# Calculation method of leaf spring stiffness

In comparison, “Common Curvature Method” and “Concentrated Load Method” are traditional calculation methods for leaf spring stiffness. In addition, the Chinese scholar Kong Hui proposed a calculation method for some inherent defects in the common curvature method-the main piece analysis method. The scholar Tian Guangyu put forward his own ideas for some inherent shortcomings of the concentrated load method. The starting point of both of them is to regard each leaf spring as a cantilever beam of equal cross-section, without considering the friction between the leaf springs and the large deformation characteristics during the deformation of the leaf spring, the classical beam formula is used to calculate the first leaf The end deflection of, and then the stiffness of the leaf spring.
The common curvature method was proposed by Parsilowski of the former Soviet Union. The basic assumption is that after the leaf spring is loaded, each blade has the same curvature in any section, that is, the entire leaf spring is regarded as a variable section beam. The formula for calculating the stiffness of the symmetrical leaf spring is as follows:

The basic assumption of the concentrated load method is that the leaves of the leaf spring only contact each other at the ends, that is, it is assumed that there is only one contact point at the end between the ith piece and the i-1th piece, the contact force is Pi, and the contact point is The deflection of two adjacent blades is equal. Among them, P1 is the external load on the first piece. Therefore, there are n-1 unknown forces in the system P2, P3,…, Pn, n-1 equations can be obtained by equal deflection at the contact point, and the unknown forces P2, P3,…, Pn, and then obtain the end deflection of the first piece based on the load on the first piece, and then the stiffness of the leaf spring can be obtained.

Based on the above assumptions, the formula for calculating leaf spring stiffness is as follows: an+2=an+1=l1.

The concentrated load method assumes that each leaf of the leaf spring is in contact with each other only at the ends, but in fact the points in the leaf spring may also be in contact with each other. Based on this idea, the improved concentrated load method puts forward the following assumptions: a. There are not only interactions at the endpoints, but also several contact points. As shown in Figure 2, there are Ni contact points between the ith piece and the i-1th piece. Record the distance between these points and the symmetry plane of the leaf spring Is lij,j=1,2,…,Ni; b. The interaction between the i-th slice and the i-1th slice only has a concentrated force at the preset Ni contact points, denoted as Pi1, Pi2, PiNi, as shown in picture 2.

Similar to the concentrated load method, there are total unknown forces in the system. From the equal deflection at the contact points, one equation can be obtained. Solving this equation system can obtain the magnitude of each unknown force. According to the force on the first piece, the end deflection of the first piece can be obtained, and then the stiffness of the leaf spring can be obtained.

Unlike the concentrated load method, the results calculated by this method cannot guarantee that each unknown force is greater than or equal to zero (that is, there can only be pressure between the contact points). For this reason, iterative algorithms are needed to solve this problem.

The formula for calculating the stiffness of the leaf spring is as follows:

The common curvature method assumes that after the leaf spring is loaded, each blade has the same curvature on any cross section. There is an obvious discrepancy in this assumption, that is, there is no concentrated bending moment at the free end of each piece. It is also impossible to have the same curvature as the previous one at the same section. For this reason, the main film analysis method has made the following assumptions. a. Each leaf spring is divided into a constrained part and a non-constrained part. The definitions of the constrained part and the non-constrained part of the i-th leaf spring; Curvature assumption, that is, the curvature of each section is the same as the previous one in this section.

The common point of the above calculation methods is that the leaves of the leaf spring are approximately equivalent to a cantilever beam, and the contact between the leaves is simulated by different methods. In fact, the leaf spring has large deformation characteristics when it is working, and there is a certain deviation in the linear cantilever beam simulation, and the contact simulation method between the leaf springs is also rough. Using the finite element method to calculate the leaf spring stiffness can overcome the above shortcomings and make the calculation more accurate, and the working stiffness of variable section springs, less leaf springs and gradient stiffness leaf springs can be obtained very well, which has practical significance.