Canister form inserts tine knife to divide the correction computation of round pressure angle

Form of canister of 1 general correction formula inserts tine knife to divide the correction of round pressure angle to should include two fields: Because of,be before cutting tool, hind the teeth shape error that horn causes; 2 because axes of circumgyrate of the cutting tool when cutting is opposite,be the places corner place to cause teeth shape error at workpiece circumgyrate axes. To this, domestic and international research is more the computational means that put forward to differ and formula. Among them, to cutting tool before, hind the general correction formula of the teeth shape error that horn causes is (in 2) type: α " -- the cutting tool cent after amending is round pressure angle γ -- pattern of the part before cutting tool (2) is applied to already outside clench the teeth inserts tine knife, also apply to inside the correction that mesh tube form inserts tine knife to divide round pressure angle. Opposite to axes of circumgyrate of the cutting tool when cutting the typical correction formula at the places corner place to cause teeth shape error of workpiece circumgyrate axes is λ of Cos of α of Tan α =tan (the α in 3) type -- to amend the cent circle after pressure angle alternate sums mood, via changing brief get form of E(4) of α of "cos of α of Tan α =tan (the general correction formula that 4) is canister form to insert tine knife to divide round pressure angle namely, the cutting tool after type is amended mediumly to undertake cutting tool teeth shape error namely should provide some to divide round pressure angle. 1.

Derivation of equation of 2 correction derivation of equation passes the correction all two afore-mentioned respects to be in same geometry graph, the author undertook canister form inserts tine knife to divide round pressure angle to amend formulary derivation. Above all, by canister form the knife that insert tine inserts the involute tooth form that make, usable also have photograph ibid, hind horn and the rack slotting tool with equal pressure angle of tooth form horn and circle of cent of the knife that insert tine is cut make, namely the correction that canister form inserts tine knife to divide round pressure angle is equivalent at horn of identical tooth form, before horn, hind of horn of tooth form of rack slotting tool amend. Accordingly, can use analytic rack to insert method of amendatory of tine tooth form to analyse canister form to insert tine knife to divide round pressure angle amend. The primitive tooth form of the equivalent rack that dotted line tooth form expresses to be in original position (namely axes of the horn before cutting tool is not had, cutting tool is opposite do not have at working place place corner to spend) , horn of its tooth form is the α of tooth form horn that the place after cutting tool is amended should have. Build on its originally to it connected coordinate is Oxy. Solid line tooth form is the real position that cutting tool works. Its circle origin from original position anticlockwise rotate λ horn, γ of the horn before be being made next, be in workpiece end panel (horizontal) umbriferous tooth form horn should be equal to workpiece to divide round pressure angle α . N-N is sectional the front face that is cutting tool, it is cutting tool has turned from original position λ horn but the tooth form of the horn before notting have is sectional. Oxy has turned coordinate department γ horn gets coordinate fastens Oxy namely. Now, the working place in cutting tool (solid line tooth form) the sectional L-L that makes parallel support at tine, respectively tooth form of face of the blade before cut is nodded at B dot and A. Be in advocate in view, it is O the centre of a circle with origin, draw circular arc to hand in Ox axis to be nodded at A for radius with OA, be equivalent to the A on sectional tooth form of cutting tool N-N selecting the A site that circles origin to rotate to primitive tooth form. Accordingly, n-N is sectional on A dot transverse tooth thickness is equal to primitive and sectional on A nods transverse tooth thickness (make its be S) . As a result of L-L sectional parallel supports at tine, certifiable the homogeneous phase of transverse tooth thickness of correspondence of each bits of place on helicoid of side of its cut tine (the process that seek testimony sees later development) . Accordingly, (Nod corresponding transverse tooth thickness to be equal to B to nod corresponding transverse tooth thickness, also namely the tooth transverse tooth thickness with corresponding dot of B dot A is equal. According to above analysis, tooth form of face of the blade before making cutting tool is in when working place of workpiece end panel umbriferous (solid line part) and cutting tool is primitive tooth form is in when original position of workpiece end panel umbriferous () of dotted line part. α of horn of correction tooth form of knowable cutting tool (α of horn of tooth form of name of 5) cutting tool (5) has H=OA-OA to be in Δ OAB, ∠ BOA= γ , ∠ BAO=(π / 2)+ α E criterion ∠ ABO= π - π of BAO=(of ∠ BOA- ∠ / 2)-(γ + α E) is gotten by sine theorem take the place of BAO of ∠ ABO, ∠ to go up type criterion has namely again (6) general type (6) generation enters type (5) , get cutting tool amends formula of computation of tooth form horn (7) general type (7) is changed brief, criterion (α of "=tan of α of 8) your Tan / () of γ of 1-tan α Etg, era enters type (9) gets λ of "cos of α of Tan α =tan (γ of 1+tan λ Tan) (the type on 9) is rack slotting tool to amend formula of pressure angle computation namely, also namely canister form inserts tine knife to amend formula of pressure angle computation. (2) proof: Change a rack on, aleatoric parallel supports at tine (or tine root) the transverse tooth thickness of correspondence of each bits of place on tooth profile of planar place cut everywhere equal. M-M, N-N is change a parallel on rack at before the random of knife face two sectional, the random that L-L carries on the head at tine for parallel is sectional and L-L hands in N-N, M-M respectively at A, B at 2 o'clock. Cross A to order N-N vertical line, hang down sufficient for C. A, B, C nods a corresponding transverse tooth thickness to be SA, SB, SC respectively. Prove former proposition, need to prove SA=sB only. Your: M-M is B to the distance between N-N, criterion on rack slotting tool from M-M sectional to sectional tooth form addendum modification Xm is Xm=-btan α E to change according to gear a principle, with in N-N sectional go up, with A the dot is in same height.

