Gear Stress Relief Hole Design And Interval Uncertainty Optimization

Gear is the key component of mechanical transmission system.Gear failure directly affects the normal operation of the transmission system.Reducing the bending stress and contact stress of the gear can effectively avoid or delay the occurrence of gear failure.Setting stress-relieving holes in the tooth and tooth root region is a method to reduce the bending stress and the contact stress,and the stress release performance is closely related to the position and size of the holes.If the position and size of the holes are not appropriate,it is very likely that the effect of stress release will not be achieved.Due to the existence of manufacturing error,the actual size of the stress-relieving holes are not exactly the same as the design size,which means the size of the holes are uncertain.In addition,in the actual process of gear transmission,the contact force and contact point position of gear pair also have a certain degree of uncertainty.When optimizing the design of stress-relieving holes,these two uncertain factors should be taken into account.(1)A design method of stress-relieving holes with straight notch shape is proposed.A total of three straight notch shaped stress-relieving holes are set in the tooth and tooth root region of the gear.Through the finite element software ANSYS,the static simulation of the gear with straight notch shaped stress-relieving holes and the gear without hole is carried out,the maximum bending stress?_F and the maximum contact stress?_H of the two gears are calculated,and the stress-relieving characteristics of the straight notch shaped holes are studied.This subject also uses the same method to study the stress-relieving characteristics of circular holes and elliptical holes.The simulation results show that the stress-relieving effect can be achieved by setting holes in these region.(2)An optimal design method of gear stress-relieving holes considering load and size uncertainty is proposed.Firstly,the Kriging approximate model is used to establish the relationship between?_F,?_H and the positioning and size parameters of the stress-relieving holes,and the torque of the driving wheel.Then the Sobol method is used to analyze the parameter sensitivity of the positioning and size parameters of the circular,elliptical and straight notch shaped stress-relieving holes and the driving wheel torque.The positioning and size parameters with high sensitivity of the stress-relieving holes and the driving wheel torque are described as interval variables,and the positioning and size parameters with low sensitivity of the stress-relieving holes are described as certain variables.A multi-objective optimization model is established to reduce the midpoint of maximum bending stress interval?_F~C,the midpoint of the maximum contact stress interval?_H~C and increase the tolerance evaluation index W.The maximum contact stress?_H was less than the allowable contact stress[?_H]and the maximum bending stress?_F was less than the allowable bending stress[?_F]as constraints.The Pareto solution of multi-objective optimization model is solved by GAPSO algorithm.After optimization,the midpoints of the maximum bending stress interval?_F~C and the maximum contact stress interval?_H~C are reduced,and the positioning and size parameters of stress-relieving holes,which are set as interval variables get appropriate tolerance range.(3)On the basis of static simulation analysis of the gear,the fatigue life with and without holes are simulated.Since most of the existing 45 steel stress-life curves(s-N curves)can only reflect the stress-fatigue life response in the range of high cycle fatigue without considering the impact of plastic strain on the fatigue life,this topic uses the local stress-strain method to calculate the gear fatigue life,calculates the fatigue parameters of Manson-Kefen equation based on the elastic modulus,tensile strength,yield strength and other information of gear material,and generates thes-N curve of gear material.The curve was imported into Workbench,and the fatigue life of the gears with and without holes are simulated.This subject also obtains thes-N curve of the gear material through the test method,and uses the same method to calculate the fatigue life of the gears with and without holes.The fatigue life simulation results show that setting stress-relieving holes can improve the contact fatigue life and bending fatigue life of the gears.