Hierarchical Control in Mechatronic Technological Systems

Abstract

The topic of hierarchical control of technological machines is one of the most relevant in mechanical engineering technology. The most difficult issue in this area is the organization of interactions between different control levels, on the one hand, and the choice of automatic control methods for each of these control levels (control by deviation, control by disturbance, mixed control, etc.), on the other. In this article, in relation to machining technology, a method and corresponding device are proposed that make it possible to implement the control of cutting force parameters (axial cutting force and cutting torque) in an automatic control system for the deviation of cutting torque by changing the axial cutting force (lower level of control). The lower-level control ensures the required quality of the surface layer (surface integrity) of the machined parts. At the same time, the required dimensional accuracy of parts is ensured at the upper level of control, which is implemented by the CNC system of the machine. At the upper level, automatic control is carried out based on the deviation of the kinematic parameters of the movement of the working parts of the CNC machine (acceleration, speed, displacement). Control switching from upper to lower level and back is carried out without using a spindle linear axial movement sensor. Instead of this expensive sensor, a limit switch (a closed and opened pair of contacts) is used, which fixes the lowest axial position of the spindle (and cutting tool). Based on the signal of closing the specified contacts of the limit switch, a transition from the lower control level to the upper one is carried out. Thus, the upper-level system operates only when these contacts are closed, and the lower-level system operates only when they are open. In relation to the upper-level system, the lower-level control system implements the control “by disturbance” principle, also known in control theory as the “disturbance compensation principle”.

1. Introduction

Conventional CNC systems on metal-cutting machines automatically maintain the kinematic parameters of the movement of the working bodies of these machines (displacement, speed, and acceleration). However, the physical and mechanical state of the surface layer (defects, such as burns and microcracks) depends on the cutting force parameters in the machining area (axial cutting force and cutting torque). For example, the quality of critical machine parts produced in various fields of industrial production is often inextricably linked with the physical and mechanical state of their surface layer (surface integrity). Such parts include, for example, compressor and turbine blades made of high-strength alloys containing titanium, chromium, cobalt, nickel and other alloying additives. Such materials provide, on the one hand, high-performance properties of finished parts, and on the other hand, have an increased tendency towards grinding burns and microcracks in the case when the values of the force (power) parameters of cutting and grinding exceed the permissible level.

Stabilization of force parameters at the required technological level is an important condition for ensuring the guaranteed quality of dimensional shaping of parts made of polymer composite materials (PCM), since their binder component is prone to melting. In addition, a non-optimal program of changing the force parameters of cutting at the entrance and exit, for example, of a drill bit, leads to “edge fraying” of the machined surface.

The quality of machining of products made of precious stones (diamond, ruby, sapphire, and emerald) due to their brittleness and tendency to microcracks cannot be guaranteed without control and limitation of the cutting force (power) parameters. That is why exclusive handmade products, which are made with low cutting forces, are so highly valued.

Simultaneous provision of programmable kinematic parameters and force parameters of cutting in the technological system is complicated by their mutual influence, in which, for example, ensuring the accuracy of parts is accompanied by a violation of the required physical and mechanical state of their surface layer (surface integrity).

Therefore, the introduction of “smart cutting” based on the regulated accounting of kinematic and force parameters of cutting, along with ensuring the required performance of technological equipment, is an urgent task in science, technology, and production. The article proposes to solve this problem through the development of a mechatronic technological system (MTS) based on CNC and intelligent mechatronic mechanism (IMM), respectively, at the upper (CNC) and lower (IMM) control levels. In such an MTS, the provision of programmatically specified kinematic and force parameters of machining is carried out by automatic CNC and IMM systems, respectively, at the upper and lower levels of control.

2. Literature Review

The theory of hierarchical control is still far from being completed. There are no established rules and criteria for the interaction of various levels in terms of achieving an acceptable control result. Significant achievements in this area include the well-known rule of authority levels according to George N. Saridis, namely that the control intelligence is hierarchically distributed according to the principle of increasing precision with decreasing intelligence (Figure 1), evident in all hierarchical control systems [1]. Analytical functions of an intelligent machine are implemented by intelligent controls, using entropy as a measure. However, various cost functions expressed in entropy terms may be used to evaluate the generated design. For instance, reliability as a property highly desirable for autonomous systems is a measure of performance expressed by entropy, which can be combined in the criterion of performance of the system design.

The response of a mechatronic deviation feedback system to the occurrence of an unforeseen deviation is delayed, and such a (closed) system is not ready for the upcoming random (unforeseen) deviation [2].

In turn, the disadvantage of the operation of a faster mechatronic system “by disturbance” when monitoring force parameters in the machining area is the fact that during the execution of the dimensional machining program, in places of changes in the physical and mechanical properties of the machining material of the part, dimensional errors occur in the form of areas of unremoved material [3]. This is also unacceptable, since the requirement to ensure the accuracy of machining in accordance with the part’ drawing is violated. Previously, some aspects of surface integrity methods were covered, but their implementation is shown without reference to the part’s geometric accuracy [3].

The possibility of regulating cutting modes in three intervals depending on the angle of inclination of the threaded groove of the mechatronic mechanism is shown with the following zones: the nano-technology (zone A), microtechnology (zone B), and microtechnology (zone C) [4].

