Belt Drive

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Belt drive with a tensioned belt connecting two pulleys.

blockType: Engee1DMechanical.Transmission.BeltDrive

Path in the library:

/Physical Modeling/1D Mechanical/Couplings & Drives/Belt Drive

Description

Block Belt Drive It consists of a pair of pulleys connected by a flexible, ideal, flat or wedge-shaped belt. If for the parameter Belt type the value is set Ideal - No slip the belt does not slip relative to the pulley surfaces.

The block takes into account the friction between the flexible belt and the pulley periphery. If the friction force is not sufficient to move the load, the block may slip. The relationship between the tension in the leading and driven branches corresponds to the Euler equation for rope friction on a cylinder, also known as the Euler—Eitelwein equation. The unit takes into account the centrifugal load on the flexible belt, the inertia of the pulley and the friction in the bearings.

Block Belt Drive It is a structural component based on a block Belt Pulley and blocks Translational Spring and Translational Damper.

Blocks Translational Spring and Translational Damper they simulate the pliability of the belt. The equations describing the dynamics of the contact between the belt and the pulley can be found in the description of the unit. Belt Pulley. The figure shows the functional block diagram of the block Belt Drive.

belt drive en

The equations

The diagrams show open and cross belt drives. If for the parameter Drive type the value is set Open belt both pulleys rotate in the same direction, with the larger pulley having a larger belt girth angle. If for the parameter Drive type the value is set Crossed belt the pulleys rotate in opposite directions and have the same girth angle.

_ Schemes of belt drives_

belt drive 1 en

The following values are shown in the figures and in the equations:

— the girth angle of the pulley A;
— the girth angle of the pulley B;
— effective radius of the pulley A;
— effective radius of the pulley B;
— the distance between the centers of pulleys A and B.

opened belt drive

If for the parameter Drive type the value is set Open belt The block calculates the belt girth angle around each pulley as follows:

The diagram shows the angles and girth parameters.

belt drive 2

the cross belt drive

If for the parameter Drive type the value is set Crossed belt, then both girth angles will be equal, and the girth angle of the belt around each pulley is

The diagram shows the angles and girth parameters.

belt drive 3

Assumptions and limitations

The pulleys do not move.
The coefficient of friction and the threshold friction velocity between the belt and each of the pulleys are the same. To parameterize individual friction interactions, use two blocks Belt Pulley.

Ports

Conserving

# A — pulley shaft A
rotational mechanics

Details

A non-directional port connected to the pulley shaft A.

Program usage name

flange_a

# B — pulley shaft B
rotational mechanics

Details

A non-directional port connected to the pulley shaft B.

Program usage name

flange_b

Parameters

Belt

# Belt type — belt parameterization
Ideal - No slip | Flat belt | V-belt

Details

Choosing the type of belt. The type of belt affects the slip conditions:

Ideal - No slip — parameterization of an ideal belt that does not slip relative to the pulley.
Flat belt — parameterization of a belt with a rectangular cross-section.
V-belt — parameterization of the wedge-shaped belt.

Values	`Ideal - No slip` \| `Flat belt` \| `V-belt`
Default value	`Ideal - No slip`
Program usage name	`belt_type`
Evaluatable	No

# Belt mass per unit length — running weight
kg/m

Details

The contribution of centrifugal force is determined by linear density, expressed as mass per unit length.

Dependencies

To use this parameter, set for the parameter Belt type meaning Flat belt or V-belt and check the box Centrifugal force.

Units	`kg/m`
Default value	`0.6 kg/m`
Program usage name	`linear_density`
Evaluatable	Yes

# Maximum tension — threshold tension parameter

Details

The ability to set the maximum tension. If you select this option, and the belt tension at any of its ends reaches or exceeds the value set for the parameter Belt maximum tension, the simulation will stop and give an error.

Dependencies

To use this parameter, set:

for the parameter Belt type meaning Ideal - No slip and a flag Compliance, or
for the parameter Belt type meaning Flat belt or V-belt.

