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CN116956601A - Design method of small-modulus helical tooth turning tool based on end face edge shape - Google Patents

Design method of small-modulus helical tooth turning tool based on end face edge shape Download PDF

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CN116956601A
CN116956601A CN202310923569.4A CN202310923569A CN116956601A CN 116956601 A CN116956601 A CN 116956601A CN 202310923569 A CN202310923569 A CN 202310923569A CN 116956601 A CN116956601 A CN 116956601A
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gear
tool
cutter
face
processed
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郭二廓
徐甲
刘畅
高婉婷
周艺涵
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Jiangsu University
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Abstract

本发明提供了基于端面刃形的小模数斜齿车齿刀具设计方法，包括：建立齿轮端面齿廓方程，计算待加工齿轮齿廓法矢；确定刀具齿数与刀具螺旋角；计算刀具安装轴交角、刀具节圆半径和刀具初始安装中心距；建立刀具与待加工齿轮齿面的啮合方程；计算与待加工齿轮齿面相共轭的车齿刀具共轭曲线簇，检查刀具共轭曲面是否存在曲面发散或交叉现象，若是，则返回修改刀具齿数，若否，则继续进行；对刀具共轭曲面插值计算得到无理论误差的刀具法面刃形；按照空间坐标变换得到刀具端面刃形；确定刀具宽度和刀具结构后角。本发明避免了小模数斜齿车齿刀具法面前刀面的刃磨工序以及刃磨时产生的齿形压力角误差，提升了刀具设计精度和使用寿命。

The invention provides a design method for a small module helical gear turning tool based on the end face blade shape, which includes: establishing a gear end face tooth profile equation, calculating the normal vector of the gear tooth profile to be processed; determining the number of tool teeth and the tool helix angle; and calculating the tool installation axis. Intersection angle, tool pitch radius and initial tool installation center distance; establish the meshing equation between the tool and the gear tooth surface to be processed; calculate the conjugate curve cluster of the turning tool that is conjugate to the gear tooth surface to be processed, and check whether the tool conjugate surface exists Surface divergence or intersection phenomenon, if yes, return to modify the number of tool teeth, if not, continue; interpolate the tool conjugate surface to obtain the tool normal surface edge shape without theoretical error; obtain the tool end face edge shape according to the spatial coordinate transformation; determine Tool width and tool structure relief angle. The invention avoids the sharpening process of the front face of the small module helical gear turning tool and the tooth profile pressure angle error generated during sharpening, and improves the design accuracy and service life of the tool.

Description

Design method of small-modulus helical tooth turning tool based on end face edge shape
Technical Field
The invention relates to the field of gear machining and cutter design, in particular to a small-modulus helical tooth turning cutter design method based on end face edge shape.
Background
Gears are key basic parts of a plurality of equipment, and the processing technology level of the gears has important significance for improving and developing high-grade gear products. Along with domestic processing demands on high-performance tooth face gears and gears with complex and compact structures, the traditional gear manufacturing process is difficult to meet the processing demands of high efficiency and high precision. The turning gear processing technology is an emerging gear processing technology, can solve the difficult problems of processing the high-grade precise harmonic speed reducer and the compact inner gear ring with thin wall or without a tool withdrawal groove on the automatic gearbox, and has the remarkable advantages of high precision, high efficiency, green environmental protection and the like.
The key of the turning technology is the design of a cutter. In the design and manufacturing process of a traditional conical helical gear turning cutter, a normal plane is usually ground into an inclined step surface to serve as a rake face, so that the cutting edges on two sides of the cutter are guaranteed to have enough working rake angles. For small-modulus helical tooth turning cutters with the modulus smaller than 1mm, the sharpening process of the front cutter face of the helical step face is complex, and the cutter sharpening process and the cutter manufacturing cost are increased. Meanwhile, due to the existence of a rear angle of the cutter structure, the front cutter surface of the sharpening method can generate asymmetric pressure angle errors on two sides of the cutter, so that the cutter edge shape precision and the gear machining precision are reduced. Therefore, aiming at the problems existing in the design and manufacture of the small-modulus turning cutter, how to optimize the sharpening process of the helical turning cutter and improve the manufacturing precision of the cutter is a problem which needs to be solved in the current small-modulus turning cutter tooth processing.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a design method of a small-modulus helical tooth turning cutter based on an end face blade shape, and the designed turning cutter not only can meet the processing requirement of a small-modulus gear, but also does not need a sharpening process of a front cutter face, thereby avoiding tooth pressure angle errors generated during sharpening.
