Method for machining face gear through cylindrical cutter

Abstract

The invention provides a method for processing a face gear by adopting a cylindrical cutter, which comprises the following specific steps of: replacing a conical cutter with a cylindrical gear turning cutter, and setting a process relief angle to avoid interference between the face gear and the cylindrical gear turning cutter; based on the meshing relation between the virtual intermediate cylindrical gear and the face gear, a face gear-cutter space coordinate system conversion model is constructed; inputting the pitch radius of the cylindrical cutter, the pitch radius of the cylindrical gear, the motion parameters of the cylindrical cutter and the face gear and the process relief angle into a face gear-cutter space coordinate system conversion model to obtain each axial offset distance of an original point of the cylindrical cutter relative to an original point of a global coordinate system when the cutter is positioned at a meshed node; and the cylindrical cutter is installed on a machine tool for face gear machining according to the axial offset distances. The cylindrical tooth turning cutter is applied to face gear tooth turning machining, the cylindrical cutter avoids machining theoretical blade type errors, and the economical efficiency and the machining precision stability are comprehensively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of gear machining, and particularly relates to a method for machining face gears by using a cylindrical cutter. Background Art

[0002] Face gear transmission is a transmission in which a cylindrical gear meshes with a face gear. According to the tooth shape, face gears can be divided into three types: straight teeth, helical teeth and arc teeth. According to the relative position relationship between the two gear shafts, it is divided into two types: intersecting and staggered. Since the face gear meshes with the cylindrical gear, the tooth thickness at the inner diameter position is thin, and the tooth tip becomes sharp at the outer diameter position. Therefore, traditional face gears are suitable for transmitting low loads. At present, face gear machining methods include cutting forming methods such as gear shaping, gear grinding, gear milling and gear turning, as well as net forming methods such as forging. Hobbing has high machining efficiency and is the mainstream research direction, but the tool manufacturing is relatively complex. Gear shaping has simple tool manufacturing but low efficiency. Gear turning can achieve both high efficiency and high precision, and the tool manufacturing is less difficult and less costly than that of spherical worm hobs. It is a face gear machining method with high efficiency, high precision and easy tool manufacturing, and it is worthy of further research to explore its potential. At present, gear turning mainly uses conical cutters and is designed according to the design method of gear shapers. There are naturally machining errors on the tooth surface, which affect the tooth surface load-bearing characteristics of face gears. Compared with conical cutters, cylindrical gear turning cutters have the advantages of unchanged cutting edge shape after flank grinding of the rake face, simple tool manufacturing and long tool life. Therefore, if a cylindrical cutter can be used to replace the conical cutter for gear turning research, the machining economy of the tool will be improved.

[0003] The face gear is formed by the meshing of a cylindrical gear, and the tooth surfaces of the two are conjugate. The pitch surface of the face gear is tangent to the pitch surface of the cylindrical gear to generate a tangent line. When the axes of the two intersect and rotate, an instantaneous axis of rotation will be generated. The intersection point of the tangent line and the instantaneous axis of rotation is the node, which is the benchmark for designing the installation model. Face gear turning machining is realized by the double-degree-of-freedom envelope of the cutting edge curve and the face gear. The cutting edge curve is conjugate to the machined tooth surface. Further understanding, the tool and the face gear are placed according to the installation model, and a virtual intermediate cylindrical gear of the face gear is introduced as the virtual intermediate cylindrical gear. The intermediate gear decomposes the face gear turning motion into the motion of cylindrical gear turning and the motion of the cylindrical gear generating the face gear. During turning machining, the cutting edge curve of the tool first cuts the tooth surface of the cylindrical gear. Taking the cylindrical gear as the virtual intermediate cylindrical gear, the machined face gear is obtained according to the face gear generation principle. However, due to the lack of structural clearance angle of the cylindrical gear turning cutter, the side of the cutter tooth will mesh with the machined tooth groove surface, resulting in meshing interference and machining failure. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention proposes a method for machining face gears using a cylindrical cutter. Compared with a conical cutter, the cylindrical cutter reduces the machining and manufacturing difficulty of the cutter, improves the service life of the cutter, avoids the machining theoretical edge profile error, and comprehensively improves the economy and the stability of machining accuracy. By adding a process back angle to the installation structure of the cutter relative to the face gear, such interference is avoided, so that the cylindrical hobbing cutter can be successfully applied to the hobbing machining of face gears.

