# Development of a New System for Attaching the Wheels of the Front Axle in the Cross-Country Vehicle

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. New Design of the Wheel Suspension

## 3. Creating A 3D Model of the Wheel Suspension and Its Modification

- The possibility of geometry adjustability and suspension rate in the largest possible range.
- The suspension must be rigid enough to fulfil the safety requirements in operation.
- The suspension must not be more rigid than the vehicle frame.
- The life span and manufacturing costs.

_{e}= 590 MPa.

## 4. Analysis of Load Forces

_{O}(N) is the gravitational force of the sprung weight for the front axle and G

_{N}(N) is the gravitational force of the unsprung weight for the wheel.

_{N}= 58.32 kg per one wheel. Then the equation for the gravitational force of the unsprung components is as follows (2):

_{N}(kg) is the weight of the unsprung axle parts per one wheel, g (m·s

^{−2}) is the constant of the gravitational acceleration. Thus,

_{1}(N) is the gravitational force for the front axle being solved determined by the equation (9), μ

_{p}(-) is the tyre adhesion coefficient, we consider μ

_{p}= 0.925 (-),

_{t}(m) is the height of the CoG of the unsprung masses, h

_{t}= 0.8 m,

_{n}(m) is the height of the CoG of the unsprung masses, h

_{n}= 0.352 m,

_{z}and F

_{y}

_{1}. The force F

_{z}forms a displacement effect to the links A, B. We assume a uniform division of this force between the links A and B. Therefore, the reaction effects develop—Figure 10a in red colour - A

_{y}and B

_{y}. Their values are detected through the exception of the equilibrium (18) respecting the vector algebra:

_{z}also continues loading the suspension by a rotational effect. The goal is to quantify the reaction force effects in the links A and B. In the geometrical centre of the links A and B, a point O was created, as Figure 10a shows. The torque of the force F

_{z}to this point is (32):

_{x}

_{1}and B

_{x}

_{1}(in red colour). As they have the same distance from the point O, we can calculate them as follows (22):

_{y}

_{1}creates a displacement effect to the considered links (A, B). We assume a uniform division of this force between the links A and B. Therefore, the reaction effects (Figure 10a—in red colour) A

_{x}

_{2}and B

_{x}

_{2}will develop. Their values will be detected by an equilibrium exception (24):

_{y}

_{1}also continues loading the suspension by a rotational effect. The goal is to quantify the reaction force effects in links A and B. In the geometrical centre of the links A and B, a point O was created, as Figure 10a shows. The torque of the force F

_{y}

_{1}to this point are (27):

_{x}

_{3}and B

_{x}

_{3}(in red colour). As they have the same distance from the point O, we can calculate them as follows (28):

_{A}) will be (32):

_{A}) will be (35):

_{B}= 3590 N affects the suspension through the pivot joint. It is oriented towards the vehicle frame in the place of suspension of the bottom knuckle bolt. In the place of suspension of the upper knuckle bolt there is a planar force of R

_{A}= 760 N. Table 2 gives the values of the geometrical parameters from Figure 10.

_{b}= 1.4 (-) is suitable for the reference vehicle (a buggy with a rear engine and distribution of the weight in favour of the rear axle). The load of the front axle during deceleration of the vehicle will be (36):

_{z}and F

_{B}

_{1}. The force F

_{z}forms a displacement effect to the links A, B. We assume a uniform division of this force between the links A and B. Therefore, the reaction effects develop—Figure 10a in red colour—A

_{y}and B

_{y}. Their values are detected through the exception of the equilibrium (38):

_{z}continues loading the suspension also by a rotational effect. It is not necessary to calculate this load because it is the same load as in the previous case (Ax

_{1}, Bx

_{1}). The force F

_{B}

_{1}creates a displacement effect to the links (A, B). We assume a uniform distribution of this force between the links A and B. Therefore, the reaction effects (Figure 10b—in red colours) A

_{x}

_{4}a B

_{x}

_{4}develop. Their values are detected by an exception from the equilibrium (41):

