This blog introduces the modeling of a twist beam suspension in Vehicle Dynamics Library, a result of a recent collaboration between Modelon and Chalmers University. This project is based on a Euler- Bernoulli beam model, which has been developed as part of an earlier project.
The post is particularly relevant for mechanical engineers, systems engineers, design engineers and simulation engineers working in automotive and in industrial equipment industries.
Industrial systems often incorporate components that are flexible by definition and functionality.
As examples, think of a twist beam axle in a car, the leaf springs or frames in a truck, the wing on an airplane and so on.
In multi body simulation they are usually modeled via flexible body models obtained by modal reduction[i] of a finite element model.
When modeling a twist beam component, this simulation method is time consuming and requires the finite element data for the component.
Further abstraction of the twist beam suspension in terms of parameterizing the cross section instead of generating a FE model can be useful during the concept design phase. The hardpoint and bushing stiffness/orientation definition, as well as parameter sensitivity analysis of vehicle dynamics performance metrics can be investigated along with the beam properties.
Currently a twist beam suspension model is available in Vehicle Dynamics Library designed for real time applications. It consists of two trailing arms mounted at the chassis using spherical joints and the cross beam is modeled as a stiffness and damping matrix. As part of this project, the suitability of the beam model for real time performance was also investigated, because it provides the user with cross section properties as input instead.
In this study of a twist beam suspension, the compliances from the bushing, the bearing and the spring all have a major effect on compliances for the lateral force steer, the camber, the lateral and longitudinal steers and the longitudinal compliance.
This goes on to show that significant improvement in the model fidelity can be obtained by using chassis mount bushings and compliant hubs.
The characteristics involved in our twist beam suspension are easily modeled in Vehicle Dynamics Library by using available components.
The first modification made in the existing Vehicle Dynamics Library implementation was to replace spherical bearings at the chassis mount with bushings instead. The second modification was the replacement of the stiffness and damping matrix based cross beam with the Euler-Bernoulli beam model.
The model was validated against a similar model in ADAMS/Car - a multibody modeling and simulation environment by MSC Software, tailored for road vehicle applications.
The geometric properties of an open V type section have been used to get realistic bending and torsional stiffness of the cross beam and the ADAMS model utilized a Modal Neutral File (MNF) flexible body, obtained from a Dassault Systèmes ABAQUS Euler-Bernoulli beam.
The rest of the parameters from the ADAMS model (hardpoints, bushings, spring, dampers) were read into Vehicle Dynamics Library using Modelon DataAccess components for TeimOrbit files, reducing the modeling time and effort required.
Both the ADAMS/Car and Vehicle Dynamics Library suspension models show close agreement from kinematics and compliance tests performed on axle rigs.
Some of the results are shown in Fig 2. The plots indicate a good agreement obtained between the reference ADAMS simulation and the Dassault Systèmes Dymola/ Modelon Vehicle Dynamics Library simulation for camber, and toe angles versus opposite wheel travels.
The twist beam suspension model was also used in a chassis model using a VDLRealTime front suspension and decouplers for evaluation of real time performance using the implicit Euler solver.
An open loop, double lane change steer maneuver was used as the test case. The evaluation indicates that the model has a turnaround time[ii] of around 1 msec for the majority of the time steps, which is a useful level for vehicle real-time applications (see Fig. 3). The model can thus be run at 1000 Hz when executed in real time.
[i] Modal reduction is the process of replacing the finite element degrees of freedom (DOFs) with modal DOFs which are typically some orders of magnitude lower. This is done by representing deformations of the finite element nodes as a linear combination of mode shapes.
[ii] Execution time for one time step
Sidharth Malik has an MSc in Automotive Engineering from Chalmers University of Technology. He has industry experience in simulation of multi body vehicle dynamics models. At Modelon he is a simulation engineer working mainly with integration of flexible bodies in models from the Vehicle Dynamics Library.
Adina Tunér is a Marketing Communications Manager at Modelon. With a keen interest in writing, a PhD in Mechanical Engineering from Romania, another one from Sweden, and with 17 years of engine research in her rucksack, Adina settled lately for the challenges of melting together innovative technologies with business and communication.