Elastic Friction


Symbol:
Identifier: Mechanics.Translation.ElasticFriction
Version: 3.6
File: Mechanics.cat
Connectors: Mechanical Connector (linear) ctr1 connectable to elements of the Linear Mechanics library
Mechanical Connector (linear) ctr2 connectable to elements of the Linear Mechanics library
Parameters: Friction Model with kindF "Stick-Slip" or "Continuous Transition"
Force of Static Friction Fst only visible if kindF=="Stick-Slip"
Force of Sliding Friction Fsl
Transfer Stiffness k not visible, if rigid=="true"
Transfer Damping b not visible, if rigid=="true"
Limit Velocity Difference dvL only visible if kindF=="Continuous Transition"
Rigid rigid if true, the element behaves as rigid
Initial Preload of Spring kindPS
  • "Unloaded"
  • "Preload Displacement Difference"
  • "Preload Force"

only visible if mode=="Elastic Friction"
Initial Displacement Difference dxSD0 only visible if kindPS=="Preload Displacement Difference"
Initial Spring Force Fs0 only visible if kindPS=="Preload Force"
Advanced: Advanced Settings adv only visible if kindF=="Stick-Slip"
Relative Minimum Difference of the Friction Forces dFfrel only visible if kindF=="Stick-Slip"
only enabled if adv=="true"
Minimum Separation Velocity Difference eps_dvsl 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"
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: Internal Force Fi
State of Friction sf
Displacement Diff. dx
Velocity Difference dv
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 Ratterschwingungen))
  • 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 the analysis of chatter vibrations))
  • Option: Rigid behavior, smooth transition in the sticking zone
  • Suitable for Analyses in time and frequency domain

Description:

The element Elastic Friction allows the modeling of the stick/slip behavior in combination with linear elasticity and damping of the friction contact. The element acts relatively between two linear mechanics components. If one of the connectors of the Elastic Friction model 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 the case, the model is identical to the Rigid Friction model.

Parameters:

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 Force of Static FrictionFst is the force, which must be exceeded in order to make the friction contact slip. It defines the point, where the element changes from the static to the sliding friction state. The Force of Sliding FrictionFsl is transmitted if the friction contact slips, i.e., if there is a speed difference in the friction element.
    See also the element type Rigid Friction for some remarks on the settings of the forces.
    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 force Fsl and the limit velocity difference dvL are required. When dvL is reached the total slipping force is acting. The meaning of these parameters in reference to the continuous transition approach is shown in the Figure 2:

    Figure 2: Sliding friction model with continuous transition
    Hint: The Sliding friction model cannot stick.
    Furthermore, the Transfer Stiffness and the Transfer Damping of the element have to be specified. The respective spring and damper act in parallel and are connected in series to the friction contact.

If rigid is set to true, the element behaves as a Rigid Friction element (same parameters, same computation 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 Displacement Difference": The spring is pre-loaded. This option activates the parameter dxSD0, the initial displacement difference.
    • "Preload Force": The spring is pre-loaded. This option activates the parameter Fs0, the pre-load force.
  • dxSD0 ... initial displacement difference of the internal spring-damper
  • Fs0 ... the initial spring force (pre-load)

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.

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

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_dvsl and eps_dI. A detailed description of both parameters can be found in the help of the 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.

Results:

  • The friction contact can either stick or slip. If the two following conditions are fulfilled:
    dv = 0 and abs(Fi) <= Fst (1)
    then the friction contact is sticking. In this case the Internal Force is defined by the spring-damper properties of the element:
  • k and b are the given stiffness and damping. dxis the displacement difference of the spring-damper, i.e. total displacement difference of the elastic friction minus the displacement difference of the friction contact at the onset of sticking.
  • In case of a sliding friction contact, the Internal Force equals the Force of Sliding Friction: Fi = Fsl * sign(dvFric) where dvFric is the velocity difference of the internal friction element which is an internal result variable. The relationship between the velocity differences at the connectors dv and dvFric take into account that the elastic friction element mainly consists of a rigid friction element and a spring-damper element in series: dv = dvFric + dvSpring where dvSpring is the velocity difference of the internal spring element which is an internal result variable.
  • 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 Displacement Difference is the difference between the current displacements of the elements which are linked to the connectors ctr1 and ctr2:
    dx = ctr1.x - ctr2.x
  • The Velocity Difference results from the velocities at the connectors:
    dv = ctr1.v - ctr2.v
  • 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 FiSis the internal force 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 FiD is the internal force of the damper.
  • In case of a Sliding friction contact the power is dissipated in the friction contact and the loss is computed as

Remarks:

The consideration of stiffness and damping distinguishes the elastic friction from the element type Rigid Friction. If, however, the transfer stiffness and/or damping are very large and if the oscillations in the friction contact are of minor effect and interest, a rigid friction should be preferred.