Study Internal Gear Contact Forces

This example studies the contact forces between inner and outer spur gears.

Internal gears are ideal in applications for high-power transmission within small overall dimensions, like robot arms. In Figure 1, the outer gear serves as the driver and applies torque to the inner gear (ring). 

Figure 1: Internal gear.

The spurGear component can be switched to an internal gear by setting the isInnerGear to true as shown in Figure 2.

Figure 2: Gear parameter tab.

Figure 3 shows the contact forces that do not get entirely loose where the next teeth pair contacts.

Figure 3: Contact forces.

The contact pressure on the gear tooth is shown in Figure 4. The maximum pressure is around 320 MPa, which is well below the typical maximum allowable limit for contact pressure on a gear tooth (for case-hardened gears, the maximum allowable contact pressure is typically 800–2000 MPa, while for through-hardened gears it can be 1000–2500 MPa.)

Figure 4: Contact pressure.

m	Value: 0.005 Type: Module (m) Description: Gear module
a	Value: (m * z1 + m * z2) / 2 Type: Distance (m) Description: Distance from wheel center 1 to wheel center 2
alpha0	Value: 20 * Modelica.Constants.pi / 180 Type: Angle (rad) Description: Reference profile angle
z1	Value: 29 Type: Integer Description: Number of teeth in wheel one
z2	Value: 80 Type: Integer Description: Number of teeth in wheel two
x1	Value: 0 Type: Real Description: Profile shift for gear wheel one
x2	Value: 5e-02 Type: Real Description: Profile shift for gear wheel two
shaftMountedAngle	Value: Modelica.Constants.pi / 4 Type: Real Description: Angle of outer wheel in inner wheel
InitialRotationWheel1	Value: shaftMountedAngle * 180 / Modelica.Constants.pi - 360 / z1 * floor(shaftMountedAngle / (2 * Modelica.Constants.pi) * z1) Type: Angle_deg (°) Description: Gear wheel initial angle of rotation shaft 1
InitialRotationWheel2	Value: shaftMountedAngle * 180 / Modelica.Constants.pi - 360 / z2 * floor(shaftMountedAngle / (2 * Modelica.Constants.pi) * z2) Type: Angle_deg (°) Description: Gear wheel initial angle of rotation shaft 2