CN115026354B - Reverse enveloping design method for complex tooth-shaped turning tool - Google Patents
Reverse enveloping design method for complex tooth-shaped turning tool Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F21/00—Tools specially adapted for use in machines for manufacturing gear teeth
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Abstract
The invention provides a reverse enveloping design method of a complex tooth-shaped turning tool, which comprises the following steps: acquiring tooth-shaped discrete data points; determining the number of teeth and helix angle of the cutter; calculating the intersection angle of the cutter mounting shaft and the initial mounting center distance of the cutter; obtaining the blade shape of the front cutter surface of the cutter based on the space meshing principle of the staggered shaft gears and the reverse enveloping movement relation of the turning gear processing; determining a cutter front angle and a top edge rear angle; calculating the variation of the cutter mounting center distance of the cutter on each axial section; calculating the cutter mounting center distance of each section, and obtaining the blade shape of the corresponding section of the cutter based on the space meshing principle of the staggered shaft gears and the reverse enveloping movement relation of turning teeth for each cutter section; and fitting the cutter front cutter surface edge shape and each section edge shape of the cutter into a cutter rear cutter surface in sequence from the near to the far from the front cutter surface. 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 complex tooth-shaped turning cutter.
Background
Gears are key basic parts in many industries, and the processing technology level of gears is significant for developing high-grade gear products. The turning gear processing technology is an emerging gear processing technology, can solve the difficult problem of processing the compact annular gear with thin wall or without a tool withdrawal groove on a high-grade precise harmonic reducer and an automatic gearbox, and has the remarkable advantages of high precision, high efficiency, green environmental protection and the like. Currently, more and more enterprises adopt a gear turning process to replace the traditional gear rolling/inserting/gear pulling-honing/gear grinding process.
The key of the tooth turning technology is the design of the cutter blade shape, and the current tooth turning cutter design method is mainly based on the conjugate theory of the curved surface and the curve of the double degrees of freedom, and is a forward design method. However, the forward design method has limitations, especially some complex tooth-shaped gears requiring tooth-shaped modification, tooth root rooting or tooth tip chamfering, and when the tooth profile diameter is smaller than the base circle diameter or the local area exceeds the curvature limit of conjugate engagement at the transition curve part of the modification, root rooting or chamfering, the problem of solution and divergence is easy to occur by adopting an engagement equation of conjugate theory to solve the cutter blade shape, so that the correct cutter blade shape cannot be designed. In practical engineering application, parameters of the gear to be processed are not complete, only CAD engineering drawings or discrete data points of the gear tooth form are available, an analytical equation of the gear tooth form cannot be obtained, and the cutter blade shape is difficult to calculate by adopting a conjugate theory. Aiming at the gears with complex tooth shapes, the existing design method of the turning cutter generally adopts rough design methods such as splicing cutting edge lines, auxiliary drawing and the like to approach the tooth shape of the gears, the design efficiency is very low, the edge shape precision of the turning cutter is affected, the design period of the turning cutter is prolonged, and the application range of the tooth shape of the turning cutter is limited.
In addition, the rear cutter surface of the existing conical turning cutter adopts a design method of equal side relief angle, and the cutter designed by the method has simple and convenient manufacturing process, but can cause the phenomenon of precision degradation of the turning cutter after repeated grinding, thereby limiting the service life of the cutter.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a reverse enveloping design method of a complex tooth-shaped turning tool, which has simple design process and high edge shape precision of the designed turning tool.
The present invention achieves the above technical object by the following means.
A reverse enveloping design method for a complex tooth-shaped turning tool comprises the following steps:
s1: acquiring tooth form discrete data points describing the gear to be processed according to the gear parameters to be processed;
s2: determining the number of teeth of the cutter and the helix 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 the space meshing principle of the staggered shaft gears and the reverse enveloping motion relation of turning gear processing, under the condition of initial installation center distance of a cutter, reversely enveloping tooth-shaped discrete data points of a gear to be processed to obtain cutter front cutter face edge-shaped profile data point clouds, carrying out layering treatment on the cutter front cutter face edge-shaped profile data point clouds, and extracting inner boundary data points of the cutter front cutter face edge-shaped profile data point clouds to obtain cutter front cutter face edge shapes;
s5: determining a cutter front angle and a top edge rear angle;
s6: determining the total weight of the cutter, equally dividing the total weight of the cutter into a plurality of equal parts, forming a plurality of equally divided sections of the cutter in the axial direction, and calculating the variation of the cutter mounting center distance on each section;
s7: superposing the variation of the cutter installation center distance on each section with the initial cutter installation center distance to obtain the cutter installation 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 installation center distance for each cutter section to obtain cutter corresponding section blade profile data point clouds, carrying out layering treatment on the cutter corresponding section blade profile data point clouds, extracting inner boundary data points of the cutter corresponding section blade profile data point clouds, and obtaining cutter corresponding section blade profiles;
s8: and fitting the cutter front cutter surface edge shape and each section edge shape of the cutter into a cutter rear cutter surface in sequence from the near to the far from the front cutter surface.
