and equals the number of non-metallic elements 3 mounted between the metal plates 10 fixed to the intermediate disk 7, and this number is equal to the maximum number of milled holes on the intermediate disk so as not to endanger the strength of the milled disk and the allocators. The milled part of the bolts allows the transmission of the movement and the torque from one half-coupling to another. The two milled areas of two bolts (one on each half-coupling) come into contact (Figure 1 on the width of the non-metallic element. There are four mounted milled bolts from a total of eight on each half-coupling; only four milled bolts work at a chosen direction of rotation.

The semi-couplings are approximately identical, the constructive differences consisting of the presence on the driven semi-coupling 2 at the level of diameter Ds, of four equidistant holes, three of them being threaded, for fixing by means of screws 8 the intermediate disk 7 of the driven semi-coupling 2, and of the fourth orifice for centering by means of the cylindrical pin 9 of the intermediate disc on the driven semi-coupling. The subassembly consists of the half-coupling (2), the milled bolts 12 fixed by the semi-coupling by means of the Grower washers 5 and the M8 nuts 6, the metal plates 10 fixed to the intermediate disc 7 by means of the screws 11 in the space between the plates and the non-metallic elements 3, which come into contact with the milled bolts that are fitted. The intermediate disk 7 is fixed to the semi-coupling driven 2 by means of the screws 8, the centering of the disk in relation to the intermediate disk being achieved by means of the cylindrical pin 9. In the coupling component, in the milled locations on the intermediate disc 7 are mounted four subassemblies plates 10, a non-metallic element 3, and screws 11, one in each milled location of the type shown in Figure 1.

The non-metallic element has various shapes presented below in the form of the letter H. The foot of the letter H ensures fastening and centering in the places of the plates.

The non-metallic element 3 that is mounted between the plates is made of the same rubber quality. Non-metallic element 3 can be made of three rubber qualities (natural rubber, NR; butadiene rubber acrylonitrile, NBR; ethylene propylene diene rubber, EPDM. When designing the coupling, the influence of the shape of the non-metallic element and the quality of the rubber on the coupling performance were taken into account.

In the optimal design process of the flexible coupling with milled bolts and nonmetallic elements, the following aspects were taken into account:


The main parameter resulting from the characteristic of the flexible couplings is the torque. Another important parameter is the rigidity, which represents the dependence of the relative rotation angle *ϕ* of the half-couplings, depending on the value of the torque *M<sup>t</sup>* .

The flexible coupling with milled bolts and non-metallic elements is characterized by damping capacity and rigidity. The existence of the flexible coupling in the mechanical systems favorably influences their behavior at oscillating loads, frequently encountered in operation, high values of the degree of damping leading to a quieter operation of the mechanical systems equipped with such a coupling. In this constructive version, by applying at the input of a torque in the direction indicated by the continuous arrow (I) (see Figure 1), the torque is transmitted from entry driver semi-coupling 1, by shape, through the milled bolts 4 to the milled bolts 12, fixed rigidly by the semi-coupling 2, in this sense, the coupling becoming rigid. In the direction of rotation indicated by the interrupted arrow (II), the milled bolts 4 act on the elastic element 3 of different constructive forms, compressing it in the direction of movement.

Figure 2 presents the 3D model of the constructive form of the milled bolt realized in Autodesk Mechanical Desktop 6 Power Pack [29] and Catia V5 [30]. The milled bolts 4 and 12 are fixed to the semi-coupled leading 1 and driven 2 by means of Grower washers and nuts that prevent the bolts from breaking. The cylindrical area of the bolt with a diameter greater than the diameter of the milled area is intended to reduce the stresses concentrators and break the bolt at the passage of diameter from the diameter of the milled area to the diameter of the cylindrical zone to the right of the threaded area. The cylindrical area with the largest diameter in the bolt component represents a shoulder, stopping on the milled end of the bolt, which is mounted in the opposite direction. The installation of the milled bolts 4 of the driver semi-coupling 1 is done easily. From right to left, the bolts are inserted into the bores processed in the driver semi-coupling 1, then Grower washers 5 and nuts 6 are mounted, and the nuts are tightened. The installation of the milled bolts 12 of the driven semi-coupling 2 (the right half-coupling, Figure 1) is easy as well. From left to right, the bolts are inserted into the handles processed in the semi-coupled driven 2, and then the Grower washers 5 and the nuts 6 are mounted, and the nuts are squeezed against the unraveling of the bolts. *Symmetry* **2021**, *13*, x FOR PEER REVIEW 7 of 16

