Slotting method of worm grinding wheel for face gear grinding

Abstract

The invention relates to the technical field of machining, in particular to a slotting method of a worm grinding wheel for face gear grinding. Comprising the following steps: establishing a tooth surface equation associated with the generating gear shaping cutter and the worm grinding wheel, calculating coordinates of any turning point on the tooth surface of the worm grinding wheel, measuring and obtaining cutting edge geometric parameters of the turning cutter, and determining a turning path of the turning cutter according to the calculated coordinates of the turning point and the measured and obtained cutting edge geometric parameters, and according to the determined turning path, a turning tool pre-installed on the numerical control turning machine tool is controlled to conduct turning slotting on the pre-installed grinding wheel blank. High-precision machining of the tooth surface of the grinding wheel is achieved through accurate control over turning points, a gear grinding machine tool is not needed, the face gear grinding precision is higher, a grinding wheel turning technology is used for replacing traditional diamond roller finishing, and the slotting efficiency of the worm grinding wheel for face gear grinding is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical processing, in particular to a grooving method of a worm grinding wheel for face gear grinding. Background Art

[0002] Face gear transmission technology is a new type of angular transmission. It is a transmission pair composed of cylindrical gears and face gears. It has unique advantages such as large transmission ratio, simple structure, stable transmission, and insensitivity to axial installation errors of cylindrical gears. However, the tooth surface of face gears is different from traditional bevel gears and cylindrical gears. Its tooth surface is a high-order complex surface, which is difficult to process and difficult to process using simple molding methods. Therefore, the precision manufacturing process of face gear tooth surface has always been a major problem.

[0003] With the deepening of research on face gear technology, the precision grinding and manufacturing of face gears has gradually been solved. The most advanced one is the worm wheel grinding tooth surface processing technology. The face gears ground by worm wheel have high tooth surface accuracy, good precision consistency, high pitch accuracy and good surface quality. Therefore, worm wheel grinding has gradually become the preferred method for precision manufacturing of face gears.

[0004] However, the worm grinding wheel used for face gear grinding is different from the worm grinding wheel used for cylindrical gear grinding. The worm grinding wheel used for the former is a special ellipsoidal grinding wheel, while the worm grinding wheel used for the latter is a standard cylindrical shape. Therefore, the manufacture of worm grinding wheels for face gear grinding has become a major problem. Due to the particularity of the tooth surface of the worm grinding wheel, the most commonly used method at present is to use a diamond roller to perform point-by-point dressing processing directly on the gear grinding machine to obtain the grinding wheel. In this process, the grinding wheel blank needs to be installed on the machine. The grinding wheel blank is generally a round cake, and then it is trimmed with a diamond roller with a small cut. However, in this process, the excess of the grinding wheel blank is very large, generally about 3-4 times the size of the gear module, and the single dressing amount of the diamond roller is small, with a maximum of about 0.05mm. Therefore, the grooving time of the worm grinding wheel is extremely long, and it takes four to five days at the fastest. This greatly increases the processing cost of the face gear and reduces the processing efficiency, which is not conducive to the batch processing of the face gear. Summary of the invention

[0005] The technical problem to be solved by the embodiments of the present invention is to provide a method for slotting a worm grinding wheel for face gear grinding, so as to solve the problem of low slotting efficiency of the worm grinding wheel for face gear grinding in the prior art.

[0006] The invention discloses a method for slotting a worm grinding wheel for face gear grinding, comprising: The tooth surface equation associated with the gear shaping tool and the worm grinding wheel is established, and the coordinates of any turning point on the tooth surface of the worm grinding wheel are calculated. The tooth surface equation associated with the gear shaping tool and the worm grinding wheel is:

[0007] In the formula, The tooth surface equation representing the coordinate transformation from the gear shaping tool to the worm wheel is: Represents the coordinate system of the cylindrical gear To the grinding wheel coordinate system The coordinate transformation matrix, The tooth surface equation of the gear shaping tool is represented by: The meshing equation between the gear shaping tool and the worm wheel is expressed as follows: represents the tooth surface normal vector of the gear shaping tool, Indicates the relative speed of the worm wheel and the gear shaping tool. represents the tooth profile parameters of the rack, represents the tooth direction parameter, Indicates the rotational motion parameters of the gear shaping tool; Measure and obtain the cutting edge geometric parameters of the turning tool, and determine the turning path of the turning tool according to the calculated turning point coordinates and the measured cutting edge geometric parameters; According to the determined turning path, a turning tool pre-installed on a CNC turning machine tool is controlled to turn and groove a pre-installed grinding wheel blank.

[0008] Optionally, the method for establishing the tooth surface equation associated with the gear shaping tool and the worm grinding wheel comprises: Configure rack parameters and define the tooth profile and corresponding normal vector at any point on the rack tooth surface; Establishing the rack coordinate system , and establish the tooth surface equation of the rack according to the defined tooth profile and the corresponding normal vector; Establishing cylindrical gear coordinate system , based on coordinate transformation, the tooth surface equation of the rack is transformed into the tooth surface equation of the shaping gear tool; Establishing the grinding wheel coordinate system , based on coordinate transformation, the tooth surface equation of the shaping gear tool is transformed into the tooth surface equation of the worm grinding wheel for face gear grinding.

[0009] Optionally, the method of establishing the tooth surface equation of the rack according to the defined tooth profile and the corresponding normal vector comprises: Get the tooth profile parameters of the rack, and define the tooth profile and the corresponding normal vector at any point on the rack tooth surface according to the tooth profile parameters. The expressions of the defined tooth profile and the corresponding normal vector are:

[0010] In the formula, Represents the tooth profile of a point on the rack tooth surface, Represents the normal vector corresponding to the tooth profile; Get the tooth parameters of the rack and transform the defined tooth profile and corresponding normal vector into the established rack coordinate system In the equation, the tooth surface equation of the rack is obtained. The tooth surface equation of the rack is expressed as:

[0011] In the formula, represents the tooth surface equation of the rack, represents the normal vector of the rack, Indicates that from the intermediate coordinate system To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To the intermediate coordinate system The coordinate transformation matrix, Representation Matrix The third-order principal minor of Representation Matrix The third-order sequential principal minor of .

[0012] Optionally, the defined tooth profile and the corresponding normal vector are converted to the established rack coordinate system The methods include: According to the configured rack, establish the rack tool coordinate system on the rack , and the intermediate coordinate system of the auxiliary coordinate transformation ; Get the normal pressure angle of the rack and the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin is established from the rack tool coordinate system To the intermediate coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0013] Get the plane helix angle of the rack, according to the established coordinate transformation matrix , establish the intermediate coordinate system To the rack coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0014] In the formula, represents the helix angle of the rack plane, represents the normal pressure angle of the rack, Represents the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin.

[0015] Optionally, it also includes obtaining the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin method: Obtain the normal pressure angle of the rack and the normal module of the forming tool, and calculate the coordinate system based on the obtained normal pressure angle and normal module Origin to coordinate system The distance from the origin is calculated as:

[0016] In the formula, is the normal module of the rack tool.

[0017] Optionally, the method of transforming the tooth surface equation of the rack into the tooth surface equation of the shaping gear shaping tool comprises: Get the rotation angle parameters of the cylindrical gear and convert the tooth surface equation of the rack into the established cylindrical gear coordinate system The tooth surface equation of the gear shaping tool is obtained:

[0018] In the formula, The tooth surface equation of the gear shaping tool is represented by: represents the normal vector of the gear shaping tool, is the rotation angle parameter of the cylindrical gear, Represents the coordinate system from the rack To cylindrical gear coordinate system The coordinate transformation matrix, Representation Matrix The third-order sequential principal minor of .

[0019] Optionally, the method of converting the tooth surface equation of the rack into the established cylindrical gear coordinate system comprises: Obtain the pitch circle radius of the cylindrical gear and the translation distance of the rack during the development process. The calculation formula for the translation distance of the rack during the development process is:

[0020]

[0021] According to the obtained pitch circle radius and translation distance, establish the rack coordinate system To cylindrical gear coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0022] In the formula, represents the translation distance of the rack during the development process, represents the rotation angle parameter of cylindrical gear, represents the helix angle of the rack plane, represents the normal pressure angle of the rack, Indicates the pitch circle radius of the cylindrical gear.

[0023] Optionally, the tooth surface equation of the gear shaping tool is converted into the established grinding wheel coordinate system. Methods in: The number of heads of the worm grinding wheel and the number of teeth of the gear shaping tool are preset to obtain the axis angle between the worm grinding wheel and the gear shaping tool. The calculation formula of the axis angle is:

[0024]

[0025] In the formula, Indicates the angle between the worm wheel and the axis of the gear shaping tool. Indicates the number of worm wheel heads, Indicates the number of teeth of the gear shaping tool. represents the helix angle of the rack plane, Indicates the left-hand helix angle of the gear shaping tool. Indicates the right-hand helix angle of the gear shaping tool. Indicates the helix angle of the left-hand worm of the worm grinding wheel. Indicates the helix angle of the right-hand worm of the worm grinding wheel; Obtain the axis distance from the axis of the worm grinding wheel to the axis of the gear shaping tool. The calculation formula for the axis distance is:

