Blade of empty axis broach grinds accident to use the research of equation

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Summary: Stated with vector blade of empty axis broach grinds the basic structure of machine, get pointed grinding parameter according to taper seat, use vector commutation derivation the athletic equation that grinds taper seat to get a tip in the blade on empty axis machine tool, beg a lever to grow vector then, regard a machine tool as athletic pilot basis. The empty axis machine tool that 90 time metaphase appears caused 0 preface the attention of whole and mechanical manufacturing industry, be called to be " this century machine tool designs first revolutionary change " . This kind of machine tool is actual it is linkage mechanism of paralell connection of a kind of space, its are basic the structure is an an activity platform, fixed platform and join 6 connecting rod of two platform. Change the length of 6 lever ceaselessly, mobile platform produces the spatial motion that 6 freedom spend, drive cutting tool to give complex three-dimensional curved surface in the treatment on workpiece. Compare with photograph of traditional machine tool, empty axis machine tool has tigidity rate of tall, motion mixes tall, precision high rigid structure is simple wait for an advantage, but its insufficient place is the traditional machine tool that working space is less than coequal dimension. Face of the knife after twist drill is complex three-dimensional curved surface, and blade is ground very little work space needs only when getting a tip, grinding the structure that empty axis machine tool uses on machine in broach blade so will be very appropriate. The article will be right the blade on machine is ground to grind taper seat to get a needle to undertake discussing in blade of empty axis broach. The vector of structure of 1 machine tool states broach blade grinds confidential to make broach opposite generation of Yu Sha annulus is given three-dimensional motion, get on broach installation in mobile platform for this, emery wheel installation is on fixed platform. Coordinate is built to fasten OBxByBzB on fixed platform, coordinate is built to fasten OPxPyPzP(graph 1) on mobile platform. Each lever uses vector Li(i=1, 2, ... , 6) expresses, each lever and the position that secure platform node use vector Bi(i=1, 2, ... , 6) expresses, each lever and the position with mobile nodical platform use vector Pi(i=1, 2, ... , 6) expresses, emery wheel center uses vector H high to express, the radius that emery wheel center nods to grinding expresses with vector R, the broach that be ground is dangerous extend a ministry to express with vector D (graph 1) . In give a structure to fall, bi is with Pi inside OBxByBzB coordinate department inside OPxPyPzP coordinate department measure for Chang Shi respectively, write down for BiB and PiP. When the 2 cone that get a tip worry the bit of cone of grinding parameter grinding of the law, the initiative and relative position of cone, broach, emery wheel sees a picture 2, the parameter that dominates this one opposite niche calls grinding parameter. Cone gets pointed grinding parameter to have 5, among them the half cone angle that Q is cone, b is broach advocate cutting blade is carried in broach sectional inside umbriferous with XP axis included angle, f is awl axes and ZB axis included angle, what H supports to get pointed topmost distance to go up in awl axis for awl is umbriferous, d1 is the distance of awl axes and broach axes. Graph the vector of structure of 1 machine tool represents an attempt the 2 cone that get a tip grind law principle graph to pursue 2 in ′ of Z of ′ of Y of ′ of O ′ X is cone coordinate is, z ′ is awl axis. Cone is in the equation in department of coordinate of ′ of Z of ′ of Y of ′ of O ′ X is 2tg2q=0(1)Oxyz of ′ of 2-z of ′ of X ′ 2+y fasten for broach coordinate, the translation that uses coordinate and rotate attainable cone is in the equation in Oxyz coordinate department (2) type 2 gave out the relation between grinding parameter Q, B, F, H, D1, optional among them 4, can beg give the 5th. Reason cone filing has 4 independent grinding parameter. Q, F, H, D1 all was recommended to regard independent grinding as parameter in a few document, need to use 4 independent equation to beg. These equation are actual the relation that is broach