In addition, modern methods of obtaining blanks have reached such a level that the technology of dimensional shaping of the finished product is reduced to removing the stock allowance in one pass. However, this does not exclude the occurrence of defects in the surface layer of the workpiece associated with the anisotropy of the physical and mechanical properties of the machining material.

From this point of view, this paper focuses on methods for stabilizing the required force parameters of machining complex-shaped surfaces and free-form surfaces that have significant deviations of the initial surface of the workpiece from the specified (according to the drawing) geometry of the finished part.

The problem of “accuracy-quality” is universal and is especially manifested in medicine. For example, drilling living bone tissue is a fundamental skill and art for maxillofacial surgeons and orthopedists in the treatment of injuries sustained as a result of an accident, illness, or aging of a person. As a result of population ageing, the prevalence of bone diseases is expected to increase dramatically. For example, to immobilize broken areas of the bone, drilling holes in the bone is used (for example, to place implants). This is a common practice in orthopedics and dentistry. However, bone drilling surgery has many problems related to the design of the medical drill [5,6,7,8,9].

Bone cutting and drilling is a well-established and mature field, and numerous factors and devices have been studied to address the aforementioned bone drilling problems, including drill bit design, drill wear, and drilling and coolant delivery parameters [5,8].

It is possible to radically change the state of affairs in the field of drilling and bone cutting if machining technology used for cutting and the drilling metals and composites, and feedback and adaptive control are often used as part of Industry 4.0 work [10].

Significant studies have been devoted to the study of defects caused by iatrogenic damage, i.e., the side traumatic effect of mechanical machining on bone tissue [11]. To ensure the safety of the tissues that surround the bone, cutting power, axial force, torque, and temperature must be kept below the critical level of osteonecrosis. Here, positive results were obtained related to the measurement and control of force parameters during drilling [6,7,12].

The idea of hierarchical (two-level) control of the axial cutting tool movement is based on a systematic approach that provides the required interaction of the upper and lower levels of control [13]. However, the design and mechanism of this interaction are not shown in this paper.

Non-contact passive SAW (surface acoustic wave) sensors can serve as transducers to measure the torque on the shaft that transmits energy from the traction motor to the cutting tool [14,15]. Actual torque information can be used to monitor the cutting torque [16]. However, there are some difficulties with the installation of these sensors on the shaft and the placement of the transmitting and receiving antennas. Furthermore, there is no information about the use of SAW sensors in the automatic torque control system.

To monitor the cutting processes, noise signals accompanying the cutting process are used, since noise always stems from transient forces that excite the structure to vibrate, emitting sound waves into the environment due to vibrations on the surface [17]. It is noted that the source of noise is the technological process itself; therefore, the noise signal carries information that can be used for technological purposes. This requires mathematical models that link the change in cutting forces over time directly with the cutting force parameters. However, the article points out that the relevant research is on the threshold of industrial application.

The methodology for optimizing cutting parameters based on the integration of a computer-aided manufacturing (CAM) system and a tool holder capable of detecting unstable process conditions during milling is of interest also in [18]. The authors compare this approach with modern adaptive process control systems. These systems provide the ability to change the feed rate and spindle rotation. This approach uses high-level CAM objects in the data processing cycle. However, it is not specified which parameters are being discussed.

A solution to the problem of regulating the feed rate during the point milling of complex-shaped parts is known [19]. When milling complex-shaped parts, the specified cutting conditions are not reached when the technological operation is set up for tools with a circular cutting edge. This is caused by the continuous change in the contact point between the tool and the workpiece, together with the fact that the cutting conditions are conventionally set to the tool reference point.

An implemented digital twin (DT) framework is presented by the orchestration of CAM-integrated and containerized technology models carrying out FEM-coupled simulations for the finishing process of a simplified blade integrated disk (blisk) demonstrator [20]. Orchestration means that the abovementioned method is made possible through the careful management and coordination of many system elements. The term blade integrated disk (Blisk) is used in the aerospace and aviation industries. A “blisk” is a monolithic part where the blades and disk are a single structure, unlike traditional turbine disks where the blades are attached to the disk as separate components. This design reduces weight, improves aerodynamics, and reduces the number of joints, making the parts more reliable.

Therefore, the purpose of this article is to develop a method and intelligent mechatronic mechanism (IMM) for the two-level (hierarchical) control of machining accuracy from the CNC system at the upper level of control of kinematic parameters, and for machining quality control from the IMM at the lower level of control of force parameters (axial cutting force and cutting torque).

3. Research Methodology

3.1. Prerequisites for Hierarchical Control

The principle of hierarchical (multi-level) control of a complex object is widespread in nature and society, starting from the organization of relationships in the systems “boss–subordinate”, “parents–children”, “senior–junior”, and “teacher–student”, and ending with the construction of complex hierarchical state and interstate structures designed to ensure the life of society and each individual.

Applied to technical automatic control systems, this principle is known as a combination of “rough” and “precise” control, which are sequentially and parallelly located in time. For example, the movement of a guided missile is first supported by its own launcher at a distance of 200–300 km; then, the missile is controlled by a long-range aircraft, which maintains control at a much greater distance, and, finally, in the immediate vicinity of the target, i.e., at a distance of 5–10 km, the missile’s own radar is turned on, which provides a hit on the target with an accuracy of 1–3 m. At the same time, an even higher level of control is possible from the corresponding satellite.

