# Brake

Brake based on Coulomb friction

## Library

Modelica/Mechanics/Translational/Components

## Description

This component models a brake, i.e., a component where a frictional force is acting between the housing and a flange and a controlled normal force presses the flange to the housing in order to increase friction. The normal force fn has to be provided as input signal f_normalized in a normalized form (0 ≤ f_normalized ≤ 1), fn = fn_max*f_normalized, where fn_max has to be provided as parameter. Friction in the brake is modelled in the following way:

When the absolute velocity "v" is not zero, the friction force is a function of the velocity dependent friction coefficient mue(v) , of the normal force "fn", and of a geometry constant "cgeo" which takes into account the geometry of the device and the assumptions on the friction distributions:

        frictional_force = cgeo * mue(v) * fn


Typical values of coefficients of friction:

      dry operation   :  mue = 0.2 .. 0.4
operating in oil:  mue = 0.05 .. 0.1


The positive part of the friction characteristic mue(v), v >= 0, is defined via table mue_pos (first column = v, second column = mue). Currently, only linear interpolation in the table is supported.

When the absolute velocity becomes zero, the elements connected by the friction element become stuck, i.e., the absolute position remains constant. In this phase the friction force is calculated from a force balance due to the requirement, that the absolute acceleration shall be zero. The elements begin to slide when the friction force exceeds a threshold value, called the maximum static friction force, computed via:

       frictional_force = peak * cgeo * mue(w=0) * fn   (peak >= 1)


This procedure is implemented in a "clean" way by state events and leads to continuous/discrete systems of equations if friction elements are dynamically coupled. The method is described in:

Otter M., Elmqvist H., and Mattsson S.E. (1999):
Hybrid Modeling in Modelica based on the Synchronous Data Flow Principle. CACSD'99, Aug. 22.-26, Hawaii.

More precise friction models take into account the elasticity of the material when the two elements are "stuck", as well as other effects, like hysteresis. This has the advantage that the friction element can be completely described by a differential equation without events. The drawback is that the system becomes stiff (about 10-20 times slower simulation) and that more material constants have to be supplied which requires more sophisticated identification. For more details, see the following references, especially (Armstrong and Canudas de Wit 1996):

Armstrong B. (1991):
Control of Machines with Friction. Kluwer Academic Press, Boston MA.

Armstrong B., and Canudas de Wit C. (1996):
Friction Modeling and Compensation. The Control Handbook, edited by W.S.Levine, CRC Press, pp. 1369-1382.

Canudas de Wit C., Olsson H., Åström K.J., and Lischinsky P. (1995):
A new model for control of systems with friction. IEEE Transactions on Automatic Control, Vol. 40, No. 3, pp. 419-425.

## Parameters

NameLabelDescriptionData TypeValid Values

mo_useSupport

useSupport

= true, if support flange enabled, otherwise implicitly grounded

Number

0
1

mo_useHeatPort

useHeatPort

=true, if heatPort is enabled

Number

0
1

mo_mue_pos

mue_pos

[v, f] Positive sliding friction characteristic (v>=0)

Matrix of size Mx2

mo_peak

peak

Peak for maximum value of mue at w==0 (mue0_max = peak*mue_pos[1,2])

Scalar

mo_cgeo

cgeo

Geometry constant containing friction distribution assumption

Scalar

mo_fn_max

fn_max

Maximum normal force

Scalar

mo_Unknown

Unknown

Value of mode is not known

Scalar

mo_Free

Free

Element is not active

Scalar

mo_Forward

Forward

v_relfric > 0 (forward sliding)

Scalar

mo_Stuck

Stuck

v_relfric = 0 (forward sliding, locked or backward sliding)

Scalar

mo_Backward

Backward

v_relfric < 0 (backward sliding)

Scalar

mo_unitAcceleration

unitAcceleration

Scalar

mo_unitForce

unitForce

Scalar

NameLabelDescriptionData TypeValid Values

mo_v_small

v_small

Relative velocity near to zero (see model info text)

Scalar

NameLabelDescriptionData TypeValid Values

mo_s_a

s_a

s_a

Structure

mo_s_a/fixed

fixed

Cell of scalars

true
false

mo_s_a/start

start

Cell of scalars

mo_s_b

s_b

s_b

Structure

mo_s_b/fixed

fixed

Cell of scalars

true
false

mo_s_b/start

start

Cell of scalars

mo_lossPower

lossPower

lossPower

Structure

mo_lossPower/fixed

fixed

Cell of scalars

true
false

mo_lossPower/start

start

Cell of scalars

mo_v_relfric

v_relfric

v_relfric

Structure

mo_v_relfric/fixed

fixed

Cell of scalars

true
false

mo_v_relfric/start

start

Cell of scalars

mo_a_relfric

a_relfric

a_relfric

Structure

mo_a_relfric/fixed

fixed

Cell of scalars

true
false

mo_a_relfric/start

start

Cell of scalars

mo_f0

f0

f0

Structure

mo_f0/fixed

fixed

Cell of scalars

true
false

mo_f0/start

start

Cell of scalars

mo_f0_max

f0_max

f0_max

Structure

mo_f0_max/fixed

fixed

Cell of scalars

true
false

mo_f0_max/start

start

Cell of scalars

mo_free

free

free

Structure

mo_free/fixed

fixed

Cell of scalars

true
false

mo_free/start

start

Cell of scalars

mo_sa

sa

sa

Structure

mo_sa/fixed

fixed

Cell of scalars

true
false

mo_sa/start

start

Cell of scalars

mo_startForward

startForward

startForward

Structure

mo_startForward/fixed

fixed

Cell of scalars

true
false

mo_startForward/start

start

Cell of scalars

mo_startBackward

startBackward

startBackward

Structure

mo_startBackward/fixed

fixed

Cell of scalars

true
false

mo_startBackward/start

start

Cell of scalars

mo_locked

locked

locked

Structure

mo_locked/fixed

fixed

Cell of scalars

true
false

mo_locked/start

start

Cell of scalars

mo_mode

mode

mode

Structure

mo_mode/fixed

fixed

Cell of scalars

true
false

mo_mode/start

start

Cell of scalars

mo_s

s

s

Structure

mo_s/fixed

fixed

Cell of scalars

true
false

mo_s/start

start

Cell of scalars

mo_f

f

f

Structure

mo_f/fixed

fixed

Cell of scalars

true
false

mo_f/start

start

Cell of scalars

mo_v

v

v

Structure

mo_v/fixed

fixed

Cell of scalars

true
false

mo_v/start

start

Cell of scalars

mo_a

a

a

Structure

mo_a/fixed

fixed

Cell of scalars

true
false

mo_a/start

start

Cell of scalars

mo_mue0

mue0

mue0

Structure

mo_mue0/fixed

fixed

Cell of scalars

true
false

mo_mue0/start

start

Cell of scalars

mo_fn

fn

fn

Structure

mo_fn/fixed

fixed

Cell of scalars

true
false

mo_fn/start

start

Cell of scalars

mo_f_normalized

f_normalized

f_normalized

Structure

mo_f_normalized/fixed

fixed

Cell of scalars

true
false

mo_f_normalized/start

start

Cell of scalars

## Ports

NameTypeDescriptionIO TypeNumber

flange_a

implicit

Flange of left shaft

input

1

flange_b

implicit

Flange of right shaft

output

1

f_normalized

implicit

Normalized force signal 0..1 (normal force = fn_max*f_normalized; brake is active if > 0)

input

2

Port 4

implicit

Support/housing of component

input

mo_useSupport

Port 5

implicit

Optional port to which dissipated losses are transported in form of heat

input

mo_useHeatPort