Big modulus hard tooth flank rolls the similar model method of shave tooth form

Summary: Be based on hard tooth flank to roll razor dentiform to produce a method, use linear, circular arc, hyperbola to plan to be opposite legally respectively roll razor law sectional tooth form had similar model. Computation of similar model error makes clear as a result, draft legal error point-blank bigger, but emery wheel nap is simple; Circular arc drafts legal error the smallest, but emery wheel nap is a bit difficult; Hyperbola drafts legal error very small and emery wheel nap is simple. The development of technology of drive of 1 foreword machinery is taller and taller to the performance demand of gear spare parts, to acquire carrying capacity ability of the big, corrode that resist a drop precision of strong, drive the gear product with good quality of tall, surface, hard tooth flank of temper by dipping in water (the research heat that technology of gear cutting of HRC48 ～ 62) already made gear manufacturing industry. Hard tooth flank rolls razor is a kind of new-style gear cutting tool that is used at hard tooth flank to be machined eventually, it withheld the characteristic of hob of hard alloy scrape already, have the advantage of close tine of dish of knife of form shave tine and first flank again, the circle that used the round hob that grind a way at the same time grinds technique. When this cutting tool machines gear of hard tooth flank, use " boil repeatedly take shave " cutting means, can obtain efficiency of taller treatment precision, cutting and inferior exterior surface roughness to be worth. One of design, technology keys that make hard tooth flank roll razor are the tooth form of knife rolling shave that wins high accuracy, roll razor to big modulus especially, because arc of tooth form curve is longer, should achieve difficulty of precision of taller tooth form bigger. Accordingly, according to hard tooth flank dentiform of knife rolling shave produces a method, through choosing reasonable tooth form similar model method rolls precision of razor tooth form with rising, it is to roll razor design, production serious content. Form of 2 tooth rolling shave makes a method roll razor dentiform to produce the method that uses a circle to grind involute worm, make roll razor the tooth form of two side edge is located in on involute worm. The axis of emery wheel is sectional and opposite at rolling the axes of razor to rotate one divides round helix to promote role, make emery wheel axis sectional the as alveolar as knife rolling shave law that divide a circle is sectional coincide, put emery wheel into chamfer of tooth rolling shave, emery wheel and roll razor to be able to undertake by respective contrail motion the circle grinds treatment. The law with round cent of chamfer of tooth rolling shave is sectional two side tooth form controls semmetry, razor will boil to turn around to grind another side again after grinding a side can. Theoretic, the basis rolls razor involute worm and osculatory line condition foregonely to try an osculatory line, wind osculatory string circumgyrate of emery wheel axes to be able to get face of emery wheel circumgyrate and its shaft again sectional appearance, but because seek the contact that go out,the line is a space complex curve, it is very difficult to press this nap emery wheel. Accordingly, use approximate method more in be operated actually, beg above all namely piece roll razor involute worm the law with alveolar round cent is sectional curve, circle this curve circumgyrate of emery wheel axes next and gain face of emery wheel circumgyrate, the error that arises from this is very small, can ignor. Because roll the law of razor,sectional curve is complex flat curve, difficulty of emery wheel nap is greater, because this can use simple curve,sectional to rolling razor law curve has similar model, it is modelling error control inside very little scope. This method can reduce difficulty of emery wheel nap already, can obtain precision of taller tooth form again. 3 roll law of razor involute worm sectional dentiform is approximate modelling pursues error of 1 linear modelling pursues error of modelling of 2 circular arc plans to be used legally point-blank plan to close point-blank roll law of razor involute worm curve of sectional tooth form can reduce difficulty of emery wheel nap apparently, but the similar model error that arises from this whether the tooth form precision that assures a requirement needs to give through computation test and verify. To make linear with roll law of razor involute worm of curve of sectional tooth form plan to close achieve best status, two node must be had between them, 3 when arise from this plan to if the graph is shown 1 times,add up to error extreme value. What E1, E3 parts to support for tine root, tine is the biggest plan to add up to an error, e2 is tine mid what some nods is the biggest plan to add up to an error. To come true best plan to close, the absolute value that should make 3 plan to add up to an error is equal, namely E1=-e2=e3, the biggest plan to add up to error E=max{| E1-e2 | , | E3-e2 | } . Can realize afore-mentioned requirements through optimizing computation. When planning to close, set linear equation to be X=kz+c above all, after the computation of affirmatory E1, E2, E3 is formulary, build target function F= | E1+e2 | + | E2+e3 | , design variable is linear slope K and invariable C, the ceaseless and mobile change that can adopt two node will mirror. Be bordering on when F hasten 0 when, achieve namely best plan to close, according to point of intersection the position can seek cost of a K, C, determine linear position thereby. Circular arc drafts legal plan 2 are shown roll law of razor involute worm to plan to close with circular arc curve of sectional tooth form. Curve of sectional tooth form still has involute worm way involute property, be apart from basic circle to exceed close drop namely its curvature radius is smaller, be apart from basic circle to exceed far drop its curvature radius is bigger. In the graph 2 show a way in sectional tooth form, a dot represents tine root, be close to basic circle, b dot supports on behalf of tine, be far from basic circle, the curvature radius that A dot nods to B by small greaten. Because the curvature radius of each bits on circular arc is identical, if choose radius of a curvature,be more than A accordingly curve of sectional tooth form drafts the dot, circular arc that is less than B dot and law combine model, can appear 3 node plan to add up to E1 of extreme value error, E2, E3, E4 with 4. To achieve best plan to close, raise modelling precision, need to change 3 nodical positions ceaselessly, make E1=-e2=e3=-e4, undertake optimizing computation accordingly. When planning to close, set plan to add up to circular arc equation to be (Z-Zc)2+(X-Xc)2=R2, plan to add up to extreme value error to be Ei=R-[(Zi-Zc)2+(X1-Xc)2]½ (i=1, 2, 3, in 4) type: R -- plan to add up to Zc of circular arc radius, xc -- the Z1 of coordinate of the centre of a circle that plans to add up to circular arc, x1 -- roll law of razor involute worm the coordinate that sectional curve drafts to add up to extreme value error to be in is built optimize target function to be F= | E1+e2 | + | E2+e3 | + | E3+e4 | + | E1+e4 | , design variable is Zc, Xc, R, the ceaseless shift that optimizes the report when computation to be 3 node changes. Be bordering on when F hasten 0 when, achieve namely best plan to close, get the biggest plan to add up to error E=max{| E1-e2 | , | E3-e2 | , | E1-e4 | , | E3-e4 | } . The basis is best the position that plans to add up to below condition 3 node, can seek cost of a Zc, Xc, R, plan to add up to the position of circular arc and radius certainly thereby. Graph 3 hyperbola plan to combine a plan the linear retrace runner shaft that hyperbola of error of 4 hyperbola modelling drafts to be H, banking angle to be A with rotor distance legally rotates, attainable the circumgyrate hyperboloid that an equation is X2/H2+y2/H2-z2/(H/tana)2=1. Sliver of direction of random of axes of edge hyperboloid circumgyrate all attainable hyperbola, press emery wheel of this linear contrail nap attainable axis is sectional the emery wheel that is hyperbola. The graph shows the way that rolls razor involute worm to plan to close with hyperbola 3 times curve of sectional tooth form. Hyperbola is to circle emery wheel axis to rotate obtain, its coordinate department is O-ZX, line segment Ab is a paragraph on hyperbola. To roll razor law curve of sectional tooth form is in coordinate is O-ZX, ab is the law that rolls razor curve of sectional tooth form, a expresses tine root, b states tine supports. When two curves plan to close, need to undertake to O-ZX coordinate department coordinate alternates, classics translation, after rotating, with OZX coordinate the department is weighed and, make the coordinate of two curves is identical. Because roll razor law,the curvature radius of curve of sectional tooth form nods B dot to greaten gradually from A, get hyperbola curvature radius to nod B to nod taper from A according to curvature radius formula, because this should choose appropriate parameter to make the A on hyperbola nods the curvature radius of area to be more than,roll the A on razor worm tooth form to nod the curvature radius of area, the curvature radius of extent of drop of the B on hyperbola is less than the curvature radius that rolls the B on razor worm tooth form to select area. When planning to close, can appear 3 node produce 4 to plan to add up to E1 of extreme value error, E2, E3, E4. If the graph is shown 4 times, should achieve best when planning to close, have E1=-e2=e3=-e4, can build from this optimize target function F= | E1+e2 | + | E2+e3 | + | E3+e4 | + | E1+e4 | . The hyperbola appearance of emery wheel is decided by parameter H, A, emery wheel position is decided by parameter Z0, X1, B. Although the appearance of emery wheel and position are decided by 5 parameter, but plan to add up to a curve to have 3 node only, can beg only namely piece among them 3 parameter. For this, when optimizing computation but will among them two parameter (X0, b) regards a tie as the condition, 3 parameter regard the others as design variable, report is 3 nodical ceaseless shift to change. Be bordering on when F hasten 0 when, achieve namely best plan to close, get the biggest plan to add up to error E=max{| E1-e2 | , | E3-e2 | , | E1-e4 | , | E3-e4 | } . By 3 affirmatory node can beg a 3 designs variable, add on two to give parameter, can determine the appearance of emery wheel and position. Example of computation of 4 modelling error sets big modulus hard tooth flank to roll the basic parameter of razor to be: Mn=14mm of method extent modulus, ° of An=20 of horn of method extent tooth form, carry D=290mm of round external diameter on the head, the helix that divide a circle rises horny G=3 ° 7, sheet head, dextral. Use methods of afore-mentioned 3 kinds of similar model sectional to rolling razor law tooth form undertakes similar model error emulates computation. Computation sees right table as a result. Error of modelling of method of modelling of watch of error of similar model emulation computation (µm)e1e2e3e4e plans to close point-blank 5.

