# Define the Friction

The friction torque resists rotation of the bodies relative to one another. The friction model supports stiction and sliding effects as well as a measured friction torque due to preload in the bushing.

The friction model is based on the LuGre model. Define the Friction Define the Friction
1. Click Activate to compute the friction torque for the bushing. When friction is active, MotionView adds to your model a control state equation and other elements that MotionSolve requires to compute the friction torque.
2. In the Mu-Static field, enter a positive real value giving the coefficient of static friction (μs).
3. In the Mu-Dynamics field, enter a positive real value giving the coefficient of dynamic (sliding) friction (μd). (μd) ≤ (μs).
4. For Transition Velocity, enter a positive real value giving the relative velocity ( ${\varsigma }_{s}$ ) on the surface of the ball at which the transition from static to dynamic (sliding) friction is complete (for example, μd). Units are length and time-1.
5. For Bristle Stiffness0), enter a positive real value for bristle stiffness. Unit is length-1.
The bristle stiffness along with the coefficient of friction (μ), ball radius (Rb) and normal force (N) determines effective torsion stiffness (Kt) of the friction: ${K}_{t}=\mu N{R}_{b}^{2}{\sigma }_{0}$
6. For Bristle Damping1), enter a positive real value giving the bristle damping coefficient of the Lugre model. The bristle damping coefficient acts on the rate-of-change of bristle deflection, which is an internal friction state dependent on the sliding velocity and bristle deflection. Units are time and length-1.
7. For Viscous Damping2), enter a positive real value giving the viscous damping coefficient of the Lugre model. The viscous damping coefficient acts on the sliding velocity. Units are time and length-1.
8. In the Torque Preload field, enter a positive real value giving the friction torque due to preload. This value is typically the friction torque measured in the bushing with no external loads applied to the bushing. The friction torque arises from preload (internal loads) created when manufacturing or installing the bushing. Units are force, length and time-1.
9. For Ball Radius, enter a positive real value for the ball radius(Rb). The friction model assumes that the bushing acts like a spherical joint and the friction arises at the contact point between the ball and socket. For a given normal force (N) in the bushing with all other parameters constant, increasing the ball radius also increases the friction torque. Unit is length.
10. Make a selection for Friction Effects.
11. Make a selection for Analysis Modes.
12. Select Use Reaction Force to force the bushing model to use the bushing force vector as the normal force when computing the friction torque.  Note that, due to preload, the resulting friction torque is never less than the friction torque.
C. Canudas De Wit, Associate, IEEE, H. Olsson, Student Member, IEEE, K. J. Åström, Fellow, IEEE, And P. Lischinsky. “A New Model For Control Of Systems With Friction.” IEEE Transactions On Automatic Control, Volume 40, NO. 3, March 1995: pp. 419-425. E. Velenis , P. Tsiotras , C. Canudas-De-Wit, “Extension Of The LuGre Dynamic Tire Friction Model To 2d Motion.” Proceedings Of The 10th Mediterranean Conference On Control And Automation. Med2002 Lisbon, Portugal,July 9-12, 2002.