[0005] To achieve the above object, the present invention provides the following technical solution: A method for machining a face gear using a cylindrical cutter, the specific steps are as follows:

[0006] Use a cylindrical hobbing cutter to replace the conical cutter, and set a process back angle to avoid interference between the face gear and the cylindrical hobbing cutter;

[0007] Based on the meshing relationship between the virtual intermediate cylindrical gear and the face gear, construct a spatial coordinate system conversion model of the face gear - cutter;

[0008] Input the pitch circle radius of the cylindrical cutter, the pitch circle radius of the cylindrical gear, the motion parameters of the cylindrical cutter and the face gear, and the process back angle into the spatial coordinate system conversion model of the face gear - cutter, and obtain the axial offsets of the origin of the cylindrical cutter relative to the origin of the global coordinate system when the cutter is at the meshing node;

[0009] Install the cylindrical cutter on the machine tool according to the axial offsets for face gear machining.

[0010] Further, the spatial coordinate system conversion model of the face gear - cutter is specifically as follows:

[0011] Face gear coordinate system O f -x f y f z f Rotate around the z f axis by the offset angle γ to obtain O1 - x1y1z1; the coordinate system O1 - x1y1z1 is moved along the z1 axis by a distance H to obtain the coordinate system O2 - x2y2z2; the coordinate system O2 - x2y2z2 is rotated around y2 by 90° - the cone angle γ f After that, move along the x2 direction by a distance S f and rotate around y3 by 90° to obtain the coordinate system O3 - x3y3z3; the coordinate system O3 - x3y3z3 is moved along the x3 direction by the pitch circle radius R of the virtual intermediate cylindrical gear pg to obtain the coordinate system O4 - x4y4z4; the coordinate system O4 - x4y4z4 is rotated around the x4 rotation axis intersection angle Σ to obtain the coordinate system O5 - x5y5z5; the coordinate system O5 - x5y5z5 is rotated around y5 by the process back angle ɑ to obtain the coordinate system O6 - x6y6z6; the coordinate system O6 - x6y6z6 is moved along the negative x6 direction by the cutter pitch circle radius Rpc Obtain the static coordinate system O of the cutting tool c -x c y c z c ;

[0012] Wherein, H is the distance between the intersection point of the axis of the virtual intermediate cylindrical gear and the axis of the face gear and the origin of the face gear; S f is the distance between the intersection point of the axis of the virtual intermediate cylindrical gear and the axis of the face gear and the origin of the virtual intermediate cylindrical gear; the cone angle γ f is the cone angle of the face gear itself; Σ is the shaft intersection angle between the virtual intermediate cylindrical gear and the cutting tool; ɑ is the process back angle set for the cylindrical cutting tool to avoid interference.

[0013] Furthermore, taking the static coordinate system O of the face gear f -x f y f z f as the global coordinate system, taking the cutting tool and the node P of the face gear as the reference, using the pitch radius R of the face gear pf 、the helix angle β of the virtual intermediate cylindrical gear pg and the pitch radius R pg 、the helix angle β of the cutting tool pc and the cone angle γ of the face gear f calculate the specific numerical values of the offset angle γ, the shaft intersection angle Σ, H, S f The relational expressions are as follows:

[0014]

[0015] Wherein, k c and k g respectively represent the helix directions of the cutting tool and the face gear, and +1, 0, -1 represent right-handed, straight-tooth and left-handed respectively.

[0016] Furthermore, an offset angle γ is formed between the connection line of the tangent point P of the cutting tool pitch circle and the face gear pitch circle and the origin O of the face gear coordinates f and the x f axis of the face gear, so that the swing axis y c of the cutter axis vector and the rotation axis z f of the face gear satisfy the orthogonal condition in space.

[0017] Furthermore, there is a shaft intersection angle Σ between the cutting tool axis and the cylindrical gear axis in the plane y4 - O4 - z4, so that the y c axis of the cutting tool is parallel to the y f axis of the face gear.

[0018] Furthermore, there is a process back angle ɑ between the cutting tool axis and the plane y4 - O4 - z4, the process back angle ɑ, the cone angle γ of the face gear fIt is directly swung out by the tool axis swing axis.

[0019] Furthermore, according to the pitch circle radius of the cylindrical tool, the pitch circle radius of the cylindrical gear, the motion parameters of the cylindrical tool and the face gear, the process back angle, the offset angle γ, the shaft intersection angle Σ, H, S f parameters, the tool origin O c relative to the static coordinate system O of the face gear f -x f y f z f There are offsets on each axis, namely the X-axis offset E x 、the Y-axis offset E y 、the Z-axis offset E z .

