Study On Cutting Stability Of Gear Shaping And Its Application

Gear shaping is an important and widely applied manufacturing process of spur gears.High processing efficiency is an eternally pursuing goal of the gear shaping technology.High speed cutting has great impact on the efficiency,Another way to further improve the efficiency is to tap the process potential by developing novel technique from the generating principle of gear shaping,such as the gear shaping technique with variational circular feed rate.Basically,cutting stability is the prerequisite of high efficient gear shaping.However,cutting stability studies of gear shaping are less mentioned and reported in references up to date.It is thus necessary to consummate the cutting stability research to support high efficient gear shaping.This thesis focuses on the cutting stability of gear shaping,to resolve the law of the cutting stability and to optimize the process of gear shaping.This will provide theoretical foundation for the application of high efficient gear shaping.The cutting stability of gear shaping is not suitable to directly test as the complexity of gear shaping and the limitation of technical specification of the gear shaper.A combination of gear shaping prototype and its similarity model is thus applied to study the stability.Dynamics equation and regenerative chatter model were set up.Stability lobes of gear shaping were predicted from the model.According to the dynamics equation of gear shaping,similarity criteria for gear shaping were deduced in terms of the similarity theory.On this base,the similarity model of gear shaping,i.e.,an interrupted turning test,was designed.The regenerative chatter feature and cutting stability of the interrupted turning(the similarity model)were obtained with theoretical modeling and experiments.The cutting stability of gear shaping(the prototype)was then deduced from that of the the interrupted turning.Based on the research of the cutting stability,process optimizing strategy and model were proposed for high efficient gear shaping via variational circular feed.Main contents and results of this thesis are as follows:Dynamics parameters of a process system are fundamental to its dynamics modeling and stability analysis.In terms of the mechanism of regenerative chatter and the modal test of a typical gear shaper(model YK5132),the radial feed direction was identified as that of the regenerative chatter in gear shaping.The dynamics parameters of the gear shaping process system in the direction of the regenerative chatter,including equivalent mass,damping ratio and stiffness,were also acquired with the modal test.Cutting force is essential to dynamics modeling and stability analysis of the process system.To model the cutting force of gear shaping,equivalent cutting width and equivalent cutting thickness in gear shaping were proposed.In a shaping stroke,the equivalent cutting width are defined as the length of contact curve between pinion cutter and gear workpice,whereas the equivalent cutting thickness are calculated from dividing the cutting area of gear shaping by the equivalent cutting width.With the help of geometric simulation of gear shaping,the cutting area,equivalent cutting width and equivalent cutting thickness corresponding to cutting position(or stroke number)were obtained in a shaping cycle(the period that the pinion cutter or the gear workpiece rotate an angular pitch).Further,a gear shaping experiment was carried out.Based on the experimental results,a cubic polynomial model of the cutting force was regressed with.The model represents the nonlinearity attribute of the cutting force respect to the equivalent cutting thickness,and thus guarantees the accuracy of regenerative chatter and cutting stability.Dynamic cutting force model of gear shaping was got based on cutting force model of gear shaping.Dynamics equation and regenerative chatter model were set up from the dynamics parameters and cutting force of the gear shaping process system.Stability lobes and optimal nominal cutting thickness of gear shaping were predicted from the model.The lobes present two high stable regions corresponding low stroke speed(less than 200 str/min,conventional gear shaping)and high stroke speed(2000–3000 str/min,high speed gear shaping),separately.The optimal equivalent nominal cutting thickness is resulted from the nonlinearity of the cutting force,and can be used to optimize the gear shaping process for high efficiency.To validate the above prediction on the cutting stability of gear shaping,similarity model test of gear shaping was designed and carried out.In order to design the similarity model test,similarity index equation for gear shaping were deduced based on the dynamics equation of gear shaping in terms of the equational analysis method in the similarity theory.Then the similarity model of gear shaping,i.e.,an interrupted turning test,was designed.Stability lobes of the similarity model(interrupted turning)were derived by solving its dynamics equation.The theoretical stability lobes were verified by the similarity model test.The cutting stability of the prototype(gear shaping)was deduced from that of the similarity model(interrupted turning).The deduced stability lobes fit well with the predicted ones from the dynamics equation of gear shaping.This represents that the stability lobes and conclusions of gear shaping in this work are reasonable and effective,which can be the foundation of process optimization of gear shaping.Based on the cutting stability lobes of gear shaping,two strategies were proposed for high efficient gear shaping via variational circular feed:(1)Constant cutting area strategy that applies to low speed(less than 200 str/min)conventional gear shaping,where the cutting area is determined via the rated working load of gear shaper and the strength limit of gear workpiece;(2)Constant nominal cutting thickness strategy that applies to high speed(2000–3000 str/min)gear shaping,where the nominal cutting thickness is the optimal nominal cutting thickness of corresponding stroke speed.Optimal models corresponding to the two strategies were put forward for efficiency improvement of gear shaping.The optimized circular feed schemes can increase the processing efficiency of gear shaping by 56% and 8.4% with the strategies of constant cutting area and constant nominal cutting thickness,separately.Gear shaping experiments validated the strategies and the optimal models.The proposed strategies are effective to improve the processing efficiency of gear shaping.