| 5-axis CNC machining has an unparalleled advantage of bringing in flexibletool-workpiece inclination angles and cutting edge contact point, especially for thecomponent of high-overlapped structures and complex free form surface. Therefore,5-axis CNC machining technology is widely used in machining high-value-addedproduct with complex surface such as mold, impeller as well as thin-walled parts inaerospace industry. However, milling chatter as well as its dynamic surface locationerror is often excited by improper milling parameters so that additional polishingprocess has to be involved, which extremely limits the improvement of productsurface quality and production efficiency. How to avoid the baneful influence ofchatter is becoming one of the most challenging targets in5-axis CNC millingfinishing.As the chip thickness regeneration effect produced on the prior and rear chipsurface is the main reason for milling chatter. Provided that the chip wave producedby the regeneration effect has phase difference with the fluctuant cutting force,milling system would probably absorb energy from cutting force and enlarge itsoscillation amplitude until chatter excited. In order to predict the chatter behavior, it isnecessary to a clearly describe the feedback effect of chip regeneration. As for5-axisball end milling, the regeneration chip wave is located on a3D chip surface withirregular shape and non-uniform chip thickness. It is a key theme to accuratelydescribe the space-time specialty about how chip thickness wave can be formed howthe regeneration effect that happens somewhere at some certain time can feed back themilling dynamics of5-axis ball-end finishing process, and how it can influence thestable milling parameters and dynamic surface location errors. Therefore, this paperwill focus on this topic with the main contents as follow:First, an accurate chip geometry modeling method is proposed for freeformsurface finishing. When the ball-end cutter is adopted in complex surface5-axismachining, the trajectory of cutting edge is a time-varying3D space curve. Thatendows the corresponding chip a significant connection between time and location,especially for the finish milling condition when low cutting depth and low cross feedare involved in and the chip shape becomes more sensitive to the detail trajectory ofcutting edge. However, the traditional chip thickness modeling methods withhemisphere path assumption and sine product assumption would result in moreprinciple error in determining chip geometry and have no idea about how to describethe time delay between the time the adjacent cutting edges pass by the two corresponding points on prior chip surface and the rear chip surface respectively.Therefore, based on the actual3D trochoidal tooth trajectory (3D3T) and the3D spacetransformation mechanism, an instantaneous time-space mapping relationship is builtto describe the varying time-delay parameter in5-axis machining. Thereby, anaccurate chip thickness model is proposed for finish process in5-axis ball-end millingwith the combination of the3D3T chip thickness model and the engagement boundaryeffect on chip thickness (EBCT).Second, the modeling and simulation methods are investigated for chipregeneration effect in5-axis ball-end milling dynamics as well as the characterizationmethod for surface machined with chatter. Using the accurate model of chip thicknessand varying delay time, the feedback mechanism of chip thickness regeneration isconstructed and thereafter a dual-flexible milling dynamic system is modeled with theconsideration of flexibilities on the tool system and the work system. With thediscretization of varying time-delay parameter, the effects of regenerative chipthickness as well as system oscillation is simulated for the ball-end finish millingsystem containing tool inclination angles. Based on the time details when the cuttingedge create the machined surface, the system dynamic response with the same timedetails is adopted to rebuild the machined surface profile. By applying themorphology method on the machined surface pattern, a kind of chattercharacterization method is proposed based on the distribution of residual height andthe connection feature. Through the chatter excitation test with a continue-varyingcutting depth, the proposed milling dynamic model and its simulation method havebeen validated.Third, a prognosis method of milling stability is proposed for5-axis ball-endfinish milling with varying time delay. Based on the accurate chip thickness model,the sensitivity factors of chip thicknesses are derived with respect to the vibrationdisplacement so that the nonlinear dynamic chip thickness and cutting force can belinearized. Focusing on how to deal with the varying time delay in constructingperiodic transfer matrix, a directly constructing method is proposed first to transferthe state variable set of time delay term to the state variable set that just happened aperiod ago. Thereby, the periodic transfer matrix from the state variable set with aperiod ahead to the current state variable set is constructed. Thus, Floquet theory isadopted to predict milling stability. In addition, the steady oscillation trajectory ismodeled as well. Validations indicate that the varying-time-delay based prognosismethod is capable of catching the left-offset effect of stability lobes in down millingcondition and right-offset effect in up milling.Fourth, chatter-free optimization strategies and methodologies are implementedfor two milling process applications based on the proposed milling dynamic modeland the stability prognosis method. At first, a new cutting force calibration method isproposed to calibrate the coefficient of cutting force with the variation of local chipthickness and cutting edge segment location. In order to traverse all the cutting edgesegments of ball part, a cylinder surface milling process is adopted with thecombination of low cutting depth and varying lead angle to replace the traditionalfull-ball-immersed method. Because the cutting depth is kept to be a constant low value, chatter risk for the traditional calibration method can be avoided. In addition,taking the axial-flow blade5-axis ball-end finish milling as an example, a modifiedgenetic algorithm is proposed accompanying with a range-internal fitness evaluationoperator. Then, milling stability prognosis method is combined with the geometricprogramming function in CAM software, which forms the5-axis process optimizationstrategy on the milling stability and the surface location error.In summary, focusing on how to predict chatter behavior to control the machinedsurface quality, the actual3D3T of cutting edge is modeled, therefore, the nominalchip shape is constructed as well as the varying time delay between the two adjacentcutting edges passed by the corresponding points on the prior and rear chip surfaces.Thereby, the varying time delay feedback of chip thickness regeneration is welldescribed and a nonlinear time varying dynamic system is established. Then, a millingstability prognostic method is proposed to improve the predict accuracy whenball-end5-axis finish milling condition is involved with the distinguishedcharacteristics of varying time-delay. In the end, a chatter free optimization strategy ispresented for ball-end5-axis milling process. |
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