At each level of control, the corresponding control principle is applied: open control without feedback, closed control with feedback “by deviation”, control “by disturbance”, or a combination of them (mixed control). In the review, it was shown that separate control of the operation of the mechatronic technological system (MTS) “by deviation” and “by disturbance” does not give an effective result, which can be achieved by symbiosis of these two methods of automatic control. That is, it is not simple arithmetic addition, but by synergistically combining them into a fundamentally new intellectual two-level hierarchical control structure.

The two-level hierarchical control structure proposed below provides the following features.

• It can react to an accidental “disturbance” that appears simultaneously with its occurrence, and not after an event that has already taken place, which can no longer be changed.
• It can automatically suspend the course of the technological process set by the upper control level (CNC) to eliminate the “disturbance” that has arisen at the lower level (IMM), putting this level into operation.
• It can eliminate the “disturbance” that has arisen at the lower level by the selected methods of gradual approximation of the actual geometry of the machining surface to the part required according to the drawing.
• After the elimination of the “disturbance” at the lower control level from the IMM, it can automatically resume the suspended course of the technological process according to the CNC program of the upper control level until the machining is complete.

In these four points, analogies are seen with the unique intellectual abilities of living organisms to adapt to the situation that has arisen and to find a way out of the created situation by means of spontaneous (non-programmed in advance) but “reasonable” actions that allow them to preserve their vital activity, maintaining a given homeostasis, i.e., maintaining the system in a stable state relative to the changing external environment. With regard to technical systems, it is necessary to add the possibility of following the pre-programmed final goal after the elimination of the “disturbance” that has arisen.

Thus, in the hierarchical MTS, there are opportunities for “delegating authority” to control the course of the technological process in the direction from the upper control level to the lower one and vice versa. This occurs when a “disturbance” occurs, about which the lower control level (IMM) signals the upper one (CNC) and suspends its operation. When the “disturbance” at the lower control level (IMM) is eliminated, the lower level allows the upper level (CNC) to continue working according to the specified upper control level program (CNC).

For example, if we take as a prototype the totality of actions of the “rational behavior” of a person, then these actions can be conditionally divided into the following types:

• Fast-moving actions at the level of the self-preservation instinct, which have an almost “explosive” character with a sudden change in the properties of the environment (lightning and thunder).
• Meaningful actions, the result of which is the search and optimization of many possible options and the adoption of a final decision to eliminate the “disturbance” that has arisen in the environment, for example, at the level of the central nervous system of a person.

Analogous to the above, IMM within the MTS performs the function of a “mechanism” that implements the “self-preservation instinct” in the event of a power overload, and the function of the “thinking apparatus” is performed by the CNC and IMM computer.

3.2. Ensuring the Maneuverability of Two-Level Control

The two-level control system should provide unified control in the MTS conditions to achieve the control goal: maximum productivity with the specified parameters of machining accuracy and the required physical and mechanical state of the surface layer (surface integrity). Based on this, we can formulate the basic requirements for MTS, an integral part of which is the new-generation IMM.

Firstly, the ability of the MTS under conditions of uncertainty to execute the “strategic” plan of surface machining when controlled by the CNC (upper control level) and to transfer the CNC system of the machine to the “standby” mode until the signal appears concerning the execution of the “tactical” machining plan (lower control level), i.e., after the elimination of the accidentally arisen “disturbance”, is essential.

Secondly, the ability to suspend the operation of the upper control level system (CNC) when receiving a signal from the lower level (IMM) about the “disturbance” that has arisen and resume it after this “disturbance” is eliminated is essential.

Thirdly, the ability of the MTS in conditions of uncertainty to transfer the lower control level (IMM) from the “standby” mode to the operating mode until the “disturbance” is eliminated and to generate a signal for the upper control level (CNC) about the completion of the “disturbance” elimination process is essential.

Fourthly, the ability of MTS to coordinate “wait” and “work” commands between the upper and lower levels of control in real time to ensure the continuous operation of both levels of control to achieve a single programmed control goal is essential.

The above capabilities are implemented in the MTS under consideration due to the development of a new generation IMM design, the description and operating principle of which are given below.

4. Construction of MTS with Two-Level Control

4.1. MTS Structure and Its Operation When Controlled by CNC

Figure 2 shows a diagram of the IMM, including a worktable (1) for the CNC machine on which the workpiece (2) is fixed. The machining tool (3) is mounted on a “floating” spindle (4), which has the possibility of simultaneous rotation and reciprocating vertical movement along its longitudinal axis, for example, in the interval of 0–5 mm [3]. The diagram in Figure 2b corresponds to the real situation that took place during the experimental studies.

In Figure 2, the following notations are used when machining a free-form surface (FFS): $Z_0$ is the current instantaneous value of the coordinate $Z$ in the $XYZ$ coordinate system of CNC machine of the upper control level, in relation to which (in coordinates $xyz$) the lower control level coordinate $z_i>0$ is counted. The course of these linear movements in the direction of the workpiece being machined is limited by rigid stops-contacts (5), to which the end face (6) of the movable armature with a winding (7), is pressed. The mechanical and electrical closure of stops-contacts (5) between themselves by the end face of armature (6) makes it possible to generate a control signal for switching on the CNC system (upper control level) for executing the CNC control program.

The armature (6) is rigidly connected to the rotating spindle (4). Therefore, the closed state of the contacts (5) means that the CNC system (upper control level) is operating, and the cutting force parameters, i.e., axial cutting force $F$ and cutting torque $M$ do not exceed the preset values of $F_0$ and $M_0$ ($F<F_0$ and $M<M_0$, respectively).

The ferromagnetic body (8) (Figure 2a) is fixed on the vertical feed slide of the machine (not shown in the diagram), so it is possible to move programmatically along the axis $Z$ of the machine in the coordinate system $XYZ$. Horizontal movements in the coordinates $X$ and $Y$ are received by the workpiece, so 3D machining of complex-shaped surfaces and free-form surfaces is possible. The use of IMM is not limited to 3D machining and can be implemented on 4- and 5-coordinate machining centers, for example, for dimensional shaping of the working surfaces of turbine blades.

The movable armature (6) provides reciprocating axial movements of the spindle (4), in case of the violation of the conditions $F<F_0$ or $M<M_0$. The winding (7) of the armature (6) receives power from the source (9) through an adjustable resistance (10), which determines the current $I$ in the armature winding (7).

The design of IMM also has a field winding (11) that lays on a magnetic core (12) (Figure 2a). When connected, it creates a magnetic flux of the desired direction and magnitude, i.e., it forms the value of magnetic field induction $B$, which, when acting on the winding (7) with an electric current $I$ (from the source (9)), creates an electrodynamic force ${\overline{F}}_{ed}$ determined from the following expression [3]:

$${\overline{F}}_{ed}=k·I\left[\overline{B},\overline{l}\right],$$

(1)

where ${\overline{F}}_{ed}$ [N] is the vector of the electrodynamic force acting on the conductor with a current $I$ in a magnetic field; $k$ is the proportionality coefficient, determined empirically (its value is entered into the passport data of each IMM design); $I$ [A] the current in the armature winding (7) (scalar value); $\left[\overline{B},\overline{l}\right]$ is the vector product of vectors $\overline{B}$ and $\overline{l}$; $\overline{B}$ [T] is the magnetic field induction vector; $\overline{l}$ [m] is the length vector of the conductor (the length of the armature winding (7)) having a direction perpendicular to the vector $\overline{B}$.

Thus, the ferromagnetic body (8), the field winding (11), and the magnetic core (12), made of soft magnetic steel [C10 and C22 according to DIN EN 10084, Germany], create a magnetic induction $\overline{B}$ that penetrates the armature winding (7) perpendicular to its turns. This, in the presence of current $I$ in the armature winding (7), causes the appearance of an electrodynamic force ${\overline{F}}_{ed}$ that presses the armature (6) against the stops-contacts (5) and ensures their rigid mechanical and electrical contact. The closing and opening of the stops-contacts (5) are, respectively, signals for the transition from the lower “tactical” control level to the upper “strategic” level and vice versa.

In the case under consideration, the break in contact between the stops-contacts (5) occurs when the current cutting torque $M$ becomes greater than the specified (programmed) $M_0$, which can be transmitted by the ball-bearing screw converter (13) (Figure 2), consisting of a “nut” (14) and a “screw” (IMM spindle) (15) [3]. When a load “disturbance” occurs, it converts the torque difference ($∆M=M-M_0$) into the linear displacement $z_i>0$ of the armature (6) relative to the body (8) (Figure 2a and Figure 3). That is, the ball-bearing screw converter (13) is simultaneously a signal source (transducer or sensor) for the magnitude of the armature’s (6) linear displacement in relation to the IMM body.

The connection between the armature (6) and ball-bearing screw converter (13) is traced along the following closed chain: armature winding (7)–movable armature (6)–duplex bearings (in Figure 2 only one bearing of two is shown)–spindle (4)–axis (15) of spindle (4)– two ball bearings (their outer rings rest on the screw groove of “nut” (14))–ball bearings (17) (their ends are rigidly connected to the IMM body). In this closed circuit, an electrodynamic force $F_{ed}$ is generated, which, after the tool comes into contact with the workpiece, is transformed into a vertical force $F<F_{ed}$ directed from top to bottom (not shown in Figure 3).

The latter force $F$ encounters an increasing counteraction of the axial cutting force $F$ until equilibrium is established between decreasing the electrodynamic force [see Equation (1)] and the axial cutting force $F$. In this case, part of the initially specified electrodynamic force ${\overline{F}}_{ed}$ is converted into an increment in torque $M$, which (the increment) by its presence ensures stabilization of the cutting torque $M$ at the required level $M_0$, i.e., $M=M_0$. This level is set by the induction $B$ from the field winding (11) and the armature (6) current $I$ in the armature winding (6) in accordance with Equation (1).

The magnitude of the elastic “spring-back” of the spindle with the tool ($z_i>0$) is directly proportional to the difference $∆M$ between the current $M$ and specified $M_0$ cutting torques (Figure 3). That is, $∆M=M-M_0$. Now it is possible to build a graph (Figure 3c), which allows for visual recommendations to be obtained for the value of the helical groove inclination angle $\mathsf{\alpha }$ for the implementation of various technological machining mode, as follows: zone A—nanotechnology; zone B—microtechnology; zone C—microtechnology [4].

