Three-axis machine tool based chamfering method for giving cutter swing angle after milling of spiral gear with any end face profile

Abstract

A chamfering method for giving a cutter swing angle after milling of a spiral gear with any end face profile based on a three-axis machine tool is characterized in that based on the structure form of the three-axis machine tool, three axes comprise a linear axis X, a linear axis Z and a rotating axis C, a cubic spline method is adopted to fit the section of a gear milling cutter head through given discrete points, and the cutter swing angle is set according to the spiral gear milling machining principle; the accurate gear end face profile and tangent vector after gear milling are calculated; a conical chamfering cutter model is established, a cutter swing angle is given, and a mathematical model of a conical cutter in a workpiece coordinate system is solved; a circle at a certain height of the appointed conical cutter is tangent to the profile of the end face of the gear, a reasonable cutting edge is fully utilized, and the requirement for the tooth profile curvature is lowered. According to the method, the discrete points of the cutter head profile are fitted by using a spline method, and the accurate gear end surface profile and tangent vector after gear milling are calculated through the cutter head profile and the gear milling track according to the space meshing principle, so that the target chamfering curve is more accurate, and the chamfering surface effect is more uniform. The method comprises the following steps: establishing a mathematical model of a conical chamfering cutter, giving a cutter swing angle, converting the cutter swing angle into a workpiece coordinate system, and calculating a cutter location point when a circle with a specified height of the conical cutter is tangent to the tooth profile of the end surface of the gear, and the method is applicable to special shapes of the end surface of the gear, such as a tooth root part with an arc or a tooth top part with a chamfer; the reasonable part cutting edge of the conical chamfering cutter is fully utilized, and the cutter loss is reduced.

Description

Technical Field

[0001] The present invention relates to a chamfering method for a given tool swing angle after milling a helical gear with an arbitrary end face profile based on a three-axis machine tool, in particular to a method for calculating an accurate target chamfering curve through a discrete point cutter head profile and a milling machining path according to the principle of spatial meshing, and a method for calculating tool trajectory points tangent to a fixed height circle of a specified conical chamfering tool and a target chamfering curve, belonging to the discipline of "numerical control technology and digital manufacturing" and the field of advanced manufacturing technology. Technical Background

[0002] Chamfering is becoming more and more common in the machining of high-quality gears. Many manufacturers require tooth profile chamfering after the gear milling process. However, there is usually a margin left in the tooth groove after the gear milling process. Due to the different profiles of the gear milling cutter, the theoretical involute tooth profile chamfering will result in mismatched chamfering trajectories and uneven chamfering surfaces. The target chamfering curve requires a more accurate expression method. The general principle of calculating the gear chamfering tool position is to make the ellipse obtained by the intersection of the cutting plane and the fixed swing angle conical tool tangent to the general end face profile to find the chamfering tool position. This cutting method requires a smaller tooth profile curvature, wastes the cutting edge, and causes serious tool loss. Summary of the invention

[0003] The purpose of the present invention is to solve the above technical problems and propose a new chamfering method based on a 3-axis machine tool, wherein the 3 axes include linear axes X, Z and a rotation axis C. The cubic spline method is used to fit the milling cutter head section, and a more accurate target chamfering curve is obtained according to the principle of spiral gear milling processing; the cross-sectional circle of a certain height of the specified conical tool is tangent to the gear end face profile. This method can be applied to the special morphology of the gear end face, fully utilize the blade in a reasonable position, reduce the requirement for the curvature of the tooth profile, and make up for the shortcomings of the general chamfering method. The present invention has good chamfering effect and high tool utilization rate.

[0004] The technical solution of the present invention is as follows:

[0005] A chamfering method for a helical gear with an arbitrary end face profile and a given tool swing angle after milling the gear based on a 3-axis machine tool, characterized by comprising the following steps:

[0006] Step 1: According to the discrete points of the cutter head, the cutter head truncation shape is fitted using the cubic spline method;

[0007] Step 2: According to the principle of spatial meshing, the accurate gear end face profile after gear milling is calculated through the cutter head section and the gear milling trajectory;

[0008] Step 3: Establish a mathematical model of the conical chamfering tool, give the tool swing angle, and convert it to the workpiece coordinate system;

[0009] Step 4, making the cross-sectional circle of a certain height of the specified conical chamfering tool tangent to the end face profile of the gear after gear milling, and calculating the chamfering tool position point;

[0010] Step five: Develop chamfering software, perform post-processing based on the chamfering principle and compare it with the actual machine tool to generate the chamfering processing program.

