Summary: Analysed the principle of clench the teeth of law of roll flute of emery wheel of annulus face worm, discussed the condition that line of bounds of clench the teeth appears, use abstain diamond to repair form gyro wheel to be on machine of roll flute of NZA worm emery wheel undertook test and verify experiments. 1 foreword is life of high speed of contented and contemporary mechanical drive, burden, low noise, longevity to wait for a requirement, the application of gear of high accuracy hard tooth flank is increasingly wide, the accurate processing technique of gear of hard tooth flank becomes gear to make one of main development way of the technology. Roll flute is at present the hard tooth flank of first selection machines craft, and law of roll flute of worm emery wheel is among them the treatment method with highest efficiency, the machine of roll flute of worm emery wheel such as NZA, RZA applies in home extensive. To reduce finished cost further, improve treatment efficiency, switzerland bilked company of Si Hao Er to roll out machine of roll flute of emery wheel of worm of RZP annulus face, its machine a principle to be: Will with by treatment gear appearance park of identical diamond gyro wheel is machined workpiece locally, through clench the teeth motion is nap of worm emery wheel annulus face, use work of grinding of emery wheel of worm of this annulus face next. Use this method to be able to simplify greatly emery wheel builds shape course, shorten nap time (share equally is 2 ～ only to the nap time of every workpiece 3 seconds) , and line contact is between emery wheel and workpiece (columnar worm is point contact) , much tine participates in grinding at the same time, osculatory coefficient is big, on the base that retains original precision, can make produce efficiency to have relatively rise substantially, the grinding time of major work can shorten less than. The article undertook an analysis to the principle of clench the teeth of law of roll flute of emery wheel of annulus face worm, diamond was abstained to repair form gyro wheel on this foundation, it is on machine of roll flute of NZA worm emery wheel undertook grinding experiments. Graph principle of 2 clench the teeth analyses sketch map of 1 coordinate department the principle of clench the teeth of law of roll flute of emery wheel of annulus face worm is to be based on open a face 2 times to include theory of subsidiary channels in the human body through which vital energy gradually, open face S Ⅰ to wrap subsidiary channels in the human body through which vital energy to give Ⅱ of S of tooth flank of worm emery wheel gradually with what diamond repairs form gyro wheel namely, reoccupy S Ⅱ wraps subsidiary channels in the human body through which vital energy to give Ⅲ of S of workpiece tooth flank. Coordinate fastens if the graph is shown 1 times,build, s(O-i, j, k) and Sp (Op-jp, jp, kp) secures dimensional coordinate department for two, among them, the rotor line coincide of Z axis and gear, the rotor line coincide of ZP axis and worm emery wheel, two axes are S(0<S<p) to the included angle between; X axis and XP gross ril load close, their direction is two axes most stone's throw direction; OOP is most stone's throw, namely the center is apart from A. Coordinate fastens S1(O1-i1, j1, k1) and gear solid couplet, coordinate fastens S2(O2-i2, j2, k2) and couplet of solid of worm emery wheel, in position of rest, they reach SP coincide with S respectively. Analysis of sth resembling a net of first time bag repairs Ⅰ of S of tooth flank of form gyro wheel the vector equation in S is written by Wu Xutang " principle of gear clench the teeth " (machinist trade publishing house 1982 publish) knowable, face of inclined tooth profile is in the equation in S1 (in 1) type: Q, v -- open face parameter P gradually -- helix parameter changes his to S in, can get (in 2) type: F1 -- N of vector of line of corner unit public law the expression in S by " principle of gear clench the teeth " knowable (3) is in relative to athletic speed V12 the expression basis in S " principle of gear clench the teeth " , set W1=1, have (the equation of clench the teeth between Ⅱ of Ⅰ of S of equation of 4) clench the teeth, S is F=nV12=0(5) type (3) , (4) generation enters type (5) , can get equation of clench the teeth of face of inclined tooth profile to be (Ⅱ of S of equation of tooth flank of 6) worm emery wheel type (1) is changed in S2 and with type (6) couplet stands, can get face of inclined tooth profile to repair the Ⅱ of S of equation of tooth flank of worm emery wheel of form to be (7) wraps subsidiary channels in the human body through which vital energy the 2nd times to analyse a bag the 2nd times in subsidiary channels in the human body through which vital energy, Ⅱ of S of tooth flank of worm emery wheel and can be stated by the equation of clench the teeth of Ⅲ of S of treatment gear tooth flank right now for Y*=n*V21=0(8) the independent parameter Q on worm emery wheel, V reachs F1 already translate into is general parameter, emery wheel of the worm in including sth resembling a net with the 2nd and be had nothing to do by the corner parameter F2* of