At the same time, a part of the force $F_{ed}$ is transferred from the ball bearing screw converter to the spindle and the tool, creating an axial load on the machining tool proportional to this force, equal in value to the following [3]:

$$F=k_F{F}_{ed}·{\mathrm{s}\mathrm{i}\mathrm{n}}^2\mathsf{\alpha }=k_F{F}_{ed}·\mathsf{\eta },$$

(2)

where $F$ [N] is the axial cutting force acting on the machining tool; $k_F$ is the proportionality coefficient, the value of which is determined empirically for each IMM design; ${\overline{F}}_{ed}$ [N] is the electrodynamic force acting on the armature (6) IMM; $\mathsf{\alpha }$ [deg] is the inclination angle of the screw groove of the ball-bearing screw converter “nut” (Figure 3c).

Vertical “spring-back” ($z_i>0$) (Figure 3) in a movable coordinate system $xyz$ (Figure 2) is a consequence of the occurrence of a “disturbance” in the cutting zone (increase in the depth of cut due to the stock allowance unevenness, blunting of the tool, etc.). It is defined in relation to the current value of the vertical coordinate of the CNC. Therefore, the actual instantaneous vertical coordinate of the tool after the appearance of a “disturbance” with respect to the technological installation base of the workpiece (the location surface or LS) is ${Z^{\prime }=Z}_0+z_i$ (Figure 3). That is, due to the appearance of a vertical “spring-back” $z_i$, the value $Z^{\prime }$ always increases.

The design of the IMM also includes a drive (16) of the rotation of the “nut” (14), which is mounted on a ball bearing (17) (Figure 2) in the IMM body (8) without the possibility of any displacements in one direction or another, except for rotation.

The hierarchical control system of the MTS also includes the CNC unit (18) of the machine, which belongs to the upper control level, while the computer (19) and electronic units (20, 21, 22, 23, and 24) (devices for receiving, converting, and transmitting signals) belong to the lower control level.

The DC power source (25) is included in the power supply circuit of the contacts (5). Depending on the state of the contacts (5)—closed or open—MTS operates in one of three modes (in accordance with the intelligent control algorithms of the computer (19)), as follows:

(1)

CNC without the IMM participation, if the force parameters do not exceed the preset values (hereinafter referred to as the “stable cutting mode”);

(2)

Alternating CNC and IMM with the removal of dimensional error in a single pass by the vertical plunge method;

(3)

Simultaneous CNC and MM operation (copying the error and its sequential removal according to the “residual stock allowance removal” program).

The DC source (26) feeds a linear displacement sensor, e.g., a variable resistor (not shown explicitly in Figure 2). The movable pointer (variable resistor slider) (27) of this sensor is rigidly connected to the movable armature (6), and the stationary element (resistor body) (28) of this sensor is rigidly connected to the fixed body (8).

The DC power source (29) provides the specified current through the field winding (11) and, as a result, the amount of electrodynamic force $F_{ed}$ that specifies the axial cutting force $F$ and cutting torque $M$ for the corresponding control mode from the computer (19).

4.2. MTS Operation in the “Stable Cutting Mode”

In this mode, the lower control level (based on IMM) does not work, and MTS is no different from the technological system based on a conventional CNC machine with all its nominal technological capabilities. The characteristic feature is as follows: the armature (6) of the IMM is rigidly pressed by the force $F_{ed}$ against the stops-contacts (5), and the spindle (4) occupies a fixed position $z_i=0$ in the moving coordinate system $xyz$ (Figure 2). The constancy of the axial cutting force $F$ and cutting torque $M$ in the “stable cutting mode” is typical for finishing operations, when “disturbances” have already been removed in the previous roughing operation steps. Therefore, the “stable cutting mode”, which is performed at the upper control level (CNC), outwardly corresponds to the finishing machining on a conventional CNC machine. Thus, the term “stable cutting mode” is relative. It indicates one of two possible operating modes.

4.3. Transition of Control from the Up Level (CNC) to the Lower One (IMM)

The machining force parameters specified according to the technology requirements are realized by IMM as a result of the interaction of the current-carrying conductor (armature winding (7)) with magnetic induction from the field winding (11). To achieve this, the power supplies (9 and 29) are turned on.

When electric currents pass through the armature winding (7) and the field winding (11), the axial force $F$ acts on the armature (6) in the axial direction. This is a part of the electrodynamic force $F_{ed}$ [N] determined by Formula (2). This axial force $F$ [N] corresponds to the cutting torque $M$ [N·m], which is a function of this force, as follows:

$$M=k_{FM}·F,$$

(3)

where $k_{FM}$ [(N·m)/N] is the empirical coefficient of the relationship between the axial force $F$ and the cutting torque $M$ (depending on the machining conditions).

The IMM operation in the “standby” mode can be represented as follows (Figure 4). A machining program is entered into the CNC unit (18) of the machine (upper control level), i.e., the trajectory and movement parameters of the machining tool in the coordinate system $XYZ$ are programmed.

Moreover, for each coordinate, the calculated (standard) machining force parameters $F_0$ and $M_0$ are assigned and this information, via the corresponding communication channels, is recorded in the computer (19) of IMM (lower control level).