The SC of transverse tooth thickness that nods correspondence is in for SC=sA-2xmtan α advocate there is BD=xmtan in the C"DB of right-angled triangle Δ of view α of α criterion SB=sC+2xmtan takes the place of SC to go up type can card gets SA=sB2 result analysis to understand canister form to insert tine knife for development each relevant geometry parameter and tooth form horn amend the relation between, regard Tan&alpha as cutting tool places horny λ , hind the function of γ of the horn before horny α E is mixed, make (be opposite only under 10) axes of cutting tool circumgyrate is opposite the λ of the variable that place part of workpiece circumgyrate axes and λ of F(of pressure angle function, α E, γ ) metabolic relation undertakes an analysis. F is right of λ first-order slant guide for (11)f is right of λ 2 rank slant guide for (12) because α " , λ , γ takes a value to all be in [0, (π / between 2)] , so 2f/ λ <0, function is protruding function, have great value. =0 of your F/ λ , as a result of,get λ ≠ (π / 2) , have namely λ = γ (the geometrical meaning of property of 13) above function is: When γ of 0< λ < , when placing the part before horn is less than cutting tool, function of correction pressure angle is add function. As the accretion of the " that place part, correction pressure angle also increases; When λ = γ (namely when cutting tool works before blade face and parallel of workpiece end panel) when, correction pressure angle reachs maximum and λ of "/cos of α of =tan of λ of Sec2 of λ of "cos of α of Tan α Max=tan (14) increases further when λ , achieve π of <(of γ < λ / when 2) , correction pressure angle is reduced gradually. When λ =2 γ , (15) type (15) explains, when the two symmetrical positions that are in horizontal when face of the blade before cutting tool, its amend pressure angle equal. In addition, from type (9) is knowable, when λ =0 namely when cutting tool photograph does not place corner to workpiece, correction pressure angle is formulary (9) evolves for λ of "cos of α of Tan α =tan (λ of 1+tan γ Tan) the type on =tan α " is namely before considering cutting tool only, hind the general correction formula of the teeth shape error that horn causes (2) . And when γ =0, type (9) turns into λ of "cos of α of Tan α =tan (λ of 1+tan γ Tan) the model of teeth shape error when the type on λ of =tan α Cos is a consideration to place part namely amends formula (3) . 3 computation example designs a tube of form to insert tine knife, the main design parameter of cutting tool is: Modulus: M=3.

5; Tine number: Z=46; Divide round pressure angle: α =30 ° ; Before horn: γ =5 ° ; Hind horn: α =5 ° 22; Basic circle diameter: D0g; The horn after root of tine of workpiece joint tine is round: 7 ° ; Computation amends D0g of basic circle diameter. Insert the working principle of tine knife according to above discussion and canister form, the rotor when the knife that insert tine works places horn to should be equal to the horn after workpiece tine root is round, from this ° of knowable λ =7. each parameter era enters type (the basic circle diameter after round pressure angle is being divided to be 176" of α =30 ° to amend after 9) must be amended is D0g=mzcos α =3.

46 × of 5 × Cos30 ° 176"=139.

The car gear that the article connects 0279 4 epilogue to analyse canister form to insert tine knife treatment to have awl too integrates the cutting principle of tine, derivation the correction that inserts tine knife to divide round pressure angle is formulary. The combinative tine tooth form that the canister form that uses this formula to design inserts tine knife to be able to cut the most adjacent and academic cost, make the union in car gear-box ages a joint that covers with tine is more accurate and reliable, the proper motion of gear of the gear-box in preventing the job effectively is taken off block. The article amends form of formulary basis canister to insert derivation of principle of tine knife job, but certifiable the tooth form that the clench the teeth outside be being applied to likewise inserts tine knife is amended. CNC Milling