CN115026354A - Reverse envelope design method for complex-tooth-shaped turning cutter - Google Patents
Reverse envelope design method for complex-tooth-shaped turning cutter Download PDFInfo
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Abstract
The invention provides a reverse enveloping design method of a turning cutter with a complex tooth shape, which comprises the following steps: acquiring a tooth profile discrete data point; determining the number of teeth and the helix angle of the cutter; calculating the intersection angle of the cutter mounting shaft and the initial mounting center distance of the cutter; based on the space meshing principle of the staggered shaft gear and the reverse enveloping motion relation of the gear machining, the edge shape of the front tool face of the tool is obtained; determining a tool rake angle and a top edge relief angle; calculating the cutter mounting center distance variation of the cutter on each section in the axial direction; calculating the mounting center distance of the cutters of each section, and obtaining the blade shapes of the corresponding sections of the cutters on the basis of the space meshing principle of the staggered shaft gear and the reverse enveloping motion relation of the turning gear processing for each cutter section; and sequentially fitting the edge shape of the front tool face of the tool and each section edge shape of the tool into a rear tool face of the tool according to the sequence from the near to the far away from the front tool face. The design process is simple and convenient, and the designed turning tooth cutter has high edge shape precision.
Description
Technical Field
The invention relates to the technical field of gear machining cutters, in particular to a reverse enveloping design method of a turning cutter with a complex tooth shape.
Background
The gear is a key basic part in various industries, and the processing technology level of the gear has great significance for developing high-grade gear products. The turning gear processing is a novel gear processing technology, can solve the processing problem of a thin-wall or tool withdrawal-free compact inner gear ring on a high-grade precise harmonic reducer and an automatic transmission, and has the remarkable advantages of high precision, high efficiency, environmental friendliness and the like. At present, more and more enterprises adopt a gear turning process to replace the traditional rolling/inserting/gear pulling-honing/gear grinding process.
The key of the gear turning technology lies in the design of the cutter edge shape, and the current gear turning cutter design method is a forward design method mainly based on the conjugate theory of two-degree-of-freedom curved surfaces and curves. However, this kind of forward design method has limitations, especially for some complex tooth gears requiring modification of tooth profile, root digging or tooth top chamfering, in the transition curve portion of modification, root digging or chamfering, when the tooth profile diameter is smaller than the base circle diameter, or the local area exceeds the curvature limit of conjugate meshing, the method of solving the cutter edge shape by using the meshing equation of conjugate theory is easy to generate the problem of solution set divergence, resulting in that the correct cutter edge shape cannot be designed. In practical engineering application, parameters of gears to be machined are incomplete, only CAD (computer aided design) engineering drawings or discrete data points of gear tooth shapes are available, analytical equations of the gear tooth shapes cannot be obtained, and the cutter edge shapes are difficult to calculate by adopting a conjugate theory. For the gears with complex tooth shapes, the existing design method of the gear turning tool generally adopts rough design methods such as piecing up edge lines, auxiliary drawing and the like to approach the tooth shapes of the gears, the design efficiency is very low, the edge shape precision of the gear turning tool is influenced, the design cycle of the gear turning tool is prolonged, and the tooth shape application range of the gear turning tool is limited.
In addition, the back tool face of the existing conical tooth turning tool adopts a design method of equal side back angles, and although the tool designed by the method is simple and convenient in manufacturing process, the precision of the tooth turning tool is reduced after repeated regrinding, and the service life of the tool is limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a reverse enveloping design method of a turning cutter with a complex tooth shape, the design process is simple and convenient, and the designed turning cutter has high edge shape precision.
The present invention achieves the above-described object by the following technical means.