[0020] Furthermore, among them, the motion parameters of the cylindrical tool and the face gear are specifically: the rotation angle corresponding to the face gear rotation motion and the rotation angle corresponding to the tool rotation motion The tool origin O c relative to the static coordinate system O of the face gear f -x f y f z f The offset relationship existing on each axis is as follows:

[0021] [E x E y E z 1] T =M dfsf ·M sf1 ·M 12 ·M 23 ·M 34 ·M 45 ·M 56 ·M 6sc ·M scdc ·

[0001] T

[0022]

[0023] Furthermore, the motion parameters of the cylindrical tool and the face gear are specifically: the rotation angle corresponding to the face gear rotation motion and the rotation angle corresponding to the tool rotation motion The specific calculation is as follows:

[0024]

[0025] Among them: f s is the feed rate, R pg is the pitch circle radius of the virtual intermediate cylindrical gear, k g is the helix direction of the face gear, βpg is the helix angle of the virtual intermediate cylindrical gear, Z g is the number of teeth of the virtual intermediate cylindrical gear, R pg is the pitch circle radius of the virtual intermediate cylindrical gear, Z f is the number of teeth of the face gear, Z c is the number of teeth of the tool, is the differential rotation angle.

[0026] Furthermore, in the step of installing the cylindrical tool on the machine tool for face gear machining according to each axial offset, the position vector of the tool origin is transformed from the static coordinate system of the face gear to the machine tool coordinate system, that is, the axial offsets of the adjusted cylindrical tool origin relative to the origin of the global coordinate system are obtained, and the adjusted axial offsets are used for installing the cylindrical tool.

[0027] Compared with the prior art, the present invention has at least the following beneficial effects:

[0028] The present invention provides a method for machining face gears using a cylindrical tool. Machining face gears with a cylindrical tool shows significant advantages in terms of tool performance and machining effect compared with traditional conical tools. In the tool manufacturing process, the manufacturing process of the cylindrical tool is simpler. Unlike the conical tool, there is no need to perform complex modification on the tool body to obtain the post-machining angle. Only by reasonably setting the process flank angle can the interference problem be effectively avoided. This characteristic not only reduces the manufacturing difficulty of the tool, but also shortens the manufacturing cycle and improves production efficiency. During the machining process, the cutting edge shape of the cylindrical tool can remain unchanged after grinding, and it can maintain a long service life, greatly reducing the tool usage cost. This enables the tool to maintain stable machining consistency throughout its entire life cycle, providing a strong guarantee for high-precision and high-efficiency machining of face gears.

[0029] Compared with the conical tool model, the spatial coordinate system transformation model of the face gear-tool in the present invention does not show a significant increase in complexity. This means that in practical applications, operators do not need to master overly complex technologies and algorithms to use this model for tool installation and machining operations, reducing the technical threshold and operation difficulty. In terms of applicability, this model has a wide range of uses. It can not only be applied to special face gear hobbing machines for face gear machining, but also can be used to machine face gears based on five-axis machine tools. This wide applicability gives enterprises greater flexibility in choosing machining equipment. They can choose the most suitable machining method according to their own production requirements and equipment conditions. Whether it is an enterprise with a special face gear hobbing machine or an enterprise with only a five-axis machine tool, they can use the model of the present invention for face gear machining, greatly improving the versatility and practicality of the model. Brief Description of the Drawings

[0030] Figure 1 is the three - view drawing of the face - gear cylindrical - cutter hobbing machining model of the present invention. Among them, Fig. 1(a) is the front view; Fig. 1(b) is the left view; Fig. 1(c) is the top view.

[0031] Figure 2 It is a schematic diagram of the realization of the present invention through a single - pendulum - head single - rotation five - axis machine tool;

[0032] Figure 3 It is a schematic diagram of the realization of the present invention through a double - cradle five - axis machine tool. Specific embodiments

[0033] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0034] The present invention proposes a method for machining face - gears using cylindrical cutters, and has established a face - gear hobbing installation model and a cylindrical - cutter hobbing machining model. The overall technical idea is briefly described as follows:

[0035] When performing face - gear hobbing machining, due to the advantages of cylindrical cutters, cylindrical cutters are selected for face - gear hobbing machining. However, it should be noted that the cylindrical cutter itself has no back - angle, so a process back - angle ɑ needs to be set in the machining and installation model of the cutter to avoid interference between the cutter tooth surface and the machined tooth surface during machining.

