Worm Gear

Worm gear with adjustable gear ratio and friction losses.

blockType: Engee1DMechanical.Transmission.Gears.Worm

Path in the library:

/Physical Modeling/1D Mechanical/Gears/Worm Gear

Description

Block Worm Gear It is a rotating gear in which two connected drive axes, a worm (W) and a gear (G), rotate together at a fixed ratio that you specify. You can choose in which direction the gear rotates – positive or negative. Right–hand rotation is a positive direction. If the worm thread is right, and they have the same sign. If the worm thread is left-handed, and they have opposite signs.

The thermal model

You can simulate the effects of heat flow and temperature changes by turning on an additional heat port. To use the thermal port, set the Friction model parameter to Temperature-dependent efficiency.

Perfect worm gear and gear ratios

Block Worm Gear imposes one kinematic constraint on two connected axes:

where

– angular velocity of the worm screw;
– gear ratio;
– angular velocity of the gear.

Two degrees of freedom are reduced to one independent degree of freedom. The forward gear pair has the following symbol .

The transmission of torque is carried out as follows:

by in the ideal case,

where

– torque transmission coefficient for the worm screw;
– the torque transmission coefficient for the gear;
– losses during transmission of torque. The losses depend on the efficiency of the device and the direction of the energy flow. To avoid sudden changes in the moment of friction when = 0, the moment of friction is introduced through a hyperbolic function.

Imperfect limitations and losses in worm gear

In an imperfect case . For more information, see the article Modeling of mechanical gears with losses.

Geometric surface contact friction

In the case of contact friction, the efficiency of torque transmission from the worm to the gear and from gear to worm are defined as follows:

The geometry of the worm gear thread, determined by the lifting angle and the angle of normal pressure .
Coefficient of surface contact friction .

Constant EFFICIENCY

In the case of constant friction, you specify and , regardless of the geometric details.

Self-locking and negative efficiency

It has two different modes, depending on the angle of elevation. , separated by a self-lock_point in which and .

In self-unscrewing mode_, , and the force acting on the nut can rotate the screw.
In self-lock mode_, , and an external torque must be applied to the screw to release the locked mechanism. The smaller the value the greater the torque must be in order to release the mechanism. conditionally positive.

Gearing efficiency

EFFICIENCY The engagement between the worm screw and the gear is maximum only if the transmitted power exceeds the threshold value.

If the power is less than the threshold, the actual efficiency is automatically adjusted to unity at zero speed.

You can set the friction loss model in the engagement:

No meshing losses - suitable for HIL simulation.
Constant efficiency.
Temperature-dependent efficiency, which simulates the variability of the efficiency of the base shaft, calculated in the mode Constant efficiency, according to the interpolation table provided by the user. The temperature-dependent setting includes a non-directional H port. This port allows you to simulate the effects of heat flow and temperature changes.

Viscous friction force

Coefficient of viscous friction determines the torque of viscous friction that occurs in a worm screw due to lubrication, imperfect gear threads and viscous losses in bearings. The torque of viscous friction on the axis of the worm gear is , where – this is the angular velocity of the worm relative to its attachment.

Coefficient of viscous friction determines the viscous friction torque experienced by the transmission, mainly due to losses in viscous bearings. The torque of viscous friction on the gear transmission axis is equal to , where – this is the angular velocity of the gear relative to its attachment.

Simulation in a hardware loop

For optimal performance of your real-time simulation, set the Friction model parameter to No meshing losses - Suitable for HIL simulation.

Assumptions and limitations

The inertia of the gears is negligible.
Gears are treated as solids.
Coulomb friction slows down the simulation (for more information, see here).

Variables

Use the Initial Targets parameter group to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# W — worm screw
`rotational mechanics

Details

A non-directional port associated with the worm.

Program usage name

worm_flange

# G — pinion
`rotational mechanics

Details

A non-directional port associated with a gear.

Program usage name

gear_flange

# 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

thermal_port

Parameters

Meshing Losses

# Worm-gear efficiency — EFFICIENCY of torque transmission from worm to gear

Details

EFFICIENCY transmission of torque from the worm to the gear.

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency and for the Friction parameterization value Efficiencies.

Default value	`0.74`
Program usage name	`worm_to_gear_efficiency_const`
Evaluatable	Yes

# Gear-worm efficiency — EFFICIENCY of torque transmission from gear to worm

Details

EFFICIENCY transmission of torque from the gear to the worm.

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency and for the Friction parameterization value Efficiencies.

Default value	`0.65`
Program usage name	`gear_to_worm_efficiency_const`
Evaluatable	Yes

# Worm-gear efficiency — an array of efficiency values for the transmission of torque from the worm to the gear

Details

An array of efficiency values for the transmission of torque from the worm to the gear. The values of the array are the efficiency at the corresponding temperature values in the Temperature parameter. Both arrays must be the same size.

Dependencies

To use this parameter, set the Friction model parameter to Temperature-dependent efficiency.

Default value	`[0.75, 0.65, 0.6]`
Program usage name	`worm_to_gear_efficiency_vector`
Evaluatable	Yes

# Gear-worm efficiency — an array of efficiency values for transferring torque from a gear to a worm

Details

An array of efficiency values for the transmission of torque from the gear to the worm. The values of the array are the efficiency at the corresponding temperature values in the Temperature parameter. Both arrays must be the same size.

Dependencies

To use this parameter, set the Friction model parameter to Temperature-dependent efficiency.