A reverse enveloping design method for a turning cutter with a complex tooth shape comprises the following steps:
s1: acquiring a tooth profile discrete data point for describing the gear to be machined according to the parameters of the gear to be machined;
s2: determining the number of teeth of the cutter and the spiral angle of the cutter;
s3: calculating the intersection angle of the cutter mounting shaft and the initial mounting center distance of the cutter;
s4: based on a staggered shaft gear space meshing principle and a reverse enveloping motion relation of gear turning machining, under the condition of an initial installation center distance of a cutter, reversely enveloping a tooth shape discrete data point of the gear to be machined to obtain a cutter front cutter edge shape profile data point cloud, carrying out layering processing on the cutter front cutter edge shape profile data point cloud, and extracting an inner boundary data point of the cutter front cutter edge shape profile data point cloud to obtain a cutter front cutter edge shape;
s5: determining a front angle and a back angle of a top edge of the cutter;
s6: determining the total regrinding quantity of the cutter, equally dividing the total regrinding quantity of the cutter into a plurality of equal parts, forming a plurality of equally divided sections on the cutter in the axial direction, and calculating the variation quantity of the installation center distance of the cutter on each section;
s7: superposing the variation of the tool mounting center distance on each section with the initial tool mounting center distance to obtain the tool mounting center distance of each section, reversely enveloping the tooth profile discrete data points of the gear to be processed under the condition of the corresponding tool mounting center distance for each tool section to obtain the blade profile data point cloud of the corresponding section of the tool, layering the blade profile data point cloud of the corresponding section of the tool, extracting the inner boundary data points of the blade profile data point cloud of the corresponding section of the tool to obtain the blade profile of the corresponding section of the tool;
s8: and sequentially fitting the edge shape of the front tool face of the tool and each section edge shape of the tool into a rear tool face of the tool according to the sequence from the near to the far away from the front tool face.
Further, the method for acquiring the discrete data points describing the tooth profile of the gear to be processed in step S1 specifically includes: the gear tooth profile is divided into n discrete points for characterization, and for any discrete point i on the tooth profile, the coordinate is (x) i ,y i ) Then the set of tooth form discrete points is represented as [ x ] i ,y i ](i＝1,2,…,n)。
Further, the intersection angle of the tool mounting shaft, the helical angle of the gear to be machined and the helical angle of the tool need to satisfy the following requirements:
Σ＝β w ±β t (1)
wherein, Σ is the intersection angle of the tool mounting shafts, β w To the helix angle, beta, of the gear to be machined t For the spiral angle of the cutter, when the gear to be machined is an internal gear, "+" is used for the opposite rotation direction of the cutter and the gear to be machined, and "-" is used for the same rotation direction of the cutter and the gear to be machined.
Further, the calculation formula of the initial installation center distance of the cutter is as follows:
a＝r pw ±r pt (2)
wherein r is pw Is the pitch radius of the gear to be machined, r pt The pitch circle radius of the cutter is taken as the pitch circle radius r of the gear to be machined, the plus value is taken for the internal gear, the minus value is taken for the external gear, and the pitch circle radius r of the gear to be machined is taken as the pitch circle radius r of the external gear pw The pitch radius r of the cutter is calculated and obtained from gear parameters pt The calculation formula of (c) is:
wherein z is t Number of teeth of gear to be machined, z w The number of teeth of the tool.
Further, the step S4 is specifically:
s4.1: establishing fixed coordinates of a gear to be machinedIs S 1 (O s1 -x s1 ,y s1 ,z s1 ) And a fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 )，z s1 The axis coincides with the axis of revolution of the gear to be machined, z s2 The axis coinciding with the axis of rotation of the tool, z s1 Axis and z s2 The included angle between the shafts is the intersection angle sigma of the cutter mounting shaft; x is the number of s1 Axis and x s2 The axes are overlapped, and the shortest distance between the gear to be processed and the rotary axis of the cutter is the initial installation center distance a of the cutter; establishing a motion coordinate system O of a gear to be machined 1 (O 1 -x 1 ,y 1 ,z 1 ) And a motion coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 ) Initial time and gear to be machined fixing coordinate system S 1 (O s1 -x s1 ,y s1 ,z s1 ) Overlapping; establishing a moving coordinate system O of the tool 2 (O 2 -x 2 ,y 2 ,z 2 ) And a motion coordinate system O 2 (O 2 -x 2 ,y 2 ,z 2 ) And the fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be machined is at uniform angular velocity omega 1 About axis z s1 Rotating, the tool being at a uniform angular velocity omega 2 About axis z s2 Rotating;