Figure 3 presents the 3D model of forms of plates on the left side and on the right

10

11

3

mounted, while the other end of the non-metallic element is mounted in the processed channel in the plate fixed on the opposite side of each milled slot located on the intermediate disk. Figure 4 shows the subassembly consisting of plates 10, non-metallic element 3 mounted between those two plates, and screws 11, the subassembly being part of the constructive variant of the prototype. For fixing the metal plate 10 of the intermediate disc 7, two screws 11 are sufficient for low execution costs for the plate and the intermediate disc, saving material and reducing the weight of the coupling. Figure 5 shows the subassembly consisting of the semi-coupling of the driver 1, the milled bolts 4, the Grower 5 washers, and the nuts 6, the subassembly being part of the constructive variant of the prototype. Semi-coupling drive 1 input transmits the torsion moment from the

**Figure 2.** 3D model of the constructive shape of milled bolt. **Figure 2.** 3D model of the constructive shape of milled bolt.

electric motor to the milled bolts 4 fixed by this semi-coupling.

10

11

**Figure 3.** Subassembly plates 10, non-metallic element 3, screws 11.

**<sup>p</sup> <sup>F</sup><sup>1</sup>**

l2

(**a**)

d

d<sup>b</sup>

D**1**

10

11

Figure 3 presents the 3D model of forms of plates on the left side and on the right side. Each plate has a milled channel, in which one end of the non-metallic element is mounted, while the other end of the non-metallic element is mounted in the processed channel in the plate fixed on the opposite side of each milled slot located on the intermediate disk. Figure 4 shows the subassembly consisting of plates 10, non-metallic element 3 mounted between those two plates, and screws 11, the subassembly being part of the constructive variant of the prototype. For fixing the metal plate 10 of the intermediate disc 7, two screws 11 are sufficient for low execution costs for the plate and the intermediate disc, saving material and reducing the weight of the coupling. Figure 5 shows the subassembly consisting of the semi-coupling of the driver 1, the milled bolts 4, the Grower 5 washers, and the nuts 6, the subassembly being part of the constructive variant of the prototype. Semi-coupling drive 1 input transmits the torsion moment from the electric motor to the milled bolts 4 fixed by this semi-coupling. Figure 3 presents the 3D model of forms of plates on the left side and on the right side. Each plate has a milled channel, in which one end of the non-metallic element is mounted, while the other end of the non-metallic element is mounted in the processed channel in the plate fixed on the opposite side of each milled slot located on the intermediate disk. Figure 4 shows the subassembly consisting of plates 10, non-metallic element 3 mounted between those two plates, and screws 11, the subassembly being part of the constructive variant of the prototype. For fixing the metal plate 10 of the intermediate disc 7, two screws 11 are sufficient for low execution costs for the plate and the intermediate disc, saving material and reducing the weight of the coupling. Figure 5 shows the subassembly consisting of the semi-coupling of the driver 1, the milled bolts 4, the Grower 5 washers, and the nuts 6, the subassembly being part of the constructive variant of the prototype. Semi-coupling drive 1 input transmits the torsion moment from the electric motor to the milled bolts 4 fixed by this semi-coupling. side. Each plate has a milled channel, in which one end of the non-metallic element is mounted, while the other end of the non-metallic element is mounted in the processed channel in the plate fixed on the opposite side of each milled slot located on the intermediate disk. Figure 4 shows the subassembly consisting of plates 10, non-metallic element 3 mounted between those two plates, and screws 11, the subassembly being part of the constructive variant of the prototype. For fixing the metal plate 10 of the intermediate disc 7, two screws 11 are sufficient for low execution costs for the plate and the intermediate disc, saving material and reducing the weight of the coupling. Figure 5 shows the subassembly consisting of the semi-coupling of the driver 1, the milled bolts 4, the Grower 5 washers, and the nuts 6, the subassembly being part of the constructive variant of the prototype. Semi-coupling drive 1 input transmits the torsion moment from the electric motor to the milled bolts 4 fixed by this semi-coupling.