Further, the method for acquiring the tooth form discrete data points describing the gear to be processed in the step S1 specifically includes: the tooth profile of the gear 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 ) The tooth form discrete point set is expressed as [ x ] i ,y i ]i＝1,2,…,n。
Furthermore, the three requirements of the cutter installation axiality angle and the helical angle of the gear to be processed and the helical angle of the cutter are satisfied:
Σ＝β w ±β t (1)
wherein Σ is the cutter mounting axis intersection angle, β w For the helix angle of the gear to be machined, beta t For the helical 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 For the pitch radius of the gear to be processed, r pt The pitch circle radius r of the gear to be processed is obtained by taking "+" for the gear to be processed as an inner gear and taking "-" for the gear to be processed as an outer gear pw Calculated by gear parameters, the pitch circle radius r of the cutter pt The calculation formula of (2) is as follows:
wherein z is t Z is the number of teeth of the gear to be processed w Is the number of teeth of the cutter.
Further, the step S4 specifically includes:
s4.1: establishing a fixed coordinate system S of a gear to be processed 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 rotation axis of the gear to be processed, z s2 The axis coincides with the axis of rotation of the tool, z s1 Axis and z s2 The included angle between the shafts is the cutter mounting shaft intersection angle sigma; x is x s1 Axis and x s2 The shafts are overlapped, and the shortest distance between the gear to be processed and the rotation 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 processed 1 (O 1 -x 1 ,y 1 ,z 1 ) Motion coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixed coordinates of the initial moment of (a) and the gear to be processedS series 1 (O s1 -x s1 ,y s1 ,z s1 ) Overlapping; establishing a motion coordinate system O of a cutter 2 (O 2 -x 2 ,y 2 ,z 2 ) Motion coordinate system O 2 (O 2 -x 2 ,y 2 ,z 2 ) Is fixed to the fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be processed has uniform angular velocity omega 1 Around axis z s1 Rotating the tool at a uniform angular velocity omega 2 Around axis z s2 Rotating;
s4.2: establishing a coordinate system S fixed by a cutter 2 To a gear to be processed fixed coordinate system S 1 Is a homogeneous transformation matrix of (1);
wherein omega 1 For the rotational angular velocity, ω, of the gear to be machined 2 The rotation angular velocity of the cutter is t is the time increment of the gear to be processed and the cutter in rotation, omega 1 And omega 2 The relation is satisfied: omega 1 ＝z w *ω 2 /z t ，z w Z is the number of teeth of the gear to be processed t The number of teeth of the cutter;
s4.3: according to the homogeneous transformation matrixes (4), (5) and (6), giving the rotation time t of the gear to be processed, and fixing the tooth profile discrete data points of the gear to be processed by the gear to be processed into a coordinate system S 1 Conversion to tool coordinate System S 2 Obtaining a space point cloud of a discrete data point envelope of the gear to be processed, and enabling a coordinate point set of the gear to be processed to be r 1 ＝[x i ,y i ,1,1]I=1, 2, …, n, and after the time t, the space point cloud obtained by enveloping the coordinate point set of the gear 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 An inverse matrix of (a);
s4.4: projecting the space point cloud on an XOY plane to enable the space point cloud [ x ] j ,y j ,z j ,1]Z in (b) j =0, obtaining a two-dimensional point cloud [ x ] of the envelope of the data point set of the gear to be processed j ,y j ]；
S4.5: two-dimensional point cloud [ x ] j ,y j ]Dividing the radial direction of the cutter into k layers, extracting the innermost boundary data point of each layer of point cloud layer by layer, and further obtaining data points [ x ] describing the edge shape of the cutter p ,y p ]，p＝1,2,…,k。
Further, the tool rake angle gamma o Is selected in the range of 5 to 20.
Further, the tool relief angle alpha o Is selected in the range of 5 to 16.
