COMSOL 6.4 - About Gear Pairs

The degrees of freedom at the gear pair are θwh and θpn. They are defined as the rotation of the wheel and pinion about the first axis of their respective local coordinate system.


	Theory for Gear Pairs

Worm and Wheel

The worm and wheel node connects a worm gear with a spur or helical gear so that at the contact point they have no relative motion along the line of action. The remaining displacements and rotations of both the gears are independent of each other.

When friction is included on a worm and wheel node, frictional forces in the plane perpendicular to the line of action are added on both the gears.

The degrees of freedom at the worm and wheel are θwm and θwh. They are defined as the rotation of the worm and wheel about the first axis of their respective local coordinate system.


	Theory for Worm and Wheel

Rack and Pinion

The rack and pinion node connects a spur or helical rack with a spur or helical gear in so that at the contact point they have no relative motion along the line of action. The remaining displacements and rotations of the rack and gear are independent of each other.

For a line contact model, one additional constraint is added to restrict the relative rotation about a line joining the rack and gear centers. If friction is included on a rack and pinion node, frictional forces in the plane perpendicular to the line of action are added on the rack and pinion.

The degrees of freedom at the rack and pinion are urk and θpn. They are defined as the displacement of rack along the third axis and the rotation of pinion about the first axis of their respective local coordinate system.


	Theory for Rack and Pinion

Gear Pair Compatibility Criteria

In a gear pair node, you can select any two gears defined for the model. For the correct tooth meshing, a set of gears must however fulfill the following compatibility criteria:

Normal Module

The normal module of the both the gears must be same.

Pressure Angle

The pressure angle of the both the gears must be same.

Configuration

For parallel axis helical gears, the sum of the helix angles must be zero.

For crossed axis helical gears, the sum of the helix angles must be nonzero.

Gear Elasticity

Gear elasticity can be added to gear pairs. In this node, elastic properties of the gear mesh such as mesh stiffness, mesh damping, and contact ratio can be specified. By default, the gear mesh is assumed to be rigid.


	Theory for Gear Elasticity

Transmission Error

A transmission error can be added to gear pairs. In this node, the static transmission error can be specified. It is added in the rotation constraint of the gear pair. By default, there is no transmission error for a gear pair and it is assumed to be an ideal pair.

The static transmission error could be due to geometrical errors and geometrical modifications such as gear runouts, misalignments, tooth tip and root relief.


	Theory for Transmission Error

Backlash

A backlash can be added to gear pairs. The transmission error due to backlash is added to the rotation constraint of the gear pair. By default, there is no backlash for a gear pair.

The backlash on a gear pair plays an important role for unloaded gears. For loaded gears, it does not affect the dynamics of gears to a large extent.


	Theory for Backlash

Friction (Gear)

Friction can be added to gear pairs. When friction is included for a gear pair, frictional forces in the plane perpendicular to the line of action are added on both the gears.

By default, there is no friction on Gear Pair and Rack and Pinion. It is, however, included for Worm and Wheel. The worm and wheel pair has always neither parallel nor intersecting configuration and in this configuration, there is always a slip even under perfect conditions.


	Theory for Gear Friction