Figure 3 presents the 3D model of forms of plates on the left side and on the right

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 7 of 16

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 7 of 16

**Figure 2.** 3D model of the constructive shape of milled bolt.

**Figure 2.** 3D model of the constructive shape of milled bolt.

**Figure 3.** Subassembly plates 10, non-metallic element 3, screws 11. **Figure 3.** Subassembly plates 10, non-metallic element 3, screws 11. **Figure 3.** Subassembly plates 10, non-metallic element 3, screws 11.

(**a**)

D**1**

(**a**) **Figure 4.** *Cont*.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 8 of 16

**Figure 4.** (**a**) Scheme of coupling; (**b**) nonmetallic elements. **Figure 4.** (**a**) Scheme of coupling; (**b**) nonmetallic elements. **Figure 4.** (**a**) Scheme of coupling; (**b**) nonmetallic elements.

**Figure 5.** The maximum deformation of nonmetallic element from natural rubber. **Figure 5.** The maximum deformation of nonmetallic element from natural rubber.

semi couplings 1 and 2 can be made from improved OLC 45 steel (improved quality rolled steel brand with 0.45% carbon content). The mechanical characteristics of the improved OLC 45 (equivalent steel is C 45) steel are: density = 8.31 g/cm<sup>3</sup> , Young's modulus = 200 GPa, Poisson's ratio = 0.287. The coupling was modeled with Computer Aid Design (CAD) in the Autodesk The milled bolts 4 and 12, the metallic elements 10, the intermediary disc 7, and the semi couplings 1 and 2 can be made from improved OLC 45 steel (improved quality rolled steel brand with 0.45% carbon content). The mechanical characteristics of the improved OLC 45 (equivalent steel is C 45) steel are: density = 8.31 g/cm<sup>3</sup> , Young's modulus = 200 GPa, Poisson's ratio = 0.287. The milled bolts 4 and 12, the metallic elements 10, the intermediary disc 7, and the semi couplings 1 and 2 can be made from improved OLC 45 steel (improved quality rolled steel brand with 0.45% carbon content). The mechanical characteristics of the improved OLC 45 (equivalent steel is C 45) steel are: density = 8.31 g/cm<sup>3</sup> , Young's modulus = 200 GPa, Poisson's ratio = 0.287.

The milled bolts 4 and 12, the metallic elements 10, the intermediary disc 7, and the

Mechanical Desktop 6 Power Pack and Catia V5. The non-metallic element is required for crushing and traction. The bolt is required The coupling was modeled with Computer Aid Design (CAD) in the Autodesk Mechanical Desktop 6 Power Pack and Catia V5. The coupling was modeled with Computer Aid Design (CAD) in the Autodesk Mechanical Desktop 6 Power Pack and Catia V5.

for bending. The non-metallic element is required for crushing and traction. The bolt is required for bending. The non-metallic element is required for crushing and traction. The bolt is required for bending.

#### **3. Calculus Element, Execution and Testing of Flexible Coupling with Milled Bolts and Non-Metallic Elements**

The numerical modeling of the performances of the designed coupling is performed on the basis of a calculation scheme, this being presented in Figure 4 [9].

According to the assembly of Figure 4a, the bolt is an integral part of the semi-coupling 1. Non-metallic elastic elements are incompressible, as they can change their shape, but they do not change their volume to a large extent.

