Elastic Friction

Identifier: Mechanics.Rotation.ElasticFriction
Version: 3.6
File: Rotary.cat
Connectors: Mechanical Connector (rotational) ctr1 connectable to elements of the Rotational Mechanics library
Mechanical Connector (rotational) ctr2 connectable to elements of the Rotational Mechanics library
Parameters: Friction Model with kindF "Stick-Slip" or "Continuous Transition"
Static Friction Torque Tst only visible if kindF=="Stick-Slip"
Sliding Friction Torque Tsl
Limit Speed Difference domL only visible if kindF=="Continuous Transition"
Transfer Stiffness k not visible, if rigid=="true"
Transfer Damping b not visible, if rigid=="true"
Rigid rigid if true, the element behaves as rigid
Steady-State Simulation: Damping kindDamping kind of damping in Steady-State Simulation and Transient Simulation
Relative Damping psi damping losses per period divided by maximal elastic deformation energy (nonlinear approximation if enabled for transient simulation)
Lehr's Damping Factor D Lehr's damping factor (nonlinear approximation if enabled for transient simulation)
Spectral Power PSpec only effective in Steady-State Simulation
Initial Preload of Spring kindPS
  • "Unloaded"
  • "Preload Angle Difference"
  • "Preload Torque"
Initial Displacement Difference dphiSD0 only visible if kindPS=="Preload Angle Difference"
Initial Spring Force Ts0 only visible if kindPS=="Preload Torque"
Advanced: Advanced Settings adv only visible if kindF=="Stick-Slip"
Relative Minimum Difference of the Friction Torques dTfrel only visible if kindF=="Stick-Slip"
only enabled if adv=="true"
Minimum Separation Speed Difference eps_domsl only visible if kindF=="Stick-Slip" and rigid=="true"
only enabled if adv=="true"
Minimum Separation Impact eps_dI only visible if kindF=="Stick-Slip" and rigid=="true"
only enabled if adv=="true"
Transition Shape of Force of Sliding Friction kindTrans
  • "Gevrey Approach (based on tanh-Function)"
  • "tanh Approach"

only visible if kindF=="Continuous Transition"
only enabled if adv=="true"
Shape Coefficient (Transition Shape) eps_sigma only visible if kindTrans=="Gevrey Approach (based on tanh-Function)"
Shape Coefficient (Transition Shape) eps_tau only visible if kindTrans=="tanh Approach"
Results: State of Friction sf
Angular Difference dphi
Speed Difference dom
Internal Torque Ti
Change of Potential Energy Pp not visible, if rigid=="true"
Power Loss Pl
  • Elastische Reibung zw. Körpern mit Berücksichtigung der Übertragungssteifigkeit und -dämpfung
  • Vorgabe veränderlicher Haft- oder Gleitreibkräfte
  • Echtes Haften: Geschwindigkeitsdifferenz ist exakt null
    (Möglichkeit zur Abbildung des Stick-Slip-Verhaltens (z.B. zur Untersuchung von Kupplungsrupfen))
  • Optional: Starres Verhalten, glatter Übergang im Haftbereich
  • Geeignet zur Analyse im Zeit- und Frequenzbereich
  • Elastic friction bw. bodies taking transfer stiffness and damping into account
  • Preset of variable static or sliding friction forces
  • Real sticking: Speed difference is exactly zero
    (representation of the stick-slip behavior (e.g. for analyses of clutch rupture))
  • Option: Rigid behavior, smooth transition in the sticking zone
  • Suitable for Analyses in time and frequency domain


The element Elastic Friction allows the modeling of the stick/slip behavior in combination with rotary elasticity and damping of the friction contact. The element acts relatively between two rotary mechanics components. If one of the connectors of the Elastic Friction remains unconnected or is connected to a fixed Preset, an absolute friction is modeled. One application example is the modeling of a rubber seal, which has elastic properties when sticking.

The element provides two friction models:

  • Friction with stick-slip and
  • Friction with Continuous Transitions.

Furthermore the model can be switched to rigid behavior. In that case, the model is identical to the Rigid Friction model.


General Parameters

The Elastic Friction element includes two friction models, which can be selected with the enumeration kindF (Friction Model with).
The two models are Friction Model with:

  • Stick-Slip:
    The Static Friction Torque is the torque, which must be exceeded in order to make the friction contact slip. It defines the point, where the element changes from the sticking to the sliding state. The Sliding Friction Torque is transmitted if the friction contact slides, i.e., if there is a speed difference in the friction element.
    See also the element type Rigid Friction (translational) for some remarks on the settings of the torques.
    Furthermore, the Transfer Stiffness and the Transfer Damping of the element have to be specified. The spring acts in parallel with the damper and they are both connected in series with the friction contact. Consequently, the spring and damper only act in the case of sticking.
  • Continuous Transition:
    This friction model is described by a continuous approach - a Gevrey function (adjusted tanh-function). For this approach, the slipping torque Tsl and the limit speed difference domL are required. When domL is reached the total slipping torque is acting.
    The meaning of theses parameters in reference to the continuous transition approach is shown in Figure 2 in the help of the translational Rigid Friction element.
    Hint: The Sliding friction model cannot stick.
    (In former versions of this element, this Sliding friction model was specified by the boolean parameter smoothApprox.)

