Coulomb friction in bearings

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This information is part of the Modelica Standard Library maintained by the Modelica Association.

This element describes Coulomb friction in bearings, i.e., a frictional torque acting between a flange and the housing. The positive sliding friction torque "tau" has to be defined by table "tau_pos" as function of the absolute angular velocity "w". E.g.

 w | tau
 0 |   0
 1 |   2
 2 |   5
 3 |   8

gives the following table:

tau_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 last two table entries is used. It is assumed that the negative sliding friction force has the same characteristic with negative values. Friction is modelled in the following way:

When the absolute angular velocity "w" is not zero, the friction torque is a function of w and of a constant normal force. This dependency is defined via table tau_pos and can be determined by measurements, e.g., by driving the gear with constant velocity and measuring the needed motor torque (= friction torque).

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

maximum_static_friction = peak * sliding_friction(w=0)  (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 which have to be solved by appropriate numerical 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 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 (5)


Value: false

Type: Boolean

Description: = true, if support flange enabled, otherwise implicitly grounded


Value: 1.0e10

Type: AngularVelocity (rad/s)

Description: Relative angular velocity near to zero if jumps due to a reinit(..) of the velocity can occur (set to low value only if such impulses can occur)


Value: false

Type: Boolean

Description: = true, if heatPort is enabled


Value: [0, 1]

Type: Real[:,2]

Description: Positive sliding friction characteristic [N.m] as function of w [rad/s] (w>=0)


Value: 1

Type: Real

Description: Peak for maximum friction torque at w==0 (tau0_max = peak*tau_pos[1,2])

Connectors (4)


Type: Flange_a

Description: Flange of left shaft


Type: Flange_b

Description: Flange of right shaft


Type: Support

Description: Support/housing of component


Type: HeatPort_a

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

Used in Examples (2)



Example to show combination of LossyGear and BearingFriction



Demonstrate the modeling of heat losses

Used in Components (2)



Motor inertia and gearbox model for r3 joints 1,2,3



Motor inertia and gearbox model for r3 joints 4,5,6