[0011] The specific method in step 1 is as follows:

[0012] According to the given cutter disc discrete points, the cutter disc truncation is obtained by using the cubic spline interpolation method to ensure that the cutter disc truncation is smooth; the width of the cutter disc is divided into n intervals [zi,zi+1], (i=1,2,…n), each interval is represented by a spline curve.

[0013] Express:

[0014] ε k (z) = a k +b k (zz i )+c k (zz i ) 2 +d k (zz i ) 3 ,(k=0,1,...n-1) (1)

[0015] The entire cubic spline curve needs to determine a k ,b k ,c k ,d k ,(k=0,1,...n-1), a total of 4n unknown coefficients.

[0016] Let h i =z i+1 -z i , according to the boundary of each spline curve:

[0017]

[0018] Let ε i (z i )=ε i , ε i (z i+1 )=ε i+1 , we can get:

[0019]

[0020] Let m i =ε i ”(z i )=2c i ,but:

[0021] d i =(m i+1 -m i ) / 6 / h i (4)

[0022] A i , c i , d i Substituting into formula (3), we can get

[0023]

[0024] Under natural boundary conditions, m0=0, m n = 0, we can get,

[0025]

[0026] According to the above matrix equation, the unique solution of the spline coefficients in each interval can be obtained, the cubic spline interpolation can be realized, and the cutter head truncation shape can be obtained.

[0027] The specific method in step 2 is as follows:

[0028] According to the principle of spatial meshing, the accurate gear end face profile after milling is calculated through the cutter head section and the milling trajectory as the target chamfer profile; during the forming milling process, the cutter head rotates around its own axis and makes a spiral motion along the workpiece axis to establish the tool coordinate system S w (O w -x w y w z w ) and gear coordinate system S p (O p -x p y p z p ); The installation angle of the cutter head is ∑; x w The shaft is aligned with the centerline of the gear tooth groove; the center distance a between the gear axis and the cutter head center is maintained constant; the gear rotation angle is When the cutter head moves along the gear axis, the distance is Thereby, the spiral motion of the cutter disc relative to the workpiece is realized;

[0029] Gear coordinate system S p The homogeneous coordinate transformation matrix to S1 is:

[0030]

[0031] The homogeneous coordinate transformation matrix from S1 to S2 is:

[0032]

[0033] The homogeneous coordinate transformation matrix from S2 to S3 is:

[0034]

[0035] S3 to cutterhead coordinate system S w The homogeneous coordinate transformation matrix is:

[0036]

[0037] Depend on Figure 2 It is easy to know that from the gear coordinate system S p To the cutterhead coordinate system S w The homogeneous coordinate transformation matrix can be expressed as

[0038] Shown as:

[0039] M wp =M w3 M 32 M 21 M 1p (11)

[0040] Right now:

[0041]

[0042] In the formula, is the gear rotation angle, ∑ is the cutter head installation angle, and a is the center distance;

[0043] By inverting (12), we can find the cutterhead coordinate system S w To S p The homogeneous coordinate transformation matrix is:

[0044]

[0045] The milling cutter rotation model can be expressed in the cutter coordinate system as follows:

[0046] r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (14)

[0047] n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T (15)

[0048] Transform the cutter head surface from the cutter head coordinate system to the gear coordinate system.

[0049] r p =M pw r w (16)

[0050] n p =M pw n w (17)

[0051] The relative speed between the cutter head and the gear is,

[0052]

[0053] in, Represents the speed of the cutter head relative to the gear. According to formula (2-22),

[0054]

[0055] In the formula,

[0056]

[0057] The contact equation is obtained,

[0058] acos(γ)+bsin(γ)=c (20)

[0059] In the formula,

[0060]

[0061] According to the above contact line solution process, the coordinates of the corresponding contact point in the tool head coordinate system are obtained. Then, according to formula (16), the coordinates of all points on the contact line in the workpiece coordinate system are obtained. The coordinates of the contact line obtained in the workpiece coordinate system are marked as (x p ,y p ,z p ), according to formula (21), the contact line spiral is projected onto the end face of the gear to obtain the gear end face profile. According to the morphology of the gear end face (such as a circular arc at the root of the tooth or a chamfer at the top of the tooth), the gear end face profile is converted into a chamfer target curve:

[0062]

[0063] In the chamfering state with tool swing angle, specify the cross-section circle at a specific height on the conical tool to be tangent to the target chamfering curve. The specific methods in step 3 and step 4 are as follows:

[0064] The conical tool surface S is expressed as:

[0065] r s =r s (u,v) (22)

[0066] The normal vector of a point on the conical tool surface S is expressed as:

[0067]

[0068] Among them, u and v are two independent surface parameters, which are coordinates that describe the shape of a single surface;

[0069] Establish an auxiliary coordinate system, such as Figure 3 , the coordinate system O1x1y1z1 is a fixed coordinate system in space, and the coordinate system O g x g y g z g Rotate around axis O1z1; when the gear rotates by angle When the coordinate system O1x1y1z1 and the coordinate system O g x g y g z g The coordinate system O1x1y1z1 is translated along the axis of O1x1 by a distance L. X Get. X It is actually the distance between the center of the cone cutter head and the center of the gear; the coordinate system O3x3y3z3 is translated by the coordinate system O2x2y2z2 along the axis of O2z2 by a distance L Z Finally, the coordinate system O3x3y3z3 is rotated around the axis O3y3 by an angle γ to obtain the tool coordinate system O w x w y w z w Here γ is the angle between the tool axis and the workpiece end face, which is selected according to the actual processing conditions;

[0070] According to the coordinate system and homogeneous coordinate transformation method, the coordinate transformation matrix between the tool coordinate system and the gear coordinate system can be obtained as follows:

[0071] M wg =M w3 M 32 M 21 M 1g (twenty four)

[0072] in,

[0073]

[0074]

[0075] According to formula (24), we can calculate:

[0076]

[0077] According to the space envelope principle, the contact equation for chamfering is:

[0078]

[0079] Among them, (x, y, z) are the three components of vector r.

[0080] Combining the above-mentioned tool mathematical model with the spatial contact conditions, the machining tool position trajectory is calculated.

[0081] According to the chamfering principle, post-processing is performed in comparison with the actual machine tool to generate the chamfering processing program.

[0082] The present invention has the following advantages:

[0083] (1) The chamfer target curve of the present invention is based on the principle of spatial meshing and is calculated according to the cross section of the milling cutter used in the actual milling process and the actual milling machining trajectory, and is more consistent with the tooth profile after actual milling;

[0084] (2) The chamfering method of the present invention can specify the tool swing angle according to the actual workpiece conditions, and can flexibly avoid various interferences.

[0085] (3) The chamfering tool position calculation method of the present invention is based on the goal of specifying the cross-sectional circle of a certain height of the conical chamfering tool to be tangent to the gear end face profile after gear milling, which rationally utilizes the tool cutting edge and reduces the curvature requirement for the target chamfered tooth profile.

[0086] (4) The chamfering tool position calculation method of the present invention can be applied to the special shape of the gear end surface.

[0087] The tooth root has a rounded shape or the tooth top has a chamfered shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 A schematic diagram of a machine tool structure applicable to the present invention;

[0089] Figure 2 The coordinate system of the profiled gear milling of the present invention;

[0090] Figure 3 is the chamfer coordinate system of the present invention;

[0091] Figure 4 It is the software parameter interface of the present invention;

[0092] Figure 5 It is the chamfer simulation and actual effect diagram of the present invention. DETAILED DESCRIPTION

[0093] The following is combined with Figure 1-5 The technical content of the present invention is explained.

[0094] A chamfering method for helical gears with arbitrary end face profiles and given tool swing angles after milling based on a 3-axis machine tool is suitable for Figure 1 machine tool.

[0095] The specific implementation steps are as follows:

[0096] Step 1: Given the discrete points of the milling cutter, the cutter head section is obtained using the cubic spline interpolation method.

[0097] According to the given disc discrete points, the disc width is divided into n intervals [zi,zi+1], (i=1,2,…n), each interval is expressed by a spline curve:

[0098] ε k (z) = a k +b k (zz i )+c k (zz i ) 2 +d k (zz i ) 3 ,(k=0,1,...n-1) (1)

[0099] The entire cubic spline curve needs to determine a k ,b k ,c k ,d k ,(k=0,1,...n-1), a total of 4n unknown coefficients.

[0100] Let h i =z i+1 -z i , according to the boundary of each spline curve:

[0101]

[0102] Let ε i (z i )=ε i , ε i (z i+1 )=ε i+1 , we can get:

[0103]

[0104] Let m i =ε i ”(z i )=2c i ,but:

[0105] d i =(m i+1 -m i ) / 6 / h i (4)

[0106] A i , c i , di Substituting into formula (3), we can get

[0107]

[0108] Under natural boundary conditions, m0=0, m n = 0, we can get,

[0109]

[0110] According to the above matrix equation, the unique solution of the spline coefficients in each interval can be obtained, the cubic spline interpolation can be realized, and the cutter head truncation shape can be obtained.

[0111] Step 2: According to the principle of spatial meshing, the accurate gear end face profile after milling is calculated through the cutter head shape and milling trajectory.

[0112] During the forming milling process, the cutter head rotates around its own axis and makes a spiral motion along the axis of the workpiece, such as Figure 2 As shown. Establish tool coordinate system S w (O w -x w y w z w ) and gear coordinate system S p (O p -x p y p z p ). The installation angle of the cutter head is ∑;x w The shaft is aligned with the centerline of the gear tooth groove; the center distance a between the gear axis and the cutter head center is maintained constant; the gear rotation angle is When the cutter head moves along the gear axis, the distance is Thereby achieving the spiral motion of the cutter disc relative to the workpiece.

[0113] Gear coordinate system S p The homogeneous coordinate transformation matrix to S1 is:

[0114]

[0115] The homogeneous coordinate transformation matrix from S1 to S2 is:

[0116]

[0117] The homogeneous coordinate transformation matrix from S2 to S3 is:

[0118]

[0119] S3 to cutterhead coordinate system S w The homogeneous coordinate transformation matrix is:

[0120]

[0121] Depend on Figure 2 It is easy to know that from the gear coordinate system S p To the cutterhead coordinate system S w The homogeneous coordinate transformation matrix can be expressed as

[0122] Shown as:

[0123] M wp =M w3 M 32 M 21 M 1p (11)

[0124] Right now:

[0125]

[0126] In the formula, is the gear rotation angle, ∑ is the cutter head installation angle, and a is the center distance.

[0127] By inverting (12), we can find the cutterhead coordinate system S w To S p The homogeneous coordinate transformation matrix is:

[0128]

[0129] The milling cutter rotation model can be expressed in the cutter coordinate system as follows:

[0130] r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (14)

[0131] n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T (15)

[0132] Transform the cutter head surface from the cutter head coordinate system to the gear coordinate system.

[0133] r p =M pw r w (16)

[0134] n p =M pw n w (17)

[0135] The relative speed between the cutter head and the gear is,

[0136]

[0137] in, Represents the speed of the cutter head relative to the gear. According to formula (2-22),

[0138]

[0139] In the formula,

[0140]

[0141] The contact equation is obtained,

[0142] acos(γ)+bsin(γ)=c (20)

[0143] In the formula,

[0144]

[0145] According to the above contact line solution process, the coordinates of the corresponding contact point in the tool head coordinate system are obtained. Then, according to formula (16), the coordinates of all points on the contact line in the workpiece coordinate system are obtained. The coordinates of the contact line obtained in the workpiece coordinate system are marked as (x p ,y p ,z p ), according to formula (21), the contact line spiral is projected onto the end face of the gear to obtain the gear end face profile. According to the morphology of the gear end face (such as a circular arc at the root of the tooth or a chamfer at the top of the tooth), the gear end face profile is converted into a chamfer target curve.

[0146]

[0147] Step 3: Establish a mathematical model of the conical chamfering tool, give the tool swing angle, and convert it to the workpiece coordinate system; the conical tool surface S is expressed as:

[0148] r s =r s (u,v) (22)

[0149] The normal vector of a point on the conical tool surface S is expressed as:

[0150]

[0151] Among them, u and v are two independent surface parameters, which are coordinates that describe the shape of a single surface;

[0152] Establish an auxiliary coordinate system, such as Figure 3 , the coordinate system O1x1y1z1 is a fixed coordinate system in space, and the coordinate system O g x g y g z g Rotates around axis O1z1. When the gear rotates by angle When the coordinate system O1x1y1z1 and the coordinate system O g x g y g z g The coordinate system O1x1y1z1 is translated along the axis of O1x1 by a distance L. X Get. X It is actually the distance between the center of the cone cutter head and the center of the gear. The coordinate system O3x3y3z3 is translated along the axis of O2z2 by the coordinate system O2x2y2z2 by a distance L Z Finally, the coordinate system O3x3y3z3 is rotated around the axis O3y3 by an angle γ to obtain the tool coordinate system O w x w y w z w Here γ is the angle between the tool axis and the workpiece end face, which is selected according to the actual processing conditions.

