Study On Thermal Contact Resistance Model Of Ball Screws Considering The Load Distribution Of Balls

The model of thermal contact resistance of ball screws is the dominating issue of determining the temperature distribution of ball screws.In the previous studies,the load on balls is considered to be uniform in the model of thermal contact resistance of ball screws.In order to determine the thermal contact resistance of ball screws accurately,a new analytical method for model of thermal contact resistance of ball screws considering uneven load distribution of balls is proposed.It has been conducted deeply,and the main research contents as follows:Firstly,the model of load on balls of ball screws is established.Based on Hertz contact theory,the contact deformation of ball screws is obtained.According to the balance of force and the coordination of deformation,the model of load on balls of ball screws is established.The load distribution on balls of ball screws is solved by the method of dichotomy and iteration.The results show that the load on balls near the spacer is larger than that far away from the spacer in double-nut ball screws only objected to preload,and the larger the preload is,the larger the load on balls is.Secondly,the model of thermal contact resistance of ball screws is established.Considering the load distribution of balls,the model of thermal contact resistance of ball screws is obtained by using the minimum excess principle and MB fractal theory.The modeling of thermal contact resistance of the ball screws is experimentally validated.On the one hand,the modeling of thermal contact resistance of the ball screws only objected to preload is experimentally studied to verify the effectiveness of this modeling.In order to decrease the heat change between the interface and the air,the internal gap of the ball screws is filled with liquid aerogels,and aerogels are coated on them.The error between the experimental results and the theoretical results is 10.34%,and the error between the experimental results and the theoretical results of the previous research method is 15.54%.The comparison of results shows that this method is an effective method to solve the thermal contact resistance of ball screws.On the other hand,the thermal contact resistance of ball screws under working condition is also tested,and the model of thermal contact resistance is further verified.Thirdly,the effects of axial load,axial pretension and nut position on the load distribution on balls and the thermal contact resistance of ball screws are discussed.The results show that with the increase of axial load,the load on balls of the left nut increases,while for the right nut,the load on balls decreases with the increase of axial load.It is concluded that thermal contact resistance of ball screws increases along with axial load increase.The load on balls all decreases with axial pretension increase,and the thermal contact resistance of ball screws decreases with the axial pretensionincrease as well.When the axial load is applied on the nut in an axial-pretension ball screw,the load distribution in Nut A or B becomes less homogenized when the nut moves from ?=0 to ?=1.When the nut moves to ?=0.25,the thermal contact resistance will reach a minimum value,and it gets a maximum value at the nut position ?=1.Finally,the influence of ball machining error on thermal contact resistance of ball screws is discussed.A non-probabilistic interval analysis method is proposed to predict the range of the load distribution of ball and the thermal contact resistance.Taking the radius of balls as the uncertainty,the range of load distribution of balls and the thermal contact resistance of ball screws under different machining errors is obtained by uncertainty analysis.The results show that when the machining error is small,the geometric error of the balls has little effect on the load distribution and thermal contact resistance of the ball screws,and theoretically,when the machining error increases,the geometric error of the balls has a greater influence on the load distribution and thermal contact resistance of the ball which is far away from the spacer.This method provides a new way to evaluate the load distribution on balls and thermal contact resistance of ball screws.