The present invention achieves the above technical object by the following means.
A design method of a small-modulus helical tooth turning tool based on an end face blade shape comprises the following steps:
step 1: according to the parameters of the gear to be processed, establishing a gear end face tooth profile equation T (1) Calculating the gear profile normal vector of the gear to be processed;
step 2: determining the number z of teeth of a tool t Helix angle beta with the tool t ；
Step 3: calculating the cutter mounting axis intersection angle sigma and the cutter pitch circle radius r pt And the initial installation center distance a of the cutter;
step 4: establishing a meshing equation T of a cutter and a tooth surface of a gear to be machined by adopting an intersecting axis double-degree-of-freedom conjugate theory (2) ；
Step 5: calculating a conjugate curve cluster T of a turning tool conjugate with the tooth surface of the gear to be processed (3) Obtaining a cutter conjugate curved surface S through curved surface fitting (1) Checking the conjugate curved surface S of the cutter (1) If the curved surface diverges or crosses, returning to the step 2 and modifying the number z of teeth of the cutter t If not, carrying out the step 6;
step 6: rotating the cutter conjugate curved surface S (1) Conjugate curved surface S of the cutter (1) The normal plane section of the cutter is overlapped with the end face of the cutter to obtain a conjugate curved surface S of the cutter (2) For the conjugate curved surface S of the cutter (2) Interpolation calculation to obtain tool normal plane blade shape T without theoretical error (4) ；
Step 7: cutting the tool to form a normal face edge shape T (4) Obtaining the cutter end face edge shape T according to the space coordinate transformation (5) ；
Step 8: determining tool width b and tool structure relief angle alpha 0 。
Further, in the step 1, the gear face tooth profile equation T (1) The method comprises the following steps:
T (1) ＝[x w (θ i ) y w (θ i ) 0 1] T
wherein ,xw 、y w The tooth profile coordinates of the end face of the gear to be processed; θ i To be treatedAnd processing gear end face tooth profile parameters.
Further, in the step 1, the tooth profile normal vector is:
wherein ,nxw For the component of the normal vector of the tooth profile of the end face of the gear to be processed along the x direction, n yw Is the component of the normal vector of the tooth profile of the end face of the gear to be processed along the y direction.
Further, in the step 3, the cutter mounting axis intersection angle Σ and the gear helix angle β to be machined w The tool helix angle beta t The three satisfy the relation: Σ= |β w -β t |。
Further, in the step 3, the initial mounting center distance a of the cutter is:
a＝r pw ±r pt
wherein ,rpw For the pitch circle radius of the gear to be machined,r pt is the pitch circle radius of the cutter,m n the normal modulus of the gear to be processed is; z g Is the number of teeth of the gear to be processed.
Further, the step 4 specifically includes:
step 4.1: establishing a fixed coordinate system O S1 (O s1 -x s1 ,y s1 ,z s1 )、O S2 (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 rotation axis of the tool, said z s1 Axis and the z s2 The included angle between the axes is the cutter mounting axis intersection angle sigma, the z s1 Axis and the z s2 The shortest distance between the shafts is the initial installation of the cutterHeart distance a, x s1 Axis and x s2 The axes are coincident; establishing a dynamic coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 )、O 2 (O 2 -x 2 ,y 2 ,z 2 )，O 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixedly connected with a gear to be processed, O 2 (O 2 -x 2 ,y 2 ,z 2 ) Fixedly connected with the cutter, O 1 (O 1 -x 1 ,y 1 ,z 1 ) Initial position of (2) and O S1 (O s1 -x s1 ,y s1 ,z s1 ) Overlap, O 2 (O 2 -x 2 ,y 2 ,z 2 ) Initial position of (2) and O S2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be machined has an angular velocity omega 1 Around said z s1 The shaft rotating and at a speed v 0 Moving the cutter at a constant speed along the direction of the rotating shaft at an angular velocity omega 2 Around said z s2 Rotation of the shaft omega 1 and ω2 The relation is satisfied:
step 4.2: deriving an equation of the meshing point M of the cutter and the tooth surface of the gear to be machined:
n m ·v 12 ＝0
wherein, the normal vector n of the tooth surface of the gear to be processed and the cutter at the meshing point M m The three components of (a) are:p w the spiral parameters of the gear to be processed are; v 12 For the relative movement speed of the tool and the tooth surface of the gear to be machined at the engagement point M +.>
Step 4.3: deriving the engagement condition according to the step S4.2:
