|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|
|Stiffness of Contact||k||only visible, if kind=="Spring" or "Spring-Damper" or "Spring-Backlash" or "Spring-Damper-Backlash"|
|Damping of Contact||b||only visible, if kind=="Damper" or "Spring-Damper" or "Damper-Backlash" or "Spring-Damper-Backlash"|
|Stiffness of Backlash||kL||only visible, if kind=="Spring-Backlash" or "Spring-Damper-Backlash"|
|Damping of Backlash||bL||only visible, if kind=="Damper-Backlash" or "Spring-Damper-Backlash"|
|Backlash||L||only visible, if kind=="Spring-Backlash" or "Damper-Backlash" or "Spring-Damper-Backlash"|
|Rigid||rigid||if true, the element behaves as rigid|
|Selection of the rigid model||kindR||if true, the element behaves as rigid|
|Coefficient of Restitution||ci||if true, the element behaves as rigid|
|Steady State Analysis:||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)|
|Advanced:||Initial Preload of Spring||kindPS||
|Initial Displacement Difference||dx0||only visible if kindPS=="Preload Displacement Difference"|
|Initial Spring Force||Fs0||only visible if kindPS=="Preload Force"|
|Initial Preload of Damper||kindPD||
|Initial Velocity Difference||dv0||only visible if kindPD=="Preload Velocity Difference"|
|Initial Damping Force||Fd0||only visible if kindPD=="Preload Force"|
|Advanced Settings||adv||only visible, if rigid=="true" and kindR<>"without Backlash"|
|Minimum Separation Force||eps_Fi||only enabled, if rigid=="true" and kindR<>"without Backlash"|
|Maximum Velocity after impact for permanent contact||eps_dv||only enabled, if rigid=="true" and kindR<>"without Backlash"|
|Change of Potential Energy||Pp||not visible, if rigid==true|
|Power Loss||Pl||not visible, if rigid==true|
|External Power||Pe||only visible, if rigid==true and kindR==Without Backlash|
|State||stop||only visible, if rigid==true and kindR <> Without Backlash|
This model implements elastic and/or damping behavior which may also contain a backlash. It is applied between two linear mechanics components. If the backlash is activated then the stiffness and damping can be independently parameterized on a user-defined interval centered on the origin of the displacement difference. The springs are always acting in parallel with the dampers.
The behavior of the component is defined by the enumeration kind. Depending on the selection the element models:
- a pure spring,
- a pure damper,
- a spring-damper.
- All of these selections can be combined with a backlash (in series), creating three further models.
The selected variant defines the required parameters for the element. The parameter dialog only shows the parameters required for the current setting. E.g., for a pure spring only the Stiffness of Contactk is required for the parametrization and thus only this parameter is accessible to the user. The maximum amount of parameters is present for a spring-damper-backlash model.
The Stiffness of Contact k and Damping of Contact b define the respective stiffness and damping of the element in cases where the backlash is exceeded or where no backlash is present. The BacklashL is an interval, which is centered on the point of zero displacement difference between the two connectors of the element i.e. the neutral position. Inside the backlash interval the element possesses a Stiffness of BacklashkL and a Damping of BacklashbL, which are different from the previously specified k and b and thus can be entered separately (see the figure below).
Ranges of validity for the parameters in the spring-damper-backlash
Thus a backlash, which occurs during a change from a tension to a compression load, can be modeled. When there is no reaction force inside the backlash interval i.e. a real backlash has to be modeled, then kL and bL must be set to zero.
|0.005 ... 0.01||for the damping in metallic materials|
|0.1 ... 0.25||for the damping in highly elastic materials|
|0.05 ... 0.15||for structural and contact damping|
(Source (German): Großmann, Knut: "Ein Beitrag zur Modellfindung und -berechnung für die dynamische Analyse von Werkzeugmaschinen-Strukturen". Technical University of Dresden, Faculty of Mechanical Science and Engineering, Dissertation A, Dresden 1976)
In this approach, is measured in the SI unit .
The element can behave as rigid when the stiffness and damping are deactivated. If rigid is true, the element models a rigid constraint or an end stop if backlash is defined.
The enumeration kindR contains the selection of rigid models:
- Without Backlash: The element has no backlash and behaves as a Constraint with dx==0
- Rigid Plastic: The element behaves as a rigid end stop with consideration of a plastic impact. The coefficient of restitution is ci = 0.
- Rigid Elastic: The element behaves as a rigid end stop with consideration of an elastic impact. The coefficient of restitution is ci = 1.