s4.2: establishing a tool-fixed coordinate system S 2 To-be-machined gear fixing coordinate system S 1 A homogeneous transformation matrix of;
wherein, ω is 1 Angular velocity of rotation, omega, of the gear to be machined 2 For the angular velocity of rotation of the tool, t is the time increment in rotation of the gear to be machined and the tool, ω 1 And omega 2 Satisfy the relation: omega 1 ＝z w *ω 2 /z t ，z w Number of teeth of gear to be machined, z t The number of teeth of the cutter;
s4.3: according to the homogeneous transformation matrixes (4), (5) and (6), the rotation time t of the gear to be machined is given, and the discrete data points of the tooth profile of the gear to be machined are fixed by a coordinate system S of the gear to be machined 1 Conversion to tool coordinate system S 2 Then, obtaining a space point cloud enveloped by discrete data points of the gear to be processed, and making a coordinate point set of the gear to be processed as r 1 ＝[x i ,y i ,1,1]And (i is 1,2, …, n), and after the time t, the spatial point cloud obtained by enveloping the gear coordinate point set to be processed is r 2 ＝[x j ,y j ,z j ,1](j ═ 1,2, …, m), and m>n；
r 2 ＝M s2-2 -1 (t)*M s1-s2 -1 *M s1-1 (t)*r 1 (7)
Wherein, M s2-2 -1 (t) represents M s2-2 Inverse matrix of (t), M s1-s2 -1 Represents M s1-s2 The inverse matrix of (d);
s4.4: projecting the spatial point cloud on XOY plane to make the spatial data point cloud [ x j ,y j ,z j ,1]Z in j Obtaining a two-dimensional point cloud [ x ] enveloped by a gear data point set to be processed as 0 j ,y j ]；
S4.5: two-dimensional point cloud [ x ] j ,y j ]Equally dividing the point cloud into k layers along the radial direction of the cutter, extracting a boundary data point of the innermost side of each layer of point cloud layer by layer, and further obtaining a data point [ x ] describing the edge shape of the cutter p ,y p ]，(p＝1,2,…,k)。
Further, the tool rake angle γ o The selection range of (A) is 5-20 degrees.
Further, the tool relief angle α o The selection range of (A) is 5-16 degrees.
Further, in step S6, the calculation formula of the variation of the center distance between the tool mounting locations and the total regrinding amount of the tool is:
Δa＝L·tanα o (8)
wherein L is the total weight grinding amount of the cutter, alpha o Is the tool relief angle.
The invention has the beneficial effects that:
1) when the cutter is designed according to the method, only simple parameters such as the number of teeth of the cutter, the helical angle, the intersection angle of the cutter installation shaft and the like need to be selected, complex analytical equations do not need to be deduced and solved, and the problem that solution set divergence is easy to generate in the traditional method for solving the cutter edge shape based on the conjugate theory is solved. The invention is suitable for the gear machining of various tooth-shaped gears such as involute, circular arc, cycloid and the like, is particularly suitable for complex tooth-shaped gears with special requirements on tooth profile modification, root digging or tooth top chamfering, and has wide applicable gear tooth profile range.
2) The edge shape of the turning gear cutter designed according to the invention can theoretically reach the edge shape precision of the turning gear cutter designed based on a conjugate method, and the edge shape of the cutter after regrinding has better precision retentivity, so that the tooth shape precision of the processed gear is ensured to be unchanged, and the cutter has longer service life.
Drawings
FIG. 1 is a flow chart of a reverse enveloping design method for a complex-tooth-shaped turning tool according to an embodiment of the present invention;
FIG. 2 is a gear tooth shape data point after discrete processing according to an embodiment of the present invention;
FIG. 3 is a coordinate system of a workpiece and a tool according to an embodiment of the invention;
FIG. 4 is a spatial point cloud obtained by reverse gear tooth profile enveloping according to the embodiment of the present invention;
FIG. 5 is a diagram illustrating an inner boundary of a two-dimensional point cloud to obtain a knife edge shape according to an embodiment of the present invention;
FIG. 6 is a view showing the tooth profile of a gear positively enveloped by the knife edge shape of the embodiment of the invention;
FIG. 7 is a gear tooth profile error curve obtained by forward enveloping of the knife edge shape of the embodiment of the invention;
FIG. 8 is a tool flank surface obtained by fitting the tool edge shape on different cross sections of an embodiment of the present invention;
fig. 9 is a gear turning tool for internally meshing a three-arc harmonic gear according to the invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather should be construed as broadly as the present invention is capable of modification in various respects, all without departing from the spirit and scope of the present invention.
