Integrating Geometric Properties Delivers Better Gear Modeling - Maplesoft

Etude de cas :
Integrating Geometric Properties Delivers Better Gear Modeling

Typically, modeling software provides a set of signal blocks or components that take basic properties into account. For dynamic modeling purposes, this approach might suffice; however, for highly complex models, having the ability to take the geometric properties of the components into account results in higher fidelity models. In the case of systems with gears, models that include the geometric properties of the gears, how the gear teeth interact with each other, and how those effects are transmitted to other components in the model will accurately predict rotational speed, power loss, and dynamic behavior of the gear. The result is a model which more accurately reflects the actual system.

Two typical gear sets used in several applications are worm drives and rack and pinion.

Worm Drive
A worm drive is an arrangement of gears consisting of a worm and worm wheel. The worm has only one tooth wrapped continuously around its circumference, much like a thread on a screw. The worm is meshed with a worm-gear or worm-wheel, whose axis is perpendicular to that of the worm. Worm drives are a simple and compact way to achieve a high torque, low speed gear ratio.

Rack and Pinion
A rack and pinion is a type of linear actuator that is used to convert rotary motion to linear motion and vice versa. A circular gear, or “pinion”, engages teeth on a linear gear bar, or “rack.” An example of its use is in rack-and-pinion steering in automobiles. The pinion is attached to the bottom end of the steering column and turns with the steering wheel. The rack meshes with the pinion and is free to move left and right in response to the angular input at the steering wheel.

Figure 1 - Worm Drive
Figure 2 - Rack and Pinion

To create a robust gear model in MapleSim, a parametrized custom component is used to enter the equations that define the gear sets. Parameters representing several aspects of the gears such as diameter factors, axial modules, and normal pressure angles allow for a more robust representation of the model. In addition, having a fully parametrized component allows the model to be customized to any standard gear specifications. Additional components are added to model additional frictional forces and loads applied to the gears to provide further information about the physics of the system and increase the fidelity of the model. Efficiency factors are then calculated from various parameter settings.

Finally, MapleSim’s 3-D visualizations for multibody systems automatically create a visual representation of the model, providing instant feedback for the model dynamics. STL images can be imported to give a more realistic look and feel to the gears, providing visual validation of the model.

With the basic gears complete, further parameters can be added to the model to define additional geometric behaviors, such as inertial losses from driving mechanisms. In addition, these high-fidelity gear models can then be added to a MapleSim custom library, making them readily available for use in other models.

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