_{B}

_{1}continues loading the suspension also by a rotational effect. The goal is to quantify the reaction force effects in the links A and B. In the geometrical centre of the links A and B a point o (Figure 10b) was created. The torque of the force F

_{B}

_{1}to this point will be (44):

_{x}

_{5}and B

_{x}

_{5}(in red colour). As they have the same distance from the point O, we can calculate them as follows (45):

_{Av}) will be (49):

_{Bv}) will be (52):

_{Bv}= 7111 N affects the suspension through the pivot joint. It is oriented towards the vehicle frame in the place of suspension of the bottom knuckle bolt. In the place of suspension of the upper knuckle bolt there is a space force of R

_{Av}= 3765 N.

## 5. Static FEM Analysis and Modal Analysis of Designed Components for Individual Driving Regimes

_{B}= 3590.0 N). However, it is a safe stress because the pivot bolt material achieves the yield strength up to R

_{e}= 590 MPa.

_{e}= 760 MPa [29]. The highest stress can be found in the point where the vertical control arm is attached in the control arm. However, the biggest force performs in the bottom part of the control arm. The fact that the largest stress is not present is caused due to attaching the knuckle bolt—this attachment together with the attachment of the control arm is in one plane. In this way the force is transferred directly to the upper control arm by pressure. In the case of the bottom control arm the situation is more complicated. The original control arm from the design (the utility model) is created from one pipe only. The component designed like this would not withstand because the maximal achieved stress is 1397.0 MPa. The designed component is placed close to the attachment base into the frame. This control arm consists of one pipe only. The design of the control arm is more sophisticated. If we compare the original (Figure 15a) and the new design (Figure 15b), a change is visible. The highest stress is not in the carrying pipe any more. It is moved into the base of the control arm attachment with the frame. The adapted control arm achieves the maximal stress of 304.69 MPa. This is again an acceptable value, if the yield strength is R

_{e}= 590 MPa. The deformation of the control arm end at the maximal load is 1.3 mm.

_{e}= 590 MPa.

_{e}= 760 MPa.

_{e}= 760 MPa.

**M**is the mass matrix,

**K**is the stiffness matrix and

**q**and $\ddot{\mathit{q}}$ are position and velocity vectors, respectively.

_{0}is the angular eigenfrequency of the system,

**y**is the vector of the amplitudes of the eigenshape oscillation of the system.

^{−1}), or a small adaptation of the eigenfrequencies of the axle oscillation f (Hz).

^{−1}. This link will be assigned the necessary damping during the dynamic simulation. No damping was considered or the modal analysis.

## 6. Sensitivity Analysis of the Vehicle

^{−1}. Before cornering the car drove straightforward 30 metres due to the numerical stabilisation of the initial conditions. The simulation itself took approximately 20 s. The task of the simulation was to follow the forces performing on the front wheels. The values of the simulated forces will serve for verifying the input data of the analytical and dimensional calculation. The diagram of the performing forces is depicted in Figure 23. The external wheel had almost a perpendicular contact with the road thanks to a zero deviation of the wheel—see the previous diagram. The smaller this force is, the stronger tendency of the car to come out of the turn is—the so called understeering.

^{−1}. The real pass of the car with the Motionview simulation will be compared. The simulated pass was based on a standardised test (Figure 24). Results of the car’s bodywork roll angle analysis are shown in Figure 25.

## 7. Dynamic Analysis of the Vehicle in the Programme Simpack

**M**is the mass matrix,

**D**is the Jacobian matrix,

**q**is the vector of generalised coordinates,

**Λ**is the vector of Lagrange multipliers and

**F**is the load vector of the system (kinematic excitation, performance of the external forces, etc.) and $\mathit{\gamma}=\mathit{D}\xb7\ddot{\mathit{q}}$ [38,39,40].

- The required model kinematics as a whole including the kinematic sub-systems—aimed at the tested front axle.
- The spring loading system of individual wheels.
- The representation of the link elements of the model.
- They dynamic forces in the tyres.
- The model must not be too complicated; the time of the calculation has to remain acceptable.

