**3. Results and Discussion**

Unlike nowadays, in the past, the seat designs were made mostly of the tubular profile. However, stamped designs of passenger bus seats still need further experimental analyses. In this case, a stamped construction with a thickness of 2 mm, made of Steel 20, was used in the 3D modeling (Figure 5). The software allowing stress distribution evaluation was the one presenting the traditional approach for solving and presenting the distribution of internal stresses in various structures. Dynamic analysis was conducted to determine the stress deformation and kinematic behavior of the mechanism with consideration of the elastic–plastic behavior of individual parts of the mechanism.

**Figure 5.** Seat model made of pressed sheet: (**a**) solid model; (**b**) Finite Element Method (FEM) model.

While building the model, the first step was to reduce weight, which weakens the supporting frame, and to increase its compliance, the model seat was cut out. The cut-out is very important for obtaining the necessary movements at checkpoints following the requirements of static tests proposed by the Economic Commission for Europe of the United Nations Regulation No. 80 [55].

The loading height H1 of load P1 was 781 mm concerning the base surface, and the loading height H2 of load P2 was 533 mm, respectively. The values of loads P1 and P2 applied to the back seat were parallel to the horizontal plane and the longitudinal axis of the bus and could be calculated as follows in Equations (6) and (7):

$$P\_1 = \frac{1000}{H\_1} \pm 50 = \frac{1000}{0.781} + 50 = 1330N \tag{6}$$

$$P\_2 = \frac{2000}{H\_2} \pm 100 = \frac{2000}{0.533} \pm 100 = 3852N\tag{7}$$

A further performance of the research on the seat frame conforming to the requirements of UNECE Regulation No. 80 [55] is the analysis of the structure strength presented in the form of a solid-state model (solid model). This would ensure higher accuracy of the calculation and would allow taking into account the plastic deformations (allowing physical non-linearity). The main advantage of the solid model is the possibility of transition from the nodal connections of the rods to the actual volumetric connections of pipes and other elements of the design corresponding to the actual scenario. In contrast to the beam performance, the solid-state model is much more complex in terms of its construction and analysis, because the model needs to be split into sets of sizes and configurations.

The study of three variants of the seats loaded with the following scenarios was carried out: with a stand (Figure 6a), with a side fixing console (Figure 6b), and with an additional handrail, which was attached to the roof frame (Figure 6c).

**Figure 6.** Three-dimensional model of a seat with a stand (**a**), a side control fixing (**b**), and a handrail attached to the roof frame (**c**).

The first example (Figure 6a) consists of a vertical rack, which was made of a 2 mm thick profile and with a hole in the center to save material; however, it was not reducing the structure's stiffness. The bottom of the rack is welded to a 3 mm thick plate with two holes of 10 mm in diameter, under a bolted connection. In the model, the welded connection of the plate is simulated, which acts as the flange fastening the base to the wheel arches of the bus and the rack's frame (Figure 6a).

The second scenario (Figure 6b) is relevant for low-entry and low-floor vehicles, allowing efficient bus floor maintenance. Its base is not fixed to the racks on the floor but is firmly tied to the side of the bus through two supporting circular pipes of 20 × 2 mm in size (Figure 6b). These pipes are welded to a steel plate (265 × 50 × 3 mm in size) with two holes for a bolted connection of 10 mm. The flanges are attached to the side of the seat at a height of 200 mm.

Starting from the fact that the second scenario (Figure 6b) is characterized by higher optimization potential, in comparison with the classical variant (Figure 6a) with a stable floor mount, which has a much smaller distance between the mount supports, and therefore a significantly greater moment of action from the forces, it is advisable to strengthen it by the introducing an additional rail attached to the roof frame (Figure 6c). It is worth noting that it is often possible to find a construction variant with a handrail attached to the frame of one of the seats. Thus, as a result of loads following UNECE Regulation No. 80, different values of displacement and absorbed energy are obtained for the back and the right-sided seats.

In general, each node has 6 degrees of free space (three linear movements and three angles of rotation), but for a particular task, certain degrees of free space may not be possible. For instance, in the solving process of deforming a flat five-point fastening of the base of the seat loaded by plane forces, the basic functions describing the displacement of the peak plane can be omitted, since their value is zero.

The description type includes here the topology of an element (flat triangle, flat quadrilateral, a polygon with curved sides, bulk element-tetrahedron, hexagon, etc.). For such shapes, the basic functions (a quadrilateral with 6 degrees of free space in the node, quadrilateral with 2 degrees of free space in the node, etc.) and formulas for calculating elastic energy are used. The solution of a set of equations of FEM (finite elements method) by the prediction of displacement will be the components of nodal displacements of the discrete design of a passenger seat.