[0036] Taking the face - gear hobbing installation model as the basic model, a face - gear hobbing machining installation model based on a cylindrical hobbing cutter is constructed, specifically through the construction of the following two models:

[0037] (i) The installation model of the face - gear and the cylindrical gear;

[0038] (ii) The installation model of the cylindrical gear and the cylindrical hobbing cutter;

[0039] Among them, during installation, ensure that the pitch circles and node positions of the face - gear and the cylindrical gear remain unchanged, and at the same time, the node of the cylindrical - hobbing - cutter - cylindrical - gear coincides with the node of the cylindrical - gear - face - gear. Taking the cylindrical - gear static coordinate system as an intermediary, establish the auxiliary coordinate systems O1 - x1y1z1 to O6 - x6y6z6 of the installation model, and correlate the cutter coordinate system O c -x c y c z c with the face - gear coordinate system O f -x f y f z f To meet the machining feasibility under the condition that the two rotating axes of the hobbing machine tool are orthogonally configured, the installation parameters need to meet the following conditions:

[0040] 1) Make the tangent point P of the cutter pitch circle and the face - gear pitch circle coincide with the origin O of the face - gear coordinate fThe connection line and face gear x f A bias angle γ is formed between the axes to ensure that the swing axis y of the cutter axis vector c and the rotation axis z of the face gear f Meet the orthogonal condition in space;

[0041] 2) The offset cutter axis is parallel to the x where the rotation axis of the face gear is located f -O f -z f plane, and the swing axis y of the cutter axis vector c is perpendicular to x f -O f -z f plane;

[0042] 3) The cutter axis has an axial intersection angle Σ with the cylindrical gear axis within the plane y4 - O4 - z4, corresponding to the bias angle γ, to ensure that the cutter y c axis is parallel to the face gear y f axis;

[0043] 4) The back angle ɑ between the cutter axis and the plane y4 - O4 - z4 and the cone angle γ existing in the face gear itself f are both directly set out by the swing axis of the cutter axis;

[0044] 5) When the cutter is at the meshing node, after being installed according to the above installation parameters, the cutter origin is relative to the static coordinate system O of the face gear f -x f y f z f There are installation offsets in each axial direction, that is, the X-axis offset E x 、the Y-axis offset E y 、the Z-axis offset E z ,and the bias angle γ.

[0045] For the above installation model, according to the basic parameters of the face gear such as the number of teeth Z of the face gear f 、the pitch circle R of the face gear pf and the basic parameters of the virtual intermediate cylindrical gear such as the helix angle β g 、the number of teeth Z g and the module m n etc., calculate the pitch circle radius R of the virtual intermediate cylindrical gear pg ; then according to the pitch circle radius R of the virtual intermediate cylindrical gear pg and the basic parameters of the cutter such as the number of teeth Z of the cutter c 、the helix angle β of the cutter c etc., calculate the pitch circle R of the cutter pc ; the bias angle γ, the axial intersection angle Σ, H, S can be calculated using the given cone angle γ of the face gear f and parameters such as the pitch circle radius fParameters; and then substituting the above parameters into the installation model, the axial offsets of the tool origin relative to the origin of the global coordinate system can be calculated, namely the X-axis offset E x , the Y-axis offset E y , the Z-axis offset E z .

[0046] Based on the hobbing machining installation model of the face gear, further apply machining motion parameters, including: the tool rotates around its own axis z c to make a rotational motion, and the corresponding rotation angle is The face gear rotates around its own axis z f to make a rotational motion, and the corresponding rotation angle is The tool makes a feeding motion from the large end to the small end along the cone angle direction of the face gear, and the feeding speed is f. Due to the helix angle of the face gear, the rotation angle of the face gear during hobbing needs to be adjusted according to the rotation angle with a certain rotational differential to machine the correct tooth groove.

[0047] The following gives specific embodiments of the present invention. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent transformations made on the basis of the technical solution of this application fall within the protection scope of the present invention.

[0048] The object of the present invention is to propose a hobbing machining model for a cylindrical tool of a face gear for the element of face gear hobbing. Compared with the conical tool, the cylindrical tool reduces the machining and manufacturing difficulty of the tool, improves the tool service life, avoids the machining theoretical edge type error, and comprehensively improves the economy and machining accuracy stability.

[0049] For the specific implementation of the present invention, the following known input conditions are as follows:

[0050] Cylindrical gear: the number of teeth Z g , helix angle β pg ;

[0051] Face gear: the number of teeth Z f , pitch circle radius R pf , cone angle γ f , helix angle β pf ;

[0052] Tool: the number of teeth Z c , helix angle β pc ;

[0053] Machining parameters: the post-cutting angle ɑ;

[0054] Based on the above input, the process of applying the machining installation model of the present invention in a double-cradle five-axis machine tool and a single-swing head single-rotation machine tool is as follows:

[0055] Step 1: Establish the installation model of the cylindrical hobbing cutter for face gears

[0056] The machining model of the cylindrical hobbing cutter for face gears in the present invention is established based on the machining model of cylindrical gears - cylindrical hobbing cutters. To reflect the generality of the model, the cone angle γ of the face gear f and the helix angle β of the face gear f are considered. First, the node is determined according to the pitch circle relationship between the face gear and the virtual intermediate cylindrical gear. Based on the node, the hobbing installation model of the face gear - cylindrical cutter as shown in Figure 1 is established.