Two hypotheses are used in the calculus:


During operation, other additional loads act on the coupling elements, such as: inertia loads, which appear in the non-stationary operating mode of the transmission equipped with coupling; shock and vibratory loads, which occur in both non-stationary and stationary operating modes; loads due to the elements of the couplings. The magnitude of the load acting on the couplings depends on: the characteristic of the motor car, the operating mode of the driven car, the influence of the coupling on the moment of inertia, the rigidity, and the vibration behavior of the kinematic chain.

Due to the fact that it is not possible to know exactly the variation of the torque over the entire operating time, the coupling calculation is performed at an imposed value of calculation torque *Mtc*. Taking into account the additional loads that may occur at installation or during operation, the so-called torsion moment of calculation *Mtc*, is calculated with the formula:

$$M\_{\rm tc} = K\_{\rm s} M\_{\rm tn} \le M\_{\rm tcn} \tag{1}$$

where *K<sup>S</sup>* is a safety factor experimentally obtained and offered by literature [1], *Mtn* is nominal torque calculated using the power of the electric motor *P* and its corresponding rotation speed *<sup>n</sup>*, with the relation *<sup>M</sup>tn* <sup>=</sup> 9.55 · <sup>10</sup><sup>6</sup> · *P* [kW] *n* [rot/min] [Nmm] [9].

Assuming that all bolts are loaded evenly and their number is *z*, the force loading a bolt is

$$F = \frac{2M\_{tc}}{zD\_1} \tag{2}$$

The crush check is performed at the bolt level. Assuming the uniform distribution of pressures along the generator and in section, the crushing between the bolt and the elastic element is determined by the relation [12].

$$
\sigma\_s = \frac{F}{A\_s} = \frac{2M\_{lc}}{zD\_1 d\_b l\_2} \le \sigma\_{as} \tag{3}
$$

where: *A<sup>s</sup>* is the crushing surface, *d<sup>b</sup>* is the bolt diameter, *l*<sup>2</sup> is the length on which the crushing occurs (*l*<sup>2</sup> = *b*, *b* being the thickness of the non-metallic element), *σas* is the permissible crushing resistance (*σas* = (5 . . . 7)MPa), and *Mtc* is the calculation torque [9,11].

Applying a traction, the stress is given by [12]:

$$
\sigma\_t = \frac{F\_t}{A\_t} = \frac{2M\_{tc}}{zD\_1 A\_t} \le \sigma\_{\text{at}} \tag{4}
$$

where: *A<sup>t</sup>* is the section area (*A<sup>t</sup>* = (*h*<sup>2</sup> − *d<sup>b</sup>* )*b*—for the shape of Figure 2), *σat* = 1.5 MPa from [9].

The bending stress is

$$
\sigma\_i = \frac{M\_i}{W\_z} = \frac{32Fl\_2}{\pi d\_b^3} = \frac{64M\_{tcap}l\_2}{\pi z D\_1 d\_b^3 l\_2} \le \sigma\_{ai} \tag{5}
$$

where *σai* = (0.25 . . . 0.4)*σ*02, *σ*<sup>02</sup> = 400 MPa—for bolt realized from improved OLC 45 steel. The values obtained applying Equation (5) is *σ<sup>i</sup>* = 9.54 MPa hh *σai* = 160MPa .

ϕ=

*r*

*M*

1

( )

<sup>Δ</sup> <sup>=</sup>

*t*

<sup>=</sup> <sup>Δ</sup>

ϕ

ϕ

Angle of relative rotation of those semi couplings is offered by: <sup>−</sup> <sup>−</sup> + <sup>−</sup> <sup>−</sup> <sup>−</sup> + + <sup>+</sup> <sup>−</sup> <sup>Δ</sup>*b b b tc b b h d arctg d h d arctg <sup>h</sup> <sup>d</sup> h d l d* 2 2 2 <sup>4</sup> <sup>4</sup> <sup>4</sup> <sup>1</sup>

Angle of relative rotation of those semi couplings is offered by:

*z b*

*<sup>i</sup> zD d l*

45 steel. The values obtained applying Equation (5) is *MPa MPa <sup>i</sup> ai*

= = = ≤

3 <sup>2</sup> 32 64

*d Fl*

π

*i*

*W M*

 , 400 σ

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 10 of 16

σ

σ

$$\Delta\varphi = \frac{4M\_{lc}}{zD\_1^2} \frac{1}{Eb} \left[ \frac{l - d\_b}{h} + 4\sqrt{\frac{h + d\_b}{h - d\_b}} \arctan\sqrt{\frac{h + d\_b}{h - d\_b}} - \frac{4d\_b}{\sqrt{h^2 - d\_b^2}} \arctan\sqrt{\frac{h + d\_b}{h - d\_b}} - \pi\right] \tag{6}$$

*ai*

=9,54

σ

π

=160 .

(5)

(6)

σ

<sup>02</sup> = MPa—for bolt realized from improved OLC

*b tcapi*

σ

2 3 1

2

*M l*

π

The rigidity is obtained by *<sup>M</sup> zD bE <sup>k</sup>* 1

where *ai <sup>02</sup>*

= (*0*,*25*...*0*,*4*)

σ

$$k\_{l} = \frac{M\_{l}(\Delta\varphi)}{\Delta\varphi} = \frac{zD\_{1}^{2}}{4} \frac{bE}{\left[\frac{l-d\_{b}}{\hbar} + 4\sqrt{\frac{l+d\_{b}}{\hbar-d\_{b}}} \operatorname{arct} g\sqrt{\frac{l+d\_{b}}{\hbar-d\_{b}}} - \frac{4d\_{b}}{\sqrt{\hbar^{2}-d\_{b}^{2}}} \operatorname{arct} g\sqrt{\frac{l+d\_{b}}{\hbar-d\_{b}}} - \pi\right]} \tag{7}$$

The non-metallic element was studied with the finite element method(FEM) [30,31]. The deformation of the non-metallic element is presented in Figure 5. Von Mises stresses appearing in the non-metallic element are presented in Figure 6. This numerical has been used to determine the elastic response of the components of the proposed coupling. A total of 13,482 octree (parabolic tetrahedron) discretization elements were used. The FEM analysis shows a non-metallic element deformation of 1.76 mm. The experimental determinations performed in static regime gave a maximum deformation of the nonmetallic element of 1.77 mm. The deformation of the non-metallic element is presented in Figure 5. Von Mises stresses appearing in the non-metallic element are presented in Figure 6. This numerical has been used to determine the elastic response of the components of the proposed coupling. A total of 13,482 octree (parabolic tetrahedron) discretization elements were used. The FEM analysis shows a non-metallic element deformation of 1.76 mm. The experimental determinations performed in static regime gave a maximum deformation of the non-metallic element of 1.77 mm.

**Figure 6.** The maximum Von Mises stress of nonmetallic element from natural rubber.

**Figure 6.** The maximum Von Mises stress of nonmetallic element from natural rubber. The maximum Von Mises stresses are presented in Figure 7. The results of the experimental tests of the coupling containing the non-metallic element 3 made of natural rubber are presented in the following figure. The static characteristic can be seen (when the The maximum Von Mises stresses are presented in Figure 7. The results of the experimental tests of the coupling containing the non-metallic element 3 made of natural rubber are presented in the following figure. The static characteristic can be seen (when the input-output shafts are collinear) with a hysteresis loop of the non-metallic element. The nonlinear character of the characteristic of the non-metallic element exists both for loading and for unloading. The experimental setup made to perform the measurement is presented in Figure 8.

input-output shafts are collinear) with a hysteresis loop of the non-metallic element. The nonlinear character of the characteristic of the non-metallic element exists both for load-Curve 1 from Figure 9 presents variation of torque of input shaft in time. Curve 2 in the same figure presents variation of output torque of output shaft during unloading. Mti represents the input torque and Mto the output torque.

**Figure 7.** The maximum Von Mises stress of intermediary disc. **Figure 7.** The maximum Von Mises stress of intermediary disc. **Figure 7.** The maximum Von Mises stress of intermediary disc.

