In the machine tool advocate in transmission system, to reduce gear number, simplify structure, shorten axial dimension, often use double public gear. But the design method that teeth of a cogwheel of active double public tine counts is to try calculate, collect is algorithmic, computation is troublesome and find out sound design program not easily. The article is passed right advocate the analysis of characteristic of double public positive drive in transmission system and research, derivation and the computation that built teeth of a cogwheel of double public tine to count a design are formulary, wrote a program to realize double public gear to age the CAD of several is calculated, rose to design efficiency apparently. If the design method that teeth of a cogwheel of 1 pair of public tine counts pursues 1 is shown, the gearshift system that has composition of series connection of A of group of gearshift of gear of slippage of two double couplet, B (or the one part) of gearshift system, among them Z1, Z2 is public gear. Graph the machine tool of gearshift system sketch map that 1 pair of public gear comprise advocate transmission system is more fall fast drive, reason needs group of before one gearshift (gearshift group A) serves as expand group, hind one gearshift group (gearshift group B) serves as main group, pursue the structural style of 1 medium gearshift system is 4=22 × 21. The tine that sets two gearshift group is counted and be Sa, Sb respectively, the level is general than be F, the least drive in gearshift group A compares for: The least drive in B of group of U=Z1/Z1 (1) gearshift compares for: If Ut=Z2/Z"2 (2) is not used change a gear and each gear modulus is identical, have: Couplet of Sa=Z1(1+u)=Z2(1+uf2) (3) Sb= Z1(1+1/(utf))= Z2(1+1/(uf)) (4) stands (3) , (4) type seeks solution, : Type of commutation of U= -f+[f2+ 4ft(f+1)]½ 2ft(f+1)(5) (5) , : T= 1-f+u F(f+1)u2(6) passes to avoid a construction big, the least drive of gearshift group B satisfies Ut ≥ 1/4 than answering, derive from this T ≥ 1/(4u) (7) type (7) generation enters type (6) , get 1/4 of ≥ of U of reassume of U ≤ 4/(f2+5f) , the span that attainable U is worth: Vertical of couplet of 4 4 F2+5f(8) of ≤ of U of 1 ≤ (1) , (8) arranges: 4Z1 4(9) is in ≤ of Z1 of Z1(f2+5f) ≤ machine tool advocate in the design of transmission system, its drive is put in certain error than allowing, transmission error is: U of A= │ is solid - ≤ of U manage │ (when drive of checking computations of │ of manage of U of │ of F-1) × 10% compares an error, because transmission comparing takes a level very hard fair compared integral Ci Mi, reason inconvenience is all to its transmission comparing undertakes checking computations. In same gearshift group, as long as among them after deputy tine number decides a pair of gear, corresponding drive is compared also decided, right now, but according to this drive deputy drive is compared and class compares the pattern, affirmatory other deputy drive compares each drive, be opposite from this other deputy actual drive compares each drive undertake checking computations. If the graph is shown 1 times, in gearshift group A, if Z1/Z1 is compared to already decided transmission, the transmission error A1 that needs checking computations Z2/Z2 only can. ≤ of │ of Z2/Z2-f2u of A1= │ (│ of F2u of │ of F-1) × 10% (10) makes: C1=1-(f-1) × 10% , c2=1-(f-1) × 10% , criterion, arrange type (10) gets: F2uc2Z2 (11) of ≤ of F2uc1Z2 ≤ Z2 manages together, in gearshift group B, if Z2/Z"2 is compared to already decided transmission, the transmission error A2 that needs checking computations Z1/Z"1 only can. ≤ of │ of Z1/Z"1-fut of A2 │ (│ of Fut of │ of F-1) × 10% (generation of 12) general C1, C2 enters type (12) , after arranging, get: Because Z1(f+1)u (1-fu)c2 (1-fu)c1(13) of ≤ of Z"1 of Z1(f+1)u ≤ is not used change a gear and each gear modulus is identical, all be M, be apart from equal principle according to the center, what beg a result to should satisfy next face relation: M(Z1+Z1)= M (Z2+Z2) 2 2m (Z1+Z"1)= M (Z2+Z"2) 