GB2585982A - Involute cylindrical gear envelope milling method taking precise characteristics of tooth surface into consideration - Google Patents
Involute cylindrical gear envelope milling method taking precise characteristics of tooth surface into consideration Download PDFInfo
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- GB2585982A GB2585982A GB2009212.8A GB202009212A GB2585982A GB 2585982 A GB2585982 A GB 2585982A GB 202009212 A GB202009212 A GB 202009212A GB 2585982 A GB2585982 A GB 2585982A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/20—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
- B23F19/002—Modifying the theoretical tooth flank form, e.g. crowning
- B23F19/005—Modifying the theoretical tooth flank form, e.g. crowning using a face-mill-type tool, e.g. a milling or a grinding tool
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/182—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by the machine tool function, e.g. thread cutting, cam making, tool direction control
- G05B19/186—Generation of screw- or gearlike surfaces
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/45—Nc applications
- G05B2219/45214—Gear cutting
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- Mechanical Engineering (AREA)
- Human Computer Interaction (AREA)
- Manufacturing & Machinery (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Gears, Cams (AREA)
- Gear Processing (AREA)
Abstract
Provided is an involute cylindrical gear envelope milling method taking the precise characteristics of a tooth surface into consideration. The method comprises the following steps: S01, choosing a milling tool, and determining the diameter of the tool and the length of a cutting edge of the tool; S02, determining a dynamic eccentricity ei of an axis of the tool relative to an axis of a gear; S03, constructing a step length formula of feeding in a tooth profile direction, constructing a curvilinear equation between an involute tooth profile extension angle and a tooth surface residual height difference, and calculating a cutter location point; and S04, planning a feeding path. According to the method, on the premise of ensuring the machining precision of a tooth surface of an involute cylindrical gear, the differential geometrical characteristics of an involute tooth surface are comprehensively taken into consideration to calculate a cutter location point and plan a tool path, such that a tool feeding trajectory is distributed as required, thereby reducing redundant feeding for the root and top of a tooth, and improving the machining efficiency of tooth envelope milling and the meshing performance of the tooth surface.
Description
FREE-FORM MILLING MACHINING METHOD FOR INVOLUTE CYLINDRICAL GEAR CONSIDERING PRECISION CHARACTERISTICS OF TOOTH SURFACE
Technical Field
The present invention relates to the field of machining technologies, and in particular, to a free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface.
Background
Gear is a critical basic part in machinery-related application industries. In recent years, in view of the long machining cycle for single-piece, small-batch, and large-modulus gear parts, and high costs of special gear making equipment and special gear cutters existing in conventional gear machining methods such as gear hobbing, gear shaping, and gear shaving, a method for free-form milling machining on a cylindrical gear using a universal tool on a universal multi-axis machining center has emerged, which can provide a flexible gear making method with low costs, high efficiency, short cycle, and fast response for single-piece, small-batch, and large-modulus gear machining of enterprises.
However, such an advanced multi-axis free-form milling machining technology still has the problem of low machining efficiency in cylindrical gear machining. The first reason is that the principle of free-form milling is fitting a tooth surface into a free curved surface and then performing tool path planning without considering differential-geometric characteristics of the tooth surface. Especially for an involute cylindrical gear, each micro-segment on a tooth profile thereof has a different curvature radius, which has certain particularity. The second reason is that such a tool path planning method based on a free curved surface also does not consider the demand for mesh precision at a pitch circle of the tooth surface. During secondary meshing of the involute cylindrical gear, the main area participating in meshing is the tooth surface close to the pitch circle, and the machining precision of this area should be preferentially guaranteed during machining. Although five-axis machining centers in the prior art can realize milling machining of a cylindrical gear, the milling method employed is treating a tooth surface as a free curved surface, resulting in contradiction between the efficiency and precision.
As a result, if the machining precision of all portions on the tooth surface is treated according to the same residual height difference without considering differential-geometric characteristics of the tooth surface and requirements for precision characteristics of the tooth surface, a large amount of redundant feed is definitely caused, resulting in low machining efficiency or low precision of the meshing area of the tooth surface.
Summary
In view of the deficiencies in the prior art, the present invention provides a free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface, which is used for improving the machining efficiency and tooth surface meshing performance for milling an involute cylindrical gear using a universal tool on a universal machining center.
The present invention achieves the aforementioned technical objective by the following technical means.
A free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface comprises: SO I: selecting a tool and determining a tool diameter and a tool cutting edge length according to parameters of a gear workpiece to be machined; S02: performing machining by means of eccentric milling, and determining a dynamic eccentricity e, of a tool axis with respect to a gear axis; S03: according to precision requirements for a main meshing area on the tooth surface of the gear, establishing a formula of a feed step length in a tooth profile direction to solve a maximum spacing,A/","), of the feed step length in the tooth profile direction, an adjacent step spacing A/, of two cutter location points, and an involute spread angle u, corresponding to each cutter location point on the tooth surface, establishing a curvilinear equation At=f (Aie,) between a spread angle of an involute tooth profile and a tooth surface residual height difference, and finally determining machining cutter location points; and SO4: planning a tool path according to the cutter location points.
Preferably, in the step SO I, an end milling cutter or a rod milling cutter is selected for a small and medium modulus involute cylindrical gear, and a conical disc milling cutter or a rod milling cutter is selected for a large-modulus involute cylindrical gear.
Preferably, in the step 501, the tool diameter Di > y910 mm, and the cutting edge length Li> 20 Preferably, a calculation formula of the eccentricity et is: formula (1) el =rb sines0 +u1 +(p)-rut cos@0 +u7 +(p7)+=' where rf, is a base radius of the gear; co is a tooth space half-angle of the base circle; u, is the involute spread angle corresponding to each cutter location point on the tooth surface; yo, is a rotation angle of a rotary table fixedly connected to the gear, and c),= 60+ ut; and Dr is the tool diameter.
Preferably, the step S03 is specifically: S03.1: dividing cutter location points of the cutter in the tooth profile direction of the gear into n equal parts, wherein the cutter location points on the tooth surface are distributed according to a parabolic equation, setting the maximum spacing of the feed step length in the tooth profile direction as Al,,,"" a minimum spacing as and the adjacent step spacing of two cutter location points as Al,, wherein the feed step length of the tool in the tooth profile direction satisfies the following formula: Al;= 9 A/11 7 t n+ A/Mitt C [0, I'] formula (2) I 5 122 \ 22 5 S03.2: obtaining a radial height II of an involute on the tooth surface according to the given gear workpiece, wherein the maximum spacing 44,u, of the feed step length in the tooth profile direction can be solved from formula (3): H E 9 A/Mal (1 n A/ 1=0 -0 112 \, 2, 5 formula (3) S03.3: substituting solved in step S03.2 into formula (2), and traversing the number of passes ie [0, n] to obtain in turn a step spacing 4/, corresponding to each cutter location point on the tooth surface; S03.4: given that A/m,, and a current number i of passes are known, obtaining the involute spread angle in on the tooth surface corresponding to each cutter location point (x7,, yp) in the parabolic equation from formula (4): 9 Alma,' . + Al ma' Vi2 y2P -0
--
r=o 5 n2 ^. 2, 5 x = rbcos(ao+u,)+1-"ts, sin(a, t) = r), sin(cr" + 13,u, cos(a " + formula (4) where rf is a root radius; rh is the base radius; and co is the tooth space half-angle of the base circle; S03.5: assuming that coordinates of two adjacent cutter location points A and B on the involute are respectively (x21, jii) and (xB, ys), and A and B intersect at a point C, the point C is a maximum residual height difference between adjacent cutter location points, assuming that coordinates of the point C are (xc, yc), and assuming that slopes of the two adjacent cutter location points A and B on the involute are respectively k.4 and k8, obtaining the following formula according to a geometric relationship between the three points A, B, and C: YE ± klX71 -kBXB kB = kA(xc-x_4)+ formula (5) according to characteristics of the involute, the slopes k4 and 103 of the two adjacent cutter location points A and B on the involute are respectively: {k 4 = tan(a0 +u,) k, = tan(a0 + uB) formula (6) where uri and ttB are respectively involute spread angles of the two adjacent cutter location points A and B; {and involute equations of the two adjacent cutter location points A and B are respectively: x, = rb cos(a0 +114)+ 411 A sin(o-, +114) y, = rh sin(o-, +714)-411 4 cos(o-, + /1 4) xB = ri, cos(a, +10 + Tilt, sin(o-, + u,) 1 y B = ri, sin(a0 +7/B)-/Abu, co s(n-, +U.3 formula (8) substituting formulas (6), (7), and (8) into formula (5) to obtain the coordinates (xc, ye) of the point C, calculating the residual height difference of the point C: formula (7) A/6 = + -- atan + atan +)
ITO
Dh formula (9) obtaining in turn tooth surface residual height differences At; between adjacent cutter location points according to formula (9), and establishing, according to the known spread angle Au, of the involute tooth profile, the curvilinear equation between the spread angle Au, of the involute tooth profile and the tooth surface residual height difference At, as: At, = ,f(Au,) formula ( I 0) S03.6: determining the machining cutter location points according to the curvilinear equation between the spread angle Au, of the involute tooth profile and the tooth surface residual height difference Ati.
Preferably, a specific method for determining the machining cutter location points in the step S03.6 is: making the tool path have a distribution from dense to sparse from a pitch circle of the tooth surface to the tooth profile on upper and lower ends, namely, making a tooth surface residual height difference At; of the main meshing area close to the pitch circle the smallest, a tooth surface residual height difference At, of a secondary meshing area far from the pitch circle gradually increase, and a tooth surface residual height difference At of a non-meshing area close to root and top portions the largest.
Preferably, the step SO4 is specifically: starting from an end surface on one side of the top portion, first feeding the tool for a first pass in a tooth direction to complete milling of an entire tooth width h; feeding by a length of Azt; to a tooth space along the involute tooth profile; then feeding for a second pass in the tooth direction; and so on until free-form milling of the entire tooth surface is completed.
The beneficial effects of the present invention are: 1) when a universal tool is used to machine an involute cylindrical gear on a multi-axis machining center, while guaranteeing the machining precision of a tooth surface of the involute cylindrical gear, the present invention considers differential-geometric characteristics of the involute tooth surface to calculate cutter location points and plan a tool path, so that the tool feed trajectory can be distributed as required, and redundant feed at the root and the top can be reduced, thereby improving the machining efficiency of free-form milling.
2) While guaranteeing the machining efficiency of the tooth surface of the involute cylindrical gear, the present invention considers precision characteristics of the involute tooth surface, so that the tool path has a distribution from dense to sparse from the pitch circle of the tooth surface to the tooth profile on two ends, which meets the requirements for high precision in the middle and low precision on two ends of the tooth surface, thereby improving the meshing performance of the tooth surface.
Brief Description of the Drawings
FIG. 1 is a view illustrating a feed step length and tool path planning of an involute tooth surface considering precision characteristics of a tooth surface according to an embodiment of the present invention.
FIG. 2 is a schematic view illustrating various motion axes of a typical four-axis machining center.
FIG. 3 is a schematic view illustrating free-form milling of an involute gear using an end milling cutter on a four-axis machining center.
FIG. 4 shows a curve illustrating a relationship between a spread angle Au, of an involute tooth profile and a tooth surface residual height difference At1 according to the embodiment of the present invention.
FIG. 5 shows cutter location points for tool envelope of the involute tooth surface according to the embodiment of the present invention, where (a) corresponds to a finish machining method considering precision characteristics of the tooth surface, and (b) corresponds to a conventional finish machining method based on an equal residual height difference method.
FIG. 6 shows a relationship between a radial length and a residual height difference of the involute tooth surface according to the embodiment of the present invention, where (a) corresponds to a finish machining method considering precision characteristics of the tooth surface, and (b) corresponds to a conventional finish machining method based on an equal residual height difference method.
1. Gear workpiece; 2. end milling cutter.
Detailed Description of the Embodiments
The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.
A free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface in the present invention is illustrated in detail by using an involute cylindrical gear part used in a transmission mechanism as an example in the present invention. The gear type is straight, the number of teeth z = 44, modulus tn"= 20 mm, the pressure angle an = 20, modification coefficient xn= 0, tooth width b = 160 mm, and the precision requirement is Class 6 in IS01328-2:1997, where the precision requirement at the pitch circle is up to ISO Class 3. For the gear, when the machining precision is ISO Class 6, the total tooth profile deviation is 27.42 pm; when the machining precision is ISO Class 3, the total tooth profile deviation is 9.69 Rm. The existing machining equipment is a four-axis free-form milling machining center. As shown in FIG. 2, three linear axes are respectively an X axis, a Y axis, and a Z axis, one rotary axis is a C axis, a workpiece is mounted on a C-axis table, a tool is mounted on a spindle SP, and the Z axis and the C axis can realize linkage.
A free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface according to an embodiment of the present invention specifically includes the following steps: S01: select a tool.
An end milling cutter 2 is preferably selected for milling machining of an involute cylindrical gear, where tool parameters are as follows: A tool diameter D1 of the end milling cutter 2: a minimum tooth space width is calculated to be 21.9 mm according to parameters of a gear workpiece I, and in order to ensure sufficient linear velocity during tool cutting, the tool diameter Dr is selected to be p I 8 mm; A tool cutting edge length L1 of the end milling cutter 2: the cutting edge length L1 is selected to be 38 mm according to the parameters of the gear workpiece 1.
S2: determine a tool eccentricity.
When the machining equipment is a four-axis free-form milling machining center, machining needs to be performed by means of eccentric milling, as shown in FIG. 2. At this time, a dynamic eccentricity e, of the tool of the end milling cutter 2 is calculated: = sin(u, + + co,)-rbt cos(o-,+u, + yo,)+ 2 formula (1) where rb is a base radius of the gear; ao is a tooth space half-angle of a base circle; u, is an involute spread angle; pi is a rotation angle of a rotary table fixedly connected to the gear, namely, a rotation angle of the C axis, and pi = Co+ u,; and Di is the diameter of the end milling cutter 2.
S3: calculate cutter location points.
According to precision requirements for a main meshing area on the tooth surface of the gear, a formula of a feed step length in a tooth profile direction is established to solve a maximum spacing Aimay of a feed step length in the tooth profile direction, solve an adjacent step spacing Al, of two cutter location points, and solve an involute spread angle u, corresponding to each cutter location point on the tooth surface, a curvilinear equation Atitt (Atti) between the spread angle of the involute tooth profile and a tooth surface residual height difference is established, and finally machining cutter location points are determined. The step S03 is specifically: S03.1: establish the formula of the feed step length in the tooth profile direction.
Cutter location points of the end milling cutter 2 in the tooth profile direction of the gear are divided into r20 equal parts, where the cutter location points on the tooth surface are distributed according to a parabolic equation. Assume that the maximum spacing of the feed step length in the tooth profile direction is a minimum spacing is and the adjacent step spacing of two cutter location points is Al,, as shown in FIG. I. At this time, the feed step length of the tool in the tooth profile direction satisfies formula (2): formula (2) 2\ A/ =9 A/ ma i +41" G [0, n] n2 S03.2: solve the maximum spacing A/,,,a, of the feed step length in the tooth profile direction. For the given gear workpiece 1, it can be known that a radial height of an involute on the tooth surface is H -45 mm. The maximum spacing 6.415 mm of the feed step length in the tooth profile direction can be solved from formula (3): formula (3) S03.3. solve a step spacing At corresponding to each cutter location point on the tooth surface of the gear 41, ax solved in step S03.2 is substituted into formula (2), the number of passes i E [0, 20] is traversed to obtain in turn a step spacing Al, of each point on the tooth surface.
S03.4: solve the involute spread angle u, corresponding to each cutter location point on the tooth surface.
Since it is known that A/,,,,,= 6.415 mm and the current total number of passes n = 20, the involute spread angle u, on the tooth surface corresponding to each cutter location point (xp, yp) in the parabolic equation is obtained from formula (4): 9 Alma A/ 1 X2 ± y2 = 0
P P n2
= ri, cos(o-0 + n I) + rhu + it!) = r, sin(0-0 +11, )- cos(u + u7) formula (4) where a root radius is rf = 415 mm; the base radius is rb = 413.645 mm; and the tooth space half-angle of the base circle is o-o= 1.192°.
S03.5: establish a curvilinear equation between the spread angle Au, of the involute tooth profile and a tooth surface residual height difference At,.
