Translational Friction (PB)

Resistive frictional contact between surfaces in position-based mechanical translational systems

Since R2024b

Libraries:
Simscape / Foundation Library / Translational / Elements

Description

The Translational Friction (PB) block represents resistive frictional contact between surfaces.

The friction force is a function of relative velocity and is assumed to be the sum of Stribeck, Coulomb, and viscous components, as shown in the figure.

Friction force diagram

The Stribeck friction, F_S, is the negatively sloped characteristics taking place at low velocities [1]. The Coulomb friction, F_C, results in a constant force at any velocity. The viscous friction, F_V, opposes motion with the force directly proportional to the relative velocity. The sum of the Coulomb and Stribeck frictions at the vicinity of zero velocity is the breakaway friction, F_brk.

You specify the normal force, F_N, which acts on the block in the direction normal to the rail, that is, normal to the direction of the motion. The block calculates the breakaway friction force and the Coulomb friction force based on the normal force and the proportionality coefficients that you also specify. The normal force can be either constant or variable.

The friction is approximated with the following equations:

$f_{f r i c t i o n} = - \sqrt{2 e} (F_{b r k} - F_{C}) \cdot \exp (- {(\frac{v}{v_{S t}})}^{2}) \cdot \frac{v}{v_{S t}} - F_{C} \cdot \tanh (\frac{v}{v_{C o u l}}) - f_{v} v$

$F_{b r k} = F_{N} \cdot K_{b r k}$

$F_{C} = F_{N} \cdot K_{C}$

$v_{S t} = v_{b r k} \sqrt{2}$

$v_{C o u l} = v_{b r k} / 10$

$v = v_{F} - v_{B}$

$l e n g t h = x_{F} - x_{B}$

$p o w e r_d i s s i p a t e d = - f_{f r i c t i o n} \cdot v$

where:

f_friction is the friction force.
F_N is the normal force, which acts on the block in the direction normal to the rail, that is, normal to the direction of the motion.
F_C is the Coulomb friction.
K_C is the Coulomb friction coefficient.
F_brk is the breakaway friction.
K_brk is the breakaway friction coefficient.
f_v is the viscous friction coefficient.
v_brk is the breakaway friction velocity.
v_St is the Stribeck velocity threshold.
v_Coul is the Coulomb velocity threshold.
v is the relative velocity.
v_B and v_F are the absolute velocities of ports B and F, respectively.
length is the friction length.
x_B and x_F are the absolute positions of ports B and F, respectively.
power_dissipated is the power dissipated through the friction.

The negative sign in the first equation reflects the force flow conventions used in the position-based mechanical translational domain. Unless the ports have inverted, a positive value of f_friction indicates that the block is in a state of compression and a negative value of f_friction indicates that the block is in a state of tension. For more information, see Two-Port Block Orientation and Force Flow Conventions.

The exponential function used in the Stribeck portion of the force equation is continuous and decays at velocity magnitudes greater than the breakaway friction velocity.

The hyperbolic tangent function used in the Coulomb portion of the force equation ensures that the equation is smooth and continuous through v = 0, but quickly reaches its full value at nonzero velocities.

Connections B and F are position-based mechanical translational conserving ports. The friction force acts from port B on port F. Positive friction force drives port F in the positive direction. You can specify the normal force either by using the Normal force parameter or by using the physical signal port N.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Examples

Gravity and Friction in the Position-Based Translational Domain

Configure gravity and gravity-induced friction effects in a position-based mechanical translational network.

Open Live Script

Ports

Input

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N — Normal force control signal, N
physical signal

Physical signal input port for the control signal that specifies the normal force. If the signal becomes negative, the block saturates the input value to 0.

Dependencies

To enable this port, set the Normal force specification parameter to Variable.

Conserving

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B — Base port
position-based mechanical translational

Position-based mechanical translational conserving port that represents the base connection.

F — Follower port
position-based mechanical translational

Position-based mechanical translational conserving port that represents the follower connection. For positive length, port F has a more positive position than port B.

Parameters

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Normal force specification — Whether normal force is constant or variable
`Constant` (default) | `Variable`

Select whether the normal force applied to the block is constant or variable:

Constant — Specify normal force by using the Normal force parameter value.
Variable — Specify normal force by using the physical signal at port N.

Normal force — Force normal to motion
`10 N` (default) | nonnegative scalar

Force applied to the block in the direction normal to the motion. The block calculates the breakaway friction force and the Coulomb friction force based on this value and the proportionality coefficients, Breakaway friction coefficient and Coulomb friction coefficient.

Dependencies

To enable this parameter, set Normal force specification to Constant.

Breakaway friction coefficient — Proportionality coefficient between normal force and breakaway friction force
`2.5` (default) | positive scalar

Coefficient for calculating the breakaway friction force, which is the sum of the Coulomb and the static frictions, based on the normal force. The parameter value must be greater than or equal to the Coulomb friction coefficient value.

Breakaway friction velocity — Peak velocity for Stribeck friction
`0.1 m/s` (default) | positive scalar

Velocity at which the Stribeck friction is at its peak. At this point, the sum of the Stribeck and Coulomb friction is the breakaway friction force. This parameter specifies the velocity threshold, which affects the tradeoff between the simulation accuracy and speed.

Coulomb friction coefficient — Proportionality coefficient between normal force and friction that opposes motion
`2` (default) | nonnegative scalar

Coefficient for calculating the Coulomb friction force, which is the friction that opposes motion, based on the normal force.

Viscous friction coefficient — Viscous losses proportionality coefficient
`0 N/(m/s)` (default) | nonnegative scalar

Proportionality coefficient between the friction force and the relative velocity. Viscous losses do not depend on the normal force.

References

[1] Armstrong, B. and C.C. de Wit, Friction Modeling and Compensation, The Control Handbook, CRC Press, 1995.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024b

Translational Friction (PB)