SupportFriction

Coulomb friction in support

    SupportFriction

Library

Modelica/Mechanics/Translational/Components

Description

This element describes Coulomb friction in support,i.e., a frictional force acting between a flange and the housing.The positive sliding friction force "f" has to be definedby table "f_pos" as function of the absolute velocity "v".E.g.

       v |   f      ---+-----       0 |   0       1 |   2       2 |   5       3 |   8

gives the following table:

   f_pos = [0, 0; 1, 2; 2, 5; 3, 8];

Currently, only linear interpolation in the table is supported.Outside of the table, extrapolation through the lasttwo table entries is used. It is assumed that the negativesliding friction force has the same characteristic with negativevalues. Friction is modelled in the following way:

When the absolute velocity "v" is not zero, the friction forceis a function of v and of a constant normal force. This dependencyis defined via table f_pos and can be determined by measurements,e.g., by driving the gear with constant velocity and measuring theneeded driving force (= friction force).

When the absolute velocity becomes zero, the elementsconnected by the friction element become stuck, i.e., the absoluteposition remains constant. In this phase the friction force iscalculated from a force balance due to the requirement, thatthe absolute acceleration shall be zero. The elements beginto slide when the friction force exceeds a threshold value,called the maximum static friction force, computed via:

   maximum_static_friction = peak * sliding_friction(v=0)  (peak >= 1)

This procedure is implemented in a "clean" way by state events andleads to continuous/discrete systems of equations if friction elementsare dynamically coupled which have to be solved by appropriatenumerical methods. The method is described in(see also a short sketch in UsersGuide.ModelingOfFriction):

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 thematerial when the two elements are "stuck", as well as other effects,like hysteresis. This has the advantage that the friction element canbe completely described by a differential equation without events. Thedrawback is that the system becomes stiff (about 10-20 times slowersimulation) and that more material constants have to be supplied whichrequires more sophisticated identification. For more details, see thefollowing 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

SupportFriction_0

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_f_pos

f_pos

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

Matrix of size Mx2

mo_peak

peak

Peak for maximum friction force at w==0 (f0_max = peak*f_pos[1,2])

Scalar

mo_startForward

startForward

startForward

Structure

mo_startForward/fixed

fixed

Cell of scalars

true
false

mo_startForward/start

start

Cell of scalars

true
false

mo_startBackward

startBackward

startBackward

Structure

mo_startBackward/fixed

fixed

Cell of scalars

true
false

mo_startBackward/start

start

Cell of scalars

true
false

mo_locked

locked

locked

Structure

mo_locked/fixed

fixed

Cell of scalars

true
false

mo_locked/start

start

Cell of scalars

true
false

mo_mode

mode

mode

Structure

mo_mode/fixed

fixed

Cell of scalars

true
false

mo_mode/start

start

Cell of scalars

SupportFriction_1

NameLabelDescriptionData TypeValid Values

mo_v_small

v_small

Relative velocity near to zero (see model info text)

Scalar

SupportFriction_2

NameLabelDescriptionData TypeValid Values

mo__nmodifiers

Number of Modifiers

Specifies the number of modifiers

Number

mo__modifiers

Modifiers

Add new modifier

Structure

mo__modifiers/varname

Variable name

Cell of strings

's_a'
's_b'
's_support'
'lossPower'
'v_relfric'
'a_relfric'
'f0'
'f0_max'
'free'
'sa'
's'
'f'
'v'
'a'

mo__modifiers/attribute

Attribute

Cell of strings

'start'
'fixed'

mo__modifiers/value

Value

Ports

NameTypeDescriptionIO TypeNumber

flange_a

implicit

Flange of left shaft

input

1

flange_b

implicit

Flange of right shaft

output

1

Port 3

implicit

Support/housing of component

input

mo_useSupport

Port 4

implicit

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

input

mo_useHeatPort

See Also