Simulation has offered tremendous progress in vehicle development. Time and effort for iterations on vehicle design have dramatically decreased. Easy access to variable ranges even outside the measurement domains has led to new engineering viewpoints. Automatic iteration processes create …time to be creative! The more it gives us, the more we need! We need our models to be flexible to meet our evolving products. We need to connect different models from different parties. We need to execute in real-time… Naturally, we in industry are attracted to Modelica and FMI.

In this blog article we introduce relevant results of a project that I, Hiroo - Toyota engineer, together with Peter - simulation engineer from Modelon, worked on during this spring within a larger Modelon team; the results were presented in May at the first Japanese Modelica Conference.

We believe this work can be interesting among others for vehicle design and development engineers, automotive test engineers, system engineers, virtual reality engineers.

Virtual Vehicle Kinematics and Compliance Test Rig

Accelerated and flexible vehicle development with virtualization

Kinematics and Compliance (K&C) rig in operation at Toyota. The vehicle body is clamped so that the rig can induce roll, pitch and bounce motion of the body.
Screenshot of a vehicle in the virtual test rig.

Why do we need virtual test rigs?

The kinematics of a suspension describes how the wheel displacement and angle change as a function of vertical travel. The wheel behavior caused by an applied force determines what we call the suspension compliance.

These characteristics are significantly important for vehicle dynamic performance and ride comfort. Kinematics and Compliance (K&C) test rigs are normally used for measuring these characteristics.

Test rigs results provide system characteristics useful to understand and analyze how the suspension works in practical cases.

Now, measurement procedures need a certain amount of time and of course, an actual vehicle. If we need to study parts exchange effects, additional iteration time is also required.

But time and vehicle availability are always limited. How can we solve this problem without compromising?

The virtualization advantage is thus clear: K&C characteristics can be acknowledged before components and vehicles come physically available. Time consuming operations such as tests setup or parts exchange are not necessary. Virtualization enables automatic optimization iteration for design values to achieve desirable system characteristics.

To develop such a complex virtual test system, we at Toyota needed specialist competence skilled not only in modeling but also in vehicle dynamics. Modelon proved to be the very company we were looking for. 

Test rig model 

The virtual rig model is based on components from Vehicle Dynamics Library and it has been developed based on a corresponding physical test rig.  

In the virtual test rig, the chassis is attached to a table that can generate roll, pitch and heave motion. The wheels are situated on pads, which can move in the ground plane to generate forces and torques. 

The rig model has several operating modes. For example, the table can be released to let the chassis settle on its own before being clamped to the table. Furthermore, the table can be controlled to achieve specific force targets on the wheels, like applying a roll motion and using heave to maintain constant total axle load.  

The virtual test rig is designed to mimic the functionality of the physical test rig and to allow tests to be operated in a consistent way, by sharing parameterization for configuration as well as data formats.

A key requirement is that the virtual rig needs to be exported as a single FMU with inputs controlling all the different operating modes. This eliminates the need for making multiple FMU exports and switching between them for different modes which greatly simplifies deployment. 

Diagram layer of the rig model including the tested vehicle model

The figure beside gives you a glimpse over the diagram layer of the rig model including the tested vehicle model. Both real and Boolean signal inputs are used to control the rig.

How are the virtual tests run?

A user interface based on the MATLAB scripting language was also developed. This interface uses functions from the FMI Toolbox for MATLAB/ Simulink to import the co-simulation FMU exported from the rig model.

A set of standard test setups is stored in an Excel spreadsheet. This spreadsheet mimics the one used for parameterizing tests on the physical test rig. There is a column for each parameter that needs to be set in the rig model, and each test is defined in one row.

To run a specific test, the specification for that test is read from the corresponding row in the spreadsheet based on a unique test number. The test specification is then loaded into a test object in the MATLAB environment, which is sent as an argument when running the test using the test rig.

test_rig = VirtualKCTestRig('FMUfile.fmu'); 

test_setup = CreateKCTest('3.3.1'); 

result =; 



The test specification can be modified after being read from the spreadsheet by changing variables in the test object.  

Application example

Let us show an example of a test run on the virtual rig. The vehicle used for the example has an elasto-kinematic McPherson front suspension and a twist beam rear suspension with bushing mounts. The test shown is a roll test with constant axle load.

During the work with the virtual rig, a new twist beam suspension model was also developed. The following plots focus on the kinematics of this rear suspension model. Parameterization is based on hard point data and other known quantities as far as possible, and some are estimated. 

The figures above show the bounce motions of the two rear wheels plotted against their longitudinal, respectively lateral displacements. Magnitudes of the signals are hidden for confidentiality reasons.

Read the full paper for all results concerning the kinematics of the rear suspension for the roll test.

Usage of the virtual test rig

There are several possible ways to use the test rig:

  • It is possible to run physical and virtual test rig tests in parallel and do correlation runs. Once good correlations are obtained, tests can be run completely on the virtual rig, since specifications and output formats are equivalent.
  • The test rig can also be used to plan tests, or dry run tests.
  • It can be used as well to do parameter tuning, typically by applying optimization methods.
  • Even more ways can be thought of for using the test rig.

Advantages of the virtual test rig are directly coupled to its usage

  • Simulation and setup time are significantly less than in the real-time tests
  • The virtual representation allows changes in the model that are very time expensive on real prototypes, and sometimes even impossible. This offers a lot of freedom and flexibility in trying different design options.
  • The user is free to change parameters in quick iterations. Depending on complexity level and length of test sequence, the execution of a complete cycle on a standard laptop normally ranges between 2 and 10 s. This allows for rapid execution of DOE, or for parameter tuning either to reach desired characteristics or to match with measurement data from the real test rig.
  • The test rig can be used to excite any vehicle that is compatible with the standard interfaces of the Vehicle Dynamics Library, which allows the user to conveniently change vehicle configuration and model fidelity level so that the K&C behavior can be predicted at any time during the design process.
  • Simulations can be distributed onto several computers with little effort, which accelerates the results even more. 

Feel free to contact us if you want to learn more details!

Hiroo Iida is a simulation engineer for chassis performance development at Toyota Motor Corporation. He spent several years to develop trade-off design methodology with virtual optimization workflow. Hiroo is currently specializing in modeling and simulation methodology with Modelica and FMI.  

Peter Sundström is a simulation engineer working with consulting and product development, mainly related to Modelon's Vehicle Dynamics Library. He has been with Modelon since 2009. The current focus is on high fidelity real-time vehicle models and various methods of model deployment. 

by Hiroo Ida and Peter Sundström