CN107977503A

CN107977503A - Worm abrasion wheel processes the multitool approach method of small size tooth top fillet

Info

Publication number: CN107977503A
Application number: CN201711208764.XA
Authority: CN
Inventors: 李国龙; 任唯贤; 何坤; 董鑫; 徐凯
Original assignee: Chongqing University
Current assignee: Chongqing University
Priority date: 2017-11-27
Filing date: 2017-11-27
Publication date: 2018-05-01
Anticipated expiration: 2037-11-27
Also published as: CN107977503B

Abstract

The invention belongs to gear manufacture field, it is related to the multitool approach method of worm abrasion wheel processing small size tooth top fillet, when solving the tooth top fillet of processing small size, worm abrasion wheel is because of radius of curvature too small the problem of can not repairing.Pass through the translation to worm abrasion wheel X-axis and Y-axis, process multistage curve, fillet curve is gone out by multistage envelope of curve, it is proposed a kind of method of point vector pairing, solve the offset of emery wheel X-axis and Y-axis, and the original reason error of approach method is analyzed, established according to the error upper limit required when designing and most preferably approach arc size and approach knife number.

Description

Worm abrasion wheel processes the multitool approach method of small size tooth top fillet

Technical field

The invention belongs to gear manufacture field, is related to the approach method with multistage orthodrome envelope small arc-shaped, solves processing During the tooth top fillet of small size (hereinafter referred to as small round corner), worm abrasion wheel can not be repaiied because minimum profile curvature radius is less than roller radius The problem of whole.

Background technology

A large amount of theory and practice show that the edge corner angle of gear can be produced and made an uproar because small colliding with easily causes flank of tooth protrusion Sound and damage mesh tooth face, and this edge corner angle easily cause stress concentration during heat treatment, influence the power of gear Learning performance causes the easy fatigue wear of gear, reduces gear life.Thus in gear manufacture field, to gear carry out chamfered edge with Rounding processing becomes one of important procedure.

Gear rounding is divided into flank profil rounding and tooth top rounding.Flank profil rounding usually on chamfering machine, by squeeze rib knife or into Type milling cutter is processed, and the effect of tooth top rounding is more important compared with flank profil rounding, because in gear drive, driving gear Tooth top cusp directly engaged with the face of driven gear, be also easy to produce impact, cause noise and vibration.

Tooth top rounding is still by the way of manual polishing at present, its main cause is that the worm abrasion wheel for processing fillet is difficult to Finishing, particularly with fillet size it is smaller when, the minimum profile curvature radius of worm abrasion wheel will be less than the radius of curvature of emery wheel, Emery wheel is caused not repair.

The content of the invention

Problem can not be repaired for the worm abrasion wheel of above-mentioned processing tooth top small round corner, the present invention provides a kind of worm abrasion wheel The multitool approach method of tooth top small round corner is processed, is realized with the tooth top in Rouno Cormer Pregrinding Wheel worm abrasion wheel processing assigned error allowed band Small round corner.

In order to solve the above-mentioned technical problem, present invention employs following technical solution：

Worm abrasion wheel process tooth top small round corner multitool approach method, by process tooth top Rouno Cormer Pregrinding Wheel worm abrasion wheel into The translation of row X-axis and Y-axis, processes the different tip curve of multistage, finally goes out tooth top small round corner by multistage envelope of curve.Approach Principle takes 5 skill in using a kitchen knife in cookery to approach the fillet that radius is 0.05 as shown in Figure 1, using the worm abrasion wheel that radius of machining is 0.5 fillet, It can be seen that Approaching Results are exactly accurate.

As a preferred embodiment of the present invention, worm abrasion wheel carries out X-axis and is translated with Y-axis, the solution of the offset of translation Method is realized by way of point vector pairing, and detailed process is to compare the production shape tooth of tooth top Rouno Cormer Pregrinding Wheel and tooth top small round corner Bar profile, the identical point vector of normal vector is matched, one group of X-axis of coordinate difference, that is, emery wheel per a pair of match point vector with The offset of Y-axis.For X-axis and the Y-axis translational movement that emery wheel converts every time is solved, a kind of method of point vector pairing is proposed, with Exemplified by 0.5 circular approximation, 0.05 circular arc, it is 0.05 to compare counterpart rack point vector that radius of machining is 0.5 fillet with radius of machining Counterpart rack point vector, the equal point vector of slope is matched, by the use of pairing point vector coordinate difference as emery wheel put down Shifting amount (△ X, △ Y)：

Wherein (X2, Y2) is the discrete point coordinates of counterpart rack that radius of machining is 0.5 fillet, and (x2, y2) is radius of machining For the 0.05 discrete point coordinates of counterpart rack.

As another preferred solution of the present invention, going out the approach method of small round corner by multistage envelope of curve, there are cusp mistake Difference, the cusp are the intersection points of adjacent two curves, and the distance in intersection point and the small round corner center of circle is cusp height, and cusp highly subtracts small Radius of corner, that is, approximate error value.For the approach method of this tangent envelope there are cusp error, which added by adjacent two knife What the flank profil intersection point that work goes out was formed, as shown in Fig. 2, error size E can use flank profil intersection point to the distance and radius in the fillet center of circle Difference represent：

Wherein (X_j, Y_j) it is flank profil intersecting point coordinate, (X₀, Y₀) fillet central coordinate of circle, r is radius of corner.

As a modification of the present invention scheme, the rounding worst error provided according to design, calculates under the error most Knife number and maximum radius of corner are approached less.The error amount produced by calculating different great circle angular radius with knife number, can obtain Volume of data point, obtains error curve using Cubic Spline Fitting to data point, multitool can be instructed to force according to error curve Nearly method chooses most suitable knife number and great circle angular radius.

The solution have the advantages that：When solving the tooth top fillet with worm abrasion wheel processing small size, because emery wheel is minimum Radius of curvature is too small and the problem of can not repair, reduced to greatest extent using suitable knife number and great circle angular radius and approach mistake Difference, improves rounding precision.

Brief description of the drawings

Fig. 1 is the schematic diagram that 0.5 fillet, five skill in using a kitchen knife in cookery approaches 0.05 fillet；

Fig. 2 is the processing of the first knife and the schematic diagram of the cusp error of the second knife processing；

Fig. 3 is the graph of a relation of great circle angular radius and approximate error under different knife numbers.

Embodiment

The present invention is described in further detail with reference to the accompanying drawings and detailed description.

Worm abrasion wheel processes the multitool approach method of tooth top small round corner, and approximation theory is as shown in Figure 1, it is first determined processing tooth The counterpart rack point vector of Rouno Cormer Pregrinding Wheel is pushed up, great circle angular radius is R, and great circle angle equation (X1, Y1) is：

Rouno Cormer Pregrinding Wheel flank profil normal vector (Nx, Ny) is：

Wherein：R_aRepresent radius of addendum, R represents chamfering radius, and α is the solution parameter of central coordinate of circle, and θ 1 represents tooth top Arc angle on circle, θ 2 represent the arc angle on flank profil involute.Substitute into mesh equation：

WhereinRepresent flank profil normal vector,Represent relative velocity, subscript 1 is illustrated respectively in different coordinates from 2 It is that A matrixes are under S1 and S2：

It is transformation matrix, (4) formula is substituted into (3) formula, solves mesh equation, obtains flank profil point and enter needed for engagement Corner φ, then obtain by coordinate transform the profile (X2, Y2) of Rouno Cormer Pregrinding Wheel counterpart rack and be：

Normal vector (the N2 of Rouno Cormer Pregrinding Wheel counterpart rack_x, N2_y) be：

(X2, Y2) and (N2_x, N2_y) composition Rouno Cormer Pregrinding Wheel counterpart rack point vector.

Then the counterpart rack point vector that small round corner approaches point of contact is solved, method for solving is with solving Rouno Cormer Pregrinding Wheel counterpart rack The method of point vector is identical.When using knife number as more skill in using a kitchen knife in cookery processing of D, the D Along ents that point of contact is selected in small round corner, small round corner are approached Radius is r, after D deciles,

Roundlet angle equation (x1, y1) is：

Small round corner normal vector (n_x, n_y) be：

(3) formula mesh equation is substituted into, and carries out coordinate transform, the profile (x2, y2) for obtaining small round corner counterpart rack is：

(x2, y2) and (N2_x, N2_y) counterpart rack at composition small round corner point of contact point vector.

Finally compare the point vector of Rouno Cormer Pregrinding Wheel counterpart rack point vector and the counterpart rack at small round corner point of contact, by normal vector The identical point vector in direction matched, i.e., found and small round corner counterpart rack normal vector direction in Rouno Cormer Pregrinding Wheel counterpart rack Identical point, considers the slope of the two normal in same section, which is (0, arctan α), and wherein α is involute pressure Power angle, thus the point vector of the counterpart rack at each small round corner point of contact can find pairing in Rouno Cormer Pregrinding Wheel counterpart rack Point vector.

The identical pairing point vector of comparison method line slope, its coordinate difference are the X-axis of required emery wheel conversion per knife, and Y-axis is inclined Shifting amount (△ X, △ Y).

If the first knife offset is (△ X1, △ Y1) according to the offset of emery wheel, you can obtains the profile after emery wheel offset Discrete point (X '₂, Y '₂):

Mesh equation is substituted into by the profile discrete point：

Wherein B matrixes are：

Mesh equation is solved, flank profil point is obtained and enters the required corner φ of engagement, then the first knife is obtained by coordinate transform Gear profile (the X ' that conversion post-processing goes out₁, Y '₁) be：

Gear profile (the X ' of the first knife processing is drawn out in CAD₁, Y '₁) matched curve, can be seen by drawing result It has no longer been circular arc to go out the curve that emery wheel translation transformation post-processing goes out, and same method can calculate tooth during next knife processing Wheel profile simultaneously draws out matched curve, the cusp of intersection point, that is, error maximum of two curves, cusp to the fillet center of circle in CAD Distance and radius difference, that is, error size E, formula is expressed as：

The maximum of these cusp errors is chosen as final approximate error all there are intersection point during processing per adjacent two knife E_m, by calculating different great circle angular radius and the error value E of knife number generation_m, volume of data point is can obtain, data point is adopted Error curve is obtained with Cubic Spline Fitting, as shown in Fig. 2, it is most suitable according to error curve multitool approximatioss can be instructed to choose Knife number and great circle angular radius；Fig. 3 is the graph of a relation of great circle angular radius and approximate error under different knife numbers.

Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with The present invention is described in detail in good embodiment, it will be understood by those of ordinary skill in the art that, can be to the skill of the present invention Art scheme technical scheme is modified or replaced equivalently, without departing from the objective and scope of technical solution of the present invention, it should all cover at this Among the right of invention.

Claims

1. worm abrasion wheel processes the multitool approach method of small size tooth top fillet, it is characterised in that by processing large scale tooth The worm abrasion wheel at tip circle angle carries out the translation of X-axis and Y-axis, the different tip curve of multistage is processed, finally by multistage curve bag Network goes out small size tooth top fillet.

2. the multitool approach method of worm abrasion wheel processing small size tooth top fillet according to claim 1, it is characterised in that snail Bar emery wheel carries out X-axis and Y-axis and translates, and the method for solving of the offset of translation is to realize have by way of point vector pairing Body process is to compare the counterpart rack profile at large scale outside circle angle and small size tooth top fillet, by the identical point vector of normal vector Matched, per the one group of X-axis of coordinate difference, that is, emery wheel and the offset of Y-axis of a pair of match point vector.

3. the multitool approach method of worm abrasion wheel processing small size tooth top fillet according to claim 2, it is characterised in that by Multistage envelope of curve goes out the approach method of small size fillet there are cusp error, which is the intersection point of adjacent two curves, hands over The distance in point and the small round corner center of circle is cusp height, and cusp highly subtracts small fillet radius i.e. approximate error value.

4. the multitool approach method of worm abrasion wheel processing small size tooth top fillet according to claim 3, it is characterised in that root The rounding worst error provided according to design, calculates and at least approaches knife number and maximum radius of corner under the error.