wherein ,xw 、y w The tooth profile coordinates of the end face of the gear to be processed; n is n xw For the component of the normal vector of the tooth profile of the end face of the gear to be processed along the x direction, n yw The component of the normal vector of the tooth profile of the end face of the gear to be processed along the y direction; t represents the time that a point on the tooth surface of the gear to be machined rotates to become an engagement point; the fixed coordinate system O S2 (O s2 -x s2 ,y s2 ,z s2 ) There is a point Q (r q cosγ,r q sin gamma, z (gamma)), so that the vector QM is normal to the meshing point M when the tool is meshed with the tooth surface of the gear to be machined m Overlap, r q Is a variable related to gamma, z q Representing the coordinate of the meshing point along the direction of the rotating shaft of the cutter under the cutter fixed coordinate system;
step 4.4: changing z according to the meshing condition obtained in the step 4.3 q Calculating to obtain conjugate curve cluster T of cutter and tooth surface of gear to be processed (2) ：
wherein ,θi Is a tooth profile parameter of the end face of the gear to be processed; gamma is r q 、z q Is a parameter of (a).
Further, in the step 5, the turning tool conjugate curve cluster T (3) The method comprises the following steps:
T (3) ＝M 2-s2 ·M s2-s1 ·T (2)
wherein ,
further, in the step 6, theConjugate surface equation S (2) The method comprises the following steps:
S (2) ＝M x2 ·M x1 ·S (1)
wherein , β x represents the tooth top helix angle of the cutter and beta x ＝arctan(r at /p t )，r at For the outside diameter of the tool, p t For the tool screw parameters->r pt Is the pitch radius of the cutter.
Further, in the step 7, the cutter end face edge shape T (5) The method comprises the following steps:
wherein ,represents M x1 Inverse matrix of>Represents M x2 Inverse matrix of M x3 Representing the projection transformation matrix of the tool normal plane blade spiral, < ->α i Is the rotation angle of the projection of the normal plane blade spiral of the cutter,z i representing the normal surface edge z of the tool s2 Coordinate values of the axes.
The invention has the beneficial effects that:
1) The turning tooth cutter based on the end face cutting edge designed by the design method disclosed by the invention has the advantages that on the basis of meeting the machining precision of the tooth wheel vehicle, particularly for the small-modulus helical tooth turning tooth cutter with the modulus smaller than 1mm, the front cutter face sharpening process is reduced, and the turning tooth cutter has great significance in improving the cutter manufacturing efficiency. Meanwhile, tooth-shaped pressure angle errors generated when the front tool face of the normal face is sharpened due to the existence of the structural relief angle are avoided, and the service life of the tool is prolonged.
2) The designed end face edge shape turning tool adopts the double-degree-of-freedom linear surface conjugate theory, the designed turning tool edge shape has no any error, the holding property after the tool edge shape is regrind is good, and the turning machining precision is high.
Drawings
FIG. 1 is a flow chart of a design method of a small-modulus helical gear turning tool based on an end face blade shape in an embodiment of the invention;
FIG. 2 is a schematic view of a tooth profile of a gear to be machined according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a motion model for generating a turning gear according to an embodiment of the present invention;
FIG. 4 shows a conjugate curve of a tool according to an embodiment of the present invention;
FIG. 5 is a schematic illustration of interpolation calculation of tool normal blade shape in accordance with an embodiment of the present invention;
FIG. 6 shows the edge shape of the end face of the cutter according to the embodiment of the present invention;
fig. 7 shows a turning tooth cutter based on an end edge shape according to an embodiment of 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. 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.
Taking tangent four-arc harmonic gear as an example of a gear 2 to be processed, wherein the gear 2 to be processed is straight-tooth, and the number of teeth is z g =100, modulus m n = 0.34836mm, helix angle β w ＝0°Radius r of addendum circle a = 17.6250mm, center coordinates of (0, 0); radius of root circle r f = 17.2130mm, center coordinates of (0, 0); radius r of first convex arc 1 =0.1200 mm, center coordinates (17.5146,0); radius r of second convex arc 2 = 0.5539mm, center coordinates (17.2366, -0.3331); radius r of first concave circular arc 3 = 2.2806mm, center coordinates (18.4523,2.2275); second concave arc radius r 4 = 0.2541mm, center coordinates are (17.4611,0.4599). The small-modulus helical gear turning tool based on the end face edge shape is designed by the small-modulus helical gear turning tool design method.
