Method and device for casting worm grinding wheel for face gear grinding

Abstract

The invention relates to the technical field of machining, in particular to a worm grinding wheel casting method and device for face gear grinding. The method comprises the steps that surface coordinates of a target grinding wheel tooth surface are obtained, a three-dimensional model of a grinding wheel is established, a mold is prepared, a casting cavity is machined in the mold according to the three-dimensional model, a casting material is injected into the casting cavity according to a preset proportion, the fully-injected casting material is cooled and solidified, and a grinding wheel blank is obtained. And sintering the grinding wheel blank to obtain a cast grinding wheel finished product. According to the method, the three-dimensional model is established, so that a casting cavity in the mold has high precision, a high-precision grinding wheel finished product is directly obtained through sintering molding finally, complex machining is not needed, the mold can be repeatedly used, and compared with traditional diamond roller finishing, the casting efficiency of the worm grinding wheel is greatly improved, and the cost is reduced. And the manufacturing cost is reduced.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical processing, in particular to a method and a device for casting 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 and a device for casting a worm grinding wheel for face gear grinding, so as to solve the problem of difficulty in manufacturing worm grinding wheels for face gear grinding in the prior art.

[0006] The invention discloses a method for casting a worm grinding wheel for face gear grinding, comprising: Acquire the surface coordinates of the target grinding wheel tooth surface, and establish a three-dimensional model of the grinding wheel according to the acquired surface coordinates; Preparing a mold, and machining a casting cavity inside the mold according to the established three-dimensional model; Preparing a casting material, and injecting the casting material into the casting cavity of the mold according to a preset proportion until the casting material fills the casting cavity; The casting in the casting cavity is cooled and solidified to obtain a grinding wheel blank, and the grinding wheel blank is sintered to obtain a cast grinding wheel finished product.

[0007] Optionally, obtaining the surface coordinates of the target grinding wheel tooth surface includes: Establish the tooth surface model of the rack; The tooth surface model of the rack is developed by coordinate transformation to obtain the tooth surface model of the shaping gear shaping tool; The tooth surface model of the gear shaping tool is developed by coordinate transformation to obtain the tooth surface model of the worm grinding wheel. The function expression of the tooth surface model of the worm grinding wheel is:

[0008] In the formula, The tooth surface equation of the worm grinding wheel is: The coordinate transformation matrix representing the gear shaping tool developing into the worm grinding wheel is: 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; The geometric parameters of any point on the tooth surface of the target grinding wheel are obtained and input into the tooth surface model of the worm grinding wheel, and the surface coordinates of the corresponding point on the tooth surface of the target grinding wheel are obtained as output.

[0009] Optionally, establishing the tooth surface model of the rack includes: Set the rack, select any point on the rack, and establish the rack tool coordinate system at the selected point ; Get the selected point in the rack tool coordinate system The tooth profile parameters and the corresponding normal vector in are obtained, and the tooth surface model of the selected point is established according to the obtained tooth profile parameters. The function expression of the tooth surface model of the selected point is:

[0010] In the formula, represents the tooth surface equation of the selected point, represents the tooth profile parameters of the selected points, Indicates the normal vector corresponding to the tooth profile parameters of the selected point; Establish a rack coordinate system on the rack , and establish an auxiliary coordinate system , through the auxiliary coordinate system Transform the selected point to the rack coordinate system In the rack coordinate system, the transformation point is obtained. Tooth direction parameters in; According to the tooth surface model of the selected point and the tooth direction parameter of the transformation point, the tooth surface model of the rack is established, and the function expression of the rack tooth surface model is:

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

[0012] Optionally, the auxiliary coordinate system Transform the tooth profile parameters and tooth direction parameters of the selected point to the rack coordinate system ,include: Get the selected point and the auxiliary coordinate system The line connecting the origins in the auxiliary coordinate system The normal pressure angle in , and the normal modulus of the selected point; The auxiliary coordinate system is obtained by calculating the normal pressure angle and the normal modulus. Origin to the rack-tool coordinate system The distance from the origin, the function expression of distance calculation is:