Default value	`false (switched off)`
Program usage name	`enable_max_tension`
Evaluatable	No

# Pre-tension — belt tension at rest
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

Belt tension when the belt and pulleys are at rest. The value must be positive.

Dependencies

To use this parameter, set:

for the parameter Belt type meaning Ideal - No slip and a flag Compliance, or
for the parameter Belt type meaning Flat belt or V-belt.

Units	`N` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
Default value	`100.0 N`
Program usage name	`F_tension_start`
Evaluatable	Yes

# Belt maximum tension — threshold value of maximum tension
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

The maximum allowable tension for each belt. When the tension at either end of the belt reaches or exceeds this value, the simulation stops and generates an error.

Dependencies

To use this parameter, set:

for the parameter Belt type meaning Ideal - No slip and checkboxes Compliance and Maximum tension, or
for the parameter Belt type meaning Flat belt or V-belt and a flag Maximum tension.

Units	`N` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
Default value	`100000.0 N`
Program usage name	`F_tension_max`
Evaluatable	Yes

# Centrifugal force — the option of accounting for centrifugal force

Details

An option to account for the effect of centrifugal force. If you check this box, the centrifugal force will reach approximately 90% of the force value at each end of the belt.

Dependencies

To use this parameter, set for the parameter Belt type meaning Flat belt or V-belt.

Default value	`false (switched off)`
Program usage name	`enable_centrifugal_force`
Evaluatable	No

# Longitudinal stiffness — effective belt stiffness
N/m | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in

Details

Effective belt stiffness.

Dependencies

To use this parameter, set:

for the parameter Belt type meaning Ideal - No slip and a flag Compliance, or
for the parameter Belt type meaning Flat belt or V-belt.

Units	`N/m` \| `mN/m` \| `kN/m` \| `MN/m` \| `GN/m` \| `kgf/m` \| `lbf/ft` \| `lbf/in`
Default value	`10000.0 N/m`
Program usage name	`k`
Evaluatable	Yes

# Drive type — belt drive type
Open belt | Crossed belt

Details

Type of belt drive. For more information, see Belt drive diagrams.

Values	`Open belt` \| `Crossed belt`
Default value	`Open belt`
Program usage name	`wrap_configuration`
Evaluatable	No

# Number of V-belts — number of straps

Details

The number of wedge-shaped straps.

The block rounds non-integer values to the nearest integer. Increasing the number of belts increases the friction force, the effective mass per unit length, and the maximum allowable tension.

Dependencies

To use this parameter, set for the parameter Belt type meaning V-belt.

Default value	`1`
Program usage name	`belt_count`
Evaluatable	Yes

# V-belt sheave angle — pulley groove angle
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The angle of the pulley groove for the wedge-shaped belt.

Dependencies

To use this parameter, set for the parameter Belt type meaning V-belt.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`30.0 deg`
Program usage name	`sheave_angle`
Evaluatable	Yes

# Compliance — an option for modeling belt compliance

Details

An option for modeling belt compliance.

If the flag is unchecked, the unit simulates an unyielding belt in which elastic deformations do not occur under the influence of force. To improve performance, uncheck the box.
If the check box is selected, the block simulates a malleable belt that elastically deforms under the action of force. To increase the accuracy, check the box.

Dependencies

To use this parameter, set for the parameter Belt type meaning Ideal - No slip.

Default value	`false (switched off)`
Program usage name	`enable_compliance`
Evaluatable	No

# Longitudinal damping — effective belt damping
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

Effective belt damping.

Dependencies

To use this parameter, set:

for the parameter Belt type meaning Ideal - No slip and a flag Compliance, or
for the parameter Belt type meaning Flat belt or V-belt.

Units	`Ns/m` \| `kgfs/m` \| `lbfs/ft` \| `lbfs/in`
Default value	`1000.0 N*s/m`
Program usage name	`C`
Evaluatable	Yes

Pulley A

Details

The moment of inertia of rotation of the pulley A.