Referring to fig. 1 to 7, a method for designing a small-modulus helical gear turning tool based on an end face blade shape according to an embodiment of the present invention specifically includes the following steps:
s1: according to the parameters of the gear 2 to be processed, a gear end face tooth profile equation T is established (1) Calculating a gear profile normal vector of the gear 2 to be processed;
as shown in fig. 2, which is a schematic diagram of the tooth profile 1 of the gear to be machined, the equation of the tooth profile 1 of the gear to be machined can be expressed as:
in the formula ,xw 、y w The tooth profile coordinates of the end face of the gear to be processed; θ i Representing the central angle range of each circular arc for the tooth profile parameter of the end face of the gear to be processed; r is (r) i Representing different arc radii; x is x i 、y i The coordinate values of the x-axis and the y-axis at which the centers of different circular arcs are positioned are shown; n is n xw 、n yw Is the normal component of the tooth profile of the end face of the gear to be processed.
So T is (1) Can be expressed as:
T (1) ＝[x w (θ i ) y w (θ i ) 0 1] T (2)
s2: determining a tool number of teeth z t =75, cutter helix angle β t ＝15°；
S3: calculating tool mounting axis intersection angle ΣRadius r of cutter pitch circle pt And the initial installation center distance a of the cutter;
cutter mounting axis intersection angle sigma and helical angle beta of gear to be processed w Helix angle beta of tool t The three formulae satisfy the following relation: Σ= |β w -β t |；
The calculation formula of the initial installation center distance a of the cutter is as follows:
a＝r pw ±r pt (3)
wherein ,rpw For the pitch radius of the gear wheel 3 to be machined, the formula can beCalculating to obtain; r is (r) pt For the radius of the tool pitch circle, the formula +.>Calculating to obtain; m is m n The normal modulus of the gear to be processed is; z g Is the number of teeth of the gear to be processed.
S4: according to the gear meshing principle, a meshing equation T of the cutter 3 and a curved surface of the gear to be processed is established by adopting an intersecting axis double-degree-of-freedom conjugate theory (2) ；
Tooth engagement equation T (2) Can be obtained by steps S4.1-S4.4, specifically:
s4.1: as shown in fig. 3, a motion model is developed for the machining of the teeth. Establishing a fixed coordinate system O S1 (O s1 -x s1 ,y s1 ,z s1 )、O S2 (O s2 -x s2 ,y s2 ,z s2 )，z s1 The axial direction coincides with the rotation axis of the gear 2 to be processed, z s2 The axis coincides with the rotation axis of the tool 3, said z s1 Axis and the z s2 The included angle between the axes is the cutter mounting axis intersection angle sigma, the z s1 Axis and the z s2 The shortest distance between the shafts is the initial installation center distance a, x of the cutter s1 Axis and x s2 The axes are coincident; establishing a dynamic coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 )、O 2 (O 2 -x 2 ,y 2 ,z 2 )，O 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixedly connected with the gear 2 to be processed, O 2 (O 2 -x 2 ,y 2 ,z 2 ) Fixedly connected with the cutter 3, O 1 (O 1 -x 1 ,y 1 ,z 1 ) Initial position of (2) and O S1 (O s1 -x s1 ,y s1 ,z s1 ) Overlap, O 2 (O 2 -x 2 ,y 2 ,z 2 ) Initial position of (2) and O S2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear 2 to be machined is at an angular velocity ω 1 Around axis z s1 Rotates and at a speed v 0 Moving at a constant speed in the direction of the axis of rotation, the tool 3 being at an angular velocity omega 2 Around axis z s2 After time t, the gear 2 to be processed rotates around z s1 Rotation of omega 1 t and move v in axial direction 0 t, the cutter 3 winds z s2 Shaft rotation omega 2t； wherein ,ω1 and ω2 The rotation speeds of the gear 2 to be processed and the cutter 3 are respectively omega 1 and ω2 The relation is satisfied:
s4.2: deriving an equation of the tooth surface of the cutter 3 and the gear 2 to be processed at the meshing point M according to the gear meshing principle:
n m ·v 12 ＝0 (4)
wherein ,nm For the normal vector of the tooth flank of the gear 2 to be machined at the meshing point M, n m The three components of (a) are:p w the spiral parameters of the gear to be processed are; v 12 For the relative speed of movement of the tool 3 with the tooth surface of the gear 2 to be machined at the engagement point M +.>
S4.3: deriving the engagement condition according to the step S4.2:
wherein ,xw 、y w The tooth profile coordinates of the end face of the gear to be processed; n is n xw For the component of the normal vector of the tooth profile of the end face of the gear to be processed along the x direction, n yw The component of the normal vector of the tooth profile of the end face of the gear to be processed along the y direction; t represents the time that a point on the tooth surface of the gear 2 to be machined rotates to become an engagement point; the fixed coordinate system O S2 (O s2 -x s2 ,y s2 ,z s2 ) There is a point Q (r q cosγ,r q sin gamma, z (gamma)), so that the vector QM coincides with the normal vector of the meshing point M when the tool 3 meshes with the tooth surface of the gear 2 to be machined, r q Is a variable related to gamma, z q The coordinates of the engagement point along the direction of the tool pivot axis in the fixed coordinate system of the tool 3 are shown.
