Belt Drive

Power transmission system with taut belt connecting two pulleys

Library

Couplings & Drives

Description

The block represents a pair of pulleys connected with a flexible flat band or V-shaped belt. The model accounts for friction between the flexible belt and the pulley periphery. If the friction force is not sufficient to drive the load, the model allows slip. The relationship between the tensions in the tight and loose branches conforms to the Euler equation. The model accounts for centrifugal loading in the flexible belt, pulley inertia, and bearing friction.

The schematics show the belt drive in its two possible configurations: open (left) and crossed (right). In the open belt configuration, both pulleys tend to rotate in the same direction, and the larger pulley tends to have a larger belt wrap angle. In the crossed belt configuration, the pulleys tend to rotate in opposite directions, and both pulleys have the same wrap angle.

In the open configuration, the wrap angle of the belt around each pulley is given by the expressions:

  • θA is the wrap angle of pulley A.

  • θB is the wrap angle of pulley B.

  • RA is the effective radius of pulley A.

  • RB is the effective radius of pulley B.

  • C is the distance between the centers of pulley A and pulley B.

The following figure shows the wrap angles and the equation parameters used in the open-configuration calculations.

In the crossed configuration, the wrap angle of the belt around each pulley is given by the following expression. The two wrap angles are equal:

The figure shows the wrap angles calculated in the crossed-configuration expression.

The Belt Drive block is a structural component based on the SimDriveline™ Belt Pulley block and Simscape™ Translational Spring and Translational Damper blocks. The Translational Spring and Translational Damper blocks model the compliance of the belt. For the equations governing the contact dynamics between the belt and the pulley, see the Belt Pulley block reference page. The following figure shows the block diagram upon which the Belt Drive block is based.

Assumptions and Limitations

  • The pulleys do not translate.

  • The friction coefficient and friction velocity threshold between the belt and each of the pulleys is the same.

Dialog Box and Parameters

Drive type

Select the type of belt drive that you want to model.

  • Open belt — (Default)

  • Crossed belt

The schematic in this page shows the two drive types.

Belt type

Type of flexible element modeled.

  • Flat band — (Default)

  • V-belt— Exposes the V-belt sheave angle and Number of V-belts parameters.

V-belt sheave angle

Sheave angle of the V-belt. Default is 30 deg.

The V-belt sheave angle parameter is visible only when the Belt type parameter is V-belt.

Number of V-belts

Number of parallel V-belts. Default is 1.

Non-integer values are rounded to the nearest integer. Increasing the number of belts increases the friction force, effective mass per unit length, and maximum allowable tension.

The Number of V-belts parameter is visible only when the Belt type parameter is V-belt.

Belt mass per unit length

Linear density of each belt. Default is 0.6 kg/m.

The model uses this to calculate the centrifugal loading.

Longitudinal stiffness

The effective stiffness of the belt. Default is 1e+4 N/m.

Longitudinal damping

Effective damping of the belt. Default is 1000 N/(m/s).

Pre-tension

Tension in the belt when the belt and pulleys are at rest. A positive value indicates that both pulley branches are initially in tension. A negative value indicates that the branches are initially slack. The default value is 100 N.

Maximum tension

Specifies whether the block throws an assertion when the belt tension is too large.

  • No maximum tension — (Default)

  • Specify maximum tension— Throws an assertion when the belt tension is too high. Exposes the Belt maximum tension parameter.

Belt maximum tension

Maximum allowable tension for each belt. Default is 1e+5 N.

When the tension on either end of the belt meets or exceeds this value, the simulation ends with an error.

The Belt maximum tension parameter is visible only when the Maximum tension parameter is Specify maximum tension.

Select the Pulley A tab to specify the characteristics of pulley attached to port A, and the Pulley B tab to specify the characteristics of pulley attached to port B.

Pulley radius

Radius of the pulley. Default is 0.15m for pulley A and 0.3 m for pulley B.

Bearing viscous friction coefficient

Viscous friction associated with the bearings that hold the axis of the pulley. Default is 0 N*m/(rad/s) for pulley A and 0.001 N*m/(rad/s) for pulley B.

Inertia

Specifies whether the block models rotational inertia of the pulley.

  • No inertia — (Default)

  • Specify inertia and initial velocity— Models rotational inertia. Exposes the Pulley inertia and Pulley initial velocity parameters.

Pulley inertia

Rotational inertia of the pulley. Default is 0.01 kg*m^2 for pulley A, and 0.03 kg*m^2 for pulley B.

The Pulley inertia parameter is visible only when the Inertia parameter is Specify inertia and initial velocity.

Pulley initial velocity

Initial rotational velocity of the pulley. Default is 0 rad/s.

The Pulley initial velocity parameter is visible only when the Inertia parameter is Specify inertia and initial velocity.

Select the Contact tab to specify contact characteristics.

Contact friction coefficient

Coulomb friction coefficient between the belt and the pulley surface. Default is 0.5.

Wrap calculations

Specifies whether the block calculates the wrap angle of the belt on the pulleys using the pulley radii, center separation, and drive type or if the wrap angles are specified directly.

  • Specify pulley center separation — (Default) The block calculates the wrap angle of the belt on the pulleys using the pulley radii, center separation, and drive type.

    Exposes the Pulley center separation parameter.

  • Specify wrap angles — Uses the wrap angles that you specify.

    Exposes the Pulley A wrap angle and Pulley B wrap angle parameters.

Pulley center separation

Distance between the centers of the pulleys. Default is 0.5 m.

The Pulley center separation parameter is visible only when the Wrap calculations parameter is Specify pulley center separation.

Pulley A wrap angle

Angle of contact between the belt and pulley attached to port A. Default is 145 deg.

The Pulley A wrap angle parameter is visible only when the Wrap calculations parameter is Specify wrap angles.

Pulley B Wrap angle

Angle of contact between the belt and pulley attached to port B. Default is 215 deg.

The Pulley B wrap angle parameter is visible only when the Wrap calculations parameter is Specify wrap angles.

Friction velocity threshold

Relative velocity required for peak kinetic friction in the contact. The friction velocity threshold improves the numerical stability of the simulation by ensuring that the force is continuous when the direction of the velocity changes. Default is 0.001 m/s.

Ports

PortDescription

A

Conserving rotational port associated with the shaft of pulley A

B

Conserving rotational port associated with the shaft of pulley B

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