Theory And Simulation Of Eccentric Lapping Of Ceramic Ball Preparation

Precision spheres are in wide demand in industries such as precision machine tools,precision instruments,and high-end equipment.For example,precision spheres are important components in precision measuring instruments such as roundness meters and gyroscopes,and are often used as benchmarks for precision measurement.Ceramic materials have the properties of low density,low thermal expansion coefficient,high thermal stability,high strength,high hardness,corrosion resistance,and good rolling fatigue resistance.These properties determine the broad application prospects of ceramic ball bearings.In the traditional lapping process of ball blank,people often rely on experience and lack scientific basis.In this way,the spheres processed by lapping will have difference in size,their accuracy can’t be guaranteed,and the cost of lapping is still high.Therefore,it is very necessary to establish scientific lapping theories to guide the lapping process of the ball blank.People have found that the eccentric lapping method has a good ball forming effect in the actual ball blank lapping process,and it is a promising method for lapping the ball blank in bulk、high-precision and low-cost.In this paper,an eccentric lapping model is established to explain the ball formation process of the eccentric lapping method,so as to guide people to use the eccentric lapping method to prepare high-precision spheres more reasonably.In this paper,a non-slip eccentric lapping model is established.Based on this model,it is found that under the condition of no-slip,the eccentric lapping method produces three rounds on the surface of the ball blank,which is inconsistent with the better ball forming effect of the eccentric lapping method,which reveals the irrationality of using a non-slip eccentric lapping model to explain the process of ball forming of the eccentric lapping.The lapping trajectory of the ball blank is an important reference for evaluating the lapping uniformity of the ball blank.Based on a rational basis,this article uses a strict mathematical description to give a calculation method for the lapping trajectory of the ball blank,and design a simple case to prove the correctness of the calculation method of the lapping trajectory.This verification case also provides a template to verify the correctness of various lapping trajectory calculation methods.In order to describe the lapping uniformity of the ball blank,two indicators,the variation coefficient of the number of grid lapping times and the area coverage of the ball blank are proposed as evaluation criteria,and the visualization of the evaluation of the lapping uniformity of the ball blank is realized in the form of cloud diagrams.The visualization method can make a more scientific evaluation of the rationality of the lapping method.In order to explain the ball formation process of the eccentric lapping method,this paper established a slip eccentric lapping model and a micro-slip groove-changing eccentric lapping model.For the slipping eccentric lapping model,with the increase of the slip distribution coefficient(slip effect),the range of the angle of the rotation axis of the ball blank becomes wider and wider,and the lapping trajectory on the ball surface gradually spreads over the spherical surface and presents a trend of random distribution.The lapping uniformity of the ball blank is getting better and better;for the micro-slip groove-changing eccentric lapping model,the lapping trajectories on the surface of the ball blank are three annular belts.As the number of groove-changes increases,the annular belt also increases and distributes on the surface of the ball blank without repetition,so that the surface of the ball blank can gradually cover the lapping trajectory.In addition,due to the random orientation of the ball blank,the lapping uniformity of the ball blank is gradually improving with the increase of the number of groove-changes.Finally,combining the slipping effect and the groove-changing mode,this article gives an explanation of the ball formation process of the eccentric lapping method.The ball blank may have a large slip effect or a micro-slip effect in the lapping process,but there is a high probability that the micro-slip effect occurs,and a large slip effect rarely occurs.There are two reasons for the obvious change in the orientation(the angle of the rotation axis)of the ball blank.One is the groove-changing mode,and the other is the greater slip effect.Once either of these two factors appears during the lapping process,the angle of the rotation axis of the ball blank will change,and the lapping trajectory on the surface of the ball blank can be diffused.The orientation of the ball blank is constantly changing during the lapping process,which finally generates lapping trajectories all over the surface of the ball blank.As the lapping process continues,the lapping uniformity of the ball blank is gradually improved.Finally,the ball blank is to be ground into a ball.