Elastic hysteresis: When a rigid ball rolls on a viscoelastic plane, due to the asymmetric deformation of the compression zone and the reverse relaxation zone, the elastic contact force is unbalanced, forming a resistance moment for the ball to roll.

Plastic deformation: A rigid ball rolls along a plastic plane. Under the combined action of compressive stress and shear stress, the contact plane undergoes plastic deformation, and the deformation resistance of the contact plane produces a tangential reaction that hinders the rolling of the ball and a normal reaction to the eccentricity, forming rolling friction.

Interfacial Adhesion: Chemical and physical adsorption occurs on solid surfaces, resulting in frictional resistance for rolling balls.

Interface micro-slip: There are three main cases of interface micro-slip;

1. Elasticity is slightly slippery. When a rigid sphere rolls on an elastic plane, due to the different elastic moduli of the material of the sphere and the contact surface, the translational distance of each revolution of the sphere is less than its circumference.

2. the geometry is slightly slippery. As the sphere rolls within the raceway, the contact area is the elliptical surface on the sphere. If the arc radius of the raceway is very close to that of the sphere, the major and minor axes of the ellipse surface are relatively large, and there is a long contact arc on the plane perpendicular to the rolling direction, the linear velocity of each point on the contact arc is different, and there are only two symmetrical points. It is an instantaneous turn of the center, and there are different degrees of micro-slip on both sides of the two points.

3. The traction is slightly slippery. When the normal force and the external moment act together on the sphere, the contact area of the sphere on the plane will be affected by static friction, which is provided by the adhesion area and the micro-slip area on the contact surface.

In a ball screw pair, the elastic modulus of the ball and the raceway are equivalent, so the elastic micro-slip between the ball and the raceway is not considered. Geometric micro-slip is the main cause of rolling resistance of balls rolling in the raceway. At the same time, considering the elastic deformation of the contact surface between the ball and the raceway under the action of the preload of the ball screw pair. Therefore, according to the superposition principle, the dynamic preload torque in the ball screw pair can be composed of the friction resistance torque caused by elastic deformation, the ball spin resistance torque, the friction resistance torque caused by geometric sliding, and the ball resistance torque generated by the loop return device .