[ 2, 5 _o H, 9 Al ",,,,( F _o 5 n-, Assume that coordinates of two adjacent cutter location points A and B on the involute are respectively (xi, yi) and (xB, yB), and A and B intersect at a point C, the point C is a maximum residual height difference between adjacent cutter location points. Assume that coordinates of the point C are ()cc, yc), and assume that slopes of the two adjacent cutter location points A and B on the involute are respectively k4 and kB, equation set (5) can be obtained according to a geometric relationship between the three points A, B, and C: formula (5) According to characteristics of the involute, the slopes ki and k8 of the two adjacent cutter location points A and B on the involute are respectively: k,, = taii(o-a + u,) k11 = tan(a0 +113) formula (6) where /LI and its are respectively involute spread angles of the two adjacent cutter location points A and B, which can be obtained from formula (4).
Moreover, involute equations of the two adjacent cutter location points A and B are respectively: x = rb cos(o-0 +u7,)+Tb7L4 sin(a0 +/44) 1 = Y, sin(a0 +ti,)-rhtiAcos(0-b+u,) formula (7) {x B = rbcos(o-b +10+v,11 sin(o-, +u11) y, = cr, sin(0-0 + ti8)-Thu, cos(o0 + t, 18) formula (8) Formulas (6), (7), and (8) are substituted into formula (5) to obtain the coordinates (xc, yc) of the point C. The residual height difference of the point C is calculated: k -ks Y"=k1(ve-x1)± Y4 2 yL AlA Vy2. e. -Yc -r atan Ye + atan xc, rb formula (9) Tooth surface residual height differences At, between adjacent cutter location points can be obtained in turn according to formula (9). As shown in FIG. 4, according to the known spread angle Au, of the involute tooth profile, the curvilinear equation between the spread angle Atti of the involute tooth profile and the tooth surface residual height difference At, is established as: At, = formula (10) S03.6: according to formula (10), make a tool path have a distribution from dense to sparse from a pitch circle of the tooth surface to the tooth profile on upper and lower ends, namely, make a tooth surface residual height difference At, of the main meshing area close to the pitch circle the smallest, a tooth surface residual height difference At, of a secondary meshing area far from the pitch circle gradually increase, and a tooth surface residual height difference At; of a non-meshing area close to root and top portions the largest.
SO4: plan the tool path.
During the machining, starting from an end surface on one side of the top portion, the tool is first fed for a first pass in a tooth direction to complete milling of an entire tooth width b; fed by a length of Au, to a tooth space along the involute tooth profile; then fed for a second pass in the tooth direction; and so on until free-form milling of the entire tooth surface is completed.
Throughout the milling, the machining step and the tooth surface precision are controlled according to a specific algorithm, so as to realize free-form milling machining of the involute cylindrical gear with high precision and high efficiency.
FIG. 5 shows cutter location points for envelope of the involute tooth surface simulated through CAM software when the numbers of the cutter location points for tool envelope of the involute tooth surface are both 20. FIG. 5(a) shows a finish machining method considering precision characteristics of the tooth surface according to the present invention, where cutter location points on the tooth surface mainly concentrate in the vicinity of the pitch circle having higher precision requirements. FIG. 5(b) shows a conventional finish machining method based on an equal residual height difference method, where cutter location points on the tooth surface show a tendency from dense to sparse from the root to the top.
FIG. 6 shows a relationship between a radial length and a residual height difference of the involute tooth surface. FIG. 6(a) shows a finish machining method considering precision characteristics of the tooth surface according to the present invention, where the obtained tooth surface residual height differences show a tendency of increasing toward the top and the root along the pitch circle, and the residual height difference near the pitch circle (435 mm < r,.< 445 mm) is At < 2.5 pm. FIG. 6(b) shows a conventional finish machining method based on an equal residual height difference method, where the obtained tooth surface residual height differences are uniformly distributed along the tooth surface. That is, the residual height difference at the pitch circle and the residual height differences at the top and the root are At = 6 Inn. Further, for an involute gear, the portion close to the pitch circle on the tooth surface is the main meshing area, while portions near the root and the top seldom participate in meshing. The finish machining method for the involute tooth surface based on the equal residual height difference method causes a large amount of redundant feed at the root and top portions, which not only reduces machining efficiency, but also fails to consider precision requirements for the meshing area at the pitch circle. Accordingly, a free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface provided in the present invention not only can improve the machining efficiency of free-form milling of the gear, but also can achieve better meshing performance for the tooth surface.
The described embodiment is a preferred embodiment of the present invention, but the present invention is not limited to the aforementioned embodiment. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essential content of the present invention shall fall within the protection scope of the present invention.
