Of arc tine bevel gear three-dimensional emulate

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Summary: Be based on Gelisen the machine tool gives equation of gear tooth flank by kinematic method and derivation of equation of clench the teeth, use I-DEAS software and give gear tooth flank according to the construction of curvature route network that gets by tooth flank equation, the three-dimensional emulation model of bevel gear of tine of make it arc. 1 foreword arc ages bevel gear applies extensively in the industry such as aviation, nautical, car, tractor, machine tool. The controls not completely in all gear wheel that serves as a kind of local point contact deputy, arc tine bevel gear is very complex on geometry, its are designed and make a method affecting gear directly quality of deputy clench the teeth. In the treatment of forge of essence of life of gear, when production forging die, tooth flank often needs bit by bit amend, have cycle long, precision is insufficient and hard the defect of appearance of accurate report tooth flank. The development of numerical control machine tool and application are the efficient, high accuracy with development helix new bevel gear to machined a method to offer a way. Because numerical control machine tool machines the requirement that is based on entity to need to know the exact figure of tooth flank, because this article developed arc tine bevel gear three-dimensional emulation model, it can the exterior appearance of product of bona fide report and structural feature, it is implementation products plan, kinematic with kinetic emulate, function analysis and optimize and the foundation of CNC Machining. The article is based on Gelisen the machine tool gives equation of gear tooth flank by kinematic method and derivation of equation of clench the teeth, use I-DEAS of software of large and general CAD/CAE/CAM, through the curvature route network that gets by tooth flank equation construction gives gear tooth flank, make it arc ages the three-dimensional emulation model of bevel gear is used at the analysis of CAE/CAM and treatment. 2 rounds of big yield that produce coordinate department to describe big rounds according to coordinate department become a process: Solid fastens even the fixed coordinate at machining a machine tool Sm, its origin Om is located in machine tool center, xmOmYm plane is located in inside machine tool plane; Solid is connected at shaking the coordinate of the stage fastens Sg, in producing a course, coordinate fastens Sg and the reference axis Zm that shake the stage circles coordinate to fasten Sm together to rotate, in initiative position Sg and Sm coincide, Øg horn is mixed for coordinate department Sg shake the current corner of the stage; Solid fastens Se at the coordinate of bit body repeatedly, its origin Om is located in bit body center, xeOeYe plane is located in plane of point of a knife (as planar as the machine tool coincide) inside, coordinate fastens Se to also originally to fasten Sg to go up at coordinate repeatedly, among them Q2 is horny Xiang Dao; Auxiliary coordinate fastens Sa to use a description to be in to machine the installation position on the machine tool by rounds treatment is big, solid fastens Sm at coordinate repeatedly, coordinate department Xa and the reference axis Xa that coordinate is Sm become γ 2 horn () of cone angle of machine tool root, horny γ 2 be equal to root cone angle big rounds; Solid is connected at be being fastened by rounds treatment is big coordinate S2, in producing a course with be machined big rounds the reference axis Xa that circles coordinate to fasten Sa together rotates, in initiative position S2 and Sa coincide, Ø2 horn fastens S2 and the current corner that are machined big rounds for coordinate, the section awl acme that is machined big rounds and coordinate fasten the origin O2 coincide of S2, XB2 is bed. Face of teeth of a cogwheel of equation of 3 tooth flank is become by sth resembling a net of biscuit of cutting tool cutting. In machining a process, the axes that bit body circles oneself rotates form cutting cone; Shake at the same time stage (taking bit body) and be machined big rounds also circle respective axes to rotate, extend range of big teeth of a cogwheel thereby. Face of cutting of rounds of will big cutting tool (cone) equation and normal equation express to fasten in coordinate in there is type of 2(1) of α of G-uGcos of θ of 2)cos of α of G](rG-uGsin of θ of Re=[(rG-uGsin α 2)sin in Se: UG, θ G -- α of curved surface variable 2 -- horn of cutting tool tooth form, inside knife (those who machine big rounds is convex) take be worth, outside knife (rounds treatment is big concave side) take negative worth, RG -- the radius of point of a knife in the magnanimity inside XeOeYe plane, by type (1) can get RG=0.

5DG ± 0.