Further, in the step S6, a calculation formula of the cutter mounting center distance variation and the cutter total weight is as follows:
Δa＝L·tanα o (8)
wherein L is the total grinding weight of the cutter, alpha o Is the rear angle of the cutter.
The invention has the beneficial effects that:
1) According to the invention, when the cutter is designed, only simple parameters such as the number of teeth, the helix angle, the intersecting angle of the cutter mounting axis and the like are required to be selected, and a complex analytical equation is not required to be deduced and solved, so that the problem that the traditional method for solving the cutter blade shape based on the conjugate theory is easy to generate solution set divergence is avoided. The invention is suitable for turning gear of various tooth-shaped gears such as involute, circular arc, cycloid and the like, in particular for complex tooth-shaped gears with special requirements on tooth-shaped modification, tooth root digging or tooth top chamfering, and has wide applicable gear tooth-shaped range.
2) The edge shape of the turning gear cutter designed according to the invention can reach the edge shape precision of the turning gear cutter designed based on the conjugate method in theory, and the edge shape of the cutter after regrinding has better precision retention, ensures the tooth shape precision of the processed gear to be unchanged, and has longer service life.
Drawings
FIG. 1 is a flow chart of a reverse enveloping design method of a complex tooth-shaped turning tool in an embodiment of the invention;
FIG. 2 is a graph of data points of tooth profile of a gear after discrete processing in accordance with 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 space point cloud obtained by reverse enveloping the tooth profile of a gear in an embodiment of the invention;
FIG. 5 is a diagram showing a method for extracting an inner boundary of a two-dimensional point cloud to obtain a cutter blade shape according to an embodiment of the present invention;
FIG. 6 is a schematic view of a cutter blade shape of an embodiment of the present invention enveloping the tooth form of a gear in the forward direction;
FIG. 7 is a graph of tooth form error of a gear obtained by a forward envelope of a cutter blade according to an embodiment of the present invention;
FIG. 8 shows the tool relief surface obtained by fitting the tool edge shape on different cross sections according to the embodiment of the invention;
fig. 9 is a turning gear of an internally meshed tri-arc harmonic gear designed according to the present invention.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit or scope of the invention, which is therefore not limited to the specific embodiments disclosed below.
The gear to be processed is an internally meshed three-arc harmonic gear, the gear to be processed is straight-tooth, and the number of teeth is z w =102, helix angle β w The reverse enveloping design method of the complex tooth-shaped turning tool is applied to the turning tool for designing the internally-meshed 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 envelope design method for a complex tooth-shaped turning tool according to an embodiment of the present invention specifically includes the following steps:
s1: according to the parameters of the gear to be processed, dividing the gear tooth profile into n discrete points for characterization, wherein for any discrete point i on the tooth profile, the coordinate is (x) i ,y i ) The tooth form discrete point set is expressed as [ x ] i ,y i ]i＝1,2,…,n；
S2: determining the number z of teeth of a tool t =68, cutter helix angle β t ＝15°；
S3: calculating the intersection angle of the cutter mounting shaft and the initial mounting center distance of the cutter;
the tool mounting axis intersection angle Σ=15° is represented by the formula Σ=β w ±β t Calculated, wherein beta w Is a known workpiece helix angle; the tool mounting center distance is represented by the formula a=r pw ±r pt Calculated as a= 6.794mm, where the pitch radius r of the gear pw The pitch circle radius of the cutter is calculated according to the gear parameters and is calculated according to the formulaAnd (5) calculating to obtain the product.