[0057] In the present invention, the virtual intermediate cylindrical gear of the hobbing machining installation model of the face gear is regarded as the virtual intermediate cylindrical gear. The following coordinate system is constructed for the hobbing machining installation model of the face gear to facilitate the calculation of spatial relationships:

[0058] Coordinate system O f -x f y f z f is the static coordinate system of the face gear. The face gear rotates around the z f axis;

[0059] Coordinate system O c -x c y c z c is the static coordinate system of the cutter. The cutter rotates around the z c axis;

[0060] The coordinate systems from O1 - x1y1z1 to O6 - x6y6z6 are intermediate auxiliary coordinate systems;

[0061] P is the tangent contact point between the pitch circle of the cutter and the pitch circle of the face gear. The axis of the virtual intermediate cylindrical gear intersects the axis of the face gear at point O2. The distance between O2 and O f is H. γ is the angle for offsetting the intermediate gear. γ f is the cone angle of the face gear itself. Σ is the shaft intersection angle between the virtual intermediate cylindrical gear and the cutter. ɑ is the process back angle set for the cylindrical cutter to avoid interference.

[0062] The correlation relationship between the coordinate systems is as follows: The face gear coordinate system O f -x f y f z f rotates around the z f axis by the offset angle γ to obtain O1 - x1y1z1; The coordinate system O1 - x1y1z1 moves along the z1 axis by a distance H to obtain the coordinate system O2 - x2y2z2; The coordinate system O2 - x2y2z2 rotates around y2 by 90° - cone angle γ f and then moves along the x2 direction by S fThe distance is rotated 90° around y3 to obtain the coordinate system O3-x3y3z3; the coordinate system O3-x3y3z3 is moved along the x3 direction by the pitch circle radius R of the virtual intermediate cylindrical gear pg to obtain the coordinate system O4-x4y4z4; the coordinate system O4-x4y4z4 is rotated around the x4 rotation axis by an included angle Σ to obtain the coordinate system O5-x5y5z5; the coordinate system O5-x5y5z5 is rotated by the post-rotation angle ɑ around y5 to obtain the coordinate system O6-x6y6z6; the coordinate system O6-x6y6z6 is moved along the negative x6 direction by the tool pitch circle R pc to obtain the coordinate system O c -x c y c z c .

[0063] Among them, H is the distance between the intersection point of the axis of the virtual intermediate cylindrical gear and the axis of the face gear and the origin of the face gear; S f is the distance between the intersection point of the axis of the virtual intermediate cylindrical gear and the axis of the face gear and the origin of the virtual intermediate cylindrical gear.

[0064] Starting from the basic model of the face gear-cylindrical gear meshing pitch circle, the following parameter design is carried out:

[0065] 1) The tangent point of the face gear pitch circle and the cylindrical gear pitch circle coincides with the tangent point of the cylindrical gear pitch circle and the tool pitch circle; the tangent point P of the tool pitch circle and the face gear pitch circle and the connection line of O f and the static coordinate system O of the face gear f -x f y f z f has an offset angle γ on the x f axis to adapt to the orthogonal configuration of each rotation axis of the machine tool, and ensure that the swing axis of the tool axis vector and the rotation axis of the face gear are orthogonal in space;

[0066] 2) The offset tool axis is parallel to the x f -O f -z f plane where the rotation axis of the face gear is located, and the swing axis y c of the tool axis vector is perpendicular to the x f -O f -z f plane; the tool axis has an included angle Σ with the cylindrical gear axis y5 in the plane y4-O4-z4; the tool axis has a post-rotation angle ɑ with the plane y4-O4-z4;

[0067] 3) At the node position of the tool and the face gear, after adjusting the relative attitude of the tool and the face gear according to the above installation parameters, the tool center point O c and the static coordinate system O of the face gear f -x f yf z f There is an installation parameter E between the axes x 、E y 、E z which are the offset E along the X-axis x 、the offset E along the Y-axis y 、the offset E along the Z-axis z ; Finally, ensure that the axis z of the face gear rotation axis f is perpendicular to the axis y of the tool angle swing c .

