CN113787235B - Method for obtaining profile of front cutter face of hobbing chamfering cutter - Google Patents

Method for obtaining profile of front cutter face of hobbing chamfering cutter Download PDF

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CN113787235B
CN113787235B CN202111162636.2A CN202111162636A CN113787235B CN 113787235 B CN113787235 B CN 113787235B CN 202111162636 A CN202111162636 A CN 202111162636A CN 113787235 B CN113787235 B CN 113787235B
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chamfering
gear
coordinate system
hobbing
tool
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CN113787235A (en
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何坤
何晓虎
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Chongqing Technology and Business University
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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
    • B23F21/12—Milling tools
    • B23F21/16—Hobs

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Abstract

The invention discloses a method for obtaining the profile of the front cutter face of a hobbing chamfering cutter, which comprises the following steps: 1) establishing a space generation motion relation coordinate system of the hobbing and chamfering tool and the cylindrical gear, 2) establishing a coordinate transformation matrix among the coordinate systems, 3) expressing the chamfering target profile of the cylindrical gear in a gear static coordinate system, and 4) establishing a contact point model of the hobbing and chamfering tool and the cylindrical gear end surface profile; 5) solving the coordinate of the contact point of the front cutter face of the hobbing and chamfering cutter and the tooth profile of the gear; 6) and smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter. The method for obtaining the profile of the front cutter face of the hobbing and chamfering cutter is based on the principle of hobbing continuous generating cutting motion, and the profile of the front cutter face of the hobbing and chamfering cutter is obtained by continuously solving the contact point of the front cutter face of the cutter and the gear chamfering target profile, so that the method can be used for designing the hobbing and chamfering cutter and improving the tooth profile chamfering efficiency of a cylindrical gear.

Description

Method for obtaining profile of front cutter face of hobbing chamfering cutter
Technical Field
The invention relates to the technical field of hobbing cutter design, and relates to a design method of a cylindrical gear hobbing chamfering cutter.
Background
The cylindrical gear is widely used in high-speed and heavy-load occasions due to compact structure, strong bearing capacity and stable transmission ratio. In order to improve the transmission precision and prolong the service life, chamfering is a common process means, burrs generated due to collision can be avoided through the chamfered cylindrical gear, and meanwhile, the noise influence of the gear is reduced.
The types of processes currently used are mainly edge grinding and edge extrusion. The edge grinding method adopts a grinding mode to perform chamfering, and has the problems of low processing efficiency, difficult control of edge grinding shape and the like; the edge-extruding method adopts the edge-extruding cutter and the gear to be processed to perform the backlash-free meshing motion to perform complete and uniform chamfering on the whole tooth profile of the gear, but the cutters need to be used in pairs, and the design of the cutters is complex. With the increasing requirements for the performance of processed gears, the research on the chamfering principle and the development of chamfering machine tools become more and more important.
At present, chamfering of spiral bevel gears is a research hotspot, a disk-shaped cutter is generally adopted to indirectly index and cut chamfers one by one for chamfering processing, but the chamfering method taking the spiral bevel gears as research objects is not suitable for chamfering processing of cylindrical gears.
Because the profile of the hobbing chamfering tool and the profile of the end face of the cylindrical gear to be machined are not conjugate tooth profiles any more, the tool profile cannot be solved by adopting an analytical method based on the gear meshing principle. And the premise of designing the hobbing chamfering tool is to obtain the profile of the front tool face of the chamfering tool correctly.
Disclosure of Invention
In view of this, the present invention provides a method for obtaining a profile of a rake face of a hobbing and chamfering tool, so as to solve the technical problem of how to obtain the profile of the rake face of the hobbing and chamfering tool for a cylindrical gear.