(**a**) (**a**)

**Figure 8.** The measurement stand (**a**) experimental stand for static and dynamic testing; (**b**) non-metallic elements from natural rubbers. **Figure 8.** The measurement stand (**a**) experimental stand for static and dynamic testing; (**b**) non-metallic elements from natural rubbers. **Figure 8.** The measurement stand (**a**) experimental stand for static and dynamic testing; (**b**) non-metallic elements from natural rubbers.

> Curve 1 from Figure 9 presents variation of torque of input shaft in time. Curve 2 in the same figure presents variation of output torque of output shaft during unloading. Mti

Curve 1 from Figure 9 presents variation of torque of input shaft in time. Curve 2 in the same figure presents variation of output torque of output shaft during unloading. Mti

represents the input torque and Mto the output torque.

represents the input torque and Mto the output torque.

linear.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 12 of 16

**Figure 9.** Measured torque in static mode. **Figure 9.** Measured torque in static mode. **Figure 9.** Measured torque in static mode.

The shock takes place by deforming the non-metallic elastic intermediate element, which transforms the shock energy into mechanical deformation work *L<sup>e</sup>* (the area under the load characteristic). Part of this energy (the area between the charging and the discharging characteristics) is transformed into heat, representing the mechanical friction work *L<sup>f</sup>* in the coupling. In non-metallic intermediate elements, friction takes place inside the elastic element (internal friction). From calculus results, mechanical deformation work *Le* = 211.94 J. The high values of the shock absorption capacity lead to the quiet operation of the transmission equipped with such a coupling, even to oscillating loads. The The shock takes place by deforming the non-metallic elastic intermediate element, which transforms the shock energy into mechanical deformation work *L<sup>e</sup>* (the area under the load characteristic). Part of this energy (the area between the charging and the discharging characteristics) is transformed into heat, representing the mechanical friction work *L<sup>f</sup>* in the coupling. In non-metallic intermediate elements, friction takes place inside the elastic element (internal friction). From calculus results, mechanical deformation work *L<sup>e</sup>* = 211.94 J. The high values of the shock absorption capacity lead to the quiet operation of the transmission equipped with such a coupling, even to oscillating loads. The flexible coupling with damping also improves the behavior in vibrational mode. The shock takes place by deforming the non-metallic elastic intermediate element, which transforms the shock energy into mechanical deformation work *L<sup>e</sup>* (the area under the load characteristic). Part of this energy (the area between the charging and the discharging characteristics) is transformed into heat, representing the mechanical friction work *L<sup>f</sup>* in the coupling. In non-metallic intermediate elements, friction takes place inside the elastic element (internal friction). From calculus results, mechanical deformation work *Le* = 211.94 J. The high values of the shock absorption capacity lead to the quiet operation of the transmission equipped with such a coupling, even to oscillating loads. The flexible coupling with damping also improves the behavior in vibrational mode.

flexible coupling with damping also improves the behavior in vibrational mode. Figure 10 shows the experimental torque at the input and the output shaft as well as for the attenuation factor of the constructive variant of the prototype tested in dynamic mode with the input shafts (collinearly output). The damping capacity of torsion shocks is the characteristic of flexible couplings to convert some of their energy into heat, the rest being converted into deformation energy, which will be returned to the system after the Figure 10 shows the experimental torque at the input and the output shaft as well as for the attenuation factor of the constructive variant of the prototype tested in dynamic mode with the input shafts (collinearly output). The damping capacity of torsion shocks is the characteristic of flexible couplings to convert some of their energy into heat, the rest being converted into deformation energy, which will be returned to the system after the shock action ceases. Figure 10 shows the experimental torque at the input and the output shaft as well as for the attenuation factor of the constructive variant of the prototype tested in dynamic mode with the input shafts (collinearly output). The damping capacity of torsion shocks is the characteristic of flexible couplings to convert some of their energy into heat, the rest being converted into deformation energy, which will be returned to the system after the shock action ceases.

shock action ceases.