[0026] In the formula, Indicates the distance from the axis of the worm wheel to the axis of the gear shaping tool. Indicates the pitch radius of the worm grinding wheel; According to the preset number of heads of the worm grinding wheel and the number of teeth of the shaping gear shaping tool, the transmission ratio of the shaping gear shaping tool and the worm grinding wheel is determined, and the rotational motion parameters of the shaping gear shaping tool and the worm grinding wheel are obtained according to the determined transmission ratio. The expression of the transmission ratio is:

[0027] In the formula, Indicates the number of worm wheels and the transmission ratio of the gear shaping tool. Indicates the rotational motion parameters of the gear shaping tool, Indicates the rotational motion parameters of the worm grinding wheel; According to the obtained rotational motion parameters, axis angle and axis distance, establish the slave coordinate system To coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0028]

[0029]

[0030]

[0031] In the formula, Represents the coordinate system of the cylindrical gear To rack tool coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack To the grinding wheel coordinate system The coordinate transformation matrix.

[0032] Optionally, a method for obtaining the relative speed of the worm grinding wheel and the shaping gear tool is also included: The angular velocities of the worm grinding wheel and the gear shaping tool are obtained respectively, and the relative speeds of the worm grinding wheel and the gear shaping tool are calculated according to the obtained angular velocities. The calculation formula of the relative speeds of the worm grinding wheel and the gear shaping tool is:

[0033] In the formula, Indicates the relative speed of the worm wheel and the gear shaping tool. Indicates the absolute speed of any point on the tooth surface of the gear shaping tool. Indicates the absolute speed of any point on the tooth surface of the worm wheel. represents the angular velocity of the gear shaping tool, represents the angular velocity of the worm wheel, Represents the rack tool coordinate system Origin and grinding wheel coordinate system Origin distance.

[0034] Optionally, the method of controlling a turning tool pre-installed on a CNC turning machine to turn and groove a pre-installed grinding wheel blank comprises: S1, installing the grinding wheel blank on the spindle of a CNC turning machine tool, and making the axis of the grinding wheel blank coincide with the axis of the spindle of the CNC turning machine tool; S2, installing the handle of the turning tool on the tool holder of the CNC turning machine tool, so that the turning tool is parallel to the end face of the grinding wheel blank, and the blade of the turning tool and the axis of the grinding wheel blank are at the same horizontal height; S3, after the grinding wheel blank and the turning tool are pre-installed, adjusting the distance between the turning tool and the grinding wheel blank according to a preset cutting depth; S4, starting the CNC turning machine to control the turning tool to turn the grinding wheel blank according to the determined turning path, and after the turning tool completes one turning, controlling the turning tool to return to the initial turning position; S5, controlling the turning tool to feed along the axis direction of the grinding wheel blank according to a preset depth, and after the turning tool reaches a target position, controlling the turning tool to turn the grinding wheel blank again according to a determined turning path; S6. Repeat steps S4 to S5 until a target tooth surface is turned on the end surface of the grinding wheel blank.

[0035] Compared with the prior art, the method for evaluating the health status of wind turbine blades provided by the embodiment of the present invention has the following beneficial effects: By establishing the tooth surface equations associated with the shaping gear shaping tool and the worm grinding wheel, the relative speed of the worm grinding wheel and the shaping gear shaping tool, the tooth profile parameters of the rack, the tooth direction parameters, the rotational motion parameters of the worm grinding wheel and the shaping gear shaping tool can be input to directly solve the turning point coordinates of the worm grinding wheel, so as to achieve high-precision machining of the grinding wheel tooth surface through precise control of the turning points, that is, the grinding wheel slotting can be achieved by using a turning machine tool, without the need for a gear grinding machine tool, which has better feasibility and higher face gear grinding accuracy. The grinding wheel turning process is used instead of the traditional diamond roller dressing, which greatly improves the slotting efficiency of the worm grinding wheel for face gear grinding and reduces the cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments, in which: Figure 1 A schematic diagram of the structure of the cooperation between a turning tool and a grinding wheel blank provided by an embodiment of the present invention; Figure 2 A schematic diagram of a state in which a turning tool provided by an embodiment of the present invention grooves a grinding wheel blank along a turning path; Figure 3 Any point on the rack provided by the embodiment of the present invention In the rack tool coordinate system Schematic diagram of coordinate positions on the Figure 4 for Figure 3 midpoint Transform to rack coordinate system midpoint Schematic diagram of coordinate position; Figure 5 for Figure 4 midpoint In the process of rack development into cylindrical gear, translation transformation to the cylindrical gear coordinate system Schematic diagram of the coordinate position of the midpoint P; Figure 6 A schematic diagram of coordinate system transformation for generating the tooth surface of a worm grinding wheel by a gear shaping tool provided in an embodiment of the present invention.

[0037] The symbols in the accompanying drawings are as follows: 1. Turning tool; 2. Grinding wheel blank; 3. Turning path. DETAILED DESCRIPTION

[0038] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. Now, in conjunction with the accompanying drawings, the preferred embodiments of the present invention are described in detail.