The invention discloses a method for obtaining the profile of the front cutter face of a hobbing chamfering cutter, which comprises the following steps:
1) establishing a space expansion motion relation coordinate system of the roll-cutting chamfering tool and the cylindrical gear according to the installation pose of the roll-cutting chamfering tool, wherein the space expansion motion relation coordinate system comprises: gear static coordinate system om-xmymzmAnd a gear moving coordinate system og-xgygzgTool static coordinate system o1-x1y1z1And the tool moving coordinate system od-xdydzd，
Gear moving coordinate system og-xgygzgIs fixedly connected with the cylindrical gear, and at the initial position, a gear moving coordinate system og-xgygzgAnd gear static coordinate system om-xmymzmOverlapping;
moving coordinate system o of toold-xdydzdFixedly connected with a hobbing chamfering tool, and a tool moving coordinate system o at an initial positiond-xdydzdAnd a tool static coordinate system o1-x1y1z1Overlapping;
2) establishing a coordinate transformation matrix M from a gear moving coordinate system to a gear static coordinate systemmg：
Figure BDA0003290809120000021
Wherein
Figure BDA0003290809120000022
For gear winding zmThe angle of counterclockwise rotation of the shaft;
establishing a coordinate transformation matrix M from a gear static coordinate system to a cutter static coordinate system1m：
Figure BDA0003290809120000023
Wherein h is the geometric center of the hobbing chamfering tool in zmThe height difference between the axial direction and the end surface of the cylindrical gear, p is xmThe distance from the axis of the cylindrical gear in the axial direction to the axis of the hobbing chamfering tool;
establishing a coordinate transformation matrix M from a tool static coordinate system to a tool moving coordinate systemd1：
Figure BDA0003290809120000024
Wherein
Figure BDA0003290809120000025
For rolling chamfering tools around z1The angle of the shaft rotating anticlockwise, the gear rotating around z in the process of continuously generating chamferingmAngle of counterclockwise rotation of the shaft
Figure BDA0003290809120000026
The roll-cutting chamfering tool is wound around z1Angle of counterclockwise rotation of the shaft
Figure BDA0003290809120000027
Figure BDA0003290809120000028
Static coordinate system x of front cutting edge and gear of chamfering tool for hobbingmomymThe included angle of the face;
Figure BDA0003290809120000031
wherein k is the tooth number of the hobbing and chamfering tool, and z is the tooth number of the cylindrical gear;
3) expressing the cylindrical gear chamfering target profile in a gear static coordinate system o on the basis of the step 2)m-xmymzmThe cylindrical gear chamfering target profile comprises a cylindrical gear chamfering target left tooth profile, a cylindrical gear chamfering target left tooth profile transition arc, a cylindrical gear chamfering target right tooth profile and a cylindrical gear chamfering target right tooth profile transition arc;
Figure BDA0003290809120000032
Figure BDA0003290809120000033
Figure BDA0003290809120000034
Figure BDA0003290809120000035
wherein
Figure BDA0003290809120000036
An equation is expressed for a cylindrical gear chamfering target left tooth profile in a gear dynamic coordinate system,
Figure BDA0003290809120000037
an equation is expressed for the right tooth profile of the cylindrical gear chamfering target in a gear dynamic coordinate system,
Figure BDA0003290809120000038
an equation is expressed for a cylindrical gear chamfering target left tooth profile transition circular arc in a gear dynamic coordinate system,
Figure BDA0003290809120000039
representing an equation for a right tooth profile transition circular arc of a cylindrical gear chamfering target in a gear dynamic coordinate system, wherein alpha is the expansion of a left tooth profile and a right tooth profileAngulation, rbThe base radius of the cylindrical gear is shown, and delta is an initial deflection angle; r is a radical of hydrogencIs the tooth profile transition arc radius, alphasIs the starting spread angle of the tooth profile transition arc, (x)c，yc) Is the circle center coordinate of the transition arc of the left tooth profile;
