THE METHOD OF SYNTHESIS OF THE GEOMETRY OF THE LONGITUDINAL PROFILE AND THE DESIGN PARAMETERS OF THE LEAF SPRING USING THE FINITE ELEMENT METHOD



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详细

BACKGROUND: In most cargo vehicles, leaf springs are used as an elastic element in the springing system, therefore, improving approaches to the calculation and synthesis of car spring suspensions to reduce vibration load and increase driving comfort is an urgent issue. Thanks to the synthesis of the longitudinal profile of the spring sheets of complex shape, it is possible to achieve high spring strength properties with a sufficiently low stiffness by applying calculations and optimizations using the finite element method (FEM), which allows you to create a more perfect spring shape in terms of smoothness of the vehicle.

AIMS: Creation of a new technique for the synthesis of a leaf spring with a variable profile of its longitudinal section and obtaining its characteristics using modern design methods based on the use of FEM.

MATERIALS AND METHODS: The solution of the task is carried out in the NX software package in the Simcenter 3D strength calculation environment. To obtain the geometry of the longitudinal profile of the leaf spring, topological optimization is applied, and then a strength test calculation is performed using FEM to obtain the characteristics of the leaf spring.

RESULTS: During the work carried out at the KAMAZ Innovation Center, a method for forming the longitudinal profile of a leaf spring (regardless of the number of sheets) was developed and the dependences of the stiffness of the leaf spring on its parameters were constructed. According to the obtained dependencies, the optimal geometry of the longitudinal profile of the spring was synthesized, in which the stiffness was reduced by 33% compared to the prototype of the spring, while maintaining the bearing capacity of the vehicle.

CONCLUSIONS: This technique of synthesis of the geometry of the longitudinal profile and the design parameters of the leaf spring can be used in the design processes of vehicle springing systems and further applied during research work.

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INTRODUCTION

The use of the finite element method is widespread in modern design methods [1-5]. This method finds the greatest application in strength calculations, which are used to verify the operability and safety of structural solutions used in vehicles [6-10]. FEM is also used to refine dynamic models of vehicles by introducing malleable elements into the system of dynamics of solids [11-15] and optimizing the design to increase strength characteristics [16-17].

Leaf springs are an essential part of vehicle springing systems that are operated in all climatic conditions [18]. Dynamic models are used to study the effect of spring suspension properties on vibration load and comfort indicators, in which an accurate description of the spring model is important in order to obtain reliable results [19]. There are many works in which FEM is used to calculate leaf springs for strength. With the help of the calculations carried out, it becomes possible to accurately determine the maximum deflections that occur in the spring sheets, stress distribution and predict the service life (resource) of the spring [20-21].

The aim of the work is to create an innovative technique for synthesizing the geometry of the longitudinal profile of the spring using topological optimization methods and further obtaining its stress-strain state to determine the dependence of the characteristics of the spring on its geometric parameters.

Methods

Formation of the longitudinal profile of the spring

The use of topological optimization in this work makes it possible to obtain the most optimal distribution of material in the direction of the spring leaf, provided that equal strength is ensured along the entire length of the spring.

When synthesizing the geometry of the longitudinal profile of the spring, the following requirements are put forward:

– achieving the greatest softness of the spring to improve vibration load and driver comfort;

– the ability of the spring to withstand dynamic load (the force acting on the spring during movement);

– the force required to hit the bump must be less than the static load on the spring;

– the mounting locations of the springs correspond to the actual mounting locations in the vehicle structure;

– when exposed to dynamic loads, the yield strength of the spring material is not exceeded;

– the stresses arising in the leaf springs are distributed evenly over the entire length of the leaf.

To obtain the geometry of the longitudinal profile of the spring, it is necessary to carry out a number of topological optimizations of the simplified blank model for further synthesis of the approximate shape of the leaf spring. As the initial model, a rectangle with attachment points located in places similar to the attachment points of the spring in the design of the springing system of a full-scale cargo vehicle was adopted. The width of the rectangle was chosen similarly to the width of the springs installed on cargo vehicles with an axle load of 9-10 tons, and the height of the rectangle was set arbitrarily. The initial model for optimizing the shape of the spring is shown in Fig. 1.