[0153] in accordance with Figure 3 The coordinate system and homogeneous coordinate transformation method shown in the figure can obtain the coordinate transformation matrix between the tool coordinate system and the gear coordinate system as follows:

[0154] M wg =M w3 M 32 M 21 M 1g (twenty four)

[0155] in,

[0156]

[0157] According to formula (24), we can calculate:

[0158]

[0159] Step 4: Make the cross-sectional circle of a certain height of the specified conical chamfering tool tangent to the end face profile of the gear after gear milling, and calculate the chamfering tool position point.

[0160] According to the spatial envelope principle, the chamfered surface is formed by the continuous motion of the conical tool surface S in space according to a certain rule. All positions occupied by the tool surface S in the space during the continuous motion form a surface family. Assume that the surface family {S t} can be expressed as:

[0161] r=r(u,v;t) (27)

[0162] Among them, t is the motion parameter (family parameter) of the surface family, which is the coordinate describing the spatial position of a single surface. When t is a certain value, S t Indicates the corresponding specific surface in the surface family.t There is generally an envelope surface Σ, which {S t Each point on the surface belongs to a unique surface S in the envelope family t points on the surface S t and the envelope surface Σ are tangent at this point. Thus, we get the surface family {S t The contact equation between} and the envelope surface Σ is:

[0163]

[0164] Among them, (x, y, z) are the three components of vector r.

[0165] The target chamfer curve is a characteristic line of the tool envelope surface, which determines the tangent direction of the contact point. At the contact point, the envelope surface normal vector is consistent with the tool surface normal vector. Combining the mathematical model of the conical tool in the workpiece coordinate system with the envelope contact condition (28), the chamfering tool position point can be obtained.

[0166] Step 5: Develop chamfering software, perform post-processing based on the chamfering principle and compare it with the actual machine tool to generate the chamfering program. Figure 4 Given basic gear parameters, tool parameters, chamfering setting parameters, etc., this method can be used to obtain the chamfering effect as follows Figure 5 shown.

Claims

1. A chamfering method for a helical gear with an arbitrary end face profile and a given tool swing angle after milling based on a 3-axis machine tool, characterized in that The steps include: Step 1: According to the discrete points of the cutter head, the cutter head truncation shape is fitted using the cubic spline method; Step 2: According to the principle of spatial meshing, the accurate gear end face profile after gear milling is calculated through the cutter head section and the gear milling trajectory; Step 3: Establish a mathematical model of the conical chamfering tool, give the tool swing angle, and convert it to the workpiece coordinate system; Step 4, making the cross-sectional circle of a certain height of the specified conical chamfering tool tangent to the end face profile of the gear after gear milling, and calculating the chamfering tool position point; Step five: Develop chamfering software, perform post-processing based on the chamfering principle and compare it with the actual machine tool to generate the chamfering processing program.

2. A chamfering method for a helical gear with a given tool swing angle after milling a tooth of any end face profile based on a three-axis machine tool as claimed in claim 1, characterized in that the specific method in step 1 is as follows: According to the given discrete points of the cutter disc, the cutter disc truncation is obtained by using the cubic spline interpolation method to ensure that the cutter disc truncation is smooth; the width of the cutter disc is divided into n intervals [zi,zi+1], (i=1,2,…n), and each interval is expressed by a spline curve: ε k (from)=a k +b k (z i )+c k (z i ) 2 +d k (z i ) 3 ,(k=0,1,...n-1) (1) The entire cubic spline curve needs to determine a k ,b k ,c k ,d k ,(k=0,1,...n-1), a total of 4n unknown coefficients. Let h i =z i+1 -z i , according to the boundary of each spline curve: Order i (z i )=e i ,he i (z i+1 )=e i+1 , available: Let m i =ε i ”(z i )=2c i ,but: d i =(m i+1 -m i ) / 6 / h i (4) A i , c i , d i Substituting into formula (3), we can get Under natural boundary conditions, m0=0, m n =0, we can get, According to the above matrix equation, the unique solution of the spline coefficients in each interval can be obtained, the cubic spline interpolation can be realized, and the cutter head truncation shape can be obtained.

