An Efficient, One-Dimensional, Finite Element Helical Spring Model for Use in Planar Multi-Body Dynamics Simulation 2013-01-1118

The helical spring is one of fundamental mechanical elements used in various industrial applications such as valves, suspension mechanisms, shock and vibration absorbers, hand levers, etc. In high speed applications, for instance in the internal combustion engine or in reciprocating compressor valves, helical springs are subjected to dynamic and impact loading, which can result in a phenomenon called “surge”. Hence, proper design and selection of helical springs should consider modeling the dynamic and impact response.

In order to correctly characterize the physics of a helical spring and its response to dynamic excitations, a comprehensive model of spring elasticity for various spring coil and wire geometries, spring inertial effects as well as contacts between the windings leading to a non-linear spring force behavior is required. In practical applications, such models are utilized in parametric design and optimization studies. For that reason, computational efficiency is also a key requirement.

In this paper, a helical spring dynamics model is presented, in which spring coils are modeled by means of one-dimensional curved beams. The displacements of these elastic components are expressed in a “floating” frame, which can undergo large rigid body motions in 2D space. The formulation thus enables modeling of planar displacements of the helical spring and captures the two-dimensional inertial effects associated with the rigid body motion/acceleration of coils but, at the same time, only requires a single degree-of-freedom per spring node. The Finite Element approach is used in order to efficiently discretize these elastic components. As compared to a more commonly used lumped mass-elastic helical spring modeling method, the proposed finite-element approach enables reduction of degrees of freedom required to accurately capture dynamic response of the spring. Furthermore, two different approaches for modeling spring coil contact and clash are presented, i.e. “lumped” and “distributed”. In the simpler, lumped coil clash model, contact forces are expressed as point loads. The distributed coil clash model treats coil contact forces as distributed loads. This results in a more efficient system since it requires fewer contact elements to correctly represent coil closure during spring compression event and, at the same time, eliminates the polygonal effect common to lumped characterization of coil-to-coil interactions.

The model has been implemented within a general-purpose multi-body dynamics analysis tool. In order to validate the model's accuracy, results from numerical simulation were compared to analytical solution of the hyperbolic partial differential equation governing helical spring dynamic response. Furthermore, experimental results from a static and dynamic spring compression tests of an automobile engine valve spring were used and compared to simulation results showing good correlation. Finally, computational efficiency of the presented model was studied in the context of a multi-body simulation of engine valvetrain system.