[0039] The present invention discloses a method for slotting a worm grinding wheel for face gear grinding, such as Figure 1 and Figure 2 As shown, including: The tooth surface equation associated with the gear shaping tool and the worm grinding wheel is established, and the coordinates of any turning point on the tooth surface of the worm grinding wheel are calculated. The tooth surface equation associated with the gear shaping tool and the worm grinding wheel is:

[0040] In the formula, The tooth surface equation representing the coordinate transformation from the gear shaping tool to the worm wheel is: Represents the coordinate system of the cylindrical gear To the grinding wheel coordinate system The coordinate transformation matrix, The tooth surface equation of the gear shaping tool is represented by: The meshing equation between the gear shaping tool and the worm wheel is expressed as follows: represents the tooth surface normal vector of the gear shaping tool, Indicates the relative speed of the worm wheel and the gear shaping tool. represents the tooth profile parameters of the rack, represents the tooth direction parameter, Indicates the rotational motion parameters of the gear shaping tool; Measure and obtain the cutting edge geometric parameters of the turning tool 1, and determine the turning path 3 of the turning tool 1 according to the calculated turning point coordinates and the measured cutting edge geometric parameters; According to the determined turning path 3, a turning tool 1 pre-installed on a CNC turning machine tool is controlled to turn and groove a pre-installed grinding wheel blank 2.

[0041] As mentioned above, in the tooth surface equations associated with the shaping gear shaping tool and the worm grinding wheel, the first column of formulas is the coordinate transformation from the shaping gear shaping tool to the worm grinding wheel, and the second column of formulas is the meshing equation between the shaping gear shaping tool and the worm grinding wheel.

[0042] By implementing the slotting method of the worm grinding wheel for face gear grinding of this embodiment, the tooth surface equation associated with the shaping gear shaping tool and the worm grinding wheel is established, and the relative speed of the worm grinding wheel and the shaping gear shaping tool, the tooth profile parameters of the rack, the tooth direction parameters, the rotational motion parameters of the worm grinding wheel and the shaping gear shaping tool, etc. can be directly solved to obtain the turning point coordinates of the worm grinding wheel, so as to achieve high-precision processing of the grinding wheel tooth surface through precise control of the turning point, that is, the grinding wheel slotting can be achieved by using a turning machine tool, without using a gear grinding machine tool, which has better feasibility and higher face gear grinding accuracy. And the grinding wheel turning process is used instead of the traditional diamond roller dressing, which greatly improves the slotting efficiency of the worm grinding wheel for face gear grinding and reduces the cost. Preferably, the turning tool 1 is an ordinary straight-edged turning tool.

[0043] Furthermore, the method of establishing the tooth surface equation associated with the gear shaping tool and the worm grinding wheel includes: Configure rack parameters and define the tooth profile and corresponding normal vector at any point on the rack tooth surface; Establishing the rack coordinate system , and establish the tooth surface equation of the rack according to the defined tooth profile and the corresponding normal vector; Establishing cylindrical gear coordinate system , based on coordinate transformation, the tooth surface equation of the rack is transformed into the tooth surface equation of the shaping gear tool; Establishing the grinding wheel coordinate system , based on coordinate transformation, the tooth surface equation of the shaping gear tool is transformed into the tooth surface equation of the worm grinding wheel for face gear grinding.

[0044] Furthermore, the method of establishing the tooth surface equation of the rack according to the defined tooth profile and the corresponding normal vector includes: Get the tooth profile parameters of the rack, and define the tooth profile and the corresponding normal vector at any point on the rack tooth surface according to the tooth profile parameters. The expressions of the defined tooth profile and the corresponding normal vector are:

[0045] In the formula, Represents the tooth profile of a point on the rack tooth surface, Represents the normal vector corresponding to the tooth profile.

[0046] Get the tooth parameters of the rack and transform the defined tooth profile and corresponding normal vector to the established rack coordinate system In the equation, the tooth surface equation of the rack is obtained. The tooth surface equation of the rack is expressed as:

[0047] In the formula, Represents the tooth surface equation of the rack, that is, the radial vector of the corresponding point on the tooth surface of the rack, represents the normal vector of the rack, Indicates that from the intermediate coordinate system To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To the intermediate coordinate system The coordinate transformation matrix, Representation Matrix The third-order principal minor of Representation Matrix The third-order sequential principal minor of .