Switching on the power source (29) provides an electric current along the field winding (11) of such a magnitude and direction that (in the presence of current $I$ in the armature winding (7)) the required electrodynamic force $F_{ed}$ arises.

By switching on the armature winding (7) and regulating the current ($I$) in it with the resistance (10), it is possible to provide a force $F_{ed}$ that guarantees a power short circuit between the end of the armature (6) and the electrical stops-contacts (5). In this case, the moving element (27) of the linear displacement sensor is in the zero position ($z_i$ = 0).

The primary signal about the force contact interaction of a tool and a workpiece in the cutting zone comes from the linear displacement sensor (resistor, capacitive, inductive, etc.). The moving element (28) of this sensor is fixed on the armature (6), while the fixed element (29) is installed on the IMM body (8).

In this way, the operation principle of the IMM new generation is implemented simultaneously in two coordinate systems, $XYZ$ and $xyz$ (Figure 4), respectively, for the upper (CNC) and lower (IMM) control levels, and the $xyz$ coordinate system is one-dimensional, i.e., the $x$ and $y$ coordinates are always equal to zero. The movable coordinate system $xyz$ is organized in such a way that the movement of the spindle (4) is possible only along the vertical axis $z$, i.e., the possibility of any displacements of the spindle along the $x$ and $y$ axes is excluded. As the stock allowance is cut off from the machined surface, a linear vertical movement of the tool is carried out down to the physical contact of the armature (6) end-face with the stops-contacts (5). The appearance of electric current from power source (25) is a signal to turn on the upper control system (CNC).

The functional expediency of this action is due to the fact that at this moment the tool is exactly in those $XYZ$ coordinates of the CNC system where the system was previously switched off. Now the CNC system continues its work until $F\le F_0$ and $M\le M_0$.

Thus, the inclusion of the force parameters of machining, as an equal component of a single two-level control system for the process of force contact interaction of the machining tool with the workpiece under uncertainty conditions (i.e., with accidentally occurring disturbances), allows for a guaranteed result to be obtained in terms of the accuracy of the dimensions performed and the workpiece surface integrity with the maximum possible machining performance. With this method, the upper control level (CNC) ensures the accuracy of the machining kinematic parameters (and accuracy of the part being machined), and the lower control level ensures the required physical and mechanical state (surface integrity) of the part surface layer and the regulated conditions for the cutting tool operation.

Such control corresponds to the well-known principles of effective control in cybernetics: (1) system decomposition (dividing a complex system into simpler subsystems, each of which is controlled independently); (2) a combination of control “in the big” (strategic control) and “in the small” (tactic control). Depending on the structure of the machined material, its physical and mechanical properties, the degree of anisotropy, etc., the MTS operation is divided as follows.

At the upper control level (CNC):

(1)

CNC program control of kinematic machining parameters (displacement, speed, acceleration);

(2)

Control “by deviation” when adjusting each kinematic parameter (cutting depth, feed, and cutting speed).

At the lower control level (IMM):

Stabilizing control “by deviation” in a closed system of automatic control of the force machining parameters (axial cutting force and cutting torque) due to a change in the axial feed of the tool, which leads to a decrease in the depth of cut.

In relation to the control system “by deviation” of kinematic parameters at the upper control level (CNC), the corresponding system of automatic control of force parameters at the lower control level (IMM) is a control system “by disturbance”. This is due to the fact that the elimination of disturbance at the lower level (IMM) contributes to the stabilization of kinematic parameters at the upper level (CNC).

At the zero position of the moving element 27 ($z_i=0$), the CNC system of the machine is started. Since the programmed (at the lower control level) force parameters $F$ and $M$ are sufficient to implement the cutting process, and there are no deviations from their values (the ideal version of a stationary cutting process), the machining technology is carried out as on a conventional CNC machine that does not have an IMM. In this case, the final result in terms of productivity and machining accuracy must correspond to the technical characteristics of the CNC machine. However, the lack of control over the values of $F$ and $M$ will inevitably lead to their deviation from the required ones. Therefore, a traditional CNC technological system containing an automatic control system for kinematic parameters should be supplemented by an automatic control system for the force parameters $F$ and $M$.

4.4. Alternating Operation of CNC and IMM

When the actual cutting torque ${M=M}_0+∆M>M_0$, i.e., it exceeds the specified value $M_0$ (the occurrence of “disturbance” $∆M$ in the cutting zone with a constant value of the axial cutting force $F_0$), then the IMM linear axial movement drive (lower control level) switches to the automatic “disturbance” elimination mode (Figure 5a).

This mode provides for the suspension of CNC control (upper control level) for all linear movements of the machine at the coordinates $XYZ$. From this point on, the IMM tracking system is in operation, e.g., in the mode of stabilization of the cutting force parameters, i.e., ${F=F}_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M=M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$. The increment ∆M leads to automatic lifting of the spindle to a certain height $z_i>0$ (Figure 4). In terms of the developed IMM design, the “screw” (15) is “screwed” into the “nut” (14) at which $∆M\to 0$. This leads to a decrease in the cutting depth (by the spindle lift height $z_i>0$) until the conditions $F_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ are achieved (met).

