Spur Rack Theory
The Spur Rack or straight rack is defined as a rigid body. A finite stiffness for the rack mesh (or rack tooth) can be specified in the Rack and Pinion node while connecting to a pinion. Similar to the rigid domain, the spur rack is a material model, which is mutually exclusive to all other material models. The only material property needed is the mass density.
Figure 3-9: Sketch of a spur rack, showing the tooth cross-section and various parameters such as center of rotation, rack axis, pitch, radial offset, tangential offset, 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.
The following section is an addition to the Spur Gear Theory section, some of which is also applicable for the spur rack.
Connection to Other Gears
A spur rack can be connected to a Spur Gear or to a Helical Gear through the Rack and Pinion node. A single rack can be connected to one or more gears.
Rack Axis
The rack axis is the axis of translation of the rack that passes through the center of rotation. This axis is used to create the rack local coordinate system in the rack and pinion node. The rack displacement, a degree of freedom in the rack and pinion node, is also interpreted about this axis.
Rack Properties
The following quantities are required on define a spur rack.
•
Pitch (p)
•
Pressure angle (α)
The normal pitch of the rack is defined as