Worm Gear
Worm gear with adjustable gear ratio and friction losses.
Description
The Worm Gear unit is a rotary gear in which two linked drive axes, a worm (W) and a pinion (G), rotate together at a fixed ratio that you set. You can choose whether the gear rotates in positive or negative direction. Right-handed rotation is the positive direction. If the worm threads are right-handed, and have the same sign. If the worm thread is left-handed, and have opposite signs.
Thermal model
You can model the effects of heat flow and temperature changes by enabling the optional thermal port. To use the thermal port, set the Friction model parameters to `Temperature-dependent efficiency'.
Ideal worm gear and gear ratios
The Worm Gear block imposes one kinematic constraint on two linked axes:
where
-
- is the angular speed of the worm screw;
-
- gear ratio;
-
- angular velocity of the pinion.
Two degrees of freedom are reduced to one independent degree of freedom. A direct drive gear pair has the following designation .
The torque is transmitted as follows:
at in the ideal case,
where
-
- is the torque transmission coefficient for a worm screw;
-
- is the torque transmission coefficient for the gear;
-
- torque transmission losses. The losses depend on the efficiency of the device and the direction of energy flow. To avoid an abrupt change in the friction torque at = 0, the friction torque is introduced through a hyperbolic function.
Non-ideal constraints and losses in a worm gear train
In the non-ideal case . For more details, see Modelling of mechanical gears with losses.
Geometric surface contact friction
In the case of contact friction, the efficiencies of torque transmission from worm to pinion and from pinion to worm are determined as follows:
-
The geometry of the worm gear threads, determined by the angle of lift and the angle of normal pressure .
-
Surface contact friction coefficient .
Constant efficiency
In the case of constant friction, you specify and , regardless of geometric details.
Self-locking and negative efficiency
has two different modes depending on the angle of lift , separated by the self-locking point, where and .
-
In the self-locking mode, , and the force acting on the nut can turn the screw.
-
In self-locking mode, , and external torque must be applied to the screw to release the locked mechanism. The smaller the value , the greater the torque must be to release the mechanism. is conditionally positive.
Gearing efficiency
The efficiency of the meshing between the worm screw and the pinion is only maximised if the transmitted power exceeds a threshold value.
If the power is less than the threshold power, the actual efficiency automatically equalises to one at zero speed.
You can set the friction loss model in the meshing:
-
`No meshing losses - suitable for HIL simulation'.
-
`Constant efficiency'.
-
`Temperature-dependent efficiency', which models the variability of the base shaft efficiency calculated in `Constant efficiency' mode according to an interpolation table provided by the user. The temperature dependency setting includes a non-directional H port. This port allows the effects of heat flux and temperature variation to be modelled.
Viscous friction force
The viscous friction coefficient determines the viscous friction torque generated in a worm screw due to lubrication, non-ideal gear threads, and viscous losses in the bearings. The viscous friction torque on the worm gear axis is , where is the angular velocity of the worm with respect to its mounting.
The viscous friction coefficient determines the viscous friction torque experienced by the gear, mainly due to viscous bearing losses. The viscous friction torque on the gear axis is , where is the angular velocity of the gear relative to its mount.
Simulation in hardware loop
For optimum performance of your real-time simulation, set the Friction model parameters to No meshing losses - Suitable for HIL simulation.
Variables
Use the Initial Targets section of the settings to set the priority and initial target values for the block parameters variables prior to simulation. For more information, see Customising physical blocks using target values.
Assumptions and constraints
-
The inertia of the gears is negligible.
-
Gears are treated as solids.
-
Coulomb friction slows down the simulation (see here for details).
Ports
Conserving
#
W
—
worm screw
`rotational mechanics
Details
A non-directional port associated with the worm.
| Program usage name |
|
#
G
—
pinion
`rotational mechanics
Details
A non-directional port associated with a gear.
| Program usage name |
|
#
H
—
heat flux
`heat
Details
A non-directional port associated with heat flow.
The heat port allows modelling the heat flow between the unit and the connected network.
Dependencies
To use this port, set Friction model to `Temperature-dependent efficiency'.
| Program usage name |
|
Parameters
Main
# Gear ratio — gear ratio
Details
The ratio of of the angular speed of the worm screw to the angular speed of the gear. The value must be greater than 1.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Worm thread type —
rotation orientation
Right-hand | Left-hand
Details
The direction of rotation of the gear corresponding to positive rotation of the worm screw.