Dependencies

To use this option, check the box Inertia.

Units	`kgm^2` \| `gm^2` \| `kgcm^2` \| `gcm^2` \| `lbmin^2` \| `lbmft^2` \| `slugin^2` \| `slugft^2`
Default value	`0.01 kg*m^2`
Program usage name	`I_pulley_a`
Evaluatable	Yes

# Pulley radius — pulley radius A
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The radius of the pulley is A.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.15 m`
Program usage name	`pulley_a_radius`
Evaluatable	Yes

# Bearing viscous friction coefficient — viscous friction of bearings
N*m*s/rad | mN*m*s/rad | kN*m*s/rad | kgf*m*s/rad | lbf*ft*s/rad

Details

Viscous friction associated with the bearings holding the pulley axis A.

Units	`Nms/rad` \| `mNms/rad` \| `kNms/rad` \| `kgfms/rad` \| `lbffts/rad`
Default value	`0.0 Nms/rad`
Program usage name	`pulley_a_viscous_coefficient`
Evaluatable	Yes

# Inertia — moment of inertia of rotation

Details

The possibility of parameterizing the moment of inertia of rotation using the initial velocity.

Default value	`false (switched off)`
Program usage name	`enable_pulley_a_inertia`
Evaluatable	No

Details

The initial rotation speed of the pulley is A.

Dependencies

To use this option, check the box Inertia.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`0.0 rad/s`
Program usage name	`w_pulley_a_start`
Evaluatable	Yes

Pulley B

Details

The moment of inertia of rotation of the pulley B.

Dependencies

To use this option, check the box Inertia.

Units	`kgm^2` \| `gm^2` \| `kgcm^2` \| `gcm^2` \| `lbmin^2` \| `lbmft^2` \| `slugin^2` \| `slugft^2`
Default value	`0.03 kg*m^2`
Program usage name	`I_pulley_b`
Evaluatable	Yes

# Inertia — moment of inertia of rotation

Details

The possibility of parameterizing the moment of inertia of rotation using the initial velocity.

Default value	`false (switched off)`
Program usage name	`enable_pulley_b_inertia`
Evaluatable	No

Details

The initial rotation speed of the pulley is B.

Dependencies

To use this option, check the box Inertia.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`0.0 rad/s`
Program usage name	`w_pulley_b_start`
Evaluatable	Yes

# Bearing viscous friction coefficient — viscous friction of bearings
N*m*s/rad | mN*m*s/rad | kN*m*s/rad | kgf*m*s/rad | lbf*ft*s/rad

Details

Viscous friction associated with the bearings holding the pulley B axis.

Units	`Nms/rad` \| `mNms/rad` \| `kNms/rad` \| `kgfms/rad` \| `lbffts/rad`
Default value	`0.001 Nms/rad`
Program usage name	`pulley_b_viscous_coefficient`
Evaluatable	Yes

# Pulley radius — pulley radius B
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The radius of the pulley is B.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.3 m`
Program usage name	`pulley_b_radius`
Evaluatable	Yes

Contact

# Pulley B wrap angle — pulley girth angle B
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The contact angle between the belt and the pulley connected to port B.

Dependencies

To use this parameter, set for the parameter Wrap angle calculation meaning Specify wrap angles.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`215.0 deg`
Program usage name	`phi_wrap_pulley_b`
Evaluatable	Yes

# Velocity threshold — contact threshold value
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The relative velocity required to achieve the peak value of kinetic friction in contact. The threshold value of the friction velocity increases the numerical stability of the simulation, ensuring the continuity of the force when changing the direction of velocity.

Dependencies

To use this parameter, set for the parameter Belt type meaning Flat belt or V-belt.