The gear to be processed is an inner meshing three-arc harmonic gear, the gear to be processed is straight teeth, the number of teeth is z w 102, helix angle β w The reverse enveloping design method of the gear turning tool with the complex tooth profile is applied to the gear turning tool for designing the internal meshing three-arc harmonic gear, wherein the diameter of the addendum circle is 44.38mm, and the diameter of the dedendum circle is 43.34 mm.
Referring to fig. 1 to 9, a reverse enveloping design method for a turning cutter with a complex tooth shape according to an embodiment of the present invention specifically includes the following steps:
s1: dividing the gear tooth profile into n discrete points for characterization according to the gear parameter to be processed, wherein the coordinate of any discrete point i on the tooth profile is (x) i ,y i ) Then the set of tooth-shaped discrete points is represented as [ x ] i ,y i ](i＝1,2,…,n)；
S2: determining the number of tool teeth z t 68, tool helix angle β t ＝15°；
S3: calculating the intersection angle of a cutter mounting shaft and the initial mounting center distance of the cutter;
the intersection angle sigma of the cutter mounting shaft is 15 degrees, which is represented by the formula sigma beta w ±β t Is calculated to obtain, wherein, beta w Is a known workpiece helix angle; the center distance for installing the cutter is defined by the formula a ═ r pw ±r pt Calculated as a 6.794mm, wherein the teethRadius of pitch circle r of wheel pw Calculated according to the gear parameters, the pitch circle radius of the cutter is calculated according to the formula
And (4) calculating.
S4: based on the space meshing principle of the crossed shaft gear and the reverse enveloping motion relation of the turning gear machining, under the condition of the initial installation center distance of the cutter, reversely enveloping the tooth shape discrete data points of the gear to be machined to obtain cutter front blade shape profile data point cloud, carrying out layering processing on the cutter front blade shape profile data point cloud, extracting the inner boundary data points of the cutter front blade shape profile data point cloud, and obtaining the cutter front blade shape as follows:
s4.1: establishing a fixed coordinate system S of a gear to be machined 1 (O s1 -x s1 ,y s1 ,z s1 ) And a fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Wherein S is 1 (O s1 -x s1 ,y s1 ,z s1 )、S 2 (O s2 -x s2 ,y s2 ,z s2 ) Respectively two spatially fixed coordinate systems, z s1 The axis coincides with the axis of revolution of the gear to be machined, z s2 The axis coinciding with the axis of rotation of the tool, z s1 Axis and z s2 The included angle between the shafts is the intersection angle sigma of the cutter mounting shaft; x is a radical of a fluorine atom s1 Axis and x s2 The axes are overlapped, and the shortest distance between the gear to be processed and the rotary axis of the cutter is the initial installation center distance a of the cutter; establishing a motion coordinate system O of a gear to be machined 1 (O 1 -x 1 ,y 1 ,z 1 ) And a motion coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 ) Initial time and gear to be machined fixing coordinate system S 1 (O s1 -x s1 ,y s1 ,z s1 ) Overlapping; establishing a motion coordinate system O of the tool 2 (O 2 -x 2 ,y 2 ,z 2 ) And a motion coordinate system O 2 (O 2 -x 2 ,y 2 ,z 2 ) And the fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be machined is at uniform angular velocity omega 1 About axis z s1 Rotating, the tool being at a uniform angular velocity omega 2 About axis z s2 Rotating;
s4.2: establishing a tool-fixed coordinate system S 2 To-be-machined gear fixing coordinate system S 1 A homogeneous transformation matrix of (a);
wherein, ω is 1 Angular velocity, omega, of the gear to be machined 2 Is the angular velocity of rotation of the tool, t is the time increment during rotation of the gear to be machined and the tool, ω 1 And ω 2 Satisfy the relation: omega 1 ＝z w *ω 2 /z t ，z w Number of teeth of gear to be machined, z t The number of teeth of the cutter;