[0048] Furthermore, the defined tooth profile and the corresponding normal vector are transformed into the established rack coordinate system The methods include: According to the configuration of the rack, such as Figure 3 As shown, the rack tool coordinate system is established on the rack , and the intermediate coordinate system of the auxiliary coordinate transformation ; Get the normal pressure angle of the rack and the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin is established from the rack tool coordinate system To the intermediate coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0049] Get the plane helix angle of the rack, according to the established coordinate transformation matrix , establish the intermediate coordinate system To the rack coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0050] In the formula, It represents the helix angle of the rack plane, and its absolute value is equal to the helix angle of the gear shaping tool; It represents the normal pressure angle of the rack, which is equal to the normal pressure angle of the gear shaping tool; Represents the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin. Figure 3 and Figure 4 As shown, Figure 3 Select any point on the rack In the rack tool coordinate system The coordinate position on the rack is transformed into the rack coordinate system through coordinate transformation. midpoint The coordinate position of .

[0051] Furthermore, it also includes obtaining the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin method: Obtain the normal pressure angle of the rack and the normal modulus of the forming tool, and calculate the intermediate coordinate system based on the obtained normal pressure angle and normal modulus Origin to rack tool coordinate system The distance from the origin is calculated as:

[0052] In the formula, It is the normal module of the forming tool, which is the same as the normal module of the face gear being processed.

[0053] Furthermore, the method of transforming the tooth surface equation of the rack into the tooth surface equation of the shaping gear shaping tool includes: Get the rotation angle parameters of the cylindrical gear and convert the tooth surface equation of the rack into the established cylindrical gear coordinate system The tooth surface equation of the gear shaping tool is obtained:

[0054] In the formula, The tooth surface equation of the gear shaping tool is represented by: represents the normal vector of the gear shaping tool, is the rotation angle parameter of the cylindrical gear, Represents the coordinate system from the rack To cylindrical gear coordinate system The coordinate transformation matrix, Representation Matrix The third-order sequential principal minor of .

[0055] As mentioned above, since the subsequent formula derivation is based on the principle of developing a rack into a cylindrical gear, the tooth surface equation of the cylindrical gear finally derived is the tooth surface equation of the shaping gear tool.

[0056] Furthermore, the method of converting the tooth surface equation of the rack into the established cylindrical gear coordinate system includes: Obtain the pitch circle radius of the cylindrical gear and the translation distance of the rack during the development process. The calculation formula for the translation distance of the rack during the development process is:

[0057]

[0058] According to the obtained pitch circle radius and translation distance, establish the rack coordinate system To cylindrical gear coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0059] In the formula, represents the translation distance of the rack during the development process, represents the rotation angle parameter of cylindrical gear, represents the helix angle of the rack plane, represents the normal pressure angle of the rack, It represents the pitch circle radius of the cylindrical gear and can be obtained by measurement.

[0060] As mentioned above, the principle and coordinate system of rack development into cylindrical gear are as follows Figure 5 As shown, Figure 4 midpoint In the process of rack development into cylindrical gear, translation transformation to the cylindrical gear coordinate system The coordinate position of the midpoint P. Because the rack and the cylindrical gear are common points at point P and have the same speed, At the same time, according to the gear meshing principle, one of the tooth conditions for the correct meshing of two gears is that the common normal of the contact point of the two tooth surfaces should be perpendicular to the relative speed. Since the cylindrical gear development process is relatively simple, the calculation formula of the cylindrical gear rotation angle parameters can be obtained by simply deducing the parameters such as the rack plane helix angle, the rack normal pressure angle, and the pitch circle radius of the cylindrical gear.

[0061] Furthermore, the tooth surface equation of the gear shaping tool is converted into the established grinding wheel coordinate system. Methods in: The number of heads of the worm grinding wheel and the number of teeth of the gear shaping tool are preset to obtain the axis angle between the worm grinding wheel and the gear shaping tool. The calculation formula of the axis angle is:

[0062]

[0063] In the formula, Indicates the angle between the worm wheel and the axis of the gear shaping tool. Indicates the number of worm wheel heads, Indicates the number of teeth of the gear shaping tool. Indicates the left-hand helix angle of the gear shaping tool. Indicates the right-hand helix angle of the gear shaping tool. Indicates the helix angle of the left-hand worm of the worm grinding wheel. Indicates the helix angle of the right-hand worm of the worm grinding wheel; Since the tooth surface equation of the cylindrical gear is the tooth surface equation of the gear shaping tool, It indicates the helix angle of the rack plane, that is, the helix angle of the gear shaping tool.

