Engee documentation

Modelling of mechanical gears

Mechanical gear modelling involves a trade-off between accuracy and speed inherent in all types of numerical modelling. Accuracy includes two different aspects: the accuracy or validity of the model and the accuracy of the modelling methods. This article discusses the complexities inherent in mechanical gear models.

For solvers and modelling methods, see the articles Getting started with solvers in Engee and Local solvers for physical networks.

Adjusting the accuracy of the model

Improving the accuracy of mechanical transmission models involves creating blocks that more accurately represent real physical components. For example, component dynamics can be described more realistically using the following options:

  • Enabling or disabling physical effects such as non-ideal gear meshing losses (gear efficiency);

  • Including or excluding pliability (including spring damping), hard stops, and time delays;

  • Incorporating or eliminating Coulomb friction of couplings and coupling-like elements;

  • Reducing or mitigating abrupt changes in physical thresholds, such as speed thresholds in couplings and non-ideal gears.

Modelling these physical effects requires additional dynamic and algebraic constraints, leads to more computationally intensive calculations and can significantly reduce the speed of the simulation.

*Model accuracy in conventional simulations:

  • Very small speed thresholds and short time delays can degrade numerical convergence or simulation performance. Consider whether these values can be increased in the simulation.

Model accuracy in fixed-step, real-time and hardware loop simulations.

With the exception of couplings, it is not recommended to use accuracy improvements in fixed step/fixed cost, real-time or hardware-in-the-loop (HIL) modelling.

For compliance or efficiency modelling, consider reducing the number of such elements by:

  • Removing unnecessary lossy elements;

  • Combining lossy elements into as few elements as possible.

If you are modelling with a fixed step solver, avoid:

  • Very small velocity thresholds;

  • Time delays that are small compared to the fixed time step.

Optimisation of simulation of rigid mechanical gears

When modelling mechanical transmissions, consider eliminating all malleable elements if it suits the purpose of your model. If some malleable elements have a more significant effect than others, try to model only those elements.

The relationship of mechanical gears to external loads - for a car this is the load from the wheel, tyre and road - is often rigid. Road conditions usually change within seconds or tens of seconds. However, internal changes in a vehicle’s drive system can occur in fractions of a second, especially during gear changes and braking. In addition, clutch locking and unlocking events create dynamic discontinuities.

For example, the tyre is 'stiff', responding slowly to applied forces and experiencing slippage. The tyre also has a wide range of frequency response. Consider tyre pliability modelling only when simulating vehicle acceleration from rest.

Optimising coupling modelling

Clutch locking and unlocking events cause jumps in the dynamics of mechanical transmissions and can lead to significant inaccuracies, especially if the system is modelled with a large tolerance variable step solver or with a large fixed time step.

  • Clutch switching changes the number and nature of the degrees of freedom of the mechanical gears during the simulation.

  • Since clutch switching is an idealised event, it causes an abrupt change in the torque of the mechanical gears as the clutch abruptly switches between static and kinetic friction.

Setting the coupling parameters

You can configure the internal parameters of each coupling unit to control when and how the coupling locks and unlocks.

Speed Tolerance Change. Most clutch units have a speed tolerance parameter ω , which controls when the clutch locks or unlocks.

  • The coupling can only lock if the relative shaft speed ω is within the range ωωω .

  • The coupling will unlock if the torque on the coupling exceeds the static friction limit, which in turn depends on the normal force on the coupling.

The values ω are set in each coupling block.

If the coupling switches between locking and unlocking too easily during simulation, consider increasing the permissible speed.

Setting solvers to eliminate coupling breaks

  • If too large an error or step size of the solver is used, clutch switching can cause serious inaccuracies.

  • If the variable pitch error is too large, it is difficult or impossible for the solver to accurately track dynamic changes due to changes in the friction moments acting on the mechanical transmission.

  • If the fixed pitch size is too large, the solver cannot accurately detect abrupt changes such as clutch locking and unlocking. The fixed pitch solver cannot adaptively reduce the pitch size to compensate.

If there are convergence problems or abrupt changes in the state (speed) of the mechanical transmission when the clutch state changes, consider reducing the solver tolerance (for a variable pitch solver) or step size (for a fixed pitch solver). Set the tolerance of the variable pitch solver or the step size of the fixed pitch solver to the smallest possible value that allows for an acceptable simulation speed (not too slow).
Setup Solver type and setting Effect on accuracy Influence on speed Influence on coupling modelling

Reduction

Variable pitch: error

Increases

Decreases

The accuracy of modelling instantaneous locking and unlocking is improved

Fixed step: step size

Increase

Variable step: error

Decreases

Increases

Deteriorates the accuracy of modelling instantaneous locks and unlocks

Fixed step: step size

  1. Modelling of mechanical gears with losses