geometry parameter and grinding parameter, to given if broach geometry parameter is  of half vertex angle, horizontal Afc of the horn after blade bevel Y, structure is circumferential, can receive corresponding expression, beg the grinding parameter that gives 4 independence thereby, next by type 2 beg a parameter of the 5th grinding. This one process all has the introduction in a lot of document, here no longer give uncecessary details. When the 3 cone that get a tip grind the athletic equation blade of the law, adjust broach according to 5 grinding parameter first initiative position, namely advocate generatrix of the cylinder outside emery wheel of cutting blade contact, broach axes and cone axes are in dimensional phase is complex, the distance is D1. Linear QQ ′ is the official vertical line of 2 axes, hang down sufficient it is Q and Q ′ respectively (graph 2) . Axes of the broach when blade is ground circles cone axes to rotate, q spot position is changeless, 2 axes included angle is F from beginning to end. It is facilitating derivation, intermediate coordinate is built to fasten O*x*y*z* on awl axis, origin O* and O nod coincide, z* and awl gross ril load close, y* is parallel at YB, if the graph is shown 2 times,X* is decided by right hand formula. O* fastens medium position to be able to decide TCB=(-bcos(q+f) by diameter arrow TCB in OBxByBzB, 0, the B=Htgq/sinf(4) in Bsin(q+f)+h+r)T (3) type, h, d1, q -- the way that affirmatory already grinding parameter ties inside O*x*y*z* department in the OPxPyPzP when blade grinds initiative position can be decided by matrix RPC0 (when 5) uses cone law to worry bit, ZP axis circles Z* to rotate, corner is - R, r calls athletic variable. According to width of valve of twist drill blade, the limits of R is 0 ° ～ about 100 ° . The directional matrix that the OPxPyPzP after roll fastens inside O*x*y*z* department turns into (the RzC(-r) in 6) type -- the axis that circle Z* turns - of R angle rotate matrix OP dot fastens medium seat in O*x*y*z* TPC of usable diameter arrow expresses, in the TPC0=(asinf when initiative position, - D1, acosf)T by the graph 2 reach form 4 visible A=d-b=d-Htgq/sinf circle Z* axis to turn - after R angle (7) is ° of  ′ =90 as a result of included angle of Z* axis and ZB axis - Q, the expression in OBxByBzB department is the directional matrix that OPxPyPzP is reason (the positional vector that 8)OP nods fastens medium expression to be TPB=RyB(-f ′ in OBxByBzB) TPC+TCB=(9) type (8) and type (the athletic equation when 9) gets a tip for grinding cone namely. 4 staff grow computation by the graph 1 visible, the opposite displacement vector that lever vector can express to the T=h+r+d in be Li=T+Pi-Bi(10) type is OP dot and OB dot, write down when the expression in OBxByBzB department for TPB. Type (the expression of each vector need in 10) is in same coordinate department, and directional matrix RPB calls changeover matrix again, the expression that reason of the PiB=RPBPiP(11) in can fastening PiP changeover to OBxByBzB gets lever vector to be fastened in OBxByBzB coordinate is LiB=TPB+RPBPiP-BiB(12) to given machine tool structure, piB and BiB all are Chang Shi to measure. Displacement vector TPB and changeover matrix RPB already all were begged piece, see pattern (8) , type (9) . Variable of the motion in grinding process changes continuously, criterion earning staff grows successive also change. What with this change the value controls each lever is adjustable, but the motion that activating platform generation books. Machine tool of axis of 5 conclusion empty is linkage mechanism of dimensional paralell connection essentially, can show the basic structure of empty axis machine tool with vector, make athletic computation very convenient. Form a principle according to what grinding parameter and cone get a tip, the translation that uses vector and rotate to state mobile platform is opposite the motion at cone and fixed platform, thereby the athletic equation that derivation grinds taper seat to get a tip in the blade on empty axis machine tool, athletic equation is comprised by the displacement vector TPB of mobile platform and directional matrix RPB. Use blade to grind athletic equation to be able to beg a lever to grow vector, in order to controls lever to grow change, make the machine tool produces blade to grind motion. CNC Milling CNC Machining