[0064] Obtain the axis distance from the axis of the worm grinding wheel to the axis of the gear shaping tool. The calculation formula for the axis distance is:

[0065] In the formula, Indicates the distance from the axis of the worm wheel to the axis of the gear shaping tool. Indicates the pitch radius of the worm grinding wheel; According to the preset number of heads of the worm grinding wheel and the number of teeth of the shaping gear shaping tool, the transmission ratio of the shaping gear shaping tool and the worm grinding wheel is determined, and the rotational motion parameters of the shaping gear shaping tool and the worm grinding wheel are obtained according to the determined transmission ratio. The expression of the transmission ratio is:

[0066] In the formula, Indicates the number of worm wheels and the transmission ratio of the gear shaping tool. Indicates the rotational motion parameters of the gear shaping tool, represents the rotational motion parameters of the worm wheel, and They rotate around their own axes respectively according to a constant transmission ratio relationship; According to the obtained rotational motion parameters, axis angle and axis distance, the cylindrical gear coordinate system is established. To the grinding wheel coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0067]

[0068]

[0069]

[0070] In the formula, Represents the coordinate system of the cylindrical gear To rack tool coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack To the grinding wheel coordinate system The coordinate transformation matrix. Figure 6 The figure shows the coordinate system transformation diagram of the gear shaping tool developing the tooth surface of the worm grinding wheel.

[0071] Furthermore, it also includes a method for obtaining the relative speed of the worm grinding wheel and the shaping gear tool: The angular velocities of the worm grinding wheel and the gear shaping tool are obtained respectively, and the relative speeds of the worm grinding wheel and the gear shaping tool are calculated according to the obtained angular velocities. The calculation formula of the relative speeds of the worm grinding wheel and the gear shaping tool is:

[0072] In the formula, Indicates the relative speed of the worm wheel and the gear shaping tool. It indicates the absolute speed of any point on the tooth surface of the gear shaping tool. It is a quantity with direction and magnitude. It represents the absolute speed of any point on the tooth surface of the worm wheel. It is a quantity with direction and magnitude. represents the angular velocity of the gear shaping tool, represents the angular velocity of the worm wheel, Represents the rack tool coordinate system Origin and grinding wheel coordinate system Origin distance.

[0073] Furthermore, the method of controlling the turning tool 1 pre-installed on the CNC turning machine to turn and groove the pre-installed grinding wheel blank 2 includes: S1, installing the grinding wheel blank 2 on the spindle of the CNC turning machine tool, and making the axis of the grinding wheel blank 2 coincide with the axis of the spindle of the CNC turning machine tool; S2, installing the tool handle of the turning tool 1 on the tool holder of the CNC turning machine tool, so that the turning tool 1 is parallel to the end surface of the grinding wheel blank 2, and the blade of the turning tool 1 and the axis of the grinding wheel blank 2 are at the same horizontal height; S3, after the grinding wheel blank 2 and the turning tool 1 are pre-installed, the distance between the turning tool 1 and the grinding wheel blank 2 is adjusted according to the preset cutting amount; S4, start the CNC turning machine to control the turning tool 1 to turn the grinding wheel blank 2 according to the determined turning path 3, and after the turning tool 1 completes one turning, control the turning tool 1 to return to the initial turning position; S5, controlling the turning tool 1 to feed along the axis direction of the grinding wheel blank 2 according to the preset depth, and after the turning tool 1 reaches the target position, controlling the turning tool 1 to turn the grinding wheel blank 2 again according to the determined turning path 3; S6. Repeat steps S4 to S5 until the target tooth surface is turned on the end surface of the grinding wheel blank 2.

[0074] As described above, in step S2, the turning tool 1 can move simultaneously along the radial and axial directions of the grinding wheel blank 2, and the position of its cutting edge can be accurately controlled. The width of the blade of the turning tool 1 is smaller than the narrowest width of the target grinding wheel tooth groove. The width of the narrowest area in the target grinding wheel tooth groove can be accurately calculated by relevant theories. Therefore, in the embodiment of the present invention, it is only necessary to ensure that the blade of the turning tool 1 is slightly smaller than the narrowest width of the target grinding wheel tooth groove. In addition, the tooth surface equation of the shaping gear tool associated with the worm grinding wheel is derived by coordinate transformation using the tooth surface of the shaping gear tool of the face gear, and the tooth surface of the shaping gear tool is derived by coordinate transformation from the tooth surface of the rack. During turning, the turning tool 1 is controlled to swing along the calculated tooth groove line, and at the same time, the lathe spindle drives the grinding wheel blank 2 to rotate, and the direction of the turning tool 1 is adjusted in real time, so that the turning tool 1 repeats the turning motion every time it feeds a certain depth along the radial direction of the grinding wheel blank 2 until the feeding depth of the turning tool 1 reaches the designed position. When the turning tool 1 is turning, the blade and the motion trajectory of the turning tool 1 are always in a tangent or overlapping relative relationship, so as to ensure that the processed grinding wheel tooth surface and the theoretical tooth surface are highly overlapped.