s4.3: according to the homogeneous transformation matrixes (4), (5) and (6), the rotation time t of the gear to be machined is given, and the discrete data points of the tooth profile of the gear to be machined are fixed in a coordinate system S by the gear to be machined 1 Conversion to tool coordinate system S 2 Then, obtaining a space point cloud enveloped by discrete data points of the gear to be processed, as shown in figure 4; in order to facilitate matrix transformation, a coordinate point set of the gear to be processed is made to be r 1 ＝[x i ,y i ,1,1]And (i is 1,2, …, n), and after the time t, the space point cloud obtained by enveloping the gear coordinate point set to be processed is r 2 ＝[x j ,y j ,z j ,1](j ═ 1,2, …, m), and m>n；
r 2 ＝M s2-2 -1 (t)*M s1-s2 -1 *M s1-1 (t)*r 1 (7)
Wherein M is s2-2 -1 (t) represents M s2-2 Inverse matrix of (t), M s1-s2 -1 Represents M s1-s2 The inverse matrix of (d);
s4.4: projecting the spatial point cloud on XOY plane to make the spatial data point cloud [ x j ,y j ,z j ,1]Z in j Obtaining a two-dimensional point cloud [ x ] enveloped by a gear data point set to be processed as 0 j ,y j ]As shown in fig. 5;
s4.5: two-dimensional point cloud [ x ] j ,y j ]Equally dividing the point cloud into k layers along the radial direction of the cutter, extracting a boundary data point at the innermost side of each layer of point cloud layer by layer to further obtain a data point [ x ] describing the edge shape of the cutter p ,y p ]，(p＝1,2,…,k)；
By the formula r 2 ＝M s2-2 -1 (t)*M s1-s2 -1 *M s1-1 (t)*r 1 The calculation formula for deducing the positive enveloping workpiece tooth profile of the cutter is as follows: r is 1 ＝M s1-1 -1 (t)*M s1-s2 *M s2-2 (t)*r 2 Wherein M is s1-1 -1 (t) represents M s1-1 The inverse matrix of (t), then 1 ＝M s1-1 -1 (t)*M s1-s2 *M s2-2 (t)*r 2 The workpiece tooth form (see figure 6) enveloped by the cutting edge shape of the gear turning cutter in the positive direction can be obtained, and whether the design of the cutting edge shape of the cutter is correct or not can be checked. FIG. 7 is the tooth profile error curve of the gear with positive envelope of the cutting edge of the turning gear cutter of the internally engaged three-arc harmonic gear designed by the method of the present invention, and the error curve shows that the tooth profile error f of the gear fα <1 μm, which shows that the turning tooth cutter designed by the method of the invention has higher edge shape precision theoretically.
S5: determining tool rake angle gamma o Angle of clearance alpha of the tool, 6 deg o ＝12°；
S6: the total regrinding amount L of the cutter is determined to be 8mm, as shown in fig. 8, a cutter tooth 9 arbitrarily cut on the cutter 3 is cut, the total regrinding amount of the cutter is divided into a plurality of equal parts, 4 equal parts in the embodiment,the amount of change in the regrinding amount of the cutter is respectively Delta L 1 ＝2mm、ΔL 2 ＝4mm、ΔL 3 ＝6mm、ΔL 4 8mm, expressed by the formula Δ a i ＝ΔL i ·tanα o Calculating the change delta a of the mounting center distance of the cutter when different regrinding amounts are obtained i ；
S7: superposing the variation of the cutter mounting center distance on each section with the initial cutter mounting center distance to obtain the cutter mounting center distance of each section, reversely enveloping the tooth profile discrete data points of the gear to be processed under the condition of the corresponding cutter mounting center distance for each cutter section to obtain the blade profile data point cloud of the corresponding section of the cutter, carrying out layering processing on the blade profile data point cloud of the corresponding section of the cutter, extracting the inner boundary data points of the blade profile data point cloud of the corresponding section of the cutter, and obtaining the blade profiles 10, 11 and 12 of the corresponding section of the cutter;
s8: the tool rake edge shape and each cross-sectional edge shape of the tool are sequentially fitted into a tool flank in the order of distance from the rake face from the near to the far, as shown in fig. 8.