89-5.

845.

86... 11.

73 circular arc plan to close 0.

326-0.

3840.

308-0.

3290.

674 hyperbola plan to close 0.

577-0.

5030.

570-0.

561.

133 by right watch knowable, the modelling error that plans to close point-blank is the biggest (E=11.

73µm) ; The modelling error that hyperbola drafts to close is minor (E=1.

133µm) ; The modelling error that circular arc drafts to close is the smallest (E=0.

674µm) . Because roll razor heretofore to have not establish relevant precision standard, accordingly but standard of precision of hob of temporary apply mechanically. The difference of tooth form allow of ISO4468-1982 and the AA class hob that GB6064-85 standard sets 16mm of modulus Mn>10 ～ is 10µm. Contrast watch 1 result is knowable, the modelling error that plans to close point-blank is more than a standard to stipulate tooth form allow is poor, cannot use; The modelling error that circular arc drafts to close to plan to close with hyperbola is far be less than standard allow difference, it is idealer modelling curve. Because hyperbola has the characteristic that presses linear nap emery wheel, because this is curve of approximate formative first selection. 5 conclusion roll razor involute worm to big modulus hard tooth flank sectional tooth form had alveolar cent round way similar model computation and analysis, the result makes clear: Draft legal error point-blank bigger, the tooth form allow that exceeds standard regulation is poor, cannot use; Circular arc drafts legal error the smallest; Hyperbola drafts legal error very small also, and can press emery wheel of linear means nap, it is better similar model method. CNC Milling