Claims (7)
- Claims What is claimed is: 1. A free-form milling machining method for an involute cylindrical gear considering precision characteristics of a tooth surface, comprising: SOl: selecting a tool and determining a tool diameter and a tool cutting edge length according to parameters of a gear workpiece to be machined; 502: performing machining by means of eccentric milling, and determining a dynamic eccentricity e, of a tool axis with respect to a gear axis; S03: according to precision requirements for a main meshing area on the tooth surface of the gear, establishing a formula of a feed step length in a tooth profile direction to solve a maximum spacing of the feed step length in the tooth profile direction, an adjacent step spacing AL of two cutter location points, and an involute spread angle ri; corresponding to each cutter location point on the tooth surface, establishing a curvilinear equation Atitt (Ant) between a spread angle of an involute tooth profile and a tooth surface residual height difference, and finally determining machining cutter location points; and SO4: planning a tool path according to the cutter location points.
- 2. The free-form milling machining method for the involute cylindrical gear considering the precision characteristics of the tooth surface according to claim 1, characterized in that, in the step S01, an end milling cutter or a rod milling cutter is selected for a small and medium modulus involute cylindrical gear, and a conical disc milling cutter or a rod milling cutter is selected for a large-modulus involute cylindrical gear.
- 3. The free-form milling machining method for the involute cylindrical gear considering the precision characteristics of the tooth surface according to claim 2, characterized in that, in the step S01, the tool diameter D, > p10 mm, and the cutting edge length Lf> 20 mm.
- 4. The free-form milling machining method for the involute cylindrical gear considering the precision characteristics of the tooth surface according to claim 1, characterized in that, a calculation formula of the eccentricity Cr is: e, = sin(cro + cos(o-o+u,+ ,)+ D, formula (1) where n is a base radius of the gear; o-0 is a tooth space half-angle of a base circle; it, is the involute spread angle corresponding to each cutter location point on the tooth surface; p, is a rotation angle of a rotary table fixedly connected to the gear, and pi = Co + u1; and Di is the tool diameter.
- 5. The free-form milling machining method for the involute cylindrical gear considering the precision characteristics of the tooth surface according to claim 1, characterized in that, the step S03 specifically comprises: S03.1: dividing cutter location points of the cutter in the tooth profile direction of the gear into /a equal parts, wherein the cutter location points on the tooth surface are distributed according to a parabolic equation, and setting the maximum spacing of the feed step length in the tooth profile direction as A/",",, a minimum spacing as A/,,,,=A/","15, and the adjacent step spacing of two cutter location points as Al, wherein the feed step length of the tool in the tooth profile direction satisfies the following formula: Al --* ""' i 9 Al 1 n + AlIllax e [0, /7] /22 2,, 5 formula (2) S03.2: obtaining a radial height H of an involute on the tooth surface according to the given gear workpiece, wherein the maximum spacing Al,. of the feed step length in the tooth profile direction can be solved from formula (3): n\2 Al 9 AlMai,. 111dX. -0 n2 2 5 formula (3) S03.3: substituting At., solved in step S03.2 into formula (2), and traversing the number of passes i E [0, n] to obtain in turn a step spacing A/1 corresponding to each cutter location point on the tooth surface; S03.4: given that A/n,",-and a current number i of passes are known, obtaining the involute spread angle th on the tooth surface corresponding to each cutter location point (xp, y,,) in the parabolic equation from formula (4): r 9 Al"", i n''' + AZ r," , 2,, cx =0 7 AIX2 ± Y2 =0 l' P __ \ . 