**Figure 10.** Variation of moments to the input and the output shaft in dynamic approach; input and output shafts are col-**Figure 10.** Variation of moments to the input and the output shaft in dynamic approach; input and output shafts are collinear. **Figure 10.** Variation of moments to the input and the output shaft in dynamic approach; input and output shafts are collinear.

Figure 10 shows the variation of the relative rotation angle between the semi-coupled and the torsion moment at the dynamic output shaft, the data recording speed at the oscillograph being 100 mm/s in time of 1 s. In this figure can be seen the Figure 10 shows the variation of the relative rotation angle between the semi-coupled and the torsion moment at the dynamic output shaft, the data recording speed at the oscillograph being 100 mm/s in time of 1 s. In this figure can be seen the Figure 10 shows the variation of the relative rotation angle between the semi-coupled and the torsion moment at the dynamic output shaft, the data recording speed at the oscillograph being 100 mm/s in time of 1 s. In this figure can be seen the dynamic characteristic with a hysteresis loop of the non-metallic element. The hysteresis loop is

smaller and more attenuated in dynamic mode. In dynamic behavior, the shocks and the vibrations are higher, and the coupling damps these shocks and vibrations very well through the non-metallic elements. The relative rotation angle between the dynamic couplings is 2.25◦ , and the input the output shafts have collinearity. In dynamic mode, the coupling must also take over the overloads that appear during starting as well as the shocks that may occur during the operation of the system equipped with coupling. For Figure 11, from calculus results, a mechanical deformation work *L<sup>e</sup>* = 394.11 J. loop is smaller and more attenuated in dynamic mode. In dynamic behavior, the shocks and the vibrations are higher, and the coupling damps these shocks and vibrations very well through the non-metallic elements. The relative rotation angle between the dynamic couplings is 2.25°, and the input the output shafts have collinearity. In dynamic mode, the coupling must also take over the overloads that appear during starting as well as the shocks that may occur during the operation of the system equipped with coupling. For Figure 11, from calculus results, a mechanical deformation work *Le* = 394.11 J.

dynamic characteristic with a hysteresis loop of the non-metallic element. The hysteresis

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 13 of 16

**Figure 11.** Measured torque in dynamic mode. **Figure 11.** Measured torque in dynamic mode.

#### **4. Discussion 4. Discussion**

Shape 1

Shape 2

Shape 3

The main parameter resulting from the characteristic of the flexible couplings is the torque. Another important parameter is the rigidity, which represents the dependence of the relative rotation angle of the half-couplings, depending on the value of the torque *Mt* . The verification of the proposed mathematical model for determining the elastic characteristic of the flexible couplings, the validation of the constructive solution, and the adopted technology are performed by comparing the theoretical diagrams with the experimental ones, determined both in static and dynamic mode. The main parameter resulting from the characteristic of the flexible couplings is the torque. Another important parameter is the rigidity, which represents the dependence of the relative rotation angle *ϕ* of the half-couplings, depending on the value of the torque *M<sup>t</sup>* . The verification of the proposed mathematical model for determining the elastic characteristic of the flexible couplings, the validation of the constructive solution, and the adopted technology are performed by comparing the theoretical diagrams with the experimental ones, determined both in static and dynamic mode.

Following the calculation using FEM for the three shapes presented in Figure 4, we obtained results presented in Table 1. Following the calculation using FEM for the three shapes presented in Figure 4, we obtained results presented in Table 1.

From the results presented for the effective stresses to traction/compression and crushing, it follows that the three constructive forms of the non-metallic element resist crush and traction, which indicates a correct design. **Table 1.** Results of verification calculations at the solicitation of traction and crushing for non-metallic element (theoretical values).


*tF*<sup>1</sup> 0,43*MPa*

torque of 188.232 Nmm.

 *tF*<sup>2</sup> 0,55*MPa at* 1,5*MPa* ; *sF*<sup>1</sup> 0,24*MPa as* 7*MPa* . *tF*<sup>2</sup> 0,35*MPa at* 1,5*MPa* ; *sF*<sup>1</sup> 0,24*MPa as* 7*MPa* . From the results presented for the effective stresses to traction/compression and crushing, it follows that the three constructive forms of the non-metallic element resist crush and traction, which indicates a correct design.

