# Calculation method of leaf spring stiffness

What are the calculation methods of leaf spring stiffness:

Traditional leaf spring stiffness calculation methods include the “common curvature method” and the “concentrated load method”. In addition, domestic scholar Guo Konghui proposed a calculation method called the main piece analysis method for the inherent defects in the common curvature method. In response to the inherent defects of the concentrated load method, Guangyu et al. proposed an improved concentrated load method. The starting point of these methods is to regard the leaves of the leaf spring as a cantilever beam of equal section, without considering the friction and the friction between the leaves of the leaf spring. For the large deformation characteristics of the leaf spring in the deformation process, the classic beam formula is used to calculate the end deflection of the first blade, and then the stiffness of the leaf spring is obtained.

The common curvature method was proposed by Parsilowski of the former Soviet Union. Its 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. From this, the formula for calculating the stiffness of the symmetric 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, and the contact force is Pi, and at the contact point The deflection of two adjacent blades is equal. Among them, P1 is the external load on the first piece. Therefore, the unknown forces in the system are P2, P3, ?, Pn, a total of n-1, and the deflection at the contact point is equal to obtain n- 1 equation, solving this equation group can get the unknown forces P2, P3, ?, Pn, and then calculate the end deflection of the first piece according to the load on the first piece, and then the stiffness of the leaf spring can be obtained. The calculation formula is as follows:

The common curvature method assumes that each blade has the same curvature on any cross-section after the leaf spring is loaded.There is an obvious inconsistency 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 leaf analysis method makes the following assumptions. a. Each leaf spring is divided into a constrained part and a non-constrained part, and the constrained part of the i-th leaf spring is The definition of the unconstrained part; b. The leaves of the leaf spring are free to deform downward in the unconstrained part, and the constrained part conforms to the common curvature assumption, that is, the curvature of each section is the same as the curvature of the previous sheet in this section.

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

The concentrated load method assumes that each leaf of the leaf spring only contacts each other at the ends, but in fact, the points in the leaf spring may also contact 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 there are several contact points.As shown in Figure 2, there are Ni contact points between the i-th 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 a total of unknown forces in the system, and an equation can be obtained from the deflection at each contact point, and the magnitude of each unknown force can be obtained by solving this equation system. According to the force on the first piece, it can be found The end deflection of the first piece is 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 common point of the above various 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, there are large deformation characteristics when the leaf spring is working, and linear There is a certain deviation in the 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, making the calculation more accurate, and for variable cross-section springs and fewer leaf springs. And the gradual stiffness leaf spring can find its working stiffness very well, which has practical significance.