treatment gear, F1* . N of vector of line of unit public law the expression in S2 is in N the expression in S (3) is changed in S2, can get (9) is in relative to athletic speed V21 the expression in S2 (equation of 10) clench the teeth type (9) , (10) generation enters type (8) , can get equation of clench the teeth (11) contacts an analysis 2 times 2 times to contact an analysis by type (6) is knowable, u=W. Analytic type (11) , the solution that can get equation of the clench the teeth that include sth resembling a net the 2nd times is (12) pursues sketch map of 2 contacts line because Tand=V/U, d=arctan(V/U) , so (13) this shows, the dot of clench the teeth of equation of contented on tooth flank of emery wheel of the worm in including sth resembling a net the 2nd times clench the teeth has two kinds: ① satisfies the dot of F2*=f2. The osculatory line that forms by these dots includes the reproduction that the line contacts on tooth flank of the worm in subsidiary channels in the human body through which vital energy for the first time namely, call former contact line, take different F2* cost, the tooth flank that forms by former contact line on workpiece tooth flank is completely as consistent as face of nap teeth of a cogwheel open face S1 Ⅲ gradually; ② satisfies the dot of F2*=f2+2d. They form line of a new contact, new the curved surface that contacts line a group of things with common features to form already was involute helicoid no longer, however Ⅲ of S2 of a new curved surface, this is caused, the line of bounds of clench the teeth that two curved surface cross at including sth resembling a net for the first time (2) seeing a picture. Line of bounds of clench the teeth is in roll flute treatment, tooth flank should be the final ideal of workpiece to open a range gradually, and should not appear new curved surface. Accordingly, need analyses the line of bounds of clench the teeth that includes sth resembling a net for the first time. (14) is begged to F1 slant derivative, have Usin(q+f1)+Vcos(q+f1)=0(15) type (14) , (15) couplet stands, can get the conditional equation of line of bounds of the clench the teeth on S Ⅰ . Solve this equation and change brief, can get (the A=(pRb-i21pRbcosS-Rbi21asinS)2-(pai21cosS+Rb2i21sinS)2(17) in 16) type type (16) and type (1) couplet stands, the equation of line of bounds of clench the teeth that can get first time to include sth resembling a net is (18) by type (18) is knowable, when A>0, nap is put in line of bounds of two clench the teeth on face of teeth of a cogwheel, and the helix angle that is basic circle cylinder to go up for 2A½cosbb(Bb along the mutual distance of Z1 axis, cosbb=p/(p2+Rb2)) ; When A<0, on face of nap teeth of a cogwheel line of bounds of nonexistent clench the teeth; When A=0, on face of nap teeth of a cogwheel only line of bounds of a clench the teeth. The criterion that whether is put in line of bounds of clench the teeth is make worm emery wheel can grinding gives whole workpiece tooth flank, should eliminate line of bounds of clench the teeth at effective job tooth flank besides. Your A=0, take the place of P=rb/tanb, can get via arranging (of S of angle of cut of the axis when roll flute of worm of 19) annulus face choose a principle to be: When S>S1 or S<When S2, nap does not have line of bounds of clench the teeth on face of teeth of a cogwheel, the workpiece tooth flank that treatment gives opens a range gradually for helix. Graph the emery wheel after 3 nap model of machine tool of condition of test of 3 grinding test: The Switzerland that factory of cent of gear of plant of Dalian machine tool uses bilks machine of roll flute of emery wheel of worm of NZA of Si Hao Er; Emery wheel norms: 294. 5mm × 104mm(grows × wide) , only head is dextral, already dynamic balancing; Test specimen: M=3mm, z=42, b=25 ° , b=20mm, a=20 ° , material is 40Cr, already quenched after crowded tine; Diamond gyro wheel: Institute of Electromechanical of university of Shandong science and technology is developed, granuality 80# , geometrical parameter is the same as test specimen. Trial measure basis afore-mentioned analysises, choose proper center to be apart from A, computation goes out not to appear the S of axial angle of cut of line of bounds of clench the teeth; Adjust a machine tool, use emery wheel of nap of diamond gyro wheel first, be apart from A(to see graph 3) to academic center till emery wheel feed, use test specimen of emery wheel grinding next. Test result makes clear, error of the tooth form of test specimen, teeth directional all has bigger improvement. The principle of clench the teeth of law of roll flute of emery wheel of worm of face of 4 conclusion annulus includes sth resembling a net to open a range 2 times gradually, may appear 2 times to contact a phenomenon; Choose proper center to be apart from A and S of axial angle of cut, can eliminate line of bounds of clench the teeth tooth flank besides, obtain ideal by treatment tooth flank; Efficiency of treatment of law of roll flute of emery wheel of annulus face worm is tall, tooth form precision is good, have good applied prospect. CNC Milling
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