- In the curve with defined parameters (Figure 27).
- On a straight path with irregularities for assessing the oscillation properties of the car.

^{−1}; R = 30 m) is 4656.592 N. On the contrary, the internal wheel (the blue curved line) is relieved and its minimal value in the followed section is 1315.121 N. The calculated values show that driving a car with the tested axle will be safe at the speed of 50 km·h

^{−1}and the curve radius 30 m. The internal wheel is still able to transfer sufficient large driving, braking and lateral forces.

- The first case: L = 0.5 m; h = 0.025 m.
- The second case: L = 0.5 m; h = 0.100 m.

^{−1}; v = 10 km·h

^{−1}; v = 25 km·h

^{−1}; v = 50 km·h

^{−1}; v = 80 km·h

^{−1}and v = 100 km·h

^{−1}.

^{−1}and v = 20 km·h

^{−1}the maximal wheel force at the moment of the run up is the same. The higher speeds, i.e., v = 50 km·h

^{−1}, v = 80 km·h

^{−1}and v = 100 km·h

^{−1}at which the car overcomes this obstacle cause a situation when the vehicle oscillation fades out more strongly behind the obstacle. It is caused by the inertia of motion of the vehicle parts in the front axle and gradual damping the oscillation. The instantaneous maximal values of the dynamic force at the moment of overcoming the obstacle (unevenness) do not represent any significant ganger from the point of view of safe driving. The most interesting case seems to be the operation of the vertical force at the speed of v = 5 km·h

^{−1}. In spite of a relatively low speed the system is oscillated most significantly just at this speed. The situation can be caused by combining the given driving speed, the amplitude and wave length of the unevenness. This excites the oscillation of the front part of the vehicle. Our optimisation will be aimed at achieving suitable oscillating properties together with the aforementioned driving conditions.

^{−1}), the operation of the vertical wheel force is not that strong. The force is then characteristic only by its current growth of its value during running up the obstacle. The simulation result for the speed on 10 km·h

^{−1}has a similar character. When the car drives at the speed of v = 25 km·h

^{−1}, v = 50 km·h

^{−1}, v = 80 km·h

^{−1}and v = 100 km·h

^{−1}a typical oscillation of the vehicle front part develops and it is typical that it fades out gradually. Similarly, as in the previous case the instantaneous values of the vertical wheel forces in the observed driving movements do not lead to any serious threat of the driving safety.