[0075] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. For those skilled in the art, the technical solutions described in the above embodiments can be modified, or some of the technical features therein can be replaced by equivalents; and all these modifications and replacements should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for slotting a worm grinding wheel for face gear grinding, characterized in that: The slotting method comprises: The tooth surface equation associated with the gear shaping tool and the worm grinding wheel is established, and the coordinates of any turning point on the tooth surface of the worm grinding wheel are calculated. The tooth surface equation associated with the gear shaping tool and the worm grinding wheel is: In the formula, The tooth surface equation representing the coordinate transformation from the gear shaping tool to the worm wheel is: Represents the coordinate system of the cylindrical gear To the grinding wheel coordinate system The coordinate transformation matrix, The tooth surface equation of the gear shaping tool is represented by: The meshing equation between the gear shaping tool and the worm wheel is expressed as follows: represents the tooth surface normal vector of the gear shaping tool, Indicates the relative speed of the worm wheel and the gear shaping tool. represents the tooth profile parameters of the rack, represents the tooth direction parameter, Indicates the rotational motion parameters of the gear shaping tool; Measure and obtain the cutting edge geometric parameters of the turning tool, and determine the turning path of the turning tool according to the calculated turning point coordinates and the measured cutting edge geometric parameters; According to the determined turning path, a turning tool pre-installed on a CNC turning machine tool is controlled to turn and groove a pre-installed grinding wheel blank.

2. The method for slotting a worm grinding wheel for face gear grinding according to claim 1, characterized in that: The method for establishing the tooth surface equation associated with the gear shaping tool and the worm grinding wheel comprises: Configure rack parameters and define the tooth profile and corresponding normal vector at any point on the rack tooth surface; Establishing the rack coordinate system , and establish the tooth surface equation of the rack according to the defined tooth profile and the corresponding normal vector; Establishing cylindrical gear coordinate system , based on coordinate transformation, the tooth surface equation of the rack is transformed into the tooth surface equation of the shaping gear tool; Establishing the grinding wheel coordinate system , based on coordinate transformation, the tooth surface equation of the shaping gear tool is transformed into the tooth surface equation of the worm grinding wheel for face gear grinding.

3. The method for slotting a worm grinding wheel for face gear grinding according to claim 2, characterized in that: The method for establishing the tooth surface equation of the rack according to the defined tooth profile and the corresponding normal vector comprises: Get the tooth profile parameters of the rack, and define the tooth profile and the corresponding normal vector at any point on the rack tooth surface according to the tooth profile parameters. The expressions of the defined tooth profile and the corresponding normal vector are: In the formula, Represents the tooth profile of a point on the rack tooth surface, Represents the normal vector corresponding to the tooth profile; Get the tooth parameters of the rack and transform the defined tooth profile and corresponding normal vector into the established rack coordinate system In the equation, the tooth surface equation of the rack is obtained. The tooth surface equation of the rack is expressed as: In the formula, represents the tooth surface equation of the rack, represents the normal vector of the rack, Indicates that from the intermediate coordinate system To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To the intermediate coordinate system The coordinate transformation matrix, Representation Matrix The third-order principal minor of Representation Matrix The third-order sequential principal minor of .

4. The method for slotting a worm grinding wheel for face gear grinding according to claim 3, characterized in that: The defined tooth profile and the corresponding normal vector are converted to the established rack coordinate system The methods include: According to the configured rack, establish the rack tool coordinate system on the rack , and the intermediate coordinate system of the auxiliary coordinate transformation ; Get the normal pressure angle of the rack and the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin is established from the rack tool coordinate system To the intermediate coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: Get the plane helix angle of the rack, according to the established coordinate transformation matrix , establish the intermediate coordinate system To the rack coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: In the formula, represents the helix angle of the rack plane, represents the normal pressure angle of the rack, Represents the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin.

5. The method for slotting a worm grinding wheel for face gear grinding according to claim 4, characterized in that: It also includes obtaining the intermediate coordinate system Origin to rack tool coordinate system The distance from the origin method: Obtain the normal pressure angle of the rack and the normal modulus of the forming tool, and calculate the intermediate coordinate system based on the obtained normal pressure angle and normal modulus Origin to rack tool coordinate system The distance from the origin is calculated as: In the formula, is the normal module of the rack tool.

6. The method for slotting a worm grinding wheel for face gear grinding according to claim 4, characterized in that: The method for transforming the tooth surface equation of the rack into the tooth surface equation of the shaping gear shaping tool comprises: Get the rotation angle parameters of the cylindrical gear and convert the tooth surface equation of the rack into the established cylindrical gear coordinate system The tooth surface equation of the gear shaping tool is obtained: In the formula, The tooth surface equation of the gear shaping tool is represented by: represents the normal vector of the gear shaping tool, is the rotation angle parameter of the cylindrical gear, Represents the coordinate system from the rack To cylindrical gear coordinate system The coordinate transformation matrix, Representation Matrix The third-order sequential principal minor of .

