Dynamic initialisation in Dymola of full vehicle models 

If you are modelling complex systems, such as full vehicle models, then you will have seen that they can include large transient periods at the start of simulation, before settling to a steady state. Colloquially this is known as the “settling phase”. Excessive settling in a model can cause the time associated with initialising the model to become excessive, as well as potentially allowing the model to reach an unintended steady state as the simulation begins. Naturally, this can impact the performance and results of the simulation; therefore, extended settling phases should be avoided. So how do we avoid this? All VeSyMA models from Claytex include aspects and features designed to promote robust initialisation, making them more intuitive and easier to use. In this blog post we will go over a couple of full vehicle examples from the VeSyMA library.

What is initialisation? And how does Dymola go about this?

In a dynamic simulation, the forces are not constant and vary with time. Within the Dymola simulation, as in real life, a multibody system model must support itself under the force of gravity or any other forces acting upon the system. If the model is not initialised at static equilibrium, i.e. all the forces within the system are equal, then it will need to find a static equilibrium during the initial phase of simulation. Otherwise known as initialisation, the model can find itself in a state that differs from the intended initial state. Care must be taken when setting the initial conditions of the model to reduce the amount of settling. Predictably, if a vehicle is not at rest, i.e. it is moving, then initialisation of the model to a steady state is more difficult, due to the additional forces acting upon the vehicle associated with its motion. Therefore, it is prudent to establish robust initialisation conditions for the model when the model is at rest.

Figure 1: Comparison of Spring Forces in a vehicle's 4 ride springs. The variables have been assigned to different axis to highlight the settling.
Figure 1: Comparison of Spring Forces in a vehicle’s 4 ride springs. The variables have been assigned to different axis to highlight the settling.

In many simulation packages, setting initialisation conditions can be a laborious task. Dymola makes this easier, by producing two models rather than one during the compilation process. The first of these models is used purely to derive the initial conditions for the second simulation model, which is the model responsible for producing the overall results of the simulation. It would be impossible otherwise, for the user to manually set all the initial conditions for all the components within the model due to the vast number of components within the model. Despite this, various primary initial forces, such as the initial force within the suspension springs, set by the user within the model have a significant impact upon the initial state the model will have. 

The initialisation setup experiment

A vehicle model with conventional suspension essentially comprises a large mass (the chassis and everything which bolts into the chassis) supported by 4 spring damper systems – the suspension systems at each vehicle corner. In VeSyMA vehicle models we specify the initial position and attitude we want the chassis to have (in terms of pitch roll, ride height) at the beginning of simulation. Each of the spring damper systems must produce a force to resist the downward force of gravity acting on the chassis; this is complicated by two factors. The first is that the load supported by the spring damper systems is not evenly distributed over the four corners due to vehicle mass distribution as well as chassis attitude. The second factor is that each of the spring damper systems supporting the chassis are themselves mounted on undamped spring systems, which is effectively how the tyres act in this scenario. All of this combines to mean that determining the static force each of the spring damper systems needs to produce to hold the chassis in the desired design location is not intuitive. 

To make determining the static spring loads (or “preload”) easier, the InitialisationSetup experiment within the StaticTests package can be used. This is a simple full vehicle experiment, derived from the mass check experiment, whereby all four wheels have been replaced with rig tyres (to remove jacking force influences) and the suspension stiffness has been dramatically increased, which minimises the amount of deflection which occurs due to the settling of the chassis on the suspension springs. This works because the vehicle hardpoint data defines the suspension when it is loaded and settled, therefore the forces must be found to allow the vehicle to rest in that condition. By minimising the deflection of the springs at initialisation, the force required to be produced by each of the springs at initialisation to support the chassis in the desired attitude can be understood. Due to this being a dynamic simulation there still will be extremely small deflections of the springs at initialisation. In turn this means that the chassis attitude (roll, pitch, yaw, right height) will differ ever so slightly with the derived suspension preloads. Therefore, the InitialisationSetup experiment also determines the initial conditions of the chassis attitude to be set within the motion block. By combining these initial conditions for the motion block and the derived suspension preloads, the vehicle as a system will initialise close to steady state. Deviation from the design condition is therefore minimised.

It is worth remembering however that this is not the only way to define initial forces. If you know the resting length of the spring, then this can also be used with the spring stiffness to define the preload required to support the vehicle at initialisation.

Figure 2: Excerpt from the simulation log of the Suspensions.Experiments.StaticTests.InitialisationSetup experiment.
Figure 2: Excerpt from the simulation log of the Suspensions.Experiments.StaticTests.InitialisationSetup experiment.

The BushTuning experiment

The same principles which govern the initialisation of the vehicle model described above, which features rigid suspension joints, extend to vehicles which have flexible suspension joints. More commonly known as bushes or bushings, these flexible joints add a further 6 degrees of deflection into each joint of the suspension linkage, by having a compliant model in each degree of freedom of the joint. Naturally, the vehicle as a system now is inherently less rigid, requiring further preload forces in each bushing degree of freedom to be calculated to support the vehicle at initialisation. 

Rather than setting the stiffness of the bushings to an extremely high value, to eliminate deflection as far as possible as previously, each bushing has an inbuilt “static tuner”. These tuners are designed to increase the force in each direction of the bushing to achieve an arbitrary target for deflection. Once the deflection criteria have been satisfied, the simulation is terminated and the six preload values for each bushing are returned to the user in the simulation window. Application of these preload values in each of the bushings within the vehicle will therefore enable the linkages to initialise as close to a steady state as possible.

Figure 3: Excerpt from the Suspensions.Experiments.StaticTests.BushTuning simulation log
Figure 3: Excerpt from the Suspensions.Experiments.StaticTests.BushTuning simulation log.

Closing remarks

By virtue of being dynamic, full vehicle dynamic simulations possess a degree of instability at initialisation if they are not initialised with the forces within a system as close to the eventual steady state as possible. Whilst there is a high number of elements within vehicle models which contribute to the dynamic nature of them, targeted application of initial forces equal to the eventual steady state forces enables the vehicle to be initialised in as stable a condition as possible. By doing so, the eventual simulation will be more robust, not to mention quicker to simulate, done if it is allowed to initialise freely without any constraints.

Written by: Theodor Ensbury – Project Engineer

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