If the contact between the tool and the workpiece occurs simultaneously, for example, in two different sections of the tool profile, then the total axial cutting force $F_0$ is composed of two forces $F_0^{\prime }$ and $F_0^{″}$ (Figure 5a), and $F_0=F_0^{\prime }+F_0^{″}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$.

With the CNC system turned off, the IMM automatic system for stabilizing the force parameters continues to operate. In this case, the cutting tool (and spindle) (under the action of force $F$, that is determined by Formula (2), is lowered vertically down with a certain vertical feed, removing the “disturbance”, i.e., $z_i$ → 0.

The value of this feed is selected automatically. It is a “manipulated variable” in the IMM lower control level system. It depends on the cutting conditions, the shape of the unevenness to be removed and the value of the “controlled parameter” $M_0$.). When $z_i=0$, mechanical and electrical closure of the stops-contacts (5) occurs (Figure 2a).

At the moment of closing the stops-contacts (5), the lower point of the tool is just on the required (according to the CNC program) surface of the workpiece, and at this point $F=0$ and $M=0$. Therefore, the closure of the stops-contacts (5) is a signal for the transfer of control to the CNC system (upper control level), which starts the previously suspended feeds $S_Z$ and $S_X$. Under the action of these feeds, the tool (in relation to a workpiece) simultaneously moves upward ($S_Z$) and to the right ($S_X$), respectively (Figure 5a).

At some point in time (due to the increase in the load on the tool from feeds $S_Z$ and $S_X$), the cutting torque receives an increment $∆M$, i.e., the situation $M=M_0+∆M>M_0$ repeats itself. At this moment, the IMM transducer 29 generates a signal $z_i>0$ and the stops-contacts (5) open. The CNC system (upper control level) is disconnected from the control of the workpiece machining process.

When the contacts (5) are open, the automatic drive for stabilization of the IMM force parameters (lower control level) comes into operation again in order to eliminate the “disturbance” $∆M$. That is, the spindle is automatically lifted to a height $z_i>0$ again. Then (in the absence of feeds $S_Z$ and $S_X$) it automatically returns down from the IMM stabilization system (lower control level), carrying out the cutting process at $F_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ (trajectory $k-d-r-e$ in Figure 5a).

The number of repetitive spindle raising and lowering cycles (from IMM without stopping the cutting process) that alternate with feeds $S_Z$ and $S_X$ from the CNC (upper control level) is an unpredictable result of automatic control and depends, for example, on the shape and dimensions of the unevenness to be removed and the IMM (lower control level) values $F_0$ and $M_0$. Note that the numerical values of $F_0$ and $M_0$ can be programmatically changed from IMM (lower level of control), i.e., they can be not only constant, but also variable: $F_0\left(z_i\right)$ and $M_0\left(z_i\right)$. This article does not address this case.

The result of the operation of the described two-level control system (when the circuits of the upper and lower control levels are sequentially and alternately included in the work) is the complete elimination of excess stock allowance and the achievement of the specified quality of the surface layer, which is guaranteed by the following fulfilled conditions: $M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $F_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}.$ It is also possible to have a variant of tracking control from the IMM lower control level, in which the cutting of the specified unevenness in the section $k-d-r-e$, (Figure 5a) occurs in accordance with the variable assignments $F_0\left(z_i\right)$ and $M_0\left(z_i\right)$ as $z_i$ → 0.

4.5. Simultaneous Operation of CNC and IMM

The MTS operation during disturbance removal under the program “residual stock removal” (Figure 5b) occurs with the simultaneous operation of CNC and IMM. Signal stops-contacts (5) (Figure 2 and Figure 4) are not involved in this case, and they are closed (Figure 2a). The tool movements $S_Z$ and $S_X$ relative to the workpiece according to the CNC program (upper control level) are not interrupted and occur simultaneously with the stabilization of force parameters ${F=F}_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M=M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ by the IMM system (lower control level).

Let us assume that in the section $k-d-r$ (Figure 5b), stable cutting is disrupted by a randomly arising “disturbance” in the form of an increased stock allowance of the free-form (arbitrary) shape.

The resulting “disturbance” in the stock allowance in the IMM system (lower control level) is reflected in the form of an increase in the cutting torque $M$, which receives some increment $∆M$, i.e., the previously described situation $M=M_0+∆M>M_0$ is repeated.

As a result, the IMM force parameters stabilization system will respond by decreasing the cutting depth by the value $∆z_i>0$, at which ${F=F}_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M=M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$. That is, the tool and spindle are again automatically raised to the height $z_i>0$, but this time without stopping the feeds $S_Z$ and $S_X$. Such simultaneous operation of the two systems—CNC (upper control level) and IMM (lower control level)—under conditions of a continuous increase in the depth of cut (without suspension of feeds $S_Z$ and $S_X$) leads to a continuous lifting of the spindle in a moving coordinate system $z_i$ while simultaneously meeting the conditions ${F=F}_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M=M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$. It looks like a tactile force (because $F_0>0$ and $M_0>0$) “scanning” the “unevenness” with the removal of the surface layer of such thickness that $F_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ and $M_0=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$. These are the cutting force and torque at which the tool bypasses unevenness. In mechanical engineering technology, this is called “copying the error”.