S4.4: changing z according to the meshing condition obtained in the step 4.3 q Calculating to obtain conjugate curve cluster T of cutter 3 and tooth surface of gear 2 to be processed (2) The equation can be expressed as:
T (2) ＝[x y z 1] T (6)
wherein, the variable cross section engagement equation T (2) The method can be concretely expressed as follows:
wherein gamma is r q 、z q Is a parameter of (a).
S5: calculating a conjugate curve cluster T of a turning cutter conjugate with the tooth surface of the gear 2 to be processed (3) Obtaining a cutter conjugate curved surface S through curved surface fitting (1) Checking the conjugate curved surface S of the cutter (1) If the curved surface diverges or crosses, returning to the step 2 and modifying the number z of teeth of the cutter t If not, carrying out the step 6;
conjugate curve cluster T of turning gear cutter (3) The calculation can be performed by the following formula:
T (3) ＝M 2-s2 ·M s2-s1 ·T (2) (7)
wherein ,
by conjugate curve cluster T of turning tooth cutter (3) Performing surface fitting to obtain a conjugate curved surface S (1) 4, as shown in FIG. 4, is a conjugate curved surface S of the cutter (1) 4。
S6: conjugate curved surface S of cutter (1) 4 rotating around the x-axis to make the cutter conjugate curved surface S (1) 4, the normal plane section coincides with the end face of the cutter to obtain a cutter conjugate curved surface S (2) 5, interpolating the cutter conjugate curved surface S by cubic spline (2) 5 interpolation calculation to obtain tool normal face blade shape T without theoretical error (4) 8；
Tool conjugate curved surface equation S obtained after rotation (2) 5 is:
S (2) ＝M x2 ·M x1 ·S (1) (8)
wherein , β x represents the tooth top helix angle of the cutter and beta x ＝arctan(r at /p t )，r at For the outside diameter of the tool, p t For the tool screw parameters->r pt Is the pitch radius of the cutter.
As shown in FIG. 5, by conjugate curved surface S of the cutter (2) Knife normal blade T calculated by 5 cubic spline interpolation (interpolation plane 7 in fig. 5) (4) 6。
S7: at the position ofTool conjugate curved surface S (1) 4, cutting the normal surface of the cutter into a blade shape T (4) 6 obtaining the cutter end face edge shape T shown in figure 6 according to the space coordinate transformation (5) 9；
Cutter end face edge shape T (5) 9 can be calculated by the following formula:
wherein ,represents M x1 Inverse matrix of>Represents M x2 Inverse matrix of M x3 Representing the projection transformation matrix of the tool normal plane blade spiral, < ->α i Is the rotation angle of the projection of the normal plane blade spiral of the cutter,z i representing the normal surface edge z of the tool s2 Coordinate values of the axes.
S8: determining tool width b and tool structure relief angle alpha 0 ；
According to the cutter end face edge shape T obtained in step S7 (5) And 9, designing and manufacturing a turning cutter based on the end face cutting edge, and carrying out turning machining on a turning machine tool according to cutter installation parameters.