4) establishing a contact point model of the roll-cutting chamfering tool and the cylindrical gear end face profile:
the axial lead of the over-rolling chamfering tool makes an inclination angle of the cylindrical gear relative to the end face
Figure BDA00032908091200000310
Plane M, plane M being the coordinate system od-xdydzdX ofdodzdPlane, plane M and coordinate system om-xmymzmX ofmomymThe faces intersect at a line L, the equation for which is:
Figure BDA0003290809120000041
the straight line L and the cylindrical gear end face profile curve are intersected at a point G, and the point G is a contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile;
5) solving the coordinates of the contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile:
solving the coordinate of the G point simultaneously with the formula (9) according to the cylindrical gear chamfered target profile equation determined by the formula (5) to the formula (8);
Figure BDA0003290809120000042
converting the obtained G point coordinate into a chamfering tool moving coordinate system to obtain the rotation angle of the hobbing chamfering tool
Figure BDA0003290809120000043
Rotation angle of cylindrical gear
Figure BDA0003290809120000044
Contour points of the hobbing chamfering tool at the positions:
Figure BDA0003290809120000045
the cylindrical gear is rotated continuously by the angle delta theta, the rolling cutting chamfering tool is rotated by the angle delta eta according to the generated motion relation,
Δη＝zΔθ/k (12)
obtain the corresponding cylindrical gear corner
Figure BDA0003290809120000046
Corner of cutter
Figure BDA0003290809120000047
Point G' of contact point; repeatedly carrying out the calculation, and continuously solving a series of contact points of the front cutter face of the roll-cutting chamfering cutter and the gear chamfering target profile;
6) and smoothly connecting the front cutter face of the roll-cutting chamfering cutter with each contact point of the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the roll-cutting chamfering cutter.
The invention has the beneficial effects that:
the method for obtaining the profile of the front cutter face of the hobbing and chamfering cutter is based on the principle of hobbing continuous generating cutting motion, obtains the profile of the front cutter face of the hobbing and chamfering cutter by continuously solving the contact point between the front cutter face and the gear chamfering target profile, can be used for designing the hobbing and chamfering cutter, and improves the chamfering efficiency of the cylindrical gear tooth profile.
Drawings
FIG. 1 is a schematic view of the installation position of a hobbing and chamfering tool relative to a cylindrical gear;
FIG. 2 is a space generation motion coordinate system of a hobbing chamfering tool and a cylindrical gear;
FIG. 3 is a model of the contact point between the hobbing and chamfering tool and the cylindrical gear;
fig. 4 is a rake face profile of a roll cutting chamfer tool.
Detailed Description
The invention is further described below with reference to the figures and examples.
The method for obtaining the profile of the rake face of the hobbing and chamfering tool comprises the following steps:
1) establishing a space expansion motion relation coordinate system of the roll-cutting chamfering tool and the cylindrical gear according to the installation pose of the roll-cutting chamfering tool, wherein the space expansion motion relation coordinate system comprises: gear static coordinate system om-xmymzmMoving coordinate system o of gearg-xgygzgTool static coordinate system o1-x1y1z1And the tool moving coordinate system od-xdydzd，
Gear moving coordinate system og-xgygzgFixedly connected with the cylindrical gear, and at the initial position, a gear moving coordinate system og-xgygzgAnd gear static coordinate system om-xmymzmOverlapping;
moving coordinate system o of toold-xdydzdFixedly connected with a hobbing chamfering tool, and a tool moving coordinate system o at an initial positiond-xdydzdAnd a tool static coordinate system o1-x1y1z1And (4) overlapping.
