February 22, 2025

Introduction to relevant theoretical research in the application of spring design

In particular, in recent years, in order to improve the high-speed performance and light weight of automobiles, automobiles have increasingly adopted leaf springs with variable cross-sections. Traditionally, the calculation of multiple leaf springs has been based on the full contact model or the chip end contact model. It has been proved that the chip end contact model is more suitable for practical use and more applications. The calculation formula of the small-section variable-section leaf spring is also used in the chip-end contact model, and the correction coefficient is introduced, but the accuracy of the formula is to be discussed. To this end, this paper discusses the possibility of finite element analysis of leaf spring by gap element method, calculates the stiffness and strength of the variable section leaf spring, and compares the calculation result with the calculation result of the formula. The accuracy was analyzed and discussed.

The finite element model considers the shape, constraint and load of the leaf spring to have symmetry. Half of the finite element analysis is carried out. Since the spring width is much larger than the sheet thickness, the plane strain unit is selected to divide the leaf spring, and the thickness is 1 mm. The contact between the pieces during spring operation is a difficult point of simulation. In this paper, the case is simulated by a gap element that can only be pressed and cannot be pulled. The gap elements are respectively connected with the corresponding nodes of the plane strain units of the adjacent two spring pieces. In order to accurately simulate the inter-chip contact, the stiffness of the gap elements should be taken as a great value. This paper is taken as 5@108N/mm. Sliding perpendicular to the axis of the gap element is allowed between the plane strain units between the sheets.

A schematic diagram of the finite element model of the leaf spring is shown. The load is applied to the end of the main piece, and the constraint is added at the center distance of the 1/4 riding bolt from the symmetry plane. The leaf spring in the figure is a straightened shape. In fact, the shape of each unit is curved. This can be used to determine the coordinates of each node by geometric calculation. Interactive modeling or programming automatic modeling using finite element analysis software. .

The calculation results are compared with the calculation results of the calculation method of the chip end contact method which is more accurately tested by practice. Content maximum stress (MPa) offset frequency (Hz) no-load full-load end-end method 500211651.887 finite element method 4892.1431.866 error 2% 1% From this point of view, the application of gap element method to simulate the calculation of the leaf spring sheet contact calculation error is small, from According to the deformation and displacement of each piece after the force, the deformation of each piece is coordinated, and there is no crowding and separation. This fully proves that it is feasible to simulate the contact between the leaf springs by applying the gap element method, which is close to the actual situation.

In order to check the accuracy of the small-section variable-section leaf spring formula, the gap element is used to calculate a small piece of variable-section leaf spring. The length of the leaf spring is 1040mm, the width of the plate is 65mm, the center distance of the riding bolt is 82mm, the number of pieces is 4 pieces, the curvature of the assembly. The radius is 1130mm, the no-load axle load is 8693N, the full-load axle load is 12446N, and the unsprung mass is 1764N. See the calculation results. Content maximum stress (MPa) Offset frequency (Hz) No-load full-load chip end method 556214311.958 Finite element method 4802.5832.080 Error 14% 6% From the results, the application of the chip end method to analyze a small number of variable-section leaf springs, the error is large. Since the stress value solved by it is too large and safe, it can be used in practice for the sake of simplicity. However, it is best to use the finite element method to accurately analyze the characteristics of a small piece of variable-section leaf spring to ensure the design quality.

Conclusion (1) The gap element method can be used to simulate the contact between the leaf springs, which is in line with the actual situation. (2) Applying the chip end method formula to calculate a small piece of variable-section leaf spring, the error is large, and the finite element method is preferred.

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