Spur Gear Theory
The Spur Gear is defined as a rigid body. A finite stiffness for the gear mesh (or gear tooth) can be specified in the Gear Pair node while connecting to other gears. Similar to the rigid domain, the spur gear is a material model, which is mutually exclusive to all other material models. The only material property needed is the mass density.
Figure 3-3: Sketch of an external spur gear., showing the tooth cross section and various parameters, such as center of rotation, gear axis, pitch radius, and pressure angle.
Figure 3-4: Sketch of an internal spur gear, showing the tooth cross section and various parameters such as center of rotation, gear axis, pitch radius, and pressure angle.
For details about the theory of a rigid body, see the Rigid Material section in the Structural Mechanics Module User’s Guide.
Connection to Other Gears
A spur gear can be connected to the following gear types:
•
Another Spur Gear or a Helical Gear through the Gear Pair node.
•
A Worm Gear through the Worm and Wheel node.
•
A Spur Rack or a Helical Rack through the Rack and Pinion node.
A single gear can be connected to one or more gears.
Mounting Methods
The motion of a spur gear can be constrained directly using its subnode. Alternatively, it can be mounted on a shaft. There are several ways through which a gear can be mounted on a shaft. Some of the commonly used methods are as follows:
•
Directly mounted on a flexible shaft
•
Mounted on a rigid or flexible shaft through a rigid or elastic fixed joint
•
Mounted on a rigid or flexible shaft through a rigid or elastic hinge joint
•
Mounted on a ground (a fixed shaft) through a rigid or elastic hinge joint
Center of Rotation
Gears are defined through rigid body degrees of freedom. These degrees of freedom are created at the center of rotation and the rotation is interpreted about this point. By default, the center of rotation is set to the center of mass, but there are other ways to define it explicitly. This is the point where you interpret the forces and moment that act on the gear due to meshing with other gears.
Gear Axis
The gear axis is the axis of rotation of the gear that passes through the center of rotation. This axis is used to create the gear’s local coordinate system in the Gear Pair node. The gear rotation, a degree of freedom in the Gear Pair node, is also interpreted about this axis.
Gear Properties
The following quantities are required to define a spur gear:
•
Number of teeth (n)
•
Pitch diameter (dp)
•
Pressure angle (α)
The transverse module of the gear is defined as:
The normal module of the gear is defined as: