Reliability Analysis Of Milling Processing System With Random Parameters

The dynamic instability in the process of milling caused by the vibration displacement delay feedback is regeneration chatter,which is a typical self-excited vibration.The occurrence of chatter can affect the surface quality of the machined parts,manufacture the excessive noise,aggravate the wear of the tool,and reduce the service life and the production efficiency of the tool.Therefore,it is especially important to study the problem of the chatter prediction in the milling process.In earlier times,the stability lobes diagram is the most widely used method of chatter prediction,which divides the plane of spindle speed-radial depth of cut into two regions that chatter and stability region,through the regions to determine whether the system is stable.The methods of obtaining the stability lobes diagram are mainly including oriented method,zeroth order approximation,semi-discretization method and full-discretization method.The parameters describing milling system are treated as certainty in the chatter prediction methods mentioned above.However,there are many uncertain factors in the actual process,including the system modal parameters,spindle speed,and cutting force coefficient.The steady boundary will change because of the uncertain parameters.So the chatter stability lobes diagram obtained by treating the uncertain parameters as certain values can’t accurately predict chatter.In this paper,the reliability theory is used to solve the chatter prediction matter of milling system with random parameters,and the main contents are as follows:a)The milling system model of two degree-of-freedoms is established in the paper,and the dynamic model of system is obtained.The four typical milling chatter prediction methods including oriented method,zeroth order approximation method,semi-discretization method and full-discretization method are reviewed in the paper.The stability lobes diagrams of milling system are draw by the four typical methods,and the results of four methods are compared and analyzed.b)Considering the chatter prediction problem of milling system with random parameters,the effects of the random parameters on the stability lobes diagram is discussed.Aiming at these effects,the reliability theory is adopted to solve chatter prediction matters of milling system with random parameters.Then,the milling system functions are obtained based on the oriented method and zero order approximation method,and the reliability models of system are established based on the reliability theory under two kinds of functions.c)Aiming at the reliability model of milling system obtained by the oriented method,the modal parameters of tool point and the inherent angular frequency are taken as the basic random variables obeying a certain distribution,the typical reliability calculation methods,including Monte-Carlo method,advanced first-order second-moment method and fourth-order moment method,are used to solve the reliability of milling system under different spindle speed and radial depth of cut.The reliability of the system is studied by the results,and the result of the three methods are compared and analyzed.The modal parameters of tool tip point of milling system are achieved by frequency response function test.d)By calculating the reliability of milling system in different spindle speed and radial depth of cut,connecting the corresponding points at the plane of spindle speed-radial depth of cut,the reliability lobes diagram of the milling system is obtained.Reliability lobes diagram is a new method to predict the chatter.The method can predict the chatter of milling system with random parameters,and the probability of chatter,ruling out the influence of random parameter.e)The sensitivity analysis of the milling system is carried on based on the advanced first-order and second-moment method and the fourth-order moment method.The performance function of milling system is obtained by oriented method,and the basic variables of the system obey the normal distribution.We can know the influence of basic variables to the reliability of system by solving the partial derivative of the system reliability to the distribution parameters of basic variables.When influence of a basic variable degree on the reliability of system is larger,the uncertainty of the variable must be into consideration when solve the reliability of system.Otherwise,the basic variable can be used as a deterministic.