[0068] Step 2 Installation parameter calculation

[0069] In the present invention, the generating cylindrical gear of the face gear hobbing model is regarded as a virtual intermediate cylindrical gear, and the number of teeth Z of the face gear f 、the pitch circle R of the face gear pf and the number of teeth Z of the virtual intermediate cylindrical gear g are used to calculate the pitch circle radius R of the virtual intermediate cylindrical gear pg with the following relationship:

[0070]

[0071] Using the pitch circle radius R of the virtual intermediate cylindrical gear pg and the helix angle β pg and the number of teeth Z of the tool c 、the helix angle β of the tool pc to calculate the pitch circle radius R of the tool pc with the following relationship:

[0072]

[0073] Between the static coordinate system O of the tool c -x c y c z c and the static coordinate system O of the face gear f -x f y f z f with the static coordinate system O of the face gear f -x f y f z f as the global coordinate system, the face gear is placed horizontally, and with the tool and the face gear node P as the reference, using the pitch circle radius R of the face gear pf 、the helix angle β of the virtual intermediate cylindrical gear pg and the pitch circle radius R pg 、the helix angle β of the tool pc and the cone angle γ of the face gear f to calculate the offset angle γ, the shaft intersection angle Σ, H, S f parameters with the following relationship:

[0074]

[0075] where k c and k g represent the helix directions of the cutting tool and the face gear respectively, and +1, 0, and -1 represent right-handed, straight-tooth, and left-handed respectively.

[0076] Adjust the tool posture according to the above offset angle γ, shaft intersection angle Σ, and back angle ɑ.

[0077] Tool origin O c relative to the face gear static coordinate system O f -x f y f z f There are offsets on each axis, namely the X-axis offset E x , Y-axis offset E y , Z-axis offset E z , and the relational expressions are as follows:

[0078] [E x E y E z 1] T = M dfsf ·M sf1 ·M 12 ·M 23 ·M 34 ·M 45 ·M 56 ·M 6sc ·M scdc ·

[0001] T

[0079]

[0080] Step 3 Implementation of installing the model on a specific machine tool

[0081] For a double-cradle machine tool as Figure 3 shown: The tool spindle of the machine tool can only move linearly along the X, Y, and Z axes and cannot rotate around the X, Y, and Z axes. There are two rotating shafts on the workbench that can rotate around two axes. It can be seen that O f -x f y f z f of the installation model is not the same as O j -x j y j z j of the machine tool coordinate system. The axial offsets in the installation model, namely the X-axis offset E x , Y-axis offset E y , Z-axis offset E zIt cannot be used directly and needs to be adjusted to Ej according to the machine tool. x and Ej y and Ej z ; The offset angle γ in the installation model is achieved by the tool moving along the negative direction of the X-axis and the positive direction of the Z-axis of the machine tool; The process back rake angle for machining requires the face gear to be swung out by rotating 90° - ɑ in the positive direction of the A-axis around the X-axis by the cradle, rather than the tool being swung out; The angle between the tool feed direction and the face gear axis during machining is the taper angle γ f , In the figure, the machine tool coordinate system requires the tool to move simultaneously in the positive direction of the X-axis, the negative direction of the Y-axis, and the negative direction of the Z-axis; During machining, the face gear is driven to rotate by the C-axis, and the rotation direction is the same as the tool spindle direction, which is clockwise rotation.

[0082] For a single pendulum head and single rotation machine tool, such as Figure 2 shown: The machine tool tool spindle can rotate around the Y-axis and swing out a specific angle, and the workbench rotates around the Z-axis. The origin of the machine tool coordinate system and the face gear coordinate system coincides with the Z-axis, which is the same as the double cradle situation, and the X-axis offset E x , Y-axis offset E y , Z-axis offset E z cannot be used directly and needs to be adjusted to Ej according to the machine tool. x and Ej y and Ej z ; The offset angle γ in the installation model is achieved by the tool moving along the negative direction of the X-axis and the positive direction of the Y-axis of the machine tool; The process back rake angle for machining requires the B-axis where the tool is located to rotate 90° - ɑ in the negative direction of the Y-axis; The angle between the tool feed direction and the face gear axis during machining is the taper angle γ f , In the figure, the machine tool coordinate system requires the tool to move simultaneously in the positive direction of the X-axis, the positive direction of the Y-axis, and the positive direction of the Z-axis; During machining, the face gear is driven to rotate by the C-axis, and the rotation direction is the same as the tool spindle direction, which is clockwise rotation.