The topological optimization of this model was carried out in the NX software package in the Simcenter 3D finite element calculation application. In the first iteration of topological optimization (Fig. 2a), the places where it is necessary to leave the material in the model to ensure less mass and maintain rigidity are visible. Most of the material that is recommended to be left is at the bottom of the model. The material that is on top arises from the fact that bending occurs and tensile stresses occur in the upper part of the original model. Therefore, the position of the upper part of the model can be changed and shifted downwards. In the lower part, the material should be removed along the edges and the distance to the bottom edge from the attachment points should be reduced so that the stresses are distributed more evenly over the lower area. Next, the geometry of the original model was iteratively changed in accordance with the results obtained, as shown in Fig. 2.

To determine the effect of the number of spring sheets on the calculated parameters of its stiffness and strength, simplified models of two-leaf and three-leaf springs were built based on the obtained topological optimization of the shape of the longitudinal profile of the spring. Figure 3 shows the resulting shapes of single-leaf spring profiles and simplified 3D models of two-leaf and three-leaf springs.

Calculation of leaf spring parameters and characteristics

The finite element spring models shown in Fig. 4 are formed from finite elements of the HEXA(8) type. Points have been created at the attachment points of the springs, which are connected to the support platform of the RBE2 spring by elements (shown in blue).

The spring eyelets have constraints applied to the nodes in the middle of the holes. The left constraint only allows rotation around the Z axis, while the right constraint allows movement along the X axis and rotation around the Z axis. A contact interaction is set between the sheets of a two-leaf and three-leaf spring. Friction is negligible, since the calculation is carried out on a simplified model used only to obtain the dependences of stiffness and strength on the geometric parameters of the spring. In modern designs, a number of design solutions are used, leading to a decrease in inter-sheet friction. In the calculations, the deflection of the spring is set as the loading, which is the same for all cases and corresponds to the maximum stroke (up to full compression of the bump) as part of the front suspension of the car.

For the presented models, FEM calculations were performed to determine the influence of geometric parameters of springs on their stiffness and strength characteristics. To build dependencies in the models, the values of the height and width of the cross section in the central part of the spring (spring package) were varied and set. The calculation results are shown in Fig. 5.

For the calculated types of springs, the dependence of stiffness on the number of spring sheets is constructed, shown in Fig. 6.

To determine the dependencies of the spring characteristics on their geometric parameters, similar calculations were performed, in which the values of the height H and width B of the springs varied.

As a result of calculations, the necessary force F was determined to create a deflection X corresponding to the full stroke of the suspension spring, the stiffness of the spring and the stresses arising in the spring. The obtained dependencies are shown in Fig. 7-10.

The dependence of the stresses arising in the spring on the width of the spring in the cross section of its central part has not been built, since the influence of width on stresses is quite small.

Figure 11 shows a technique for synthesizing the geometry of the longitudinal profile of the spring in the form of a block diagram. Thanks to the obtained dependencies, using the compiled algorithm for synthesizing the shape of the spring, we can choose the most suitable configuration for the vehicle, based on the requirements: the weight of the vehicle on which the spring will be used; the required service life; the required coefficient of dynamism, depending on the operating conditions.

According to the calculations carried out, 3 spring configurations can be distinguished, which have the most advantageous characteristics for use on cargo vehicles with an axle load of 9-10 tons:

– single leaf spring 43 mm high, 90 mm wide;

– double leaf spring 60 mm high, 90 mm wide;

– a three-leaf spring with a height of 70 mm, a width of 90 mm.

When using a single-leaf spring, it is possible to avoid the occurrence of inter-leaf friction, however, the coefficient of dynamism decreases and Mises stresses increase. For a single leaf spring, a 33% reduction in stiffness was achieved compared to the prototype. When using two-leaf and three-leaf springs, there is inter-leaf friction in the spring sheets, but due to the described geometric parameters of the spring, it is possible to reduce the stiffness of the spring.

Results

As a result of the calculations, the following results were obtained:

1. The dependence of the full compression forces, stiffness and stresses of the spring on its geometric parameters.
2. Spring stiffness characteristics depending on the number of sheets.
3. A new method for synthesizing the geometry of the longitudinal profile and selecting the required characteristics of suspension springs used on vehicles is proposed.
Conclusion

With the increasing requirements for vehicle springing systems, it is necessary to introduce new design methods. The paper presents a new approach to the synthesis of springs, which are an important part of the springing system. The developed design approach allows you to select the optimal geometry of the longitudinal profile of the spring and calculate the characteristics of the spring, as well as use them to create dynamic models of springing systems used in vehicles for further calculations of vehicle dynamics.