In general, the base model with a stand consists of 19 constituent elements. Its weight is 15.1 kg. The number of finite elements of the FEM model approaches 40,000 and the number of nodes is 85,376. The results of the calculations indicate that despite being identical to one another, the left and right seats are divided into different amounts of finite elements (FE): the left consists of 16,160 elements joined by 33,265 nodes and the right consists of 16,189 items with 33,309 nodes. Similar conditions can be observed for absolutely identical M8 bolts fastening the base. There may be several explanations: firstly, the Ansys Workbench algorithm generates a grid every time individually (adapting to the set conditions of the calculation), and may start, for example, not from the seat mounting area, but its upper part, showing signs of an artificial neural network. Secondly, the base to which the seat is fixed is not symmetrical (different degrees of detail in its various areas).

The model of the seat with a console mount consists of 19 constituent elements and is heavier by 0.6 kg. The number of end-points of the FEM model increases to 42,699, and the number of the corresponding nodes is almost 5000 units.

All elements that are part of the seat model have nonlinear characteristics of the material, including its physical nonlinearity (Nonlinear Effects = Yes). For example, one of the M8 bolts consists of 198 elements and 408 knots, and the corresponding nut consists of 66 elements and 473 knots. The contact sensitivity parameter that is automatically set in the Ansys Workbench environment is 3.4712 mm (Tolerance Value). In general, the model is more complex, concerning the rack sample, and it requires a more detailed breakdown of key elements: the degree of detail in the partition is determined by the Relevance parameter, which is assumed to be 0.35 for the model under study (as part of the Ansys Workbench software functionality, the maximum value for Relevance is −100). Compared with the first scenario (Figure 5a) and despite the absence of a rack mount to the floor, the overall height of the model (Length Y) increased from 791.09 to 1184 mm. The difference in overall height is due to the presence of a high rail, which is fixed to the system of railings on the roof of the cabin. Compared with the second scenario (Figure 5b), the number of FEs increased by 7%, and the number of nodes increased by 7.5%, respectively.

The weight of the model with a handrail is 16.6 kg, and the number of constituent elements of assembly increased not as much. Data on the FEM-wire rail were as follows: the number of FE railings is 3792, and the number of nodes is 7426. Its dimensional height was 971.5 mm, and the weight of the whole model was 0.9 kg.

During the computer simulation of seat frame tests, the behavior of the component elements with the corresponding steel–steel friction pairs has also been determined. For steel–steel pairs, the coefficient of friction is set to 0.2, which corresponds to the typical value in rest. In addition to the bolted joints, all contact pairs have a friction coefficient of 0.2. The hard type bonded (motionless) joint provides a bolted connection (for example, Bonded—M8 bolt to bolt connection).

It should be noted that the statement about the direct correlation of the growth of relevance to the accuracy of the calculation is false. In the split configuration on the FE, the Relevance Center parameter is set to Fine, which means an improved detail of the element at the curves of the model and complex transitions (bolted connections, etc.). The minimum value of the edge length of the finite element was 5,8838e−004 mm.

Firstly, the stress values of the base model with the rack were analyzed. The maximum value reached was 431.74 MPa. The rack was fixed using the bolted connection at the left bracket, which was mounted along with the movement of the seat to the base in its front part. At the same time, the maximum stress value of mounting bolts was 199.43 MPa. In the place where the seat frame was fixed with a bolted connection, the stress value was 240 MPa. The constituent elements reached maximum stresses at different times, which is presented in Figure 7.

**Figure 7.** Tension diagrams depending on load steps: (**a**) nut; (**b**) bolt.

When considering the stress–strain state of the design at the stage of full absorption of the impact energy presented in Figure 7, the maximum stress value, equal to 374.74 MPa, is recorded in the frame of the right-hand drive of the bus in the area of the seat bend. This is as expected due to the greatest bending moments passing through this area. The stress values in the rack vary from 5 MPa in the flange with an increase of 45 MPa in the bolted joints and up to 270 MPa in the rack (Figure 8). Structurally, the seat leg is a welded structure consisting of a pressed sheet with a thickness of 2 mm and a flat flange fastened to the floor with a thickness of 3 mm.

Together with the base of the seat (welded square tube frame), the rack and flange mounted to the bracket of the seat arch forms a single inseparable structure. The structure demonstrated a maximum stress value of 339.81 MPa, which is fixed in the right seat mount bracket.