[0083] Step 4 Motion description of the face gear cylindrical cutter hobbing model

[0084] Apply motion parameters to the tool and the face gear in the installation model. The face gear rotates around its own axis z f to make a rotational motion, and the tool rotates around its own axis z c to make a rotational motion, and at the same time, it makes a feed motion from the large end to the small end along the taper angle direction of the face gear. The feed speed is f. Considering the influence brought by the spiral angle of the virtual intermediate cylindrical gear and the face gear, the rotational motion of the face gear needs to cooperate with a certain rotational differential speed to machine a tooth groove with the correct structure. When the feed amount is f s , the rotation angle corresponding to the rotational motion of the face gear corresponding to the rotational motion of the tool and the differential rotation angle

[0085]

[0086] Where: f s is the feed rate, R pg is the pitch radius of the virtual intermediate cylindrical gear, k g is the helix direction of the face gear, β pg is the helix angle of the virtual intermediate cylindrical gear, Z g is the number of teeth of the virtual intermediate cylindrical gear, R pg is the pitch radius of the virtual intermediate cylindrical gear, Z f is the number of teeth of the face gear, Z c is the number of teeth of the tool, is the differential rotation angle.

[0087] During machining, the radial feed of the tool causes the offsets of the tool origin relative to the axes of the static coordinate system of the face gear to change in real time along with the feed. After the change, the offset E of the X-axis xf , the offset E of the Y-axis yf , and the offset E of the Z-axis zf vary with time t according to the following relationships:

[0088]

[0089] For a general face gear conical tool, compared with a cylindrical tool, there are problems such as difficult machining and manufacturing and low tool service life. The cylindrical tool is simple to manufacture and does not need to modify the tool body like a conical tool to obtain the post-machining angle. Only by setting the process flank angle can interference be avoided; after the cylindrical tool is ground, the shape of its cutting edge remains unchanged, and the machining consistency within the entire life cycle of the tool can be maintained. Due to the natural theoretical error in the flank shape design of the conical tool, the change in the flank shape after grinding leads to fluctuations in the machining error of the face gear tooth profile; compared with the conical tool, after being ground a certain number of times, the flank error exceeds the acceptable range of the face gear tooth profile accuracy and fails, while the cylindrical tool can maintain a long service life, so it has good economy; and compared with the conical tool model, the complexity of the installation model of the cylindrical turning tool for face gears does not increase too much; the installation model of the face gear cylindrical turning tool of the present invention has a wide range of applications and can be realized based on a five-axis machine tool, and does not necessarily have to be used on a special hobbing machine for face gear machining. Therefore, this method has extremely high application value and is worthy of popularization and use.

Claims

1. A method for machining face gears using a cylindrical cutter, characterized in that, The specific steps are as follows: Replace the conical tool with a cylindrical hobbing cutter, and set the process back angle to avoid interference between the face gear and the cylindrical hobbing cutter; Based on the meshing relationship between the virtual intermediate cylindrical gear and the face gear, construct a spatial coordinate system transformation model of the face gear - tool; Input the pitch circle radius of the cylindrical tool, the pitch circle radius of the cylindrical gear, the motion parameters of the cylindrical tool and the face gear, and the process back angle into the spatial coordinate system transformation model of the face gear - tool to obtain the axial offsets of the origin of the cylindrical tool relative to the origin of the global coordinate system when the tool is at the meshing node; Install the cylindrical tool on the machine tool according to the axial offsets for face gear machining.

2. A method for machining face gears using a cylindrical cutter according to claim 1, characterized in that The spatial coordinate system transformation model of the face gear - tool is specifically as follows: Face gear coordinate system O f -x f y f z f Rotate about z f Axis by the offset angle γ to obtain O1-x1y1z1; The coordinate system O1-x1y1z1 is moved along the z1 axis by a distance H to obtain the coordinate system O2-x2y2z2; The coordinate system O2-x2y2z2 is rotated about y2 by 90° - cone angle γ f After that, move along the x2 direction by S f Of distance, and rotate about y3 by 90°, to obtain the coordinate system O3-x3y3z3; The coordinate system O3-x3y3z3 is moved along the x3 direction by the virtual intermediate cylindrical gear pitch circle radius R pg To obtain the coordinate system O4-x4y4z4; The coordinate system O4-x4y4z4 is rotated about the x4 rotation axis intersection angle Σ to obtain the coordinate system O5-x5y5z5; The coordinate system O5-x5y5z5 is rotated about y5 by the machining back angle ɑ to obtain the coordinate system O6-x6y6z6; The coordinate system O6-x6y6z6 is moved along the negative x6 direction by the tool pitch circle radius R pc To obtain the tool static coordinate system O c -x c y c z c ; Among them, H is the distance between the intersection point of the axis of the virtual intermediate cylindrical gear and the axis of the face gear and the origin of the face gear; S f is the distance between the intersection point of the axis of the virtual intermediate cylindrical gear and the axis of the face gear and the origin of the virtual intermediate cylindrical gear; the cone angle γ f is the cone angle of the face gear itself; Σ is the shaft intersection angle between the virtual intermediate cylindrical gear and the tool; ɑ is the process back angle set for the cylindrical tool to avoid interference.