Units	`m/s` \| `mm/s` \| `cm/s` \| `km/s` \| `m/hr` \| `km/hr` \| `in/s` \| `ft/s` \| `mi/s` \| `ft/min` \| `mi/hr` \| `kn`
Default value	`0.001 m/s`
Program usage name	`v_threshold`
Evaluatable	Yes

# Pulley center separation — the distance between the centers of the pulleys
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The distance between the centers of the pulleys.

Dependencies

To use this parameter, set for the parameter Wrap angle calculation meaning Specify pulley center separation.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`0.5 m`
Program usage name	`center_distance`
Evaluatable	Yes

# Kinetic friction coefficient — coefficient of kinetic friction

Details

Belt friction when slipping.

Dependencies

To use this parameter, set for the parameter Friction model meaning Modal.

Default value	`0.42`
Program usage name	`kinetic_friction_coefficient`
Evaluatable	Yes

# Static friction coefficient — coefficient of static friction

Details

Belt friction while maintaining static contact.

Dependencies

To use this parameter, set for the parameter Friction model meaning Modal.

Default value	`0.5`
Program usage name	`static_friction_coefficient`
Evaluatable	Yes

# Contact friction coefficient — coefficient of contact friction

Details

The coefficient of Coulomb friction between the belt and the pulley surface.

Dependencies

To use this parameter, set for the parameter Friction model meaning Continuous.

Default value	`0.5`
Program usage name	`friction_coefficient`
Evaluatable	Yes

# Wrap angle calculation — type of angle calculation
Specify pulley center separation | Specify wrap angles

Details

The ability to calculate the girth angle based on the distance between the centers of the pulleys or directly specify these values.

Specify pulley center separation — The unit calculates the belt girth angle using the radii of the pulleys, the distance between the centers and the type of transmission.
Specify wrap angles — The block uses the girth angles you set.

Dependencies

To use this parameter, set for the parameter Belt type meaning Flat belt or V-belt.

Values	`Specify pulley center separation` \| `Specify wrap angles`
Default value	`Specify pulley center separation`
Program usage name	`wrap_parameterization`
Evaluatable	No

# Pulley B initial state — initial condition of pulley B
Unlocked | Locked

Details

The ability to initialize the simulation with a locked or unlocked pulley B.

Dependencies

To use this parameter, set for the parameter Friction model meaning Modal.

Values	`Unlocked` \| `Locked`
Default value	`Unlocked`
Program usage name	`belt_pulley_b_initial_state`
Evaluatable	No

# Pulley A wrap angle — pulley girth angle A
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

The contact angle between the belt and the pulley connected to the A port.

Dependencies

To use this parameter, set for the parameter Wrap angle calculation meaning Specify wrap angles.

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`145.0 deg`
Program usage name	`phi_wrap_pulley_a`
Evaluatable	Yes

# Friction model — choosing the friction method
Continuous | Modal

Details

The possibility of parameterization of continuous or modal friction.

Dependencies

To use this parameter, set for the parameter Belt type meaning Flat belt or V-belt.

Values	`Continuous` \| `Modal`
Default value	`Modal`
Program usage name	`friction_model`
Evaluatable	No

# Pulley A initial state — the initial state of the pulley A
Unlocked | Locked

Details

The possibility of initializing the simulation with the locked or unlocked pulley A.

Dependencies

To use this parameter, set for the parameter Friction model meaning Modal.

Values	`Unlocked` \| `Locked`
Default value	`Unlocked`
Program usage name	`belt_pulley_a_initial_state`
Evaluatable	No

# Force threshold — force threshold value
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

The relative force required to achieve the peak value of kinetic friction in contact.

Dependencies

To use this parameter, set for the parameter Belt type meaning Flat belt or V-belt.

Units	`N` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
Default value	`0.01 N`
Program usage name	`F_threshold`
Evaluatable	Yes

Additional Info

Hardware and software modeling

Details

For optimal simulation performance in the parameter group Belt uncheck the box Centrifugal force.

Literature

Johnson, Kenneth L. Contact Mechanics. Cambridge: Cambridge Univ. Press, 2003.