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作者简介

Pavel Rubanov

KAMAZ Innovation Center

编辑信件的主要联系方式.
Email: rubanov_ps@bk.ru
ORCID iD: 0009-0000-2055-2046

Design Engineer, Engineering Calculations and Modeling Service

俄罗斯联邦, 121205, Moscow, Skolkovo Innovation Center, Bolshoy blvd., 62.

Roman Maksimov

Federal State Autonomous Educational Institution of Higher Education "Moscow Polytechnic University";
KAMAZ Innovation Center.

Email: romychmaximov@gmail.com
ORCID iD: 0009-0003-4947-790X
SPIN 代码: 7384-6758

Postgraduate student of the Department, "Ground vehicles";

Design Engineer, Engineering Calculations and Modeling Service

俄罗斯联邦, 38 Bolshaya Semyonovskaya str., Moscow, 107023; 121205, Moscow, Skolkovo Innovation Center, Bolshoy blvd., 62.

Michael Chetverikov

Federal State Autonomous Educational Institution of Higher Education "Moscow Polytechnic University";
KAMAZ Innovation Center.

Email: mihchet@gmail.com
ORCID iD: 0000-0003-3723-1171
SPIN 代码: 7949-0814

Postgraduate student of the Department, "Ground vehicles";

Design Engineer, Engineering Calculations and Modeling Service

俄罗斯联邦, 38 Bolshaya Semyonovskaya str., Moscow, 107023; 121205, Moscow, Skolkovo Innovation Center, Bolshoy blvd., 62.