S4: based on the space meshing principle of the staggered shaft gears and the reverse enveloping motion relation of turning gear processing, under the condition of initial installation center distance of a cutter, the tooth-shaped discrete data points of the gear to be processed are reversely enveloped to obtain cutter front cutter blade-shaped profile data point clouds, the cutter front cutter blade-shaped profile data point clouds are subjected to layering treatment, inner boundary data points of the cutter front cutter blade-shaped profile data point clouds are extracted to obtain cutter front cutter blades, and the method comprises the following specific steps:
s4.1: establishing a fixed coordinate system S of a gear to be processed 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 ) Two spatially-fixed coordinate systems, z s1 The axis coincides with the rotation axis of the gear to be processed, z s2 The axis coincides with the axis of rotation of the tool, z s1 Axis and z s2 The included angle between the shafts is the cutter mounting shaft intersection angle sigma; x is x s1 Axis and x s2 The shafts are overlapped, and the shortest distance between the gear to be processed and the rotation 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 processed 1 (O 1 -x 1 ,y 1 ,z 1 ) Motion coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 ) Is fixed with a fixed coordinate system S of the gear to be processed 1 (O s1 -x s1 ,y s1 ,z s1 ) Overlapping; establishing a motion coordinate system O of a cutter 2 (O 2 -x 2 ,y 2 ,z 2 ) Motion coordinate system O 2 (O 2 -x 2 ,y 2 ,z 2 ) Is fixed to the fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be processed has uniform angular velocity omega 1 Around axis z s1 Rotating the tool at a uniform angular velocity omega 2 Around axis z s2 Rotating;
s4.2: establishing a coordinate system S fixed by a cutter 2 To a gear to be processed fixed coordinate system S 1 Is a homogeneous transformation matrix of (1);
wherein omega 1 For the rotational angular velocity, ω, of the gear to be machined 2 The rotation angular velocity of the cutter is t is the time increment of the gear to be processed and the cutter in rotation, omega 1 And omega 2 The relation is satisfied: omega 1 ＝z w *ω 2 /z t ，z w Z is the number of teeth of the gear to be processed t The number of teeth of the cutter;
s4.3: according to the homogeneous transformation matrixes (4), (5) and (6), giving the rotation time t of the gear to be processed, and fixing the tooth profile discrete data points of the gear to be processed by the gear to be processed into a coordinate system S 1 Conversion to tool coordinate System S 2 Obtaining a space point cloud of a discrete data point envelope of the gear to be processed, as shown in fig. 4; in order to facilitate matrix transformation, let the coordinate point set of the gear to be processed be r 1 ＝[x i ,y i ,1,1]I=1, 2, …, n, and after the time t, the space point cloud obtained by enveloping the coordinate point set of the gear 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 An inverse matrix of (a);
s4.4: projecting the space point cloud on an XOY plane to enable the space point cloud [ x ] j ,y j ,z j ,1]Z in (b) j =0, obtaining a two-dimensional point cloud [ x ] of the envelope of the data point set of the gear to be processed j ,y j ]As shown in fig. 5;
s4.5: two-dimensional point cloud [ x ] j ,y j ]Dividing the cutter into k layers along the radial direction of the cutter, and extracting the innermost layer of each layer of point cloud layer by layerA boundary data point of the side, and further a data point [ x ] describing the edge shape of the cutter is obtained p ,y p ]，p＝1,2,…,k；
From formula r 2 ＝M s2-2 -1 (t)*M s1-s2 -1 *M s1-1 (t)*r 1 The calculation formula for the tooth form of the workpiece with the forward enveloping of the cutter can be deduced as follows: r is (r) 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) is represented by the formula r 1 ＝M s1-1 -1 (t)*M s1-s2 *M s2-2 (t)*r 2 The workpiece tooth profile (see fig. 6) enveloped by the turning tool edge shape in the forward direction can be obtained, and whether the tool edge shape design is correct or not is checked. FIG. 7 is a graph showing the tooth form error f of the forward envelope of the edge of the turning tool of the internally meshed tri-arc harmonic gear designed by the method of the present invention, as can be seen from the error graph fα <1 mu m, the turning tooth cutter designed by the method has higher edge shape precision in theory.
S5: determining the tool rake angle gamma o =6°, tool relief angle α o ＝12°；
S6: determining the total weight l=8mm of the cutter, as shown in fig. 8, which is a cutter tooth 9 arbitrarily cut off from the cutter 3, equally dividing the total weight of the cutter into a plurality of equal parts, in this embodiment, 4 equal parts, and then changing the weight of the cutter to Δl respectively 1 ＝2mm、ΔL 2 ＝4mm、ΔL 3 ＝6mm、ΔL 4 =8mm, expressed by the formula Δa i ＝ΔL i ·tanα o Calculating to obtain the variation delta a of the mounting center distance of the cutter when the regrinding amount is different i ；
S7: superposing the variation of the cutter installation center distance on each section with the initial cutter installation center distance to obtain the cutter installation 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 installation center distance for each cutter section to obtain cutter corresponding section blade profile data point clouds, carrying out layering treatment on the cutter corresponding section blade profile data point clouds, extracting inner boundary data points of the cutter corresponding section blade profile data point clouds, and obtaining cutter corresponding section blade profiles 10, 11 and 12;
s8: the cutter rake face edge shape and each cross-section edge shape of the cutter are fitted into the cutter flank face in sequence from the near to the far from the rake face, as shown in fig. 8.