2) Establishing a coordinate transformation matrix M from a gear moving coordinate system to a gear static coordinate systemmg：
Figure BDA0003290809120000051
Wherein
Figure BDA0003290809120000052
For gear winding zmThe angle of counterclockwise rotation of the shaft;
establishing a coordinate transformation matrix M from a gear static coordinate system to a cutter static coordinate system1m：
Figure BDA0003290809120000053
Wherein h is the geometric center of the roll-cutting chamfering tool in zmThe height difference between the axial direction and the end surface of the cylindrical gear, p is xmThe distance from the axis of the cylindrical gear in the axial direction to the axis of the hobbing chamfering tool;
establishing a coordinate transformation matrix M from a tool static coordinate system to a tool moving coordinate systemd1：
Figure BDA0003290809120000061
Wherein
Figure BDA0003290809120000062
For rolling chamfering tools around z1The angle of the shaft rotating anticlockwise, the gear rotating around z in the process of continuously generating chamferingmAngle of counterclockwise rotation of the shaft
Figure BDA0003290809120000063
The roll-cutting chamfering tool is wound around z1Angle of counterclockwise rotation of the shaft
Figure BDA0003290809120000064
Figure BDA0003290809120000065
Static coordinate system x of front cutting edge and gear of chamfering tool for hobbingmomymThe included angle of the face;
Figure BDA0003290809120000066
wherein k is the tooth number of the hobbing and chamfering tool, and z is the tooth number of the cylindrical gear.
3) Expressing the cylindrical gear chamfering target profile in a gear static coordinate system o on the basis of the step 2)m-xmymzmChamfering target profile of middle and cylindrical gearThe shape comprises a cylindrical gear chamfered target left tooth profile, a cylindrical gear chamfered target left tooth profile transition arc, a cylindrical gear chamfered target right tooth profile and a cylindrical gear chamfered target right tooth profile transition arc;
Figure BDA0003290809120000067
Figure BDA0003290809120000068
Figure BDA0003290809120000069
Figure BDA00032908091200000610
wherein
Figure BDA00032908091200000611
An equation is expressed for a cylindrical gear chamfering target left tooth profile in a gear dynamic coordinate system,
Figure BDA00032908091200000612
an equation is expressed for the right tooth profile of the cylindrical gear chamfering target in a gear dynamic coordinate system,
Figure BDA00032908091200000613
an equation is expressed for a cylindrical gear chamfering target left tooth profile transition circular arc in a gear dynamic coordinate system,
Figure BDA0003290809120000071
representing an equation for a right tooth profile transition circular arc of a cylindrical gear chamfering target in a gear dynamic coordinate system, wherein alpha is an expansion angle of a left tooth profile and a right tooth profile, and r isbThe base radius of the cylindrical gear is adopted, and delta is an initial deflection angle; r iscIs the tooth profile transition arc radius, alphasIs the starting spread angle of the tooth profile transition arc, (x)c，yc) Is the center coordinate of the transition arc of the left tooth profile.
4) Establishing a contact point model of the hobbing chamfering tool and the cylindrical gear end face profile:
the axial lead of the over-rolling chamfering tool makes an inclination angle of the cylindrical gear relative to the end face
Figure BDA0003290809120000072
Plane M, plane M being the coordinate system od-xdydzdX ofdodzdPlane, plane M and coordinate system om-xmymzmX ofmomymThe faces intersect at a line L, the equation for which is:
Figure BDA0003290809120000073
the straight line L intersects with the profile curve of the cylindrical gear end face at a point G, and the point G is a contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile.
5) Solving the coordinates of the contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile:
solving the coordinate of the G point simultaneously with the formula (9) according to the cylindrical gear chamfered target profile equation determined by the formula (5) to the formula (8);
Figure BDA0003290809120000074
converting the obtained G point coordinate into a chamfering tool moving coordinate system to obtain the rotation angle of the hobbing chamfering tool
Figure BDA0003290809120000075
Rotation angle of cylindrical gear
Figure BDA0003290809120000076
Contour points of the hobbing chamfering tool at the positions:
Figure BDA0003290809120000077
the cylindrical gear is rotated continuously by the angle delta theta, the rolling cutting chamfering tool is rotated by the angle delta eta according to the generated motion relation,
Δη＝zΔθ/k (12)
obtain the corresponding cylindrical gear corner
Figure BDA0003290809120000078
Corner of cutter
Figure BDA0003290809120000079
The contact point G' of (1); and repeating the calculation, and continuously solving a series of contact points of the front cutter surface of the roll-cutting chamfering cutter and the gear chamfering target profile.