3. The chamfering method of a helical gear with a given tool swing angle after milling a helical gear with any end face profile based on a three-axis machine tool as claimed in claim 1, characterized in that the specific method in step 2 is as follows: According to the principle of spatial meshing, the accurate gear end face profile after milling is calculated through the cutter head section and the milling trajectory as the target chamfer profile; during the forming milling process, the cutter head rotates around its own axis and makes a spiral motion along the workpiece axis to establish the tool coordinate system S w (O w -x w y w z w ) and gear coordinate system S p (O p -x p y p z p ); The installation angle of the cutter head is ∑;x w The shaft is aligned with the centerline of the gear tooth groove; the center distance a between the gear axis and the cutter head center is constant; the gear rotation angle is When the cutter head moves along the gear axis, the distance is Thereby, the spiral motion of the cutter disc relative to the workpiece is realized; Gear coordinate system S p The homogeneous coordinate transformation matrix to S1 is: The homogeneous coordinate transformation matrix from S1 to S2 is: The homogeneous coordinate transformation matrix from S2 to S3 is: S3 to cutterhead coordinate system S w The homogeneous coordinate transformation matrix is: It is easy to see from Figure 2 that the gear coordinate system S p To the cutterhead coordinate system S w The homogeneous coordinate transformation matrix can be expressed as: M wp =M w3 M 32 M 21 M 1p (11) Right now: In the formula, is the gear rotation angle, ∑ is the cutter head installation angle, and a is the center distance; By inverting (12), we can find the cutterhead coordinate system S w To S p The homogeneous coordinate transformation matrix is: The milling cutter rotation model can be expressed in the cutter coordinate system as follows: r w (R,γ)=[Rcos(γ),Rsin(γ),f(R),1] T (14) n w (R,γ)=[Rf'(R)cosγ,Rf'(R)sinγ,-R,0] T (15) Transform the cutter head surface from the cutter head coordinate system to the gear coordinate system. r p ＝M pw r w (16) n p =M pw n w (17) The relative speed between the cutter head and the gear is, in, Indicates the speed of the cutter head relative to the gear. According to formula (2-22), In the formula, The contact equation is obtained, acos(γ)+bsin(γ)=c (20) In the formula, According to the above contact line solution process, the coordinates of the corresponding contact point in the tool head coordinate system are obtained. Then, according to formula (16), the coordinates of all points on the contact line in the workpiece coordinate system are obtained. The coordinates of the contact line obtained in the workpiece coordinate system are marked as (x p ,y p ,z p ), according to formula (21), the contact line spiral is projected onto the end face of the gear to obtain the gear end face profile. According to the morphology of the gear end face (such as a circular arc at the root of the tooth or a chamfer at the top of the tooth), the gear end face profile is converted into a chamfer target curve: 。 4. A chamfering method for a helical gear with an arbitrary end face profile and a given tool swing angle after milling based on a 3-axis machine tool as claimed in claim 1, characterized in that in the chamfering state with the tool swing angle, a cross-sectional circle at a specific height on the specified conical tool is tangent to the target chamfering curve, and the specific methods in step 3 and step 4 are as follows: The conical tool surface S is expressed as: r s =r s (u,v) (22) The normal vector of a point on the conical tool surface S is expressed as: in, u and v are two independent surface parameters, which are coordinates that describe the shape of a single surface; Establish an auxiliary coordinate system, as shown in Figure 3, the coordinate system O1x1y1z1 is a fixed coordinate system in space, and the coordinate system O g x g y g z g Rotate around axis O1z1; when the gear rotates by angle When the coordinate system O1x1y1z1 and the coordinate system O g x g y g z g The coordinate system O1x1y1z1 is translated along the axis of O1x1 by a distance L. X Get. X It is actually the distance between the center of the cone cutter head and the center of the gear; the coordinate system O3x3y3z3 is translated by the coordinate system O2x2y2z2 along the axis of O2z2 by a distance L Z Finally, the coordinate system O3x3y3z3 is rotated around the axis O3y3 by an angle γ to obtain the tool coordinate system O w x w y w z w Here γ is the angle between the tool axis and the workpiece end face, which is selected according to the actual processing conditions; According to the coordinate system and homogeneous coordinate transformation method, the coordinate transformation matrix between the tool coordinate system and the gear coordinate system can be obtained as follows: M wg =M w3 M 32 M 21 M 1g (24) in, According to formula (24), we can calculate: According to the space envelope principle, the contact equation for chamfering is: Among them, (x, y, z) are the three components of vector r. Combining the above-mentioned tool mathematical model with the spatial contact conditions, the machining tool position trajectory is calculated.

5. A chamfering method for a helical gear with an arbitrary end face profile and a given tool swing angle after milling based on a three-axis machine tool as described in claim 1, characterized in that according to the chamfering principle, post-processing is performed in comparison with the actual machine tool to generate a chamfering processing program.

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