参考

  1. Khlepitko, A. S. Features of the use of rational methods of designing the load-bearing system of a truck / A. S. Khlepitko, I. R. Mavleev // XII Kama readings : collection of reports of the All-Russian scientific and practical conference of students, postgraduates and young scientists, Naberezhnye Chelny, November 20, 2020 / Kazan Federal University, Naberezhnye Chelny Institute ; executive editor L. A. Simonova. – Naberezhnye Chelny, 2020. – pp. 361-367. – EDN EAAWRV.
  2. Taupek, I. M. Analysis of finite element modeling of the forging process at the RKM / I. M. Taupek, K. A. Polozhentsev // Modern problems of the mining and metallurgical complex. Science and Production : Proceedings of the Nineteenth All-Russian Scientific and Practical Conference with international participation, Stary Oskol, December 07, 2022. – Stary Oskol: National Research Technological University "MISIS", 2023. – pp. 309-314. – EDN DUJGZJ.
  3. Fischev, A.V. Investigation of stress concentrations in nodes of metal structures / A.V. Fischev // Fundamental principles of mechanics. - 2023. – No. 11. – pp. 64-67. – doi: 10.26160/2542-0127-2023-11-64-67. – EDN OCNHND.
  4. Dergachev, D. A. Improving product quality through design automation / D. A. Dergachev // SNK-2022 : Proceedings of the LXXII open International Student Scientific Conference of the Moscow Polytechnic University, Moscow, April 04-22, 2022. – Moscow: Federal State Budgetary educational Institution of Higher Education "Moscow Polytechnic University", 2022. – pp. 90-94. – EDN PUFAVD.
  5. Sutyagin, A. N. On the issue of specialized software performing calculations based on the finite element method / A. N. Sutyagin, V. I. Kolesova // Bulletin of the Russian State University named after P. A. Solovyov. – 2022. – № 4(63). – Pp. 107-112. – EDN XKGSLE.
  6. Gonzalez, A. A. V. Physico-mathematical modeling of the process of interaction of a passenger car airbag with an anthropomorphic mannequin / A. A. V. Gonzalez, R. B. Goncharov, A.V. Petyukov // Bulletin of the Bauman Moscow State Technical University. The Natural Sciences series. – 2022. – № 4(103). – Pp. 4-21. – doi: 10.18698/1812-3368-2022-4-4-21. – EDN NJQZLI.
  7. Chetverikov, M. V. Investigation of the residual stress-strain state of the mini-loader load-bearing system under repeated loading according to the requirements of the ROPS safety standard / M. V. Chetverikov, R. B. Goncharov, D. O. Butarovich // Proceedings of NAMI. – 2023. – № 1(292). – Pp. 46-55. – doi: 10.51187/0135-3152-2023-1-46-55. – EDN DETBGE.
  8. Goncharov, R. B. Improving the structures of truck cabins at the design stage to ensure the requirements of passive safety in case of impact and minimizing mass / R. B. Goncharov, V. N. Zuzov // Proceedings by US. – 2019. – № 4(279). – Pp. 28-37. – EDN XXVGQA.
  9. Goncharov, R. B. Features of the search for optimal parameters of amplifiers of the rear part of the cabin of a truck based on parametric and topological optimization in order to ensure the requirements for passive safety according to international rules and obtain its minimum mass / R. B. Goncharov, V.N. Zuzov // Proceedings of the NSTU named after R.E. Alekseev. – 2019. – № 2(125). – Pp. 163-170. – doi: 10.46960/1816-210X_2019_2_163. – EDN ZTSJEL.
  10. Levenkov, Ya. Yu. Development of ROPS from aluminum alloys for front loaders / Ya. Yu. Levenkov, D. S. Vdovin, D. A. Alexandrov // Machines and installations: design, development and operation. – 2023. – No. 3. – pp. 1-15. – EDN ALZYPP.
  11. Vdovin, D. S. Forecasting the fatigue life of semi-trailer suspension elements at the early stages of design / D. S. Vdovin, I. V. Chichekin, Ya. Yu. Levenkov // Proceedings of NAMI. – 2019. – № 2(277). – Pp. 14-23. – EDN QTMBXK.
  12. Analysis of the loads of a truck frame by the method of dynamics of body systems using a finite element model / V. A. Gorelov, A. I. Komissarov, D. S. Vdovin, O. I. Chudakov // Transport systems. – 2020. – № 4(18). – Pp. 4-14. – doi: 10.46960/62045_2020_4_4. – EDN GLXUZD.
  13. Zhu, S.H. Vehicle frame fatigue life prediction based on finite element and multi-body dynamic [Text] / S.H. Zhu, Z.J. Xiao, X.Y. Li // Applied Mechanics and Materials. Trans Tech Publications Ltd, 2012.T. 141. pp. 578-585.
  14. A.A. Yudakov, "Principles of constructing general equations of dynamics of elastic bodies based on the Craig–Bampton model and their practically significant approximations", Vestn. Udmurtsk. un-ta. Matem. Fur. Computer science, 2012, № 3, 126-140.
  15. Goncharov, R. B. Methodology for calculating the loads acting in the guiding elements of the car suspension when overcoming obstacles / R. B. Goncharov, D. M. Ryabov // Izvestiya MSTU MAMI. – 2015. – Vol. 1, No. 3(25). – pp. 129-135. – EDN UXKHEZ.
  16. Goncharov, R. B. Topological optimization of the car bumper design under impact from the standpoint of passive safety / R. B. Goncharov, V. N. Zuzov // Izvestiya MGTU MAMI. – 2018. – № 2(36). – Pp. 2-9. – EDN XUWXVB.
  17. Shabolin, M. L. Reducing the requirements for the strength of the material of the truck subframe with independent suspension by topological optimization of the structural and power circuit / M. L. Shabolin, D. S. Vdovin // Izvestiya MGTU MAMI. – 2016. – № 4(30). – Pp. 90-96. – EDN XDEHED.
  18. The influence of structural changes on the resistance to brittle fracture of the metal of the KAMAZ car springs during operation in the conditions of the North / S. P. Yakovleva, I. I. Buslaeva, S. N. Makharova, A. I. Levin // Problems of mechanical engineering and machine reliability. – 2019. – No. 3. – pp. 65-73. – doi: 10.1134/S0235711919030155. – EDN WBWKBG.
  19. Rykova, O. A. Issues of friction modeling in leaf springs / O. A. Rykova // Proceedings of the Fraternal State University. Series: Natural and Engineering Sciences. - 2022. – Vol. 1. – pp. 207-213. – EDN UIEXYO.
  20. Artyomov, I. I. Experimental studies of destruction of leaf springs of vehicles / I. I. Artyomov, V. V. Kelasyev, A. A. Generalova // News of higher educational institutions. The Volga region. Technical sciences. – 2009. – № 2(10). – Pp. 145-155. – EDN KWKSHH.
  21. Chekurda, V. V. Durability of a multi-leaf car spring / V. V. Chekurda, M. A. Nozdrin // Reliability and durability of machines and mechanisms : Collection of materials of the XIII All-Russian scientific and practical conference, Ivanovo, April 14, 2022. Ivanovo: Federal State Budgetary Educational Institution of Higher Education "Ivanovo Fire and Rescue Academy of the State Fire Service of the Ministry of the Russian Federation for Civil Defense, Emergencies and Elimination of Consequences of Natural Disasters", 2022. – pp. 426-431. – EDN COUUUW.

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