6) And smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter.
In the method for obtaining the profile of the front cutter face of the hobbing and chamfering tool in the embodiment, based on the principle of hobbing continuous generating cutting motion, the profile of the front cutter face of the hobbing and chamfering tool is obtained by continuously solving the contact point between the front cutter face and the gear chamfering target profile, and the method can be used for designing the hobbing and chamfering tool and improving the chamfering efficiency of the cylindrical gear tooth profile.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (1)

1. A method for obtaining the profile of the front tool face of a hobbing chamfering tool is characterized by comprising the following steps: the method comprises the following steps:
1) establishing a space expansion motion relation between the roll-cutting chamfering tool and the cylindrical gear according to the installation pose of the roll-cutting chamfering toolA coordinate system, the spatially-generated kinematic relationship coordinate system comprising: gear static coordinate system om-xmymzmMoving coordinate system o of gearg-xgygzgTool static coordinate system o1-x1y1z1And the tool moving coordinate system od-xdydzd，
Gear moving coordinate system og-xgygzgFixedly connected with the cylindrical gear, and at the initial position, a gear moving coordinate system og-xgygzgAnd gear static coordinate system om-xmymzmOverlapping;
moving coordinate system o of toold-xdydzdFixedly connected with a hobbing chamfering tool, and a tool moving coordinate system o at an initial positiond-xdydzdAnd a tool static coordinate system o1-x1y1z1Overlapping;
2) establishing a coordinate transformation matrix M from a gear dynamic coordinate system to a gear static coordinate systemmg：
Figure FDA0003290809110000011
Wherein
Figure FDA0003290809110000012
For gear winding zmThe angle of counterclockwise rotation of the shaft;
establishing a coordinate transformation matrix M from a gear static coordinate system to a cutter static coordinate system1m：
Figure FDA0003290809110000013
Wherein h is the geometric center of the hobbing chamfering tool in zmThe height difference between the axial direction and the end surface of the cylindrical gear, p is xmCylindrical gear shaft in axial directionThe distance from the center line to the axis of the hobbing chamfering tool;
establishing a coordinate transformation matrix M from a tool static coordinate system to a tool moving coordinate systemd1：
Figure FDA0003290809110000014
Wherein
Figure FDA0003290809110000015
For rolling chamfering tools around z1The angle of the shaft rotating anticlockwise, the gear rotating around z in the process of continuously generating chamferingmAngle of counterclockwise rotation of the shaft
Figure FDA0003290809110000016
The roll-cutting chamfering tool is wound around z1Angle of counterclockwise rotation of the shaft
Figure FDA0003290809110000017
Static coordinate system x of front cutting edge and gear of chamfering tool for hobbingmomymThe included angle of the face;
Figure FDA0003290809110000021
wherein k is the tooth number of the hobbing and chamfering tool, and z is the tooth number of the cylindrical gear;
3) expressing the cylindrical gear chamfering target profile in a gear static coordinate system o on the basis of the step 2)m-xmymzmThe cylindrical gear chamfering target profile comprises a cylindrical gear chamfering target left tooth profile, a cylindrical gear chamfering target left tooth profile transition arc, a cylindrical gear chamfering target right tooth profile and a cylindrical gear chamfering target right tooth profile transition arc;
Figure FDA0003290809110000022
Figure FDA0003290809110000023
Figure FDA0003290809110000024
Figure FDA0003290809110000025
wherein
Figure FDA0003290809110000026
An equation is expressed for a cylindrical gear chamfering target left tooth profile in a gear dynamic coordinate system,
Figure FDA0003290809110000027
an equation is expressed for the right tooth profile of the cylindrical gear chamfering target in a gear dynamic coordinate system,
Figure FDA0003290809110000028
an equation is expressed for a cylindrical gear chamfering target left tooth profile transition circular arc in a gear dynamic coordinate system,
