The maths that centrifugal force affects to turning machining error is analysed

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Summary: From mathematical angle centrifugal force is opposite the round influence outside turning undertook an analysis, the round dimension outside thinking it won't be affected and appearance. In turning treatment, especially when high speed turning, because high speed rotates of the spare parts lopsided, inevitable meeting produces centrifugal power, analysis and understanding leave mental efforts is the problem that people often pays close attention to to the influence of machining error. Integrated all sorts of conclusion, have two kinds of different views commonly. One of, think centrifugal force can make the circle outside workpiece produces on size error, namely radius error: Another kind of view thinks to meet the round appearance error outside the influence. The article undertakes an analysis to this problem from mathematical angle, offer the view that differs completely with afore-mentioned conclusion. The mathematical expression of 1 centrifugal force and its analysis set the W that be by the gravity of treatment workpiece, the rotate speed of lathe main shaft is N, lopsided quality M arrives rotate central distance is R, leave mental efforts FQ to be: FQ=mrw2=Wr(2pn)2g60(1) sets machining complex stiffness to be KXT, the deflection that issues main shaft axes in the action of centrifugal force measures Ar to be: Ar=Fo/KXT(2) because the direction of FQ is constant change, what it is us to answer to study through building coordinate to fasten its change the rule. If attached drawing place is shown, build YOZ of world coordinate system, o chooses the ideal axle center that gives priority to an axis, and hypothesis main shaft does not have circumgyrate error. Because leave the action of mental efforts, make the O1(yo1 of actual circumgyrate axes of main shaft, zo1) rotates with W of main shaft angular velocity inside YOZ plane change, we are built with O1 instantaneous axes move coordinate system VO1W, the mathematical expression that the axes of main shaft instantaneous that causes from mental efforts changes is: The F in {yo1=Arcoswt=Arcosfzo1=Arsinwt=Arsinf(3) type is the instantaneous corner of centrifugal force. All of world coordinate system and move the coordinate between coordinate system to alternate relation is: (When Y)=(yo1)+(cosf-sinf)(V)zzo1sinfcosfw(4)(v)=(y-yo1)(cosfsinf)wz-zo1-sinfcosf(5) turning is machined, because add workpiece,rotate together along with main shaft, accordingly, the geometrical appearance of workpiece cross section is formed in moving coordinate to fasten by cutting tool relative to orbit. Set cutting tool to be in the coordinate position in world coordinate system: The R in {y=rz=0(6) type machines radius for workpiece. type (6) and type (5) type generation enters type (5) gets: {v=(r-Arcosf)cosf-Arsin2f=rcosf-Arw=(r-Arcosf)(-sin F)-Arsinfcosf=rsinf(7) by type (7) can get: (V+Ar)2+w2=r2(8) attached drawing by type (8) can see apparently, by the circle that the cross section of treatment workpiece remains radius to be R, without on size error of any appearance sum of errors, the centre of a circle that is this circle only locates relatively fiducial O deflection the distance of Ar, consequently generation coaxial spends an error between treatment surface and fixed position tool reference plane. When 2 conclusion turning is machined, because workpiece is lopsided,the centrifugal force of generation won't cause the on size error that processes a face and appearance error, the coaxial that can create treatment face and fixed position area only spends an error, its coaxial spends the deflection Ar that the error causes for centrifugal force. When measuring the dimension that machines the surface and appearance, should choose correctly to measure fiducial. Dimension should measure a diameter, if want to measure,radius is mixed outside circular shape, be about to press include the principle is measured certainly fiducial. Centrifugal force can cause the vibration of machining complex, the influence machines exterior quality and coaxial to spend an error, answer treatment workpiece quality is lopsided adopt technology measure to give limitation. The circle outside the turning when afore-mentioned conclusion apply to odd dial to drive workpiece to rotate likewise (the circle outside grinding) circumstance. CNC Milling CNC Machining