7. The method for slotting a worm grinding wheel for face gear grinding according to claim 6, characterized in that: The method for converting the tooth surface equation of the rack into the established cylindrical gear coordinate system includes: Obtain the pitch circle radius of the cylindrical gear and the translation distance of the rack during the development process. The calculation formula for the translation distance of the rack during the development process is: According to the obtained pitch circle radius and translation distance, establish the rack coordinate system To cylindrical gear coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: In the formula, represents the translation distance of the rack during the development process, represents the rotation angle parameter of cylindrical gear, represents the helix angle of the rack plane, represents the normal pressure angle of the rack, Indicates the pitch circle radius of the cylindrical gear.

8. The method for slotting a worm grinding wheel for face gear grinding according to claim 7, characterized in that: It also includes the conversion of the tooth surface equation of the gear shaping tool into the established grinding wheel coordinate system. Methods in: The number of heads of the worm grinding wheel and the number of teeth of the gear shaping tool are preset to obtain the axis angle between the worm grinding wheel and the gear shaping tool. The calculation formula of the axis angle is: In the formula, Indicates the angle between the worm wheel and the axis of the gear shaping tool. Indicates the number of worm wheel heads, Indicates the number of teeth of the gear shaping tool. represents the helix angle of the rack plane, Indicates the left-hand helix angle of the gear shaping tool. Indicates the right-hand helix angle of the gear shaping tool. Indicates the helix angle of the left-hand worm of the worm grinding wheel. Indicates the helix angle of the right-hand worm of the worm grinding wheel; Obtain the axis distance from the worm wheel axis to the gear shaping tool axis. The calculation formula for the axis distance is: In the formula, Indicates the distance from the axis of the worm wheel to the axis of the gear shaping tool. Indicates the pitch radius of the worm grinding wheel; According to the preset number of heads of the worm grinding wheel and the number of teeth of the shaping gear shaping tool, the transmission ratio of the shaping gear shaping tool and the worm grinding wheel is determined, and the rotational motion parameters of the shaping gear shaping tool and the worm grinding wheel are obtained according to the determined transmission ratio. The expression of the transmission ratio is: In the formula, Indicates the number of worm wheels and the transmission ratio of the gear shaping tool. Indicates the rotational motion parameters of the gear shaping tool, Indicates the rotational motion parameters of the worm grinding wheel; According to the obtained rotational motion parameters, axis angle and axis distance, the cylindrical gear coordinate system is established. To the grinding wheel coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: In the formula, Represents the coordinate system of the cylindrical gear To rack tool coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack To the grinding wheel coordinate system The coordinate transformation matrix.

9. The method for slotting a worm grinding wheel for face gear grinding according to claim 7, characterized in that: It also includes a method for obtaining the relative speed of the worm grinding wheel and the gear shaping tool: The angular velocities of the worm grinding wheel and the gear shaping tool are obtained respectively, and the relative speeds of the worm grinding wheel and the gear shaping tool are calculated according to the obtained angular velocities. The calculation formula of the relative speeds of the worm grinding wheel and the gear shaping tool is: In the formula, Indicates the relative speed of the worm wheel and the gear shaping tool. Indicates the absolute speed of any point on the tooth surface of the gear shaping tool. Indicates the absolute speed of any point on the tooth surface of the worm wheel. represents the angular velocity of the gear shaping tool, represents the angular velocity of the worm wheel, Represents the rack tool coordinate system Origin and grinding wheel coordinate system Origin distance.

10. The method for slotting a worm grinding wheel for face gear grinding according to any one of claims 1 to 9, characterized in that: The method for controlling a turning tool pre-installed on a CNC turning machine tool to turn and groove a pre-installed grinding wheel blank comprises: S1, installing the grinding wheel blank on the spindle of a CNC turning machine tool, and making the axis of the grinding wheel blank coincide with the axis of the spindle of the CNC turning machine tool; S2, installing the handle of the turning tool on the tool holder of the CNC turning machine tool, so that the turning tool is parallel to the end face of the grinding wheel blank, and the blade of the turning tool and the axis of the grinding wheel blank are at the same horizontal height; S3, after the grinding wheel blank and the turning tool are pre-installed, adjusting the distance between the turning tool and the grinding wheel blank according to a preset cutting depth; S4, starting the CNC turning machine to control the turning tool to turn the grinding wheel blank according to the determined turning path, and after the turning tool completes one turning, controlling the turning tool to return to the initial turning position; S5, controlling the turning tool to feed along the axis direction of the grinding wheel blank according to a preset depth, and after the turning tool reaches a target position, controlling the turning tool to turn the grinding wheel blank again according to a determined turning path; S6. Repeat steps S4 to S5 until a target tooth surface is turned on the end surface of the grinding wheel blank.

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