- Coefficient of Restitution: The element behaves as a rigid end stop with consideration of a plastic-elastic impact. The coefficient of restitution ci can be defined by the user: 0 <= ci <= 1.
The group Initial Values contains the enumerations kindPS and kindPD as well as (depending on their settings) the parameters dx0, dv0 and Fs0, Fd0 for the definition of an initial preload of the spring-damper element.
- The enumeration kindPS holds a selection of initial states of the spring:
- "No Preload or Preload from Environment": This is the default selection. The spring is initially unloaded or will be pre-loaded by the environmental conditions (i.e. initial values at the connections at ctr1 or ctr2).
- "Preload Displacement Difference": The spring is pre-loaded. This option activates the parameter dx0, the initial displacement difference.
- "Preload Force": The spring is pre-loaded. This option activates the parameter Fs0, the pre-load force.
- dx0 ... initial displacement difference of the spring
- The value of this parameter must be consistent with the initial values of the connections at ctr1 (-> x10) and ctr2 (-> x20):
dxSD0 == x10 - x20
To fulfill this constraint, it is recommend to unfix x10 or x20 (-> the corresponding initial values of the connections).
- Also the initial speeds must be consistent, because
dv0 = v10 - v20(initial velocity difference)
der(dx0) = dvand
dv = 0
- Fs0 ... the initial spring force or pre-load
- Here, dx0 will be computed internally by dx0 = Fs0/k taking the stiffness k into account.
- Note: Also here the initial values must be consistent (see above).
- The enumeration kindPD holds a selection of initial states of the damper:
- "No Preload or Preload from Environment": This is the default selection. The damper is initially unloaded or will be pre-loaded by the environmental conditions (i.e. initial values at the connections at ctr1 or ctr2).
- "Preload Velocity Difference": The damper is pre-loaded. This option activates the parameter dv0, the initial velocity difference.
- "Preload Force": The damper is pre-loaded. This option activates the parameter Fd0, the pre-load force.
- dv0 ... initial velocity difference of the damper
- The value of this parameter must be consistent with the initial values of the connections at ctr1 (-> v10) and ctr2 (-> v20):
dv0 == v10 - v20
To fulfill this constraint, it is recommend to unfix v10 or v20 (-> the corresponding initial values of the connections).
- Fd0 ... the initial damping force or pre-load
- Here, dv0 will be computed internally by
dv0 = Fd0/btaking the damping b into account.
- Note: Also here the initial values of the velocities must be consistent (see above).
If rigid=="true" and kindR<>"without Backlash" the element models a rigid end stop. In this case some further advanced parameters are offered to the user: eps_Fi and eps_dv, which are tolerance limits, and adv, which enables these tolerance limits. A detailed description can be found in the help of the End Stop element.
The parameter settings and extra results on tab Steady-State Simulation are documented in the section Special Properties of Model Elements, which is part of the description of the topic Periodic Steady-State Simulation.
If the element acts as damper kind=="Damper", then the switch onlyRelDamp appears. For a detailed description of the meaning of this switch, see chapter Damper, section "Steady State Analysis".
- The Internal Force Fi, the Spring Force Fs, and the Damper ForceFd are computed using the following formulas (see also the figure above):
- The Displacement Difference is the difference between the current displacements of the elements which are linked to the connectors ctr1 and ctr2:
- The Velocity Difference results from the speeds at the connectors:
- The Change of Potential Energy (power delivered to the spring) is computed with:
- The Power Loss (power dissipated in the damper) is:
- If rigid==true and kindR is set to "Without Backlash", the external power Pe is computed (Constraint behavior):
If this power is positive, the element acts as a power source, otherwise it consumes power.
If the element is switched to rigid and a backlash is considered, the element behaves as a rigid end stop. In this case the state variable stop can be analyzed. For a description of stop, see the help of the Stop element.
If, after a complete parameterization, the element is changed to a kind with less parameters e.g., from a Spring-Damper-Backlash to a Spring, the following simulation runs are, of course, performed with a reduced set of parameters. Nevertheless the disabled parameters continue to carry their last values. So, after changing back to the previous kind all hidden parameters are restored to their original values.
By entering a negative backlash a pre-tensioned system can be modeled. In the backlash interval, which becomes the pretension interval here, a twice as high stiffness and damping are obtained. Outside the interval stiffness and damping are as specified, see figure below.
Pre-tensioned spring with k = 1 Nm/mm, b = 1 Ns/mm, L = -1 mm.