## 8. Conclusions

- This article presents the design of the front wheel suspension in a cross-country vehicle according to our patents SK 7945 Y1 and SK 7960 Y1.
- During creating the 3D models, we found out that collisions of individual components could occur. This fact led the authors to a thorough analysis of the 3D model of the wheel suspension.
- The authors decided to implement this design in a prototype of a cross-country vehicle built at their workplace because all necessary technical data inevitable for creating a design and technical calculations was available.
- The suspension components were checked by the finite element analysis for defining the driving regimes. The finite element analysis proved the unsuitability of the original design of the bottom control arm. The new and optimised form is already an alternative for the usage in the given vehicle.
- Through the modal analysis we identified the basic dynamic characteristics of the axle, i.e., its eigenmodes and eigefrequencies.
- The authors carried out the sensitivity analysis of the car through the programme Altair Motionview. The next step of solving this area consisted in creating the MBS model of the axle and its implementation to model of the car in the MBS programme Simpack. The dynamic analyses were also realised in this programme. Based on the dynamic analyses we detected the operations of the wheel forces in the designed axle for various driving regimes.
- The obtained results will serve for verifying the design functionality, experimental comparison between the mathematical model and data detected from the built prototype operation.
- The presented and developed technical solution of an independent wheel suspension for a sport car will improve its driving qualifies during driving on various surfaces. The spring compression is dimensioned in such a way it will enable driving on a low quality surface with big unevenness by high speed—this will ensure a constant contact of the wheels with the surface. This will maintain the transmission ability of the driving, steering and braking forces which significantly affects the increased safety of the designed vehicle. Except for this the character of the suspension will guarantee a sufficient level of the driving comfort for the crew.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Acantar, J.V.; Assadian, F. Vehicle dynamics control of an electric-all-wheel-drive hybrid electric vehicle using tyre force optimisation and allocation. Veh. Syst. Dyn.
**2019**, 57, 1897–1923. [Google Scholar] - Goh, J.Y.; Goel, T.; Gerdes, J.C. Toward automated vehicle control beyond the stability limits: Drifting along a general path. J. Dyn. Syst. Meas. Control Trans. ASME
**2020**, 142, 21004. [Google Scholar] [CrossRef] [Green Version] - Yang, Z.; Yong, C.; Li, Z.; Yin, K.S. Simulation analysis and optimization of ride quality of in-wheel motor electric vehicle. Adv. Mech. Eng.
**2018**, 10, 76543. [Google Scholar] [CrossRef] - Bae, S.; Lee, J.M.; Chu, C.N. Axiomatic design of automotive suspension systems. CIRP Ann. Manuf. Technol.
**2002**, 51, 115–118. [Google Scholar] [CrossRef] - Lee, J.K.; Shim, J.K. Application of screw Theory to the Analysis of Instant Screw Axis of Vehicle Suspension System. Int. J. Automot. Technol.
**2019**, 20, 137–145. [Google Scholar] [CrossRef] - Zauner, C.; Edelmann, J.; Plochl, M. Modelling, validation and characterisation of high-performance suspensions by means of a suspension test rig. Int. J. Veh. Des.
**2019**, 79, 107–126. [Google Scholar] [CrossRef] - Dodok, T.; Cubonova, N.; Kuric, I. Workshop programming as a part of technological preparation of production. Adv. Sci. Technol. Res. J.