Fig. 7 shows a turning tooth cutter based on an end edge shape according to the invention. Compared with the traditional method for sharpening the front cutter surface by using the helical tooth turning cutter, the method can directly adopt the end surface cutting edge as the cutting edge to avoid the error of the tooth form pressure angle of the cutter, the cutter edge shape precision is higher, the service life is longer, the sharpening process of the front cutter surface is not needed, and the cutter manufacturing process is reduced.
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 (9)

1. The design method of the small-modulus helical tooth turning tool based on the end face edge shape is characterized by comprising the following steps of:
step 1: according to the parameters of the gear to be processed, establishing a gear end face tooth profile equation T (1) Calculating the gear profile normal vector of the gear to be processed;
step 2: determining the number z of teeth of a tool t Helix angle beta with the tool t ；
Step 3: calculating the cutter mounting axis intersection angle sigma and the cutter pitch circle radius r pt And the initial installation center distance a of the cutter;
step 4: establishing a meshing equation T of a cutter and a tooth surface of a gear to be machined by adopting an intersecting axis double-degree-of-freedom conjugate theory (2) ；
Step 5: calculating a conjugate curve cluster T of a turning tool conjugate with the tooth surface of the gear to be processed (3) Obtaining a cutter conjugate curved surface S through curved surface fitting (1) Checking the conjugate curved surface S of the cutter (1) If the curved surface diverges or crosses, returning to the step 2 and modifying the number z of teeth of the cutter t If not, carrying out the step 6;
step 6: rotating the cutter conjugate curved surface S (1) Conjugate curved surface S of the cutter (1) The normal plane section of the cutter is overlapped with the end face of the cutter to obtain a conjugate curved surface S of the cutter (2) For the conjugate curved surface S of the cutter (2) Interpolation calculation to obtain tool normal plane blade shape T without theoretical error (4) ；
Step 7: cutting the tool to form a normal face edge shape T (4) Obtaining the cutter end face edge shape T according to the space coordinate transformation (5) ；
Step 8: determining tool width b and tool structure relief angle alpha 0 。
2. The method for designing a small-modulus helical gear turning tool based on end face edge shape according to claim 1, wherein in the step 1, the gear end face tooth profile equation T (1) The method comprises the following steps:
T (1) ＝[x w (θ i ) y w (θ i ) 0 1] T
wherein ,xw 、y w The tooth profile coordinates of the end face of the gear to be processed; θ i Is a tooth profile parameter of the end face of the gear to be processed.
3. The method for designing a small-modulus helical gear turning tool based on an end face blade shape according to claim 2, wherein in the step 1, the tooth profile normal vector is:
wherein ,nxw For the component of the normal vector of the tooth profile of the end face of the gear to be processed along the x direction, n yw Is the component of the normal vector of the tooth profile of the end face of the gear to be processed along the y direction.
4. The method for designing a small-modulus helical turning tool based on end face edge shape according to claim 1, wherein in the step 3, the tool mounting axis intersection angle Σ and the helical angle β of the gear to be machined w The tool helix angle beta t The three satisfy the relation: Σ= |β w -β t |。
5. The method for designing a small-modulus helical gear turning tool based on an end face blade shape according to claim 1, wherein in the step 3, the initial installation center distance a of the tool is:
a＝r pw ±r pt
wherein ,rpw For the pitch circle radius of the gear to be machined,r pt is the pitch circle radius of the cutter,m n the normal modulus of the gear to be processed is; z g Is the number of teeth of the gear to be processed.