**Figure 8.** Strength map of the rack.

The variant of the seat base, designed for the installation in low-entry buses, has a one-way mount attached to the bus sidewall, and therefore, in theory, it has a lower equilibrium than the previous design. The maximum value of stresses recorded during the loading process was 434.33 MPa. It corresponds to the contact area of the anterior nut with the left seat frame. Such conditions and detection of the maximum stress design fully correspond with the previous case. In both cases, the nut will withstand the force reactions transmitted from the bolt while maintaining the design integrity. The maximum stress value is 390.02 MPa, which is 3–5% more compared to the previous version. This value corresponds to the area of the left-hand drive of the seated bus, which is the opposite of the seat with a stand (the right seat was more loaded).

In a reverse case, the value of the maximum stress occurs at the base of the seat, with 305.81 MPa versus 339.81 MPa for the rack variant. Although the area where the extremum of stress is fixed coincides with the same seat mount bracket. Thus, the bracket is in lower load conditions as part of the console construction. Even though the absolute value of stresses is lower in the console variant, the average value of stresses is 30–35% higher when referring to 270–300 MPa for pipe profiles (25 × 2 mm) against 220–250 MPa for a variant providing a stable mounting.

In general, the console structure in terms of stresses has a sufficient margin of safety, but a significant part of the constituent elements is outside the yield strength of the material (Steel 20–250 MPa). This is because the seat performs the bearing function, which may result in increased displacement under regular loads following UNECE Regulation No. 80.

For the third variant of the base with a console fastening and additional armor with a stress map, a decrease by 5% in the value of stresses was noticed. The maximum value corresponds to the area of the left seat bend. In general, the relative equilibrium of the construction of the seat together with an additional handrail may be estimated: the oscillation of the voltage value is at 30–40% between the model components, meaning there are no overloaded elements or those with an excess safety margin.

Although the seat base showed a maximum stress value of 5 MPa more than in two other cases, the average value of stresses in round profiles, 20 × 2 mm in size, at 15–20% is lower due to stress redistribution. A significant contribution to stress redistribution has a vertical additional handrail, absorbing a significant part of the energy when struck. The voltage map of this handhold shows the effectiveness of its work: the maximum stress value was 266.77 MPa. As expected, this value is fixed in the area of the seat mounting to its base.

#### **4. Conclusions**

Bearing in mind that there is a number of factors influencing the general performance of bus seats, the present paper aimed to focus on an aspect considered crucial in urban public transportation, which is safety and comfort. The comfort analyses were performed using purpose-built models on seat profiles occupied by an adult (M50) and a young (M10) passenger. The safety analyses were based on analyzing the frame strength and stress distribution for three variants of seat mounts: a seat with a stand, a side control seat fixing, and a seat-supporting handrail attached to the roof frame.

All considered models were solid-based and created using computer-aided design and a computer-aided engineering software environment; then, they were imported into the software package for Finite Element Method analysis. In general, the base model with a stand consists of 19 constituent elements. The number of finite elements of the Finite Element Method model approached 40,000, and the number of nodes exceeded 80,000.

The simulation of different scenarios for seat loading complies with Economic Commission for Europe of the United Nations Regulation No. 80 [54]. The common seat frame types with various mounting types used in standard or low floor buses were tested, giving a promising correlation between the simulation and test results according to the Economic Commission for Europe of the United Nations Regulation No. 80. For different seat mounting scenarios, the achieved maximum stresses were 431.74 MPa for a base model, 374.74 MPa at the stage of full absorption of the impact energy, and 339.8 MPa for the rack and flange mounted to the bracket of the seat arch. For the variant of the seat base, which was designed for installation in low-floor buses, the maximum value of stresses recorded during the loading process was 434.33 MPa.

The present study is a primary investigation focusing on particular events concerning two passengers with assumed seating locations and coordinates. The study should be further developed to evaluate seating comfort and safety for all passengers located at different seating spots. Bearing in mind that the results of the present study could be applied in urban public transportation only, the outcomes would allow understanding how to improve the comfort zone preventing potential physical discomfort or injuries.

**Author Contributions:** Conceptualization, I.K., O.H. and E.K.; methodology, O.H. and M.R.; software, Y.Y., M.R., R.H. and Y.S.; validation, Y.V., P.O. and K.R.; formal analysis, I.K. and O.H.; investigation, I.K., Y.Y., M.R., R.H., Y.S. and Y.V.; resources, I.K., O.H. and M.R.; data curation, P.O. and K.R.; writing—original draft preparation, O.H. and P.O.; writing—review and editing, P.O. and E.K.; visualization, R.H., Y.S., Y.V. and Ł.M.; supervision, E.K. 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.

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

#### **References**

