MiL testing involves using a mathematical model of a system component as the testing environment.
This allows engineers to evaluate and validate the behavior and functionality of specific aspects of a system before the actual hardware implementation takes place.
Driving simulators have boosted the vehicle design with the introduction of human beings in the simulation loop.
For a realistic functioning, the steering system must provide an accurate behaviour, since the hand wheel is a crucial human interface.
Despite a large diffusion of steering models, this paper deals with the creation of a specific solution for real-time applications, characterized by precise features as numerical stability and low computational cost.
The mechanical model is composed by two DOF:
- The first one composed by the: steering wheel, steering column and hooke joints
- The second one is composed by the pinion, rack and tie rods.
The two masses are connected by the torsion bar modelled as a simple torsional spring and damper.
The HPS is modelled by a simple function in two variables which are the torsion bar torque and vehicle velocity plus a first order delay to approximate the system dynamic response.
Superior understanding of the phenomena
Deployment of the specification framework
Easy and quick benchmark of different architectures
Human-centred design from scratch with driving simulators
Case study: Real-time steering system model
Development of an Angle-Driven 2 DOF steering system model specific for
real-time applications
Model requirements
- Accurate steering wheel angle to rack position relation
- Accurate power steering assistance modelling
- Friction effects properly modelled
- Real-time features
- High numerical stability
- Ease of parametrization
- Implementation at the simulator possible
Modelled components
- Rack: friction force, viscous coefficient, stribeck velocity, inertia
- Torsion bar: stiffness, damping
- Steering column: friction force, viscous coefficient, inertia
HPS Hydraulic Power Steering
- Steady state curves
- Time constant
Modelled key phenomena
- System elasticities
- Power steering effects
- Friction hysteresis
Case study: Real-time suitable steering system model
Model validation: Objective Assessment
Model comparison
- Proving ground data
- 2 DOF Model
- 1 DOF Model
Slow ramp steer ISO 4138
- Constant velocity
- Constant slope steering wheel ramp profile
Weave test ISO 13674
- Constant velocity
- Constant sine amplitude
- Constant sine frequency
Results
- High fidelity steer torque reproduction from low to high lateral acceleration
- On center stability
- Effective reproduction of hysteresis effects
- Accurate Steering wheel angle to vehicle lateral acceleration relation
Reference
Development of a real-time steering system model for driving simulators – Cesare Certosini, Francesco Vinattieri, Renzo Capitani, Claudio Annicchiarico, 2019