2 2(14) by type (9) is knowable, when fair more certain than F, give value of a Z1 to be able to define the scope that a Z1 is worth, then by type (3) decides Z2, by type (the extraction of 11) affirmatory Z2 is worth limits. After affirmatory Z2, by type (2) decides Z"2, then by type (the extraction of 13) affirmatory Z"1 is worth limits, finally by (result of 14) type test and verify. Can request the plan that gives more choice to age teeth of a cogwheel is counted so, with facilitating the architect has much plan compare and optimize a design. Graph 2 computation the computer that teeth of a cogwheel of 2 pairs of public tine counts flow chart of program of number of teeth of a cogwheel of double public tine assists computation and example the computational formula according to afore-mentioned derivation and design method, use Visual Basic language to wrote a program to realize double public gear to age the CAD of several is calculated, convenient apace requests the design plan that gives teeth of a cogwheel of more double public tine to count, created necessary premise and good condition to undertake plan is compared and optimizing a design more. Graph 2 it is flow chart of CAD calculative program. Set one machine tool advocate transmission system, progression of main shaft rotate speed is 8, if be in the first, double public gear is used in group of the 2nd gearshift, its structure style is: 21 × of 8=22 × 24, fair than F=1.
12, to this transmission system medium double public gear ages number undertakes the CAD is calculated now. The tine number that can reach through computation 968 accord with transmission to compare a requirement devises plan, partial plan data sees a table 1. If the other condition in system of this advocate transmission is changeless, change only fair the cost that compares F, likewise calculable the design plan that gives number of corresponding teeth of a cogwheel of double public tine. Express 1 F=1.
12 Shi Chi Lun Chi Shu De Xuan Ze Fang An Z1 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 19 19 19 19 19 19 20 20 20 20 21 21 21 21 22 22 Z1 32 34 36 37 38 39 40 41 42 43 44 45 46 47 48 37 38 39 40 41 42 33 34 35 36 37 38 35 36 37 38 32 33 34 35 32 33 Z2 29 31 33 34 35 36 37 38 38 40 41 42 43 44 45 34 35 36 37 38 39 30 31 32 33 34 35 32 33 34 35 29 30 31 32 29 30 Z2 87 80 75 73 71 69 69 66 65 64 63 62 61 60 59 83 80 78 76 74 73 112 106 102 98 94 91 86 84 80 78 84 82 80 78 85 83 Zai Shang Shu Ji Suan Chu Jiao Duo De Chi Shu She Ji Fang An Ji Chu Shang , design a machine tool according to place advocate the specific requirement of transmission system, can put forward different tie condition and target function, the numerous gear that reachs to CAD computation then ages several plan undertake compare and be optimizinged designing, beg an optimal gear to age number devises plan from which. The article passes 3 conclusion to the machine tool advocate the analysis of characteristic of double public positive drive in transmission system and research, in gear changeless below the circumstance, reach the following conclusion: Be based on pair of machine tools advocate the analytic research of characteristic of double public positive drive in transmission system, put forward teeth of a cogwheel of a kind of tine to count the new method of the design, and derivation the computation that tine teeth of a cogwheel counts is formulary. To falling the gearshift system of fast drive, the least drive compares the series of before one gearshift that introduces double public gear is not random given, should satisfy a requirement however (≤ of 1/4) ≤ U [4/(f2+5f)] , otherwise, group of the 2nd gearshift because drive is less than passing and cannot come true. Through the computer auxiliary computation can go to the lavatory apace begs a more gear that accords with a requirement to age number devises plan, on this foundation, build optimize design target function and tie condition accordingly, can have much plan compare and optimize a design, in order to get optimal design program. CNC Milling