Knowledge Bank

Multi-directional stiffness matrices of elastic joints, such as elastomeric bushing in automotive suspensions, are not easily quantified and are often simplified as diagonal matrices, ignoring effects of coupling among the different directions contained in off-diagonal terms in the matrices. The purpose of this study is to examine two procedures to quantify the complete two-dimensional stiffness matrices of different elastic joints. The procedures are both based on dynamic measurements on a rigid body with well-known inertia properties supported by a flexible joint with known center of motion. The first method uses the known inertia properties, measured resonant frequencies and the corresponding mode shapes of the system to calculate the stiffness matrix of the joint. The second method directly calculates the stiffness matrix using the known inertia properties and accelerance measurements collected over a range of frequencies. A controlled experiment with a system with known stiffness matrix, kinetic constraints, and inertia properties was created. Using accelerances from impulse hammer measurements, a unique stiffness matrix was obtained for a variety of joints and analyzed using each method. The sources of error are discussed along with ways in which to potentially minimize the effects of these errors.