Default value	`[0.5, 0.45, 0.4]`
Program usage name	`gear_to_worm_efficiency_vector`
Evaluatable	Yes

# Friction model — the friction model
No meshing losses - Suitable for HIL simulation | Constant efficiency | Temperature-dependent efficiency

Details

The model of friction in transmission. Set as:

No meshing losses - Suitable for HIL simulation – gear engagement is considered ideal.
Constant efficiency – the transmission of torque between the worm screw and the gear is reduced by a constant amount of efficiency, , such that .
Temperature-dependent efficiency – the transmission of torque between pairs of gears is determined by the interpolation table of temperature correspondence and the efficiency of torque transmission.

Values	`No meshing losses - Suitable for HIL simulation` \| `Constant efficiency` \| `Temperature-dependent efficiency`
Default value	`No meshing losses - Suitable for HIL simulation`
Program usage name	`friction_model`
Evaluatable	No

# Friction parameterization — friction losses due to imperfect engagement
Friction coefficient and geometrical parameters | Efficiencies

Details

Friction losses due to imperfect engagement. Set as:

Friction coefficient and geometrical parameters – friction is determined by the contact friction between the surfaces.
Efficiencies – friction is determined by constant efficiency .

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency.

Values	`Friction coefficient and geometrical parameters` \| `Efficiencies`
Default value	`Friction coefficient and geometrical parameters`
Program usage name	`friction_parameterization`
Evaluatable	No

# Normal pressure angle — normal pressure angle
rad | deg | rev | mrad | arcsec | arcmin | gon

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 for the Friction parameterization value Friction coefficient and geometrical parameters.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`17.5 deg`
Program usage name	`thread_pressure_angle`
Evaluatable	Yes

# Lead angle — lifting angle
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

Thread lifting angle , where:

– the thread stroke of the worm.
– the average thread diameter.

The value must be greater than zero.

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency and for the Friction parameterization value Friction coefficient and geometrical parameters.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`20.0 deg`
Program usage name	`lead_angle`
Evaluatable	Yes

# Friction coefficient — coefficient of friction of the thread

Details

The dimensionless coefficient of normal friction in the thread. The value must be greater than zero.

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency and for the Friction parameterization value Friction coefficient and geometrical parameters.

Default value	`0.08`
Program usage name	`friction_coefficient`
Evaluatable	Yes

Details

A vector of temperature values used to construct an interpolation table of temperature and torque transmission efficiency. The elements of the vector should increase monotonously.

Dependencies

To use this parameter, set the Friction model parameter to Temperature-dependent efficiency.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`[280.0, 300.0, 320.0] K`
Program usage name	`temperature_vector`
Evaluatable	Yes

# Power threshold — minimum threshold power value
W | uW | mW | kW | MW | GW | V*A | HP_DIN

Details

The power threshold value, when exceeded, the value of the total torque transmission efficiency is applied. If the value is lower than the specified value, the efficiency value is smoothed using a hyperbolic tangent function.

If you set the Friction model parameter to Constant efficiency The unit reduces losses to zero when no power is transmitted.
If you set the Friction model parameter to Temperature-dependent efficiency The unit smooths the efficiency between zero at rest and the values indicated in the interpolation tables of temperature correspondence and efficiency of torque transmission.

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency or Temperature-dependent efficiency.

Units	`W` \| `uW` \| `mW` \| `kW` \| `MW` \| `GW` \| `V*A` \| `HP_DIN`
Default value	`0.001 W`
Program usage name	`power_threshold`
Evaluatable	Yes

Main

# Gear ratio — Gear ratio

Details

Relationship the angular velocity of the worm screw is relative to the angular velocity of the gear. The value must be higher 1.

Default value	`25.0`
Program usage name	`ratio`
Evaluatable	Yes

# Worm thread type — rotation orientation
Right-hand | Left-hand

Details

The direction of rotation of the gear corresponding to the positive rotation of the worm screw.

If the value is set to Left-hand. rotating the worm screw in the positive direction will cause the gear to rotate in the negative direction.

Values	`Right-hand` \| `Left-hand`
Default value	`Right-hand`
Program usage name	`thread_handedness`
Evaluatable	No

Viscous Losses

# Worm-carrier and sun-carrier viscous friction coefficients — vector of viscous friction coefficients between worm and gear
N*m*s/rad | mN*m*s/rad | kN*m*s/rad | kgf*m*s/rad | lbf*ft*s/rad

Details

Vector of viscous friction coefficients, for the movement of the worm and gear, respectively.

Units	`Nms/rad` \| `mNms/rad` \| `kNms/rad` \| `kgfms/rad` \| `lbffts/rad`
Default value	`[0.0, 0.0] Nms/rad`
Program usage name	`viscous_coefficient_vector`
Evaluatable	Yes

Thermal Port

# Thermal mass — heat capacity
J/K | kJ/K

Details

The thermal energy required to change the temperature of a component by one degree of temperature. The higher the heat capacity, the more resistant the component is to temperature changes.

Dependencies

To use this parameter, set the Friction model parameter to Temperature-dependent efficiency.

Units	`J/K` \| `kJ/K`
Default value	`50.0 J/K`
Program usage name	`thermal_mass`
Evaluatable	Yes

Worm Gear

Description

The thermal model

Perfect worm gear and gear ratios

Imperfect limitations and losses in worm gear

Geometric surface contact friction

Constant EFFICIENCY

Self-locking and negative efficiency

Gearing efficiency

Viscous friction force

Simulation in a hardware loop

Assumptions and limitations

Variables

Ports

Conserving

Parameters

Meshing Losses

Main

Viscous Losses

Thermal Port

See also