6. The method for designing the small-modulus helical gear turning tool based on the end face edge shape according to claim 1, wherein the step 4 is specifically:
step 4.1: establishing a fixed coordinate system O S1 (O s1 -x s1 ,y s1 ,z s1 )、O S2 (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 rotation axis of the tool, said z s1 Axis and the z s2 The included angle between the axes is the cutter mounting axis intersection angle sigma, the z s1 Axis and the z s2 The shortest distance between the shafts is the initial installation center distance a, x of the cutter s1 Axis and x s2 The axes are coincident; establishing a dynamic coordinate system O 1 (O 1 -x 1 ,y 1 ,z 1 )、O 2 (O 2 -x 2 ,y 2 ,z 2 )，O 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixedly connected with a gear to be processed, O 2 (O 2 -x 2 ,y 2 ,z 2 ) Fixedly connected with the cutter, O 1 (O 1 -x 1 ,y 1 ,z 1 ) Initial position of (2) and O S1 (O s1 -x s1 ,y s1 ,z s1 ) Overlap, O 2 (O 2 -x 2 ,y 2 ,z 2 ) Initial position of (2) and O S2 (O s2 -x s2 ,y s2 ,z s2 ) Overlapping; the gear to be machined has an angular velocity omega 1 Around said z s1 The shaft rotating and at a speed v 0 Moving the cutter at a constant speed along the direction of the rotating shaft at an angular velocity omega 2 Around said z s2 Rotation of the shaft omega 1 and ω2 The relation is satisfied:
step 4.2: deriving an equation of the meshing point M of the cutter and the tooth surface of the gear to be machined:
n m ·v 12 ＝0
wherein, the normal vector n of the tooth surface of the gear to be processed and the cutter at the meshing point M m The three components of (a) are:p w the spiral parameters of the gear to be processed are; v 12 For the relative movement speed of the tool and the tooth surface of the gear to be machined at the engagement point M +.>
Step 4.3: deriving the engagement condition according to the step S4.2:
wherein ,xw 、y w The tooth profile coordinates of the end face of the gear to be processed; n is n xw For the component of the normal vector of the tooth profile of the end face of the gear to be processed along the x direction, n yw The component of the normal vector of the tooth profile of the end face of the gear to be processed along the y direction; t represents the time that a point on the tooth surface of the gear to be machined rotates to become an engagement point; the fixed coordinate system O S2 (O s2 -x s2 ,y s2 ,z s2 ) There is a point Q (r q cosγ,r q sin gamma, z (gamma)), in the tool and to be machinedNormal vector n of vector QM and meshing point M when tooth surfaces of gears mesh m Overlap, r q Is a variable related to gamma, z q Representing the coordinate of the meshing point along the direction of the rotating shaft of the cutter under the cutter fixed coordinate system;
step 4.4: changing z according to the meshing condition obtained in the step 4.3 q Calculating to obtain conjugate curve cluster T of cutter and tooth surface of gear to be processed (2) ：
wherein ,θi Is a tooth profile parameter of the end face of the gear to be processed; gamma is r q 、z q Is a parameter of (a).
7. The method for designing a small-modulus helical gear turning tool based on end face edge shape according to claim 6, wherein in the step 5, the turning tool is conjugate to a curve cluster T (3) The method comprises the following steps:
T (3) ＝M 2-s2 ·M s2-s1 ·T (2)
wherein ,
8. the method for designing a small-modulus helical gear turning tool based on end face edge shape according to claim 1, wherein in the step 6, the conjugate curved surface equation S (2) The method comprises the following steps:
S (2) ＝M x2 ·M x1 ·S (1)
wherein ,β x represents the tooth top helix angle of the cutter and beta x ＝arctan(r at /p t )，r at For the outside diameter of the tool, p t For the tool screw parameters->r pt Is the pitch radius of the cutter.
9. The method for designing a small-modulus helical gear turning tool based on end face edge shape according to claim 1, wherein in the step 7, the tool end face edge shape T (5) The method comprises the following steps:
wherein ,represents M x1 Inverse matrix of>Represents M x2 Inverse matrix of M x3 Representing the projection transformation matrix of the tool normal plane blade spiral, < ->α i For the rotation angle of the projection of the normal face blade spiral of the tool, +.>z i Representing the normal surface edge z of the tool s2 Coordinate values of the axes.
CN202310923569.4A 2023-07-25 2023-07-25 Design method of small-modulus helical tooth turning tool based on end face edge shape Pending CN116956601A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118123138A (en) * 2024-02-01 2024-06-04 大连理工大学 A design method for the cutting edge of a gear end face tooth profile chamfering tool
CN118951172A (en) * 2024-08-06 2024-11-15 哈尔滨工业大学 A method for optimizing the machining of spiral gear teeth
CN119337533A (en) * 2024-12-02 2025-01-21 重庆大学 A design method for cutting edge profile of gear turning tools

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118123138A (en) * 2024-02-01 2024-06-04 大连理工大学 A design method for the cutting edge of a gear end face tooth profile chamfering tool
CN118951172A (en) * 2024-08-06 2024-11-15 哈尔滨工业大学 A method for optimizing the machining of spiral gear teeth
CN119337533A (en) * 2024-12-02 2025-01-21 重庆大学 A design method for cutting edge profile of gear turning tools

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