HuntCrossleyForce Class Reference

This class models the forces generated by simple point contacts, such as between two spheres, or a sphere and a half space. More...

#include <HuntCrossleyForce.h>

Inheritance diagram for HuntCrossleyForce:

List of all members.

Public Member Functions
	HuntCrossleyForce (GeneralForceSubsystem &forces, GeneralContactSubsystem &contacts, ContactSetIndex contactSet)
	Create a Hunt-Crossley contact model.
void	setBodyParameters (int bodyIndex, Real stiffness, Real dissipation, Real staticFriction, Real dynamicFriction, Real viscousFriction)
	Set the material parameters for a body in the contact set.
Real	getTransitionVelocity () const
	Get the transition velocity (vt) of the friction model.
void	setTransitionVelocity (Real v)
	Set the transition velocity (vt) of the friction model.
	SimTK_INSERT_DERIVED_HANDLE_DECLARATIONS (HuntCrossleyForce, HuntCrossleyForceImpl, Force)

Detailed Description

This class models the forces generated by simple point contacts, such as between two spheres, or a sphere and a half space.

This includes components for the normal restoring force, dissipation in the material, and surface friction. This force is only applied to point contacts. Other contacts, such as those involving triangle meshes, are ignored.

This class relies on a GeneralContactSubsystem to identify contacts, then applies forces to all contacts in a single contact set. To use it, do the following:

Add a GeneralContactSubsystem and GeneralForceSubsystem to a MultibodySystem.
Create a contact set within the GeneralContactSubsystem, and add ContactGeometry::Sphere and ContactGeometry::HalfSpace objects to it.
Add a HuntCrossleyForce to the GeneralForceSubsystem, and call setBodyParameters() on it once for each body in the contact set.

Normal Force Components

The force in the normal direction is based on a model due to Hunt & Crossley: K. H. Hunt and F. R. E. Crossley, "Coefficient of Restitution Interpreted as Damping in Vibroimpact," ASME Journal of Applied Mechanics, pp. 440-445, June 1975. This is a continuous model based on Hertz elastic contact theory, which correctly reproduces the empirically observed dependence on velocity of coefficient of restitution, where e=(1-cv) for (small) impact velocity v and a material property c with units 1/v. Note that c can be measured right off the coefficient of restitution-vs.-velocity curves: it is the absolute value of the slope at low velocities.

Given a collision between two spheres, or a sphere and a plane, we can generate a contact force from this equation f = kx^n(1 + 3/2 cv) where k is a stiffness constant incorporating material properties and geometry (to be defined below), x is penetration depth and v = dx/dt is penetration rate (positive during penetration and negative during rebound). Exponent n depends on the surface geometry. For Hertz contact where the geometry can be approximated by sphere (or sphere-plane) interactions, which is all we are currently handling here, n=3/2.

Stiffness k is defined in terms of the relative radius of curvature R and effective plane-strain modulus E, each of which is a combination of the description of the two individual contacting elements:

          R1*R2                                         E2^(2/3)
     R = -------,  E = (s1 * E1^(2/3))^(3/2),  s1= ------------------- 
         R1 + R2                                   E1^(2/3) + E2^(2/3)

c = c1*s1 + c2*(1-s1) k = (4/3) sqrt(R) E f = k x^(3/2) (1 + 3/2 c xdot) pe = 2/5 k x^(5/2) Also, we can calculate the contact patch radius a as a = sqrt(R*x)

In the above, E1 and E2 are the *plane strain* moduli. If you have instead Young's modulus Y1 and Poisson's ratio p1, then E1=Y1/(1-p1^2). The interface to this subsystem asks for E1 (pressure/strain) and c1 (1/velocity), and E2,c2 only.

Friction Force

The friction force is based on a model by Michael Hollars:

f = fn*[min(vs/vt,1)*(ud+2(us-ud)/(1+(vs/vt)^2))+uv*vs]

where fn is the normal force at the contact point, vs is the slip (tangential) velocity of the two bodies at the contact point, vt is a transition velocity (see below), and us, ud, and uv are the coefficients of static, dynamic, and viscous friction respectively. Each of the three friction coefficients is calculated based on the friction coefficients of the two bodies in contact:

u = 2*u1*u2/(u1+u2)

Because the friction force is a continuous function of the slip velocity, this model cannot represent stiction; as long as a tangential force is applied, the two bodies will move relative to each other. There will always be a nonzero drift, no matter how small the force is. The transition velocity vt acts as an upper limit on the drift velocity. By setting vt to a sufficiently small value, the drift velocity can be made arbitrarily small, at the cost of making the equations of motion very stiff. The default value of vt is 0.01.

Constructor & Destructor Documentation

HuntCrossleyForce	(	GeneralForceSubsystem &	forces,
		GeneralContactSubsystem &	contacts,
		ContactSetIndex	contactSet
	)

Create a Hunt-Crossley contact model.

Parameters:

	forces	the subsystem which will own this HuntCrossleyForce element
	contacts	the subsystem to which this contact model should be applied
	contactSet	the index of the contact set to which this contact model will be applied

Member Function Documentation

Real getTransitionVelocity ( ) const

Get the transition velocity (vt) of the friction model.

void setBodyParameters	(	int	bodyIndex,
		Real	stiffness,
		Real	dissipation,
		Real	staticFriction,
		Real	dynamicFriction,
		Real	viscousFriction
	)

Set the material parameters for a body in the contact set.

Parameters:

	bodyIndex	the index of the body within the contact set
	stiffness	the stiffness constant (k) for the body
	dissipation	the dissipation coefficient (c) for the body
	staticFriction	the coefficient of static friction (us) for the body
	dynamicFriction	the coefficient of dynamic friction (ud) for the body
	viscousFriction	the coefficient of viscous friction (uv) for the body

void setTransitionVelocity ( Real v )

Set the transition velocity (vt) of the friction model.

SimTK_INSERT_DERIVED_HANDLE_DECLARATIONS	(	HuntCrossleyForce	,
		HuntCrossleyForceImpl	,
		Force
	)

The documentation for this class was generated from the following file:

HuntCrossleyForce.h