Figure FDA0003290809110000029
representing an equation for a right tooth profile transition circular arc of a cylindrical gear chamfering target in a gear dynamic coordinate system, wherein alpha is an expansion angle of a left tooth profile and a right tooth profile, and r isbThe base radius of the cylindrical gear is shown, and delta is an initial deflection angle; r iscIs the tooth profile transition arc radius, alphasIs the starting spread angle of the tooth profile transition arc, (x)c，yc) Is the circle center coordinate of the transition arc of the left tooth profile;
4) establishing a contact point model of the hobbing chamfering tool and the cylindrical gear end face profile:
the axial lead of the over-rolling chamfering tool is relative to the cylindrical gearEnd face inclination angle of
Figure FDA0003290809110000031
Plane M, plane M being the coordinate system od-xdydzdX ofdodzdPlane, plane M and coordinate system om-xmymzmX ofmomymThe faces intersect at a line L, the equation for which is:
Figure FDA0003290809110000032
the straight line L and the cylindrical gear end face profile curve are intersected at a point G, and the point G is a contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile;
5) solving the coordinates of the contact point of the front cutter face of the hobbing chamfering cutter and the gear tooth profile:
solving the coordinate of the G point simultaneously with the formula (9) according to the cylindrical gear chamfered target profile equation determined by the formula (5) to the formula (8);
Figure FDA0003290809110000033
converting the obtained G point coordinate into a chamfering tool moving coordinate system to obtain the rotation angle of the hobbing chamfering tool
Figure FDA0003290809110000034
Rotation angle of cylindrical gear
Figure FDA0003290809110000035
Contour points of the hobbing chamfering tool at the positions:
Figure FDA0003290809110000036
the cylindrical gear is rotated continuously by the angle delta theta, the rolling cutting chamfering tool is rotated by the angle delta eta according to the generated motion relation,
Δη＝zΔθ/k (12)
obtain the corresponding cylindrical gear corner
Figure FDA0003290809110000037
Corner of cutter
Figure FDA0003290809110000038
Point G' of contact point; repeatedly carrying out the calculation, and continuously solving a series of contact points of the front cutter face of the roll-cutting chamfering cutter and the gear chamfering target profile;
6) and smoothly connecting each contact point of the front cutter face of the hobbing and chamfering cutter and the gear chamfering target profile to obtain a cutting edge curve of the front cutter face of the hobbing and chamfering cutter.
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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101439461A (en) * 2008-12-31 2009-05-27 山西大同齿轮集团有限责任公司 Technique for producing and processing chamfering tool for cylindrical gear double-side tooth profile
CN109014439A (en) * 2018-08-30 2018-12-18 中国重汽集团大同齿轮有限公司 Plate-like topping gear chamfering knife and manufacturing method for cylindrical gear profile chamfered edge
CN109190313A (en) * 2018-10-30 2019-01-11 长江大学 A kind of spiral bevel gear tooth top chamfered edge calculation method based on Surface tessellation
DE102018113962A1 (en) * 2017-07-11 2019-01-17 Komatsu Ltd. HOBS
CN110705064A (en) * 2019-09-20 2020-01-17 天津大学 Design method of rotary chamfering tool, tool designed by design method and use method of tool

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Publication number Priority date Publication date Assignee Title
CN101439461A (en) * 2008-12-31 2009-05-27 山西大同齿轮集团有限责任公司 Technique for producing and processing chamfering tool for cylindrical gear double-side tooth profile
DE102018113962A1 (en) * 2017-07-11 2019-01-17 Komatsu Ltd. HOBS
CN109014439A (en) * 2018-08-30 2018-12-18 中国重汽集团大同齿轮有限公司 Plate-like topping gear chamfering knife and manufacturing method for cylindrical gear profile chamfered edge
CN109190313A (en) * 2018-10-30 2019-01-11 长江大学 A kind of spiral bevel gear tooth top chamfered edge calculation method based on Surface tessellation
CN110705064A (en) * 2019-09-20 2020-01-17 天津大学 Design method of rotary chamfering tool, tool designed by design method and use method of tool

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