**2017**, 11, 111–116. [Google Scholar] [CrossRef] [Green Version] - Kuric, I. New methods and trends in product development and planning. In Proceedings of the 1st International Conference on Quality and Innovation in Engineering and Management, Cluj Napoca, Romania, 17–19 March 2011. [Google Scholar]
- Kanchwala, H. Vehicle suspension model development using test track measurements. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2020**, 234, 1442–1459. [Google Scholar] [CrossRef] - Larocca, A.; Youssef, M.; Gadbois, A.; Zamfir, D.; Kubo, P. Influence of shock absorber damping rates on the fatigue of anti-roll bars of a commercial vehicle. Int. J. Heavy Veh. Syst.
**2020**, 27, 180–201. [Google Scholar] [CrossRef] - Lee, U.K.; Lee, S.H.; Han, C.S.; Hedrick, K.; Catala, A. Active geometry control suspension system for the enhancement of vehicle stability. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2008**, 222, 979–988. [Google Scholar] [CrossRef] - Su, Z.Y.; Xu, F.X.; Hua, L.; Chen, H.; Wu, K.Y.; Zhang, S. Design optimization of minivan MacPherson-strut suspension system based on weighting combination method and neighborhood cultivation genetic algorithm. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2019**, 233, 650–660. [Google Scholar] [CrossRef] - Bartolozzi, R.; Frendo, F. Stiffness and strength aspects in the design of automotive coil springs for McPherson front suspensions: A case study. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2011**, 225, 1377–1391. [Google Scholar] [CrossRef] - Gao, Q.; Feng, J.Z.; Zheng, S.L. Optimization design of the key parameters of McPherson suspension systems using generalized multi-dimension adaptive learning particle swarm optimization. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2019**, 233, 3403–3423. [Google Scholar] [CrossRef] - Romero, N.; Florez, E.; Mendoza, L. Optimization of a multi-link steering mechanism using a continuous genetic algorithm. J. Mech. Sci. Technol.
**2017**, 31, 3183–3188. [Google Scholar] [CrossRef] - Colombo, D.; Gobbi, M.; Mastinu, G.; Pennati, M. Analysis of an unusual McPherson suspension failure. Eng. Fail. Anal.
**2009**, 16, 1000–1010. [Google Scholar] [CrossRef] - Zhou, G.; Kim, H.S.; Choi, Y.J. A new method of identification of equivalent suspension and damping rates of full-vehicle model. Veh. Syst. Dyn.
**2019**, 57, 1573–1600. [Google Scholar] [CrossRef] - Osipowicz, T.; Abramek, K.F.; Barta, D.; Drozdziel, P.; Lisowski, M. Analysis of possibilities to improve environmental operating parameters of modern compression-ignition engines. Adv. Sci. Technol. Res. J.
**2018**, 12, 206–213. [Google Scholar] [CrossRef] - Barta, D.; Mruzek, M. Factors influencing the hybrid drive of urban public transport buses. Manag. Syst. Prod. Eng.
**2015**, 20, 213–218. [Google Scholar] - Abbas, A.H.; Mohammed, A.-W.A. Dune Buggy Design. Bachelor’s Thesis, University of Khartoum, Khartoum State, Sudan, 2015. [Google Scholar]
- Tarkowski, S.; Nieoczym, A.; Caban, J.; Gardynski, L.; Vrabel, J. Reconstruction of road accident using video recording. In Proceedings of the 3rd International Conference of Computational Methods in Engineering Science, Kazimierz Dolny, Poland, 22–24 November 2018; Lublin University of Technology: Lublin, Poland, 2018. [Google Scholar]
- Dobrodenka, P.; Dobrodenka, A.; Dobrodenka, M.; Gerlici, J.; Lack, T.; Blatnicky, M.; Dizo, J.; Harusinec, J.; Suchanek, A.; St’astniak, P. Attachment of Front Axle Wheels of Cross-Country Vehicles. Patent SK 7960 Y1, 26 October 2017. [Google Scholar]
- Dobrodenka, P.; Dobrodenka, A.; Dobrodenka, M.; Gerlici, J.; Lack, T.; Blatnicky, M.; Dizo, J.; Harusinec, J.; Suchanek, A.; St’astniak, P. Attachment of Front Axle Wheels of Cross-Country Vehicles. Patent SK 7945 Y1, 20 October 2017. [Google Scholar]
- Leitner, B.; Decky, M.; Kovac, M. Road pavement longitudinal evenness qualification as stationary stochastic process. Transport