The knife outside correspondence of the positive sign in 5PW(2) type (namely) of rounds of big concave side, the knife inside minus correspondence (namely rounds of big convex) , PW is apart from for knife top. Equation of face of cutting of rounds of will big cutting tool expresses to be being machined big rounds there is R2(rG in coordinate department S2, θ G, in Øg)=[M2e]re(3) type [M2e] -- rounds of coordinate commutation matrix is big treatment that the coordinate department that solid has even Yu Dao goes to to be fastened by rounds of treatment is big coordinate has equation of clench the teeth to hold water in the process, namely in type of Nm · Vmg2=0(4) : M -- the Nm in showing its vector fastens Sm in coordinate -- the normal Vmg2 of face of cutting tool cutting -- be machined big rounds seek solution with the opposite motion rate that produces form annulus to be nodded in cutting above is various can expunction parameter UG, g of θ of R2(of equation of rounds of those who get Øg is curved surface parameter be mixinged with θ G is big tooth flank, Øg) . The three-dimensional model of bevel gear of 4 arc tine because G of θ of R2(of tooth flank equation, the curved surface with Øg) definite place is dimensional curved surface, form is more complex, be discontinuous inside certain limits, face of big teeth of a cogwheel is the one part of curved surface only, because this must decide G of θ of R2(of tooth flank equation, g of two variable θ in Øg) , the span of Øg. The dot on face of big teeth of a cogwheel (X, y, z) what go up in Xoy plane is umbriferous and inevitable be located in line of root of top line of tine teeth of a cogwheel, tine, outside what awl is apart from line and inner cone to be apart from a line to form is quadrangular inside. The space is nodded (X, y, z) what go up in Xoy plane is umbriferous the coordinate of gotten point is (X1, y1) , among them X1=x, y1=(y2+z2)½ . With these 4 the edge is attrib border condition, judge by G of θ of R2(of tooth flank equation, whether is the point with Øg) certain place inside this limits, the extraction that gets G of two variable θ , Øg thereby is worth limits. To facilitate from the back make a plan, the extraction that should increase variable θ G, Øg appropriately is worth limits. Will age line of root of top line, tine, outside what awl is apart from line, inner cone to be apart from a line to form is quadrangular outside enlarge, peripheral line draw a frame round. peripheral line draw a frame round OX of line of the axle that circle tine rotates, become entity to age namely the circle is hypostatic. According to G of θ of R2(of tooth flank equation, Øg) , it is variable with a parameter, another parameter is changed ceaselessly take a cost, can get a series of curves. The density of reticle is worth density to decide by the extraction of variable θ G, Øg, reseau is closer, curved surface is more accurate. Net of this parameter curve is curvature route network namely, right now curved surface assumes office to was along the tangent of two parameter curve this a little bit advocate direction. Use I-DEAS software the function that reseau of the curve in design of advanced curved surface builds curved surface parts to build network of route of parameter of convex, concave side slick curved surface (tooth flank face piece) . Encircle tine entity and convex (concave side) tooth flank face piece those who take be mixed to get gear namely is convex (concave side) . Will convex the new entity that forms with command of attrib border suture with concave side. To get accurate tine root, need undertakes correction to tine root. Line of the arbor in winding tine root string rotates form root awl entity, substance of the awl that use a root goes excising the new entity that forms by attrib border suture, make accurate tine base substance, amend the awl that use a root the hypostatic array that pass, array number is counted for tine teeth of a cogwheel, the substance after using array goes excising gear annulus base, get the three-dimensional emulation model of arc tine bevel gear namely. The top is apart from knife of round of radius of base parameter point of a knife that expresses bevel gear of 1 arc tine pressure angle of concave side of concave side pressure angle annulus way of base installation part answers a knife horny Xiang Dao bed of machine of ratio of roll 228.

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02 right 5 conclusion this modelling method basis cutting tool, machine tool and process of the cutting that be reached by the mutual motion of treatment gear go equation of gear tooth flank by kinematic method and derivation of equation of clench the teeth, construction gives curvature route network and generate tooth flank by tooth flank equation again. The tooth flank definition that makes by curvature route network is high, information of tooth flank of can accurate report. Method of this kind of modelling is to be based on Gelisen essentially the machine tool generates tooth flank by cutter track contrail. The model that this kind of modelling method that is based on craft gets is in on numerical control machine tool when treatment, what can assure tooth flank is successional with consistency, raise tooth flank precision. CNC Milling CNC Machining