High-ratio speed reducer based on cycloidal disk motion

Gears

This block represents a compact, high-ratio, speed-reduction mechanism that contains four key components:

Eccentric cam

Cycloidal disk

Ring-gear housing

Pin rollers

The eccentric cam, which extends from the base shaft, sits inside the cycloidal disk. This disk meshes with the ring-gear housing. The pin rollers, which extend from the follower shaft, sit in matching holes on the cycloidal disk.

During normal operation, the base shaft drives the eccentric cam. The cam spins inside the cycloidal disk, causing it to rotate in an eccentric pattern about an offset axis. As it moves, the cycloidal disk engages the internal teeth of the ring-gear housing. The internal meshing reverses the rotational velocity direction.

Pin rollers extending from cycloidal disk holes transmit rotational motion to the follower shaft. This shaft spins counter to the base shaft at a highly reduced speed. The large reduction ratio results from the near-equal cycloidal disk and ring gear tooth numbers. The effective gear reduction ratio is

$$r=\frac{{n}_{R}-{n}_{C}}{{n}_{C}},$$

where:

*r*is the gear reduction ratio.*n*_{R}is the number of teeth on the ring gear.*n*_{C}is the number of teeth on the cycloidal disk.

The gear reduction ratio constrains the angular velocities of the base and follower shafts according to the expression

$${\omega}_{F}=-r{\omega}_{B},$$

where:

*ω*_{F}is the angular velocity of the follower shaft.*ω*_{C}is the angular velocity of the base shaft.

The gear reduction ratio also constrains the torques acting on the base and follower shafts, according to the expression

$${T}_{B}=r{T}_{F}+{T}_{f},$$

where:

*T*_{B}is the net torque at the base shaft.*T*_{F}is the net torque at the follower shaft.*T*_{f}is the torque loss due to friction.

The magnitude of the frictional torque depends on the torque transfer efficiency and power flow direction according to the expression

$${T}_{f}=\{\begin{array}{cc}f\xb7\text{\hspace{0.17em}}abs\left({T}_{B}\right)\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\left(\frac{1}{{\eta}_{BF}}-1\right),& {T}_{B}\xb7{\omega}_{B}\le 0\\ f\xb7\text{\hspace{0.17em}}abs\left({T}_{B}\right)\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\left(1-{\eta}_{FB}\right),& {T}_{B}\xb7\text{\hspace{0.17em}}{\omega}_{B}>0\end{array},$$

where:

*f*is a blending factor that smooths the frictional torque function near zero (e.g., during reversal of the rotational velocity direction).*η*_{BF}is the torque transfer efficiency from the base shaft to the follower shaft.*η*_{FB}is the torque transfer efficiency from the follower shaft to the base shaft.

The blending factor *f* is a hyperbolic function
of the cycloidal disk angular velocity:

$$f=\mathrm{tanh}\left(\frac{4{\omega}_{B}}{{\omega}_{Th}}\right),$$

where:

*ω*_{Th}is the angular velocity threshold at the base shaft above which full efficiency losses are in effect.

The figure shows the cycloidal drive in front and side views. The kinematics of the drive system cause a reversal of the base and follower shaft angular velocities so that the two shafts spin in opposite directions.

The cycloidal drive can operate in reverse mode, e.g., with
power flowing from the follower shaft to the base shaft. In this mode,
torque transfer efficiencies are typically negligible. You can adjust
the efficiency value in the block dialog box using the **Efficiency
from follower shaft to base shaft** parameter.

You can model the effects of heat flow and temperature change
through an optional thermal conserving port. To expose the thermal
port, right-click the block and select **Simscape** > **Block choices** > **Show thermal
port**. Exposing the thermal port causes
new parameters specific to thermal modeling to appear in the block
dialog box.

**Number of teeth on cycloid disk**Total number of teeth projecting outward from the cycloidal disk perimeter. This number should be slightly smaller than the number of teeth or pins on the ring gear. The ratio of the gear tooth numbers defines the relative angular velocities of the base and follower shafts. The default value is

`20`

.**Number of teeth on ring gear**Total number of teeth or pins projecting inward from the ring gear housing. This number should be slightly larger than the number of teeth on the cycloidal disk. The ratio of the two gear tooth numbers defines the relative angular velocities of the base and follower shafts. The default value is

`24`

.

Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.

**Thermal mass**Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change. The default value is

`50`

J/K.**Initial temperature**Component temperature at the start of simulation. The initial temperature influences the starting meshing or friction losses by altering the component efficiency according to an efficiency vector that you specify. The default value is

`300`

K.

Port | Description |
---|---|

B | Rotational conserving port representing the base shaft |

F | Rotational conserving port representing the follower shaft |

H | Thermal conserving port for thermal modeling |

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