Engee documentation

Simulation of mechanical gears

Mechanical transmission modeling implies a compromise between accuracy and speed, which is inherent in all types of numerical modeling. Accuracy includes two aspects: the reliability of the model and the accuracy of numerical methods. The article discusses the difficulties typical for models with manual transmissions.

For more information about solvers and modeling 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 is to create blocks that more accurately represent real physical components. For example, the dynamics of components can be described more realistically using the following options:

  • Enabling or disabling physical effects such as imperfect gear engagement losses (gear efficiency).

  • Enabling or excluding ductility (including spring damping), rigid stops, and time delays.

  • Inclusion or exclusion of Coulomb friction of couplings and similar elements.

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

Modeling these physical effects requires additional dynamic and algebraic constraints, leads to more resource-intensive calculations, and can significantly reduce the simulation speed.

Model accuracy in conventional modeling

Very small speed thresholds and short time delays can degrade numerical convergence or simulation performance. Check if these values can be increased during the simulation.

Model accuracy in fixed-step, real-time, and hardware cycle simulation

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

To verify compliance or simulate effectiveness, consider reducing the number of such elements by:

  • removing unnecessary items with losses;

  • combining lossy elements into as few elements as possible.

If you are modeling with a fixed-step solver, avoid:

  • very small speed thresholds;

  • time delays that are small compared to a fixed time step.

Optimization of simulation of rigid mechanical gears

When modeling mechanical transmissions, consider eliminating all malleable elements if this is consistent with the purpose of your model. If some malleable elements have a more significant impact than others, model only them.

The connection of mechanical gears with external loads — for a car, this is the load from the wheel, tires and road — is often rigid. Road conditions usually change within a few seconds or tens of seconds. However, internal changes in a car’s drive system can occur in fractions of a second, especially when shifting gears and braking. In addition, coupling lock and unlock events create dynamic breaks.

For example, a tire is «tough» reacting slowly to applied forces and experiencing slippage. The bus also has a wide range of frequency characteristics. Simulate tire compliance only when simulating vehicle acceleration from rest.

Optimization of coupling modeling

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

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

  • Since clutch shifts are idealized events, they cause a dramatic change in the torque of mechanical gears: 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.

Change the speed tolerance. Most coupling units have a speed tolerance parameter , which determines when the clutch is locked or unlocked.

  • The coupling can lock only if the relative speed of the shaft is in the range of .

  • The clutch is unlocked if the torque on it exceeds the limit of static friction, which, in turn, depends on the normal force on the clutch.

Values they are set in each coupling block.

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

Setting up solvers to eliminate coupling breaks

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

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

  • If the fixed step size is too large, the solver cannot accurately detect abrupt changes such as locking and unlocking the coupling. A fixed-step solver cannot adaptively reduce the step size to compensate.

If there are problems with convergence or sudden changes in the state (speed) of the mechanical transmission at the moment of coupling switching, consider reducing the tolerances of the solver (for a variable-pitch solver) or the 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 lowest possible value to ensure an acceptable simulation speed (not too slow).
Customization Solver type and configuration Impact on accuracy Impact on speed Influence on coupling modeling

Decrease

Variable pitch: error

Increases

Decreasing

The accuracy of modeling instant locks and unlocks is improved.

Fixed step: step size

Increase

Variable pitch: error

Decreasing

Increases

Degrades the accuracy of modeling instant locks and unlocks

Fixed step: step size

  1. Modeling of mechanical gears with losses