The tool design method has the characteristics of simple design process and wide applicable tooth form range, and the tool design method considers the blade shape change after the tool is regrinded, adopts the enveloping of the sections to obtain the blade shapes on different sections of the tool, can ensure that the blade shapes of the regrinded tool have good precision retention, ensures that the tooth form precision of the machined gear is unchanged, has more regrinding times and longer service life.
The foregoing examples illustrate only a few embodiments of the invention and are described in detail herein without thereby limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (8)
1. A reverse enveloping design method of a complex tooth-shaped turning tool is characterized by comprising the following steps:
s1: acquiring tooth form discrete data points describing the gear to be processed according to the gear parameters to be processed;
s2: determining the number of teeth of the cutter and the helix 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 the space meshing principle of the staggered shaft gears and the reverse enveloping motion relation of turning gear processing, under the condition of initial installation center distance of a cutter, reversely enveloping tooth-shaped discrete data points of a gear to be processed to obtain cutter front cutter face edge-shaped profile data point clouds, carrying out layering treatment on the cutter front cutter face edge-shaped profile data point clouds, and extracting inner boundary data points of the cutter front cutter face edge-shaped profile data point clouds to obtain cutter front cutter face edge shapes;
s5: determining a cutter front angle and a top edge rear angle;
s6: determining the total weight of the cutter, equally dividing the total weight of the cutter into a plurality of equal parts, forming a plurality of equally divided sections of the cutter in the axial direction, and calculating the variation of the cutter mounting center distance on each section;
s7: superposing the variation of the cutter installation center distance on each section with the initial cutter installation center distance to obtain the cutter installation 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 installation center distance for each cutter section to obtain cutter corresponding section blade profile data point clouds, carrying out layering treatment on the cutter corresponding section blade profile data point clouds, extracting inner boundary data points of the cutter corresponding section blade profile data point clouds, and obtaining cutter corresponding section blade profiles;
s8: and fitting the cutter front cutter surface edge shape and each section edge shape of the cutter into a cutter rear cutter surface in sequence from the near to the far from the front cutter surface.
2. The method for designing the reverse envelope of the complex-tooth-shaped turning tool according to claim 1, wherein the method for acquiring the tooth-shaped discrete data points describing the gear to be machined in the step S1 is specifically as follows: the tooth profile of the gear 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 ) The tooth form discrete point set is expressed as [ x ] i ,y i ]，i＝1,2,…,n。
3. The method for designing the reverse envelope of the complex-tooth-shaped turning tool according to claim 1, wherein the three requirements of the tool mounting axis intersection angle, the helical angle of the gear to be machined and the helical angle of the tool are as follows:
Σ＝β w ±β t (1)
wherein Σ is the cutter mounting axis intersection angle, β w Is the helix angle of the gear to be processed，β t For the helical 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 method for designing the reverse envelope of the complex tooth form turning tool 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 For the pitch radius of the gear to be processed, r pt The pitch circle radius r of the gear to be processed is obtained by taking "+" for the gear to be processed as an inner gear and taking "-" for the gear to be processed as an outer gear pw Calculated by gear parameters, the pitch circle radius r of the cutter pt The calculation formula of (2) is as follows:
wherein z is t Z is the number of teeth of the gear to be processed w For the number of teeth, beta w For the helix angle of the gear to be machined, beta t Is the helix angle of the cutter.