-
When set to `Left-hand', rotating the worm screw in the positive direction will cause the pinion to rotate in the negative direction.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
Meshing Losses
#
Friction model —
friction model
No meshing losses - Suitable for HIL simulation | Constant efficiency | Temperature-dependent efficiency
Details
A model of friction in a transmission. Defined as:
-
No meshing losses - Suitable for HIL simulation- the gearing is assumed to be perfect. -
Constant efficiency- torque transmission between worm screw and pinion is reduced by a constant efficiency value, , such that . -
Temperature-dependent efficiency- torque transmission between pairs of toothed gears, determined from an interpolation table of the correspondence between temperature and torque transmission efficiency.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
#
Friction parameterization —
friction losses in non-ideal meshing
Friction coefficient and geometrical parameters | Efficiencies
Details
Friction loss in non-ideal meshing. Defined as:
-
Friction coefficient and geometrical parameters- friction is determined by contact friction between surfaces. -
Efficiencies- friction is determined by constant efficiency .
Dependencies
To use this parameter, set the Friction model parameters to Constant efficiency.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
No |
#
Normal pressure angle —
normal pressure angle
deg | rad | rev | mrad
Details
Pressure angle on the thread in the normal plane. The value must be in the range (0, 90)°.
Dependencies
To use this parameter, set the Friction model parameter to Constant efficiency and the Friction parameterization parameter to Friction coefficient and geometrical parameters.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Lead angle —
lift angle
deg | rad | rev | mrad
Details
Thread lift angle , where:
-
- worm thread stroke.
-
- average diameter of the thread.
The value must be greater than zero.
Dependencies
To use this parameter, set Friction model to `Constant efficiency' and Friction parameterization to `Friction coefficient and geometrical parameters'.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Friction coefficient — thread friction coefficient
Details
Dimensionless coefficient of normal friction in the thread. The value must be greater than zero.
Dependencies
To use this parameter, set Friction model to `Constant efficiency' and Friction parameterization to `Friction coefficient and geometrical parameters'.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Worm-gear efficiency — Efficiency of torque transmission from the worm to the pinion gear
Details
Efficiency of torque transmission from worm to pinion.
Dependencies
To use this parameter, set the Friction model parameters to Constant efficiency and the Friction parameterization to Efficiencies.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Gear-worm efficiency — Efficiency of torque transmission from pinion to worm
Details
Efficiency of torque transmission from pinion to worm.
Dependencies
To use this parameter, set the Friction model parameters to Constant efficiency and the Friction parameterization to Efficiencies.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Temperature —
vector of temperature values
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Details
A vector of temperature values used to construct an interpolation table of temperature and torque transmission efficiency. The elements of the vector should be monotonically increasing.
Dependencies
To use this parameter, set the Friction model parameters to `Temperature-dependent efficiency'.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Worm-gear efficiency — array of efficiency values of torque transmission from worm to pinion
Details
An array of worm-to-pinion torque transfer efficiencies. The array values are the efficiencies at the corresponding temperature values in the Temperature parameters. Both arrays must be of the same size.
Dependencies
To use this parameter, set the Friction model parameters to `Temperature-dependent efficiency'.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
# Gear-worm efficiency — array of efficiency values of torque transmission from gear to worm
Details
An array of torque transmission efficiencies from the gear to the worm. The array values are the efficiencies at the corresponding temperature values in the Temperature parameters. Both arrays must be of the same size.
Dependencies
To use this parameter, set the Friction model parameters to `Temperature-dependent efficiency'.
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
#
Power threshold —
minimum threshold power value
W | GW | MW | kW | mW | uW | HP_DIN
Details
The power threshold value above which the full torque transmission efficiency value is applied. Below this value, the efficiency value is smoothed using a hyperbolic tangent function.
-
If the Friction model parameters are set to `Constant efficiency', the unit reduces losses to zero when no power is transmitted.
-
If the Friction model parameters are set to `Temperature-dependent efficiency', the unit smooths the efficiency between zero at rest and the values specified in the interpolation tables for temperature and torque transfer efficiency.
Dependencies
To use this parameter, set the Friction model parameters to `Constant efficiency' or `Temperature-dependent efficiency'.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Viscous Losses
#
Worm-carrier and sun-carrier viscous friction coefficients —
vector of viscous friction coefficients between worm and pinion
N*m/(rad/s) | ft*lbf/(rad/s)
Details
Vector of viscous friction coefficients, for worm and pinion motion respectively.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |
Thermal Port
#
Thermal mass —
heat capacity
J/K | kJ/K
Details
The heat energy required to change the temperature of a component by one degree of temperature. The greater the heat capacity, the more resistant the component is to temperature change.
Dependencies
To use this parameter, set the Friction model parameters to `Temperature-dependent efficiency'.
| Values |
|
| Default value |
|
| Program usage name |
|
| Evaluatable |
Yes |