THE METHOD OF SYNTHESIS OF THE GEOMETRY OF THE LONGITUDINAL PROFILE AND THE DESIGN PARAMETERS OF THE LEAF SPRING USING THE FINITE ELEMENT METHOD
- Authors: Rubanov P.S.1, Maksimov R.O.2,3, Chetverikov M.V.2,3
-
Affiliations:
- KAMAZ Innovation Center
- Federal State Autonomous Educational Institution of Higher Education "Moscow Polytechnic University"
- KAMAZ Innovation Center.
- Section: Theory, designing, testing
- Submitted: 17.01.2024
- Accepted: 27.06.2024
- Published: 26.07.2024
- URL: https://journals.eco-vector.com/0321-4443/article/view/625745
- DOI: https://doi.org/10.17816/0321-4443-625745
- ID: 625745
Cite item
Abstract
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.
Full Text
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.
About the authors
Pavel S. Rubanov
KAMAZ Innovation Center
Author for correspondence.
Email: rubanov_ps@bk.ru
ORCID iD: 0009-0000-2055-2046
Design Engineer, Engineering Calculations and Modeling Service
Russian Federation, 121205, Moscow, Skolkovo Innovation Center, Bolshoy blvd., 62.Roman O. 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-code: 7384-6758
Postgraduate student of the Department, "Ground vehicles";
Design Engineer, Engineering Calculations and Modeling Service
Russian Federation, 38 Bolshaya Semyonovskaya str., Moscow, 107023; 121205, Moscow, Skolkovo Innovation Center, Bolshoy blvd., 62.Michael V. 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-code: 7949-0814
Postgraduate student of the Department, "Ground vehicles";
Design Engineer, Engineering Calculations and Modeling Service
Russian Federation, 38 Bolshaya Semyonovskaya str., Moscow, 107023; 121205, Moscow, Skolkovo Innovation Center, Bolshoy blvd., 62.References
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