If rigid is set to true, the element behaves as Rigid Friction element (same parameters, same calculation basics). In this case, stiffness and damping are deactivated.

Initial Values

Preload of the internal spring in sticking state

An elastic friction model represents a spring-damper of the friction contact. This spring-damper acts in the sticking state.
For some applications or analyses, it is required to start the simulation in the sticking state. And then it is possible to configure a pre-loaded spring.

  • The enumeration kindPS holds a selection of initial states of the internal spring:
    • "Unloaded": This is the default selection. The spring is initially unloaded.
    • "Preload Angle Difference": The spring is pre-loaded. This option activates the parameter dphiSD0, the initial angle difference.
    • "Preload Torque": The spring is pre-loaded. This option activates the parameter Ts0, the pre-load torque.
  • dphiSD0 ... initial displacement difference of the internal spring-damper
  • Ts0 ... the initial spring torque or pre-load

Steady-State Simulation:

The parameters on the additional page Steady-State Simulation only effect the Periodic Steady-State Simulation. The setting of the enumeration kindDamping determines the friction model and the calculation of the damping torque.

  • Steady State as Time Simulation: The damping force is computed as in the time simulation.
    Note, that the Sliding friction model (kindF=="Continuous Transition") should be used for the Periodic Steady-State Simulation since discontinuities may cause convergence problems.
  • Relative Damping psi (
  • Lehr's Damping Factor D: The internal torque is computed in the same way as for Relative Damping but with substituted by where D is Lehr's damping factor.

More information about Relative Damping and Lehr's Damping Factor is given in section "Special Properties of Model Elements" of the help for the Periodic Steady-State Simulation.

Advanced Parameters:

The tab Advanced contains several parameters for a more detailed definition of the models with static and sliding friction.

Advanced setting for models with static and sliding friction

These parameters define numerical limits for the model. They can only be entered, if adv (Advanced Settings) is set to true. Else, the element takes the default values which suit most cases. This means that it is usually not required to change the values.

  • dTfrel ... This parameter defines the relative ratio between the forces of static and sliding friction. As the hint of the translational Rigid Friction element explains the value of Tst must be greater than Tsl. If the supplied Tst is equal or smaller than Tsl, the model computes a new Tst and in this case, the current value of the parameter Tst will be ignored. The new value is computed with: dTfrel = (Tst - Tsl) / Tsl and Tst = Tsl*(1+dTfrel)

In the case of a friction model with stick-slip and rigid=="true" the element behaves as a Rigid Friction element. For this case two more advanced parameters can be set: eps_domsl and eps_dI. A detailed description of the both corresponding parameters can be found in the help of the translational Rigid Friction model.

Advanced setting for friction models with continuous transition

The enumeration kindTrans provides a selection of two continuous transition models, which can be selected if adv is set to "true".

  • "Gevrey Approach (based on tanh-Function)":
    This approach and the meaning of the corresponding shape parameter eps_sigma are described in chapter Continuous transition between two signals by Gevrey approach.
    The advantage of this approach is, that the output becomes a real zero before the transition and real one after the transition (see figure in the linked chapter).
    Disadvantage is, that there are small discontinuities at the transition start and end. If these discontinuities cause problems (caused rarely), please try the next transition approach ...
  • "tanh Approach":
    This approach and the meaning of the corresponding shape parameter eps_tau are described in chapter Continuous transition between two signals by a hyperbolic tangent approach.
    The advantage of this approach is, that there are no discontinuities (see figure in the linked chapter).
    Disadvantage is, that the output is only in the near of zero or one, resp.


  • The friction contact can either stick or slip. If the two following conditions are fulfilled:
    dom = 0 and abs(Ti) <= Tst (1)
    then the friction contact is sticking. In this case the Internal Torque is defined by the spring-damper properties of the element:
  • k and b are the given stiffness and damping, is the torsion angle, of the spring-damper, i.e. total angular difference of the elastic friction minus the angular difference of the friction contact at the onset of sticking. Furthermore, is the angular velocity of the spring damper, i.e. the time-derivative of .
  • In the case of a Sliding friction contact the Internal Torque equals the Sliding Friction Torque:
    Ti = Tsl * sign(dom).
  • The current state of the friction contact can be observed using the result variable State of Friction (sf): see Table 1 in chapter Rigid Friction of the Linear Mechanics library
  • The result variable sf is suited for triggering other model's events which depend on the state of friction contact. The value can be accessed by referencing the output variable of the friction element.
  • The Angular Difference is the difference between the current angles of the elements which are linked to the connectors ctr1 and ctr2:
    dphi = ctr1.phi - ctr2.phi
  • The Speed Difference results from the speeds at the connectors:
    dom = ctr1.om - ctr2.om
  • For a Static friction contact the Change of Potential Energy (i.e., the amount of power fed into the spring component of the element), is calculated as
    where TiS is the internal torque of the spring. There is no change of potential energy if the friction contact is slipping.
  • The power loss of the element for the case of a Static friction contact is the power which is dissipated in the damper component
    where TiD is the internal torque of the damper.
  • In case of a Sliding friction contact the power is dissipated in the friction contact and the loss is computed as


The remarks given for the Linear (translatory) Elastic Friction element type hold equivalently.