brake

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brake

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Iconic Diagrams\Mechanical\Rotation\Components

Implementations

C

V

CV

SCVS

LuGre

Use

Domains: Continuous. Size: 1-D. Kind: Iconic Diagrams (Rotation).

Introduction

The brake models represent a disk brake or other type of brake where a rotation is stopped by applying a friction force. The amount of friction depends on the normal force that is applied and the friction function that is used. The normal force is given by the input signal Fn. The brake is mounted to the fixed world.

DiskBreak

The model has only one initial port p defined. Because any number of connections can be made, successive ports are named p1, p2, p3 etc. 20-sim will automatically create equations such that the resulting torque p.T is equal to the sum of the torques of all connected ports p1 .. pn. The angular velocities of all connected ports are equal to p.omega.

 

p.T = sum(p1.T, p2.T, ....)

p.omega = p1.omega = p2.omega = ....

 

Due to the use of normal force, the brake models all have a fixed torque out causality. The constitutive equations are therefore described as:

 

p.T = Fn * f(p.omega);

 

with f the friction function.

Description - C

This model represents a brake with braking force described as coulomb friction. The brake is mounted to the fixed world. The amount of friction depends on the normal force that is applied:

 

p.T = Fn*mu_c*tanh(slope*p.omega);

 

Fn: normal force (given by the input signal Fn)

mu_c: the coulomb friction coefficient

slope: the steepness of the coulomb friction curve.

 

CoulombFriction

 

Interface - C

Ports

Description

p[any]

Any number of connections can be made (Rotation).

Causality

 

Fixed torque out

 

Input

 

Fn

Normal force [N]

Parameters

 

mu_c

slope

Coulomb friction coefficient [m]

Steepness of Coulomb friction curve [s/rad]

Description - V

This model represents a brake with braking force described as viscous friction. The brake is mounted to the fixed world. The amount of friction depends on the normal force that is applied:

 

p.T = Fn*mu_v*p.omega;

 

Fn: normal force (given by the input signal Fn)

mu_v: the viscous friction coefficient

 

ViscousFriction

 

Interface - V

Ports

Description

p[any]

Any number of connections can be made (Rotation).

Causality

 

Fixed torque out

 

Input

 

Fn

Normal force [N]

Parameters

 

mu_v

Viscous friction coefficient [m.s/rad]

 

Description - CV

This model represents a brake with braking force described as coulomb plus viscous friction. The brake is mounted to the fixed world. The amount of friction depends on the normal force that is applied:

 

p.T = Fn*(mu_c*tanh(slope*p.omega) + mu_v*p.omega);

 

Fn: normal force (given by the input signal Fn)

mu_v: the viscous friction coefficient

mu_c: the coulomb friction coefficient

slope: the steepness of the coulomb friction curve.

CoulombViscousFriction

Interface - CV

Ports

Description

p[any]

Any number of connections can be made (Rotation).

Causality

 

Fixed torque out

 

Input

 

Fn

Normal force [N]

Parameters

 

mu_v

mu_cv

slope

Viscous friction coefficient [ms/rad]

Coulomb friction coefficient [m]

Steepness of Coulomb friction curve [s/rad]

Description - SCVS

This model represents a brake with braking force described as static plus coulomb plus viscous plus Stribeck friction. The brake is mounted to the fixed world. The amount of friction depends on the normal force that is applied:

 

p.T = Fn *

(( mu_c + (mu_st*abs(tanh( slope*p.omega )) - mu_c)

* exp( -((p.omega / v_st)^2 )) ) * sign(p.omega)

+ mu_v * p.omega);

 

Fn: normal force (given by the input signal Fn)

mu_s: the static friction coefficient

mu_v: the viscous friction coefficient

mu_c: the coulomb friction coefficient

slope: the steepness of the coulomb and static friction curve.

v_st: the characteristic Stribeck velocity.

 

StaticCoulombViscousFriction

 

Interface - SCVS

Ports

Description

p[any]

Any number of connections can be made (Rotation).

Causality

 

Fixed torque out

 

Input

 

Fn

Normal force [N]

Parameters

 

mu_s

mu_v

mu_cv

slope

v_st

Static friction coefficient [m]

Viscous friction coefficient [m.s/rad]

Coulomb friction coefficient [m]

Steepness of Coulomb friction curve [s/rad]

Characteristic Stribeck velocity [rad/s]

Description - LuGre

This model represents a brake with braking force described by the LuGre friction model. The brake is mounted to the fixed world. The amount of friction depends on the normal force that is applied:

 

p.T = FN*f_lg(p.omega);

 

Fn: normal force (given by the input signal Fn)

f_lg: the LuGre friction model

Interface - LuGre

Ports

Description

p[any]

Any number of connections can be made (Rotation).

Causality

 

Fixed Torque out

 

Input

 

Fn

Normal force [N]

Parameters

 

mu_c

mu_s

mu_v

v_st

mu_k

Coulomb friction coefficient

Static friction coefficient [m]

Viscous friction coefficient [ms/rad]

Characteristic Stribeck velocity [rad/s]

rotational stiffness coefficient at zero speed [m/rad]