A Multibody Dynamics Approach to Leaf Spring Simulation for Upfront Analyses
Published June 15, 2015 by SAE International in United States
Annotation of this paper is available
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.
CitationAddepalli, K., Remisoski, N., Sleath, A., and Liu, S., "A Multibody Dynamics Approach to Leaf Spring Simulation for Upfront Analyses," SAE Technical Paper 2015-01-2228, 2015, https://doi.org/10.4271/2015-01-2228.
- Society of Automotive Engineers, Inc., “Manual on Design and Application of Leaf Springs,” (Warrendale, Society of Automotive Engineers, Inc., 1980), doi:10.4271/HS-788.
- Figure from Road Module, The Contact Patch, www.the-contact-patch.com, Creative Commons framework
- Society of Automotive Engineers, Inc., “Universal Joint and Driveshaft Design Manual,” (Warrendale, Society of Automotive Engineers, Inc., 1979), doi:10.4271/AE-07.
- Wellmann, T. and Govindswamy, K., “Development of a Multi-Body Systems Approach for Analysis of Launch Shudder in Rear Wheel Driven Vehicles,” SAE Technical Paper 2009-01-2073, 2009, doi:10.4271/2009-01-2073.
- Sugiyama, H., Shabana, A. A., Omar, M., Loh, W., “Development of Nonlinear Elastic Leaf Spring Model for Multibody Vehicle Systems,” Computational Methods in Applied Mechanics and Engineering, 195 (2006), doi:10.1016/j.cma.2005.02.032.
- Kat, C. J., “Validated Leaf Spring Suspension Models,” Ph.D. Dissertation, University of Pretoria, 04-23-2012
- Rill, G., “Vehicle Modeling by Susbystems,” J. of the Brazilian Society of Mechanical Sciences and Engineering, 4-28, 10/12-2006, doi:10.1590/S1678-58782006000400007.
- Philipson, N., “Leaf Spring Modeling,” The Modelica Association, ideon Science Park, SE-22370 Lund, Sweden
- Omar, M.A., Shabana, A.A., Mikkola, A., Loh, W. and Basch, R., “Mutlibody System Modeling of Leaf Springs,” J. of Vibration and Control, 10(11), 1601-1638, 11-2004, doi:10.1177/1077546304042047.
- Wasfy, T. M. and Noor, A. K., “Computational Strategies for Modeling Flexible Multibody Systems,” ASME J. of Applied Mechanics. 6-56, 11-2003, doi:10.1115/1.1590354.
- Yang, Y., Ren, W., Chen, Jiang, M. and Yang, Y., “Study on Ride Comfort of Tractor with Tandem Suspension Based on Multi-body System Dynamics,” Applied Mathematical Modeling, 33(1), 01-2009, doi:10.1016/j.apm.2007.10.011.
- Pickhaver, J.A., “Beam Elements,” Numerical Modeling of Building Response to Tunnelling,” Ph.D. Dissertation, University of Oxford, 2006.
- ADAMS User Guide, “Discrete Flexible Links”, V. 2013.2
- Cowper, G. R., “The Shear Coefficient in Timoshenko's beam Theory,” J. of Applied Mechanics 33(2), 335-340, 1966, doi:10.1115/1.3625046.
- Gillespie, T., “Fundamentals of Vehicle Dynamics,” (Warrendale, Society of Automotive Engineers, Inc., 1992), doi:10.4271/R-114.
- Ming, Q., “Vehicle Dynamics,” Sliding Mode Controller Design for ABS System, Department of Electrical Engineering, Virginia Polytechnic Institute and State University, 04-18-1997