What effect will differential slip have on linear bearings?

Linear bearings using ball or roller are usually chosen because they are able to withstand high loads with very low friction.But rolling elements(including linear bearings)are not frictionless.One of the factors that cause friction in linear bearings(along with characteristics such as surface roughness,elastic hysteresis and lubrication of materials)is a phenomenon called differential slip.

Under ideal conditions,the load-bearing ball of a linear bearing will experience point contact with the raceway.(Similarly,linear bearings using rollers experience linear contact between rollers and raceways.In reality,however,the ball(or roller)and raceway materials are slightly elastic and deform slightly under load,thus transforming point(or line)contacts into small elliptical regions.This small,concentrated load-bearing region generates Hertzian contact stress between the two surfaces,and the elliptical geometry of the contact region leads to differential slip.Although differential sliding does occur in bearings using cylindrical rollers,it is much smaller than bearings using ball bearings.

When a load is applied to the ball,the ball and raceway undergo some deformation,resulting in an elliptical contact area.

When the ball is rolling along the raceway,the velocity at any point in the contact area must be equal to the angular velocity of the bearing multiplied by the radius from that point to the Y-axis(the axis of ball rolling).But because the area of contact is elliptical,the radius from the Y-axis will vary at different points in the ellipse.For example,in the figure below,the radius from the Y-axis at points "a" and "b" is different from the radius from the Y-axis at points "c" and "d".

The central band of the contact region(theoretically)does not slip,while the outer band slips due to the larger radius or distance from the axis of rotation.

This means that various points along the contact area have different speeds,with the result that the ball does not roll as it travels along the raceway,but slides or slips.

Of course,not all points slip along the contact area.There is a radius at which non-slip rolling occurs.However,if the radius of any point to the Y-axis is greater or less than this value,the point will slip.In fact,the contact area can theoretically be divided into three "rolling bands,"with the inner band experiencing pure rolling and the two outer zones experiencing sliding.(In fact,some slippage does occur in the inner band,while some rolling occurs in the outer band.The higher the consistency between the ball and the raceway,the higher the overall slip.

Differential slip will lead to increased friction and heating,which will affect the performance of linear bearings.In the aspect of linear bearing design and construction,the bearing with Gothic arched raceway geometry has higher differential slip than that with circular arc geometry.This is because the Gothic arch geometry produces a relatively large difference in the area of contact between the rolling diameters of the ball.

For Gothic arch geometry,the ball's rolling diameter varies greatly,resulting in higher differential slip and therefore higher friction.

Differential slip also affects the preload that can be applied to bearings with Gothic arched raceway geometry,as the preload increases the contact area between the ball and raceway,thereby further increasing friction and heat generation.

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