3. A method for machining face gears using a cylindrical cutter according to claim 2, characterized in that, Taking the static coordinate system O of the face gear f -x f y f z f as the global coordinate system, taking the tool and the face gear node P as the reference, using the face gear pitch circle radius R pf , the helix angle β of the virtual intermediate cylindrical gear pg and the pitch circle radius R pg , the tool helix angle β pc and the cone angle γ of the face gear f to calculate the specific numerical values of the offset angle γ, the shaft intersection angle Σ, H, and S f The specific numerical relationships of the parameters are as follows: where k c and k g represent the helix directions of the cutting tool and face gear respectively, and +1, 0, -1 represent right-handed, straight teeth and left-handed respectively.

4. A method for machining face gears using a cylindrical cutter according to claim 2, characterized in that At the tangent point P between the pitch circle of the cutter and the pitch circle of the face gear and the origin O of the face gear coordinates f The connecting line between and the x-axis of the face gear f Form an offset angle γ, so that the swing axis y of the cutter axis vector c And the rotation axis z of the face gear of the face gear f Meet the orthogonal condition in space.

5. A method for machining face gears using a cylindrical cutter according to claim 2, characterized in that, The tool axis has an angular offset Σ with respect to the axis of the cylindrical gear within the plane y4 - O4 - z4, such that the y c axis of the tool is parallel to the y f axis of the face gear.

6. A method for machining face gears using a cylindrical cutter according to claim 2, characterized in that, The machining clearance angle ɑ between the tool axis and the plane y4 - O4 - z4, the machining clearance angle ɑ, and the face gear cone angle γ f It is directly swung out by the tool axis swing shaft.

7. A method for face gear machining using a cylindrical cutter according to claim 2, characterized in that According to the pitch circle radius of the cylindrical cutter, the pitch circle radius of the cylindrical gear, the motion parameters of the cylindrical cutter and the face gear, the technological back rake angle, the offset angle γ, the shaft intersection angle Σ, H, and S f parameters, the tool origin O is obtained c relative to the static coordinate system O of the face gear f -x f y f z f When there are offsets on each axis, i.e., the X-axis offset E x , the Y-axis offset E y , and the Z-axis offset E z .

8. A method for face gear machining using a cylindrical cutter according to claim 7, characterized in that, Among them, The motion parameters of the cylindrical cutter and the face gear are specifically as follows: the rotation angle of the face gear corresponding to the rotational motion and the rotation angle of the cutter corresponding to the rotational motion The origin O of the cutter c relative to the static coordinate system O of the face gear f -x f y f z f The offset relationships existing on each axis are as follows: [E x E y E z 1] T = M dfsf ·M sf1 ·M 12 ·M 23 ·M 34 ·M 45 ·M 56 ·M 6sc ·M scdc ·[0001] T 9. A method for machining face gears using a cylindrical cutter according to claim 1, characterized in that The specific motion parameters of the cylindrical cutter and the face gear are as follows: the rotation angle corresponding to the rotational motion of the face gear and the rotation angle corresponding to the rotational motion of the cutter The specific calculation is as follows: Where: f s is the feed rate, R pg is the pitch radius of the virtual intermediate cylindrical gear, k g is the helix direction of the face gear, β pg is the helix angle of the virtual intermediate cylindrical gear, Z g is the number of teeth of the virtual intermediate cylindrical gear, R pg is the pitch radius of the virtual intermediate cylindrical gear, Z f is the number of teeth of the face gear, Z c is the number of teeth of the cutter, is the differential rotation angle.

10. A method for face gear machining using a cylindrical cutter according to claim 1, characterized in that, In the step of installing the cylindrical tool on the machine tool according to the axial offsets for face gear machining, the position vector of the tool origin is transformed from the face gear static coordinate system to the machine tool coordinate system, that is, the axial offsets of the adjusted origin of the cylindrical tool relative to the origin of the global coordinate system are obtained, and the adjusted axial offsets are used for installing the cylindrical tool.

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