**2019**, 34, 195–203. [Google Scholar] [CrossRef] [Green Version] - Kostrzewski, M. Analysis of selected acceleration signals measurements obtained during supervised service conditions—Study of hitherto approach. J. Vibroeng.
**2018**, 20, 1850–1866. [Google Scholar] [CrossRef] [Green Version] - Liščák, Š.; Matějka, R.; Rievaj, V.; Šulgan, M. Chassis of Road Vehicles, 1st ed.; University of Žilina: Žilina, Slovak Republic, 2006; 136p. (In Slovak) [Google Scholar]
- Jakubovicova, L.; Sapietova, A.; Moravec, J. Static analysis of transmission tower beam structure. In Proceedings of the 3rd International Scientific Conference on Innovative Technologies in Engineering Production, Bojnice, Slovakia, 11–13 September 2018; University of Zilina: Zilina, Slovakia, 2018. [Google Scholar]
- Leitner, B. Autoregressive Models in Modelling and Simulation of Transport Means Working Conditions. In Proceedings of the 14th International Conference on Transport Means, Kaunas, Lithuania, 21–22 October 2010; Ostasevicius, V., Ed.; Kaunas University of Technology: Kaunas, Lithuania, 2010. [Google Scholar]
- Bajla, J.; Bronček, J.; Antala, J.; Sekerešová, D. Engineering Tables, 3rd ed.; Slovak Office of Standards, Metrology and Testing: Bratislava, Slovak Republic, 2014; 488p. (In Slovak) [Google Scholar]
- Svoboda, M.; Schmid, V.; Soukup, J.; Sapieta, M. Modal analysis of the vehicle model. Springer Proc. Math. Stat.
**2018**, 249, 351–362. [Google Scholar] - Klimenda, F.; Soukup, J.; Zmindak, M.; Skocilasova, B. Dissemination of shock waves in thin isotropic plates. In Proceedings of the 23rd Polish-Slovak Scientific Conference on Machine Modelling and Simulations, Rydzyna, Poland, 4–7 September 2018. [Google Scholar]
- Reimpell, J.; Stoll, H.; Betzler, J. The Automotive Chassis: Engineering Principles, 2nd ed.; Butterworth-Heinemann: Warrendale, PA, USA, 2001; 456p. [Google Scholar]
- Bulej, V.; Uricek, J.; Eberth, M.; Kuric, I.; Stancek, J. Modelling and simulation of machine tool prototype with 6DOF parallel mechanism in Matlab/Simulink. In Proceedings of the 23rd Polish-Slovak Scientific Conference on Machine Modelling and Simulations, Rydzyna, Poland, 4–7 September 2018. [Google Scholar]
- Tlach, V.; Cisar, M.; Kuric, I.; Zajačko, I. Determination of the industrial robot positioning performance. Matec Web Conf.
**2017**, 137, 01004. [Google Scholar] [CrossRef] [Green Version] - Melnik, R.; Sowinski, B. Analysis of dynamic of a metro vehicle model with differential wheelsets. Transp. Probl.
**2017**, 12, 13–124. [Google Scholar] - Koziak, S.; Chudzikiewicz, A.; Opala, M.; Melnik, R. Virtual software testing and certification of railway vehicle from the point of view of their dynamics. Transp. Res. Procedia
**2019**, 40, 729–736. [Google Scholar] [CrossRef] - Kostrzewski, M. Sensitivity analysis of selected parameters in the order picking process simulation model, with randomly generated orders. Entropy
**2020**, 22, 423. [Google Scholar] [CrossRef] [Green Version] - Shevtsov, Y.I. Wheel/Rail Interface Optimization; University of Technology: Delft, The Netherlands, 2008; 218p. [Google Scholar]
- Hauser, V.; Nozhenko, O.; Kravchenko, K.; Loulova, M.; Gerlici, J.; Lack, T. Proposal of a steering mechanism for tram bogie with three axle boxes. Procedia Eng.
**2017**, 192, 289–294. [Google Scholar] [CrossRef] - Sapietova, A.; Bukovan, J.; Sapieta, M.; Jakubovicova, L. Analysis and implementation on input load effects on an air compressor piston in MSC.ADAMS. In Proceedings of the 21st Polish-Slovak International Scientific Conference on Machine Modeling and Simulations, Hucisko, Poland, 6–8 September 2016; Czestochowa University of Technology: Czestochowa, Poland, 2016. [Google Scholar]