The described process of “scanning” the unevenness is accompanied by the operation of the CNC program (upper control level) of the “residual stock allowance removal”, namely the algorithm for storing the current value of the “residual stock allowance “with an instantaneous value ${z_i(X}_1{Y}_1{Z}_1)>0$ (Figure 6a). For this purpose, the IMM force parameters stabilization system “measuring unit” is used, including the signal stops-contacts (5), which control the situation ${z_i(X}_n{Y}_n{Z}_n)=0$, where $n$ is the serial number of the last working pass, after which the “disturbance” in the form of an increased stock allowance is completely removed.

In this case, the “residual stock allowance removal” program “remembers” the following situation: on the section $k^{\prime }-m-n-r^{\prime }$ there was an unpredictable movement of the spindle along the axis $z_i$, i.e., $z_i\left(X,Y,Z\right)>0$, and in this area there is an uncut layer of material with geometry $k^{\prime }-z_i\left(X,Y,Z\right)-r^{\prime }$ (Figure 5b and Figure 6).

After the first working pass (Figure 6a), the residual stock allowance fixed in the CNC system memory (upper control level) is sequentially removed as the current geometry of the residual stock changes. For example, after the second working pass, the surface takes on the appearance ${z_i(X}_2{Y}_2{Z}_2)$ (Figure 6b). Thus, the tool is programmatically reciprocated relative to the workpiece only in the area of the remaining (not cut) material layer, e.g., on the section $k^{\prime }-d-r^{\prime }$ (Figure 5b).

This machining continues until the condition $z_i=0$ is met for each point of the surface being machined. This means that the actual geometric shape of the surface being processed will have dimensions in accordance with the tolerance specified in the drawing, including a very small tolerance, for example, several nanometers, since it became possible to change the specified value $F_0>0$ according to the IMM program at $z_i\to 0$, tending it towards zero, i.e., $F_0\to 0$. This means working with shallow depths of cut in the nanometer range.

After the machining error $z_i(X,Y,Z)$ on the section $k^{\prime }-d-r^{\prime }$ is completely eliminated, the CNC system (upper control level) moves to smoothing (nursing) working passes not only on this but also in all other areas of the surface being machined. The specified values of force parameters $F_0$ and $M_0$ can be reduced according to the IMM program of the stabilization system to very small (almost zero) values. At the same time, the positioning of the tool relative to the part is carried out according to the CNC program (upper control level), and the stabilization of force parameters $F_0$ and $M_0$ is carried out from the IMM system (lower control level). In fact, the final precision machining of the part is performed

5. Conclusions

• A methodology of hierarchical (two-level) control in a mechatronic technological system (MTS) containing at the upper and lower control levels a CNC device and an intelligent mechatronic mechanism (IMM), respectively, has been created and tested. From the CNC device, the automatic regulation of the machining kinematic operating parameters (depth of cut, feed, cutting speed, and tool position) is carried out “by deviation”. From the IMM device, the force cutting parameters (axial cutting force and cutting torque) are automatically adjusted by changing the vertical feed in such a way as to ensure the preset value of axial cutting force and cutting torque.
• The interaction of the control levels is carried out in such a way that when the lower level is working, the upper level is in standby mode and is switched on when a ready signal is received from the lower control level. In turn, when the upper control level is activated, the vertical feed value found at the lower level is taken as a new set value (the influence of the lower control level on the upper one).
• In relation to the upper control level, the stabilization or program change (tracking mode) of the force cutting parameters (axial cutting force and cutting torque) at the lower control level is controlled by “disturbance”, in which this “disturbance”, in the form of the deviation of the current cutting torque from its preset value, is measured and eliminated.
• In relation to the lower control level, the axial cutting force and cutting torque are maintained at a predetermined level by adjusting the vertical tool feed in a closed stabilizing or track automatic control system “by deviation”.
• The proposed structure of the hierarchical (two-level) control system consisting of CNC (upper control level) and IMM (lower control level) is due to the fact that the simultaneous achievement of the required geometry of the part being machined and the absence of defects in its surface layer cannot be achieved when the force cutting parameters—axial cutting force and cutting torque—exceed their permissible values (constant or variable as the machining stock allowance is removed).
• Two schemes of hierarchical (two-level) control have been developed: sequential and parallel.

In the first case (sequential scheme), the operation of the upper (CNC) and lower (IMM) contours of hierarchical control takes place in a sequential “start–stop mode”. The automatic control system of the upper level (CNC) is periodically turned off by the signal of the open state of the IMM signal contacts. Moreover, the excess stock allowance is removed when the axial cutting tool runs vertically down. This method is characterized by a higher machining performance, since the axial tool (grinding or milling) moves along its vertical axis of rotation (plunge grinding or plunge milling, respectively). At the same time, the rigidity of the technological system is at its maximum (no lateral deflection of the tool) and the operation is accompanied by stabilization (or change according to the program in the tracking mode) of the axial cutting force and cutting torque.

In the second case (parallel scheme), both control levels (CNC and IMM) operate simultaneously in time. The CNC (upper control level) positions the tool according to the CNC control program, maintaining the kinematic cutting parameters at a predetermined level, and the IMM (lower control level) stabilizes or changes the axial cutting force and cutting torque in the tracking mode. In this case, there is a “copying of the error”, but the value of the residual stock is recorded each time, and then the residual stock allowance is removed at subsequent working passes in those places where the IMM signal contacts were open at previous working passes.