Cycloidal Drive
High-ratio speed reducer based on cycloidal disk motion
Description
The Cycloidal Drive 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
where:
r is the gear reduction ratio.
nR is the number of teeth on the
ring gear.
nC 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
where:
The gear reduction ratio also constrains the torques acting on the base
and follower shafts, according to the expression
where:
TB is the net torque at the base
shaft.
TF is the net torque at the
follower shaft.
Tf is the torque loss due to
friction. For more information, see Model Gears with Losses.
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, that is, with power flowing from the
follower shaft to the base shaft. In the reverse mode, torque transfer efficiencies are
typically negligible. You can adjust the efficiency by changing the value of the
Efficiency from follower shaft to base shaft parameter.
Friction Model
You can set the meshing losses friction model to:
No meshing losses - suitable for HIL
simulation.
Constant efficiency, which is the default
friction setting for block versions prior to R2020b.
Temperature-dependent efficiency, which
models variability in the base-shaft efficiencies calculated in the
Constant efficiency setting according to
a user-supplied look-up table. The temperature-dependency setting
enables a thermal conserving port H. This port
receives the heat flow into the block, which is translated into the
block temperature according to the gear Thermal
mass.
Thermal Model
You can model
the effects of heat flow and temperature change by exposing an optional thermal port. To expose
the port, in the Meshing Losses tab, set the Friction
model parameter to Temperature-dependent
efficiency.
Variables
Use the Variables settings to set the priority and initial target
values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.
DependenciesVariable settings are exposed only when, in the Meshing Losses
settings, the Friction model parameter is set to
Temperature-dependent efficiency.
Ports
Conserving
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B — Base shaft
mechanical rotational
Rotational conserving port representing the base shaft.
F — Follower shaft
mechanical rotational
Rotational conserving port representing the follower shaft.
H — Heat flow
thermal
Thermal conserving port associated with heat flow.
Dependencies
This port is enabled when Meshing Losses is
set to Temperature-dependent
efficiency.
Parameters
expand all
Main
Number of teeth on cycloid disk — Number of cycloid disk teeth
20 (default) | positive scalar integer
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.
Number of teeth on ring gear — Number of ring gear teeth
24 (default) | positive scalar integer
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.
Meshing Losses
Friction model — Model for meshing losses
No meshing losses - Suitable for HIL
simulation (default) | Constant efficiency | Temperature-dependent efficiency
No meshing losses — Suitable for HIL
simulation — Gear meshing is
ideal.
Constant efficiency —
Transfer of torque between worm and gear is reduced by
friction.
Temperature-dependent efficiency
— Torque transfer is determined from user-supplied data
for meshing efficiency and temperature.
Temperature — Temperature
[280 300 320]
K (default) | increasing vector
Array of temperatures used to construct 1-D temperature-efficiency
lookup tables. The array element values must increase left to right. The
number of elements in the array must match the number of elements in the
arrays specified for these parameters:
Dependencies
To enable this parameter, set Friction model
to Temperature-dependent
efficiency.
Efficiency from base shaft to follower shaft — Efficiency
0.90 (default) | [0.95 0.85 0.80] | scalar or array of elements between 0 and 1
Torque transfer efficiency in normal operation mode, that is, with the
base shaft driving the follower shaft. Efficiency values must fall in
the interval [0, 1]. Larger efficiency values correspond to greater
torque transfer between the base and follower shafts. Values approaching
unity are typical.
For the
Non-thermal model — Specify the value as a
scalar.
Thermal model — Specify the value as an array in
which each element is the ratio of output power to input
power at the corresponding the temperature element in the
temperature array. The number of elements in the array must
match the number of elements in the arrays specified for the
Temperature parameters.
Dependencies
This parameter is specified as an array when you select a thermal
model. For more information, see Thermal Model.
Efficiency from follower shaft to base shaft — Efficiency
0.05 or [0.10 0.05
0.03] (default) | scalar or array of elements between 0 and 1
Torque transfer efficiency in reverse operation mode, that is, with
the follower shaft driving the base shaft. Efficiency values must fall
in the interval [0, 1]. Larger efficiency values correspond to greater
torque transfer between the base and follower shafts. Values approaching
zero are typical.
For the
Non-thermal model — Specify the value as a
scalar.
Thermal model — Specify the value as an array in
which each element is the ratio of output power to input
power at the corresponding the temperature element in the
temperature array. The number of elements in the array must
match the number of elements in the arrays specified for the
Temperature parameters.
Dependencies
This parameter is specified as an array when you select a thermal
model. For more information, see Thermal Model.
Power threshold — Power threshold
0.001W (default) | scalar
Absolute value of the cycloidal disk power above which the full
efficiency factor applies.
For the non-thermal model, when power is below the specified value, a
hyperbolic tangent function smooths the efficiency factor to one, such
that the efficiency losses go to zero at the resting state.
For the thermal model, a hyperbolic tangent function smooths the
efficiency factor between zero when at rest and the value provided by
the temperature-efficiency lookup table when at the specified power
threshold.
As a guideline, the power threshold should be lower than the expected
power transmitted during simulation. Higher values can cause the block
to underestimate efficiency losses. However, very low values may
increase the computational cost of simulation.
Thermal Port
These settings are exposed when you select a thermal model. For more information,
see Thermal Model.
Thermal mass — Thermal mass
50
J/K (default) | scalar
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.
Dependencies
To enable this parameter, set Friction model
to Temperature-dependent
efficiency.
Initial temperature — Initial temperature
300
K (default) | scalar
Component temperature at the start of simulation. The initial
temperature alters the component efficiency according to an efficiency
vector that you specify, affecting the starting meshing or friction
losses.
Dependencies
This parameter is exposed when you select a thermal model. For
more information, see Thermal Model.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Introduced in R2014a