The cutter design method has the characteristics of simple design process and wide applicable tooth form range, and the cutter design method considers the edge shape change of the reground cutter, adopts the sectional envelope to obtain the edge shapes on different sections of the cutter, can ensure that the reground cutter edge shape has good precision retentivity, ensures that the tooth form precision of the processed gear is not changed, has more reground times of the cutter and has longer service life.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (8)
1. A reverse enveloping design method for a turning cutter with a complex tooth shape is characterized by comprising the following steps:
s1: acquiring a tooth profile discrete data point for describing the gear to be machined according to the parameters of the gear to be machined;
s2: determining the number of teeth of the cutter and the spiral angle of the cutter;
s3: calculating the intersection angle of the cutter mounting shaft and the initial mounting center distance of the cutter;
s4: based on a staggered shaft gear space meshing principle and a reverse enveloping motion relation of gear turning machining, under the condition of an initial installation center distance of a cutter, reversely enveloping a tooth shape discrete data point of the gear to be machined to obtain a cutter front cutter edge shape profile data point cloud, carrying out layering processing on the cutter front cutter edge shape profile data point cloud, and extracting an inner boundary data point of the cutter front cutter edge shape profile data point cloud to obtain a cutter front cutter edge shape;
s5: determining a front angle and a back angle of a top edge of the cutter;
s6: determining the total regrinding quantity of the cutter, equally dividing the total regrinding quantity of the cutter into a plurality of equal parts, forming a plurality of equally divided sections on the cutter in the axial direction, and calculating the variation quantity of the installation center distance of the cutter on each section;
s7: superposing the variation of the cutter mounting center distance on each section with the initial cutter mounting center distance to obtain the cutter mounting center distance of each section, reversely enveloping the tooth profile discrete data points of the gear to be processed under the condition of the corresponding cutter mounting center distance for each cutter section to obtain the blade profile data point cloud of the corresponding section of the cutter, layering the blade profile data point cloud of the corresponding section of the cutter, and extracting the inner boundary data point of the blade profile data point cloud of the corresponding section of the cutter to obtain the blade profile of the corresponding section of the cutter;
s8: and sequentially fitting the edge shape of the front tool face of the tool and each section edge shape of the tool into a rear tool face of the tool according to the sequence from the near to the far away from the front tool face.
2. The reverse envelope design method of the complex-tooth-shaped turning gear tool according to claim 1, wherein the method for acquiring discrete data points describing the tooth shape of the gear to be machined in the step S1 is specifically as follows: dividing gear tooth profile into n discrete points for performing tableFor any discrete point i on the tooth form, the coordinate is (x) i ,y i ) Then the set of tooth form discrete points is represented as [ x ] i ,y i ](i＝1,2,…,n)。
3. The reverse envelope design method of the complex-tooth-shaped turning gear tool according to claim 1, wherein the intersection angle of the tool mounting shaft, the helix angle of the gear to be machined and the helix angle of the tool are satisfied:
Σ＝β w ±β t (1)
wherein, Σ is the intersection angle of the tool mounting axis, β w To the helix angle, beta, of the gear to be machined t For the spiral angle of the cutter, when the gear to be machined is an internal gear, "+" is used for the opposite rotation direction of the cutter and the gear to be machined, and "-" is used for the same rotation direction of the cutter and the gear to be machined.
4. The reverse envelope design method of a turning tool with a complex tooth shape according to claim 1, wherein the calculation formula of the initial installation center distance of the tool is as follows:
a＝r pw ±r pt (2)
wherein r is pw Is the pitch radius of the gear to be machined, r pt The pitch circle radius of the cutter is taken as the pitch circle radius r of the gear to be machined, the plus value is taken for the internal gear, the minus value is taken for the external gear, and the pitch circle radius r of the gear to be machined is taken as the pitch circle radius r of the external gear pw The pitch radius r of the cutter is calculated and obtained from gear parameters pt The calculation formula of (2) is as follows:
wherein z is t Number of teeth of gear to be machined, z w The number of teeth of the tool.
5. The reverse envelope design method of the turning tool with the complicated tooth shape according to claim 1, wherein the step S4 is specifically as follows:
s4.1: establishing a fixed coordinate system S of a gear to be machined 1 (O s1 -x s1 ,y s1 ,z s1 ) And a fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 )，z s1 The axis coinciding with the axis of revolution of the gear to be machined, z s2 The axis coinciding with the axis of rotation of the tool, z s1 Axis and z s2 The included angle between the shafts is the intersection angle sigma of the cutter mounting shaft; x is the number of s1 Axis and x s2 The axes are overlapped, and the shortest distance between the gear to be processed and the rotary axis of the cutter is the initial installation center distance a of the cutter; establishing a motion coordinate system O of a gear to be machined 1 (O 1 -x 1 ,y 1 ,z 1 ) And a motion coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 ) Initial time and gear to be machined fixing coordinate system S 1 (O s1 -x s1 ,y s1 ,z s1 ) Overlapping; establishing a motion coordinate system O of the tool 2 (O 2 -x 2 ,y 2 ,z 2 ) And a motion coordinate system O 2 (O 2 -x 2 ,y 2 ,z 2 ) And the fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be machined is at uniform angular velocity omega 1 About axis z s1 Rotating, the tool being at a uniform angular velocity omega 2 About axis z s2 Rotating;
s4.2: establishing a tool-fixed coordinate system S 2 To-be-machined gear fixing coordinate system S 1 A homogeneous transformation matrix of;
wherein, ω is 1 Angular velocity, omega, of the gear to be machined 2 For the angular velocity of rotation of the tool, t is the time increment in rotation of the gear to be machined and the tool, ω 1 And ω 2 Satisfy the relation: omega 1 ＝z w *ω 2 /z t ，z w Number of teeth of gear to be machined, z t The number of teeth of the cutter;
s4.3: according to the homogeneous transformation matrixes (4), (5) and (6), the rotation time t of the gear to be machined is given, and the discrete data points of the tooth profile of the gear to be machined are fixed by a coordinate system S of the gear to be machined 1 Conversion to tool coordinate system S 2 Then, obtaining a space point cloud enveloped by discrete data points of the gear to be processed, and making a coordinate point set of the gear to be processed as r 1 ＝[x i ,y i ,1,1]And (i is 1,2, …, n), and after the time t, the space point cloud obtained by enveloping the gear coordinate point set to be processed is r 2 ＝[x j ,y j ,z j ,1](j ═ 1,2, …, m), and m>n；
r 2 ＝M s2-2 -1 (t)*M s1-s2 -1 *M s1-1 (t)*r 1 (7)
Wherein M is s2-2 -1 (t) represents M s2-2 Inverse matrix of (t), M s1-s2 -1 Represents M s1-s2 The inverse matrix of (d);
s4.4: projecting the spatial point cloud on XOY plane to make the spatial data point cloud [ x j ,y j ,z j ,1]Z in j Obtaining a two-dimensional point cloud [ x ] enveloped by a gear data point set to be processed as 0 j ,y j ]；
S4.5: two-dimensional point cloud [ x ] j ,y j ]Equally dividing the point cloud into k layers along the radial direction of the cutter, extracting a boundary data point at the innermost side of each layer of point cloud layer by layer to further obtain a data point [ x ] describing the edge shape of the cutter p ,y p ]，(p＝1,2,…,k)。
6. Vehicle with complex tooth profile according to claim 1The reverse envelope design method of the tooth cutter is characterized in that the rake angle gamma of the cutter o The selection range of (A) is 5-20 degrees.
7. The reverse envelope design method for a complex-tooth-shaped turning tool according to claim 1, wherein a tool relief angle α is o The selection range of (2) is 5-16 degrees.
8. The reverse envelope design method for a turning tool with a complicated tooth profile according to claim 1, wherein in step S6, the calculation formula of the variation of the tool mounting center distance and the total regrinding amount of the tool is as follows:
Δa＝L·tanα o (8)
wherein L is the total weight grinding amount of the cutter, alpha o Is the tool relief angle.
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