 1,5*MPa* ; 

*sF*<sup>1</sup> 0,24*MPa*

*as* 7*MPa* .

*at*

The torque that can be transmitted and that resulted in the three cases is presented in Figure 12. The maximum torque that can be transmitted by the coupling is determined by the traction conditions. The torque that can be transmitted and that resulted in the three cases is presented in Figure 12. The maximum torque that can be transmitted by the coupling is determined by the traction conditions.

The third case, presented in Figure 4, allows the coupling to transmit a maximum

**5. Conclusions** The following criteria must be taken into account when designing such a coupling: The third case, presented in Figure 4, allows the coupling to transmit a maximum torque of 188.232 Nmm.

#### the coupling must take axial, radial, and/or angular deviations; the relative movement **5. Conclusions**

between the semi-couplings to be done without shocks; the coupling must have a low rigidity; feature to have an increasing slope and high damping capacity; changing the non-metallic elastic elements to achieve the modification of the coupling elasticity; in case of damage to a non-metallic element, the coupling can continue to operate; destroyed elastic elements can be easily replaced; the component elements of the coupling must not have protrusions/roughness, thus increasing the safety in operation. The study permits us to draw the following conclusions: the coupling has the possibility to transmit the torque in any direction; The following criteria must be taken into account when designing such a coupling: the coupling must take axial, radial, and/or angular deviations; the relative movement between the semi-couplings to be done without shocks; the coupling must have a low rigidity; feature to have an increasing slope and high damping capacity; changing the non-metallic elastic elements to achieve the modification of the coupling elasticity; in case of damage to a non-metallic element, the coupling can continue to operate; destroyed elastic elements can be easily replaced; the component elements of the coupling must not have protrusions/roughness, thus increasing the safety in operation.

 the proposed solution of coupling ensures compensation of radial and angular de-The study permits us to draw the following conclusions:


The main objective was the level of performance of the coupling, namely the torque of being transmitted by the coupling. Experimental determinations were made in different cases by loading and unloading. Another objective was to carry out tests in different modes (static and dynamic, respectively) taking into account the situation that the two input and output shafts are collinear. From the point of view of functional performance (the torque transmitted by coupling to a load-discharge cycle and the torque to input shaft I and output shaft II, respectively), the coupling performed well, the values obtained experimentally being close to the theoretical ones.

The tested construction variant has a very good shock and vibration attenuation factor of up to 9%.

Figures 9 and 11 show the non-linear characteristic of non-metallic elements at loading and unloading, which means that the flexible coupling with milled bolts and non-metallic elements has the non-linear characteristic, and the coupling is with variable rigidity. Damping occurs if there is a difference between the elastic loading characteristic and the elastic unloading characteristic of the coupling. The hysteresis loop is smaller and more attenuated in dynamic mode. In dynamic mode, the shocks and the vibrations are higher, and the coupling damps these shocks and vibrations very well through the non-metallic elements.

From the dynamic variation of the torsion moment at the output shaft according to the relative angle of rotation between the two semi-couples it can be observed that the non-metallic element has a negligible hysteretic loss, on a small portion of the discharge characteristic practically coinciding with the loading. Note the non-linear nature of the non-metallic element feature when loading and unloading.

**Author Contributions:** Conceptualization, M.G.; methodology, M.G.; software, I.-M.G. and M.G.; validation, M.G., I.-M.G.; formal analysis, S.V., I.-M.G., M.G., P.N.B.; investigation, I.-M.G.; resources, M.G. and I.-M.G.; data curation, M.G. and I.-M.G.; writing—original draft preparation, M.G. and I.-M.G.; writing—review and editing, S.V., M.G. and I.-M.G.; visualization, S.V., M.G. and I.-M.G.; supervision, S.V., M.G., I.-M.G., P.N.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article*
