Ch3 Contact Stiffness
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Advanced Contact Training Manual 3. Contact Stiffness
Transcript of Ch3 Contact Stiffness
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3. Contact Stiffness
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Contact Stiffness
A. Basic Concepts
Review:
• Recall that all ANSYS contact elements use a penalty stiffness (contact stiffness) to help enforce compatibility at the contact interface.
• Some finite amount of penetration, , is required mathematically to maintain equilibrium.
• However, physical contacting bodies do not interpenetrate ( = 0).
The contact spring will deflect an amount , such that equilibrium is satisfied:
F = k where k is the contact stiffness.
F
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Contact Stiffness
... Basic Concepts
• As an analyst, you face a dilemma:
– Minimum penetration gives best accuracy.
• Therefore, the contact stiffness should be very great.
– However, too stiff a value causes convergence difficulties.
• The model can oscillate, with contacting surfaces bouncing off of each other.
Iteration n Iteration n+1
F
F
FcontactF
Iteration n+2
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Contact Stiffness
... Basic Concepts
• The contact stiffness is the most important parameter affecting both accuracy and convergence behavior.
• You must carefully determine an appropriate value for contact stiffness.
– Balance the convergence efficiency against the required level of accuracy.
– The “best” value is problem dependent, and must often be determined by trial-and-error.
• Estimate a trial value to use, then examine the convergence behavior and accuracy.
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Contact Stiffness
B. Determining a value
• Frequently, you can estimate a good value for the contact stiffness as a function of the relative stiffness of the areas in contact.
• The stiffness of a bulky solid will generally be greater than that of a springy, bending-dominated structure. The contact stiffness will typically be correspondingly greater for bulky solid structures.
– Examples of bulky contact include metal forging, wheel-on-rail, pin in a bearing block, etc.
– Examples of bending-dominated contact include leaf springs, sheet metal forming, etc.
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Contact Stiffness
... Determining a value
• For bulky solids, the Hertz contact stiffness often provides an appropriate basis for the penalty stiffness. This stiffness can be estimated from the element size and Young’s modulus.
• For a uniformly-shaped 3D element, the Hertz stiffness would be approximately kHertz a x E, where a is the characteristic element size, and E is the Young’s modulus.
• For 2D elements with thickness (t), Hertz stiffness would be approximately kHertz t x E.
– For 2D axisymmetric elements, the “thickness” is 1 radian x r, giving a Hertz stiffness of approximately kHertz r x E.
a
a
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a
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Contact Stiffness
... Determining a value
• As a practical matter, a good first trial value for bulky contact stiffness would be kcontact = fbulk x kHertz, where fbulk is a factor usually between 0.1 and 10 for bulky solids.
– Because the starting estimated value of fbulk ranges over at least two orders of magnitude, and because kcontact will be adjusted by trial-and-error anyway, it is usually not justifiable to worry about the element’s size when estimating the penalty stiffness.
• For bulky solids, simply estimate the penalty stiffness by
k = fbulk x E
– where the factor fbulk is usually between 0.1 and 10, and a good starting value for fbulk is often fbulk = 1.0.
– This estimate assumes an approximate “unit” element size; for very large or very small elements, you might need to adjust the starting value of fbulk accordingly.
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Contact Stiffness
... Determining a value
• If your contact involves two different materials, use E of the softer contacting material.
• Account for the reduced tangent modulus if plasticity will be active.
• For Mooney-Rivlin hyperelastic materials, the material law does not use a value of E. You will therefore have to estimate E for such materials.
– You can simply scale a modulus value from the appropriate portion of the stress-strain curve.
– Or, estimate an initial modulus by E = 6(a + b) where a and b are the first two Mooney-Rivlin constants.
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Contact Stiffness
... Determining a value
• For flexible components (beam-like and shell-like models) the stiffness of the system may be much lower than the Hertz contact stiffness.
• In this situation you might run a static analysis with a unit load applied to the expected area of contact to determine the local stiffness of the model. The contact stiffness can then be estimated from:
k = fbend(P/)
• where P is the applied unit load, is the corresponding deflection, and for flexible body contact, fbend is a factor between 1 and 100. Setting fbend = 1 is usually a good starting value.
• For practical simplicity, you might merely estimate the contact stiffness by:
k = fbend x E/10
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Contact Stiffness
... Determining a value
• In addition to transmitting normal action (pressure) between surfaces, contact elements also transmit tangential action (friction).
• The contact elements use a tangential penalty stiffness to enforce compatibility in the tangential direction.
Ftangent
Ftangent = ktangent
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Contact Stiffness
... Determining a value
• The tangential penalty stiffness affects convergence and accuracy in exactly the same way as the normal penalty stiffness.
– Too soft a value leads to inaccurate results.
– Too stiff a value causes convergence difficulties.
– A “best” value should be determined by trial-and-error.
• As a starting estimate, try using
ktangent = 0.01 knormal
– This is the default value for most ANSYS contact elements.
• Of course, the tangent stress is limited by the value at which
sliding occurs: xp– Friction is discussed in the next chapter.
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Contact Stiffness
... Determining a value
• For node-to-node and node-to-surface elements, you specify the value of penalty stiffness directly, in units of Force/Length.
– For variable mesh densities, the overall surface stiffness will be greater where the mesh is denser, and will be less where the mesh is coarser.
• This could lead to uneven contact pressures.
(Surfaces shown separated for clarity)
F
Stiffer at dense meshSofter at coarse mesh
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Contact Stiffness
... Determining a value
• For surface-to-surface elements, you specify the penalty stiffness as a factor to be applied to a function of the underlying element stiffness.
– Alternatively, you can specify an absolute stiffness value, in units of (Force/Length)/Area.
– Because stiffness is specified per unit area, the overall surface stiffness varies much less with varying mesh density.
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Contact Stiffness
... Determining a value
• Determining a good stiffness value usually requires some experimentation. The following procedure may be used as a guideline:– 1. Use a low value of stiffness to start.
– 2. Run the analysis to a fraction of the final load.
– 3. Check the penetration and number of equilibrium iterations used in each substep.
• As a rough, quick check, if you can visually detect penetration in a true-scale displaced plot of the entire model, the penetration is probably excessive. Increase the stiffness and restart.
• If many iterations are needed for convergence (or if convergence is never achieved), reduce the stiffness and restart.
– Note: Penalty stiffness can be modified from one load step to another, and can be adjusted in a restart.
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Contact Stiffness
... Determining a value
• Remember: The contact stiffness is the most important parameter affecting both accuracy and convergence behavior.
– If you can fully grasp this idea, you will be able to master most contact difficulties!
• If you are having convergence problems, reduce the stiffness value, and rerun.
• You should also verify the validity of your results by varying the penalty stiffness value in a sensitivity study.
– Tighten the stiffness in successive analyses, until important results items (contact pressure, max. SEQV, etc.) cease to change significantly.
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Contact Stiffness
... Determining a value
… contact stiffness
• As an example, FKN was varied for an interference-fit analysis of a collar on a shaft. Maximum equivalent von Mises stress was monitored.
• In this particular case, a value of FKN = 1.0 proved to give adequate accuracy.
FKN Max. SEQV0.001 4,0000.01 20,0000.1 65,0001 91,000
10 92,900100 93,000
