A Multibody Dynamics Approach to Leaf Spring Simulation for Upfront Analyses

Drivelines used in modern pickup trucks commonly employ universal joints. This type of joint is responsible for second driveshaft order vibrations in the vehicle. Large displacements of the joint connecting the driveline and the rear axle have a detrimental effect on vehicle NVH. As leaf springs are critical energy absorbing elements that connect to the powertrain, they are used to restrain large axle windup angles. One of the most common types of leaf springs in use today is the multi-stage parabolic leaf spring. A simple SAE 3-link approximation is adequate for preliminary studies but it has been found to be inadequate to study axle windup. A vast body of literature exists on modeling leaf springs using nonlinear FEA and multibody simulations. However, these methods require significant amount of component level detail and measured data. As such, these techniques are not applicable for quick sensitivity studies at design conception stage. This paper bridges this gap in the literature by developing a spring model at the conceptual phase using the multibody dynamics (MBD) tool Adams based on a minimal parameter set to define leaf geometry and profile. Linear Timoshenko beam theory is employed to model the leaves thus accounting for the beam cross-section rotation which facilitates simulation of bending and shear effects. This is essential for simulating spring seat angle changes during acceleration and braking under different vertical loads. A mono leaf spring case study is presented to demonstrate the modeling capability along with a sensitivity study to provide insights on factors that affect axle windup. The effect of drive torque and longitudinal load on the windup behavior of both symmetric and asymmetric springs is demonstrated. Two-stage symmetric and asymmetric spring models are validated against test data for windup. This methodology will help develop spring simulations quickly during the design conception phase and thereby provide valuable information regarding the response of integrated vehicle systems. This in turn will help drive the design from an early stage thereby preventing expensive and time-consuming design changes later in the product development phase.