**Figure 4.**Arrangement kinematics of the wheel attachment design (

**a**) and principal scheme of the design function (

**b**).

**Figure 5.**Direction of the impact forces towards the A column of the car (

**a**) and graphical dependence of driving into an obstacle (

**b**).

**Figure 11.**The boundary conditions of the static calculation (

**a**) and the overall shift of the axle from the car self-weight regarding to the parameters of the spring (

**b**).

**Figure 12.**The vertical shift of the wheel suspension from the car self-weight regarding to spring parameters (

**a**) and stress distribution HMH in the suspension from the self-weight of the vehicle (

**b**).

**Figure 14.**Distribution of the equivalent von Misses stresses of the wheel pivot bolt (

**a**) and the vertical control arm (

**b**) during driving in the curve.

**Figure 15.**Distribution of the equivalent von Misses stresses of the original (

**a**) and the new (

**b**) bottom control arm for the given vehicle during driving in the curve.

**Figure 16.**Distribution of the equivalent von Misses stresses of the wheel pivot bolt (

**a**) and vertical control arm (

**b**) during the braking process.

**Figure 17.**Distribution of the equivalent von Misses stresses of the original (

**a**) and the new (

**b**) upper control arm for the given vehicle during driving in the curve.

**Figure 18.**The types of the used links (

**a**) and contact surfaces (

**b**) for the modal analysis purposes.

**Figure 19.**The first (

**a**), the second (

**b**), the third (

**c**), the fourth (

**d**), the fifth (

**e**) and the sixth (

**f**) eigenfrequency of the engineering design.

**Figure 21.**The view of the model in the Motorview interface (

**a**), the Motorview graphical output of the wheel deviation of the designed suspension (

**b**).

**Figure 22.**The characteristics of the changes of the wheel deviations from the vertical motion of the car.

**Figure 23.**The simulated values of the vertical wheel forces of the front axle—the considered vehicle in the Motionview programme.

**Figure 30.**The motion of the wheels of the front axle during driving over an obstacle: (

**a**) driving on the obstacle, (

**b**) overcoming the obstacle.

**Figure 31.**The operation of the vertical wheel forces of the right wheel of the front axle during overcoming an obstacle with a height of h = 0.025 m.

**Figure 32.**The operation of the vertical wheel forces of the right wheel of the front axle during overcoming an obstacle with a height of h = 0.100 m.

Parameter | Indication | Value | Unit |
---|---|---|---|

maximal weight | m_{max} | 780 | kg |

wheel width | a | 245 | mm |

wheel radius | r | 376 | mm |

wheelbase of wheel axes | z | 2350 | mm |

Spacing of wheel axes | o | 1500 | mm |

vehicle dead weight | m_{p} | 640 | kg |

considered load of the front axle | m | 300 | kg |

perpendicular distance of control arms joints | i | 300 | mm |

designed weight of control arm | m_{kr} | 6 | kg |

designed weight of vertical control arm | m_{zr} | 3.45 | kg |

weight of wheel body (8E0501611J) | m_{nk} | 3.28 | kg |

total weight of non-suspended material belonging to one wheel | m_{N} | 5.35 | kg |

weight wheel journal | m_{c} | 6.1 | kg |

Quantity | Value |
---|---|

a | 245 mm |

b | 381 mm |

c | 92 mm |

d | 150 mm |

e | 150 mm |

i | 300 mm |

k | 226 mm |

r | 376 mm |

s | 32 mm |

γ | 17° |

Angular Eigenfrequency | Eigenfrequency | |||
---|---|---|---|---|

Eigenmode | Designation | Value (rad∙s^{−1}) | Designation | Value (Hz) |

1st | Ω_{1} | 13.758 | f_{1} | 2.195 |

2nd | Ω_{2} | 576.893 | f_{2} | 91.862 |

3rd | Ω_{3} | 751.025 | f_{3} | 119.590 |

4th | Ω_{4} | 1350.765 | f_{4} | 215.090 |

5th | Ω_{5} | 2088.288 | f_{5} | 332.530 |

6th | Ω_{6} | 2143.866 | f_{6} | 341.380 |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dižo, J.; Blatnický, M.; Sága, M.; Harušinec, J.; Gerlici, J.; Legutko, S.
Development of a New System for Attaching the Wheels of the Front Axle in the Cross-Country Vehicle. *Symmetry* **2020**, *12*, 1156.
https://doi.org/10.3390/sym12071156

**AMA Style**

Dižo J, Blatnický M, Sága M, Harušinec J, Gerlici J, Legutko S.
Development of a New System for Attaching the Wheels of the Front Axle in the Cross-Country Vehicle. *Symmetry*. 2020; 12(7):1156.
https://doi.org/10.3390/sym12071156

**Chicago/Turabian Style**

Dižo, Ján, Miroslav Blatnický, Milan Sága, Jozef Harušinec, Juraj Gerlici, and Stanisław Legutko.
2020. "Development of a New System for Attaching the Wheels of the Front Axle in the Cross-Country Vehicle" *Symmetry* 12, no. 7: 1156.
https://doi.org/10.3390/sym12071156