5. The method for designing the reverse envelope of the complex tooth form turning tool according to claim 1, wherein the step S4 is specifically:
s4.1: establishing a fixed coordinate system S of a gear to be processed 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 rotation axis of the gear to be processed, z s2 The axis coincides with the axis of rotation of the tool, z s1 Axis and z s2 The included angle between the shafts is the cutter mounting shaft intersection angle sigma; x is x s1 Axis and x s2 The shafts are overlapped, and the shortest distance between the gear to be processed and the rotation axis of the cutter is the initial installation of the cutterCenter distance a; establishing a motion coordinate system O of a gear to be processed 1 (O 1 -x 1 ,y 1 ,z 1 ) Motion coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 ) Is fixed with a fixed coordinate system S of the gear to be processed 1 (O s1 -x s1 ,y s1 ,z s1 ) Overlapping; establishing a motion coordinate system O of a cutter 2 (O 2 -x 2 ,y 2 ,z 2 ) Motion coordinate system O 2 (O 2 -x 2 ,y 2 ,z 2 ) Is fixed to the fixed coordinate system S of the tool 2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be processed has uniform angular velocity omega 1 Around axis z s1 Rotating the tool at a uniform angular velocity omega 2 Around axis z s2 Rotating;
s4.2: establishing a coordinate system S fixed by a cutter 2 To a gear to be processed fixed coordinate system S 1 Is a homogeneous transformation matrix of (1);
wherein omega 1 For the rotational angular velocity, ω, of the gear to be machined 2 The rotation angular velocity of the cutter is t is the time increment of the gear to be processed and the cutter in rotation, omega 1 And omega 2 The relation is satisfied: omega 1 ＝z w *ω 2 /z t ，z w Z is the number of teeth of the gear to be processed t The number of teeth of the cutter;
s4.3: according to the homogeneous transformation matrixes (4), (5) and (6), giving the rotation time t of the gear to be processed, and obtaining the gear to be processedThe tooth-shaped discrete data points are fixed by a gear to be processed in a coordinate system S 1 Conversion to tool coordinate System S 2 Obtaining a space point cloud of a discrete data point envelope of the gear to be processed, and enabling a coordinate point set of the gear to be processed to be r 1 ＝[x i ,y i ,1,1]I=1, 2, …, n, and after the time t, the space point cloud obtained by enveloping the coordinate point set of the gear 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 An inverse matrix of (a);
s4.4: projecting the space point cloud on an XOY plane to enable the space point cloud [ x ] j ,y j ,z j ,1]Z in (b) j =0, obtaining a two-dimensional point cloud [ x ] of the envelope of the data point set of the gear to be processed j ,y j ]；
S4.5: two-dimensional point cloud [ x ] j ,y j ]Dividing the radial direction of the cutter into k layers, extracting the innermost boundary data point of each layer of point cloud layer by layer, and further obtaining data points [ x ] describing the edge shape of the cutter p ,y p ]，p＝1,2,…,k。
6. The method for reverse envelope design of complex tooth form turning tool according to claim 1, wherein the tool rake angle γ o Is selected in the range of 5 to 20.
7. The method for reverse envelope design of complex tooth form turning tool according to claim 1, wherein the tool relief angle α o Is selected in the range of 5 to 16.
8. The method for designing the reverse envelope of the complex tooth form turning tool according to claim 1, wherein in the step S6, the calculation formula of the variation of the tool mounting center distance and the total weight of the tool is:
Δa＝L·tanα o (8)
wherein L is the total grinding weight of the cutter, alpha o Is the rear angle of the cutter.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102744469A (en) * | 2012-07-30 | 2012-10-24 | 浙江工商职业技术学院 | Hob design method |
| CN110465706A (en) * | 2019-07-10 | 2019-11-19 | 西安理工大学 | Hardened face gear smart car technique and its skiving devising method of cutting tool |
| CN112157321A (en) * | 2020-08-07 | 2021-01-01 | 江苏大学 | Design method of powerful gear scraping cutter for large-profile gear |
| CN112705794A (en) * | 2020-12-31 | 2021-04-27 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Tooth cutting tool for machining cycloid gear and design method thereof |
| 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 |
| CN114101807A (en) * | 2021-10-28 | 2022-03-01 | 西安交通大学 | Edge shape design method of gear workpiece end face continuous equidistant chamfering cutting tool |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| DE102013012797A1 (en) * | 2013-07-31 | 2015-02-19 | Gleason-Pfauter Maschinenfabrik Gmbh | Process for machining tooth edges and designed processing station |
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Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102744469A (en) * | 2012-07-30 | 2012-10-24 | 浙江工商职业技术学院 | Hob design method |
| CN110465706A (en) * | 2019-07-10 | 2019-11-19 | 西安理工大学 | Hardened face gear smart car technique and its skiving devising method of cutting tool |
| CN112157321A (en) * | 2020-08-07 | 2021-01-01 | 江苏大学 | Design method of powerful gear scraping cutter for large-profile gear |
| CN112705794A (en) * | 2020-12-31 | 2021-04-27 | 天津职业技术师范大学(中国职业培训指导教师进修中心) | Tooth cutting tool for machining cycloid gear and design method thereof |
| 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 |
| CN114101807A (en) * | 2021-10-28 | 2022-03-01 | 西安交通大学 | Edge shape design method of gear workpiece end face continuous equidistant chamfering cutting tool |
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