Tham khảo tài liệu 'nano - and micro eelectromechanical systems - . lyshevski part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | phenomenon that is difficult to model. The classical Coulomb friction is a retarding frictional force for translational motion or torque for rotational motion that changes its sign with the reversal of the direction of motion and the amplitude of the frictional force or torque are constant. For translational and rotational motions the Coulomb friction force and torque are X dx Coulomb kFc sgn v k sgnl è dt 0 TCoulomb kTc sgn w kTc sgn dq I è dt 0 where kFc and kTc are the Coulomb friction coefficients. Figure illustrates the Coulomb friction. F T 1 Coulomb 1 Coulomb kFc kTc kFc kTc dx dỡ v w dt dt F Static T Static Ft- Tt - F_. - T_. 1 St - 1 St dx dỡ v w dt dt a c Figure . Functional representations of a Coulomb friction b viscous friction c static friction Viscous friction is a retarding force or torque that is a linear function of linear or angular velocity. The viscous friction force and torque versus linear and angular velocities are shown in Figure . The following expressions are commonly used to model the viscous friction dx Fỵi B v B for translational motion viscous v v dt and Tv. s B w B . - for rotational motion viscous m m dt where Bv and Bm are the viscous friction coefficients. The static friction exists only when the body is stationary and vanishes as motion begins. The static friction is a force FStatic or torque TStatic and we have the following expressions Fstatic Fst v dL 0 dt and Tstatic Tst w de 0. dt 2001 by CRC Press LLC One concludes that the static friction is a retarding force or torque that tends to prevent the initial translational or rotational motion at the beginning see Figure . In general the friction force and torque are nonlinear functions that must be modeled using frictional memory presliding conditions etc. The empirical formulas commonly used to express Fstatic and Tstatic are Ffr f - kfr2e kfr3 v sgn vt -kỉx kri - kr2e dt kfr 3 dx dt and kfr3 de dt Tfr kfri k ra kfr3 ffl sgn f -k de kf-i - .