5 n = I;, COS(0-0 ± I I,) ± rbl I, sin(a, + tc) yr = ri, sin(ra + 112)-r"u, cos(0-0 +112) formula (4) where ty is a root radius; ry is the base radius; and ao is the tooth space half-angle of the base circle; S03.5: assuming that coordinates of two adjacent cutter location points A and B on the involute are respectively (z4, yA) and (xis, yB), and A and B intersect at a point C, the point C is a maximum residual height difference between adjacent cutter location points, assuming that coordinates of the point C are (rc, yr), and assuming that slopes of the two adjacent cutter location points A and B on the involute are respectively ki.4 and kB, obtaining the following formula according to a geometric relationship between the three points A, B, and C: y -y + cAx -&ix is k_1-kB = -x3)+y1 formula (5) according to characteristics of the involute, the slopes k4 and Icy of the two adjacent cutter locationH 1=0{points A and B on the involute are respectively: kA = tan(a, + //A) kg = tan(o-0 +u8) formula (6) where ki and uB are respectively involute spread angles of the two adjacent cutter location points A and B; and involute equations of the two adjacent cutter location points A and B are respectively: Tx, = rb cos(o-c, + up, )+ rb'Asin(60+ {ty, = Th siner" + rhu cos(a0 + u formula (7) x = r, cos(a0 + u 8) + r,u8 sin(a0 + u8) yB =rbsin(c0 + un)-rbu "cos(a0 +u11) formula (8) substituting formulas (6), (7), and (8) into formula (5) to obtain the coordinates (xc, yc) of the point C, calculating the residual height difference of the point C: + "-11,1 In formula (9) obtaining in turn tooth surface residual height differences At; between adjacent cutter location points according to formula (9), and establishing, according to the known spread angle Au, of the involute tooth profile, the curvilinear equation between the spread angle Au, of the involute tooth profile and the tooth surface residual height difference At, as: At = (Au, ) formula (10) S03.6: determining the machining cutter location points according to the curvilinear equation between the spread angle Au; of the involute tooth profile and the tooth surface residual height difference At,.
- 6. The free-form milling machining method for the involute cylindrical gear considering the precision characteristics of the tooth surface according to claim 5, characterized in that, a specific method for determining the machining cutter location points in the step S03.6 comprises: making the tool path have a distribution from dense to sparse from a pitch circle of the tooth surface to the tooth profile on upper and lower ends, namely, making a tooth surface residual height difference At, of the main meshing area close to the pitch circle the smallest, a tooth surface residual height difference At, of a secondary meshing area far from the pitch circle gradually increase, and a tooth surface residual height difference At, of a non-meshing area close to root and top portions the largest. ye cAt, = xc + - r, atan + atan Co
- 7. The free-form milling machining method for the involute cylindrical gear considering the precision characteristics of the tooth surface according to claim 1, characterized in that, the step SO4 specifically comprises: starting from an end surface on one side of the top portion, first feeding the tool for a first pass in a tooth direction to complete milling of an entire tooth width h; feeding by a length of Au; to a tooth space along the involute tooth profile; then feeding for a second pass in the tooth direction; and so on until free-form milling of the entire tooth surface is completed.
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| CN201910059324.5A CN109663991B (en) | 2019-01-22 | 2019-01-22 | Involute cylindrical gear enveloping milling method considering tooth surface precision characteristic |
| PCT/CN2020/073343 WO2020151683A1 (en) | 2019-01-22 | 2020-01-21 | Involute cylindrical gear envelope milling method taking precise characteristics of tooth surface into consideration |
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| CN110125490B (en) * | 2019-05-17 | 2020-05-22 | 淮阴工学院 | Method for finish milling of gear surface of Niemann worm gear by using full-edge side edge of flat-bottom taper milling cutter |
| CN111687495B (en) * | 2020-05-25 | 2022-04-22 | 西安交通大学 | Stepped feed rough cutting method for herringbone gear with narrow clearance groove |
| CN111687496B (en) * | 2020-05-25 | 2021-10-08 | 西安交通大学 | Narrow clearance groove herringbone gear offset forming processing method |
| CN113283025B (en) * | 2021-05-11 | 2022-09-06 | 北京理工大学 | Involute tooth profile error modeling method containing system error |
| CN114043012A (en) * | 2021-09-15 | 2022-02-15 | 南京工业大学 | Flexible envelope machining method for cutter path of gear milling cutter head |
| CN113885432B (en) * | 2021-10-26 | 2023-11-17 | 辽宁科技学院 | Cutter path planning method for few-axis numerical control machining face gear |
| CN114309820B (en) * | 2022-01-04 | 2022-08-02 | 南京工业大学 | Gear single-side forming machining method combining customized cutter and specific path |
| CN114770217B (en) * | 2022-05-05 | 2024-01-26 | 清华大学 | Processing method and device of asymmetric bionic fish scale type microstructure |
| CN115657602B (en) * | 2022-12-03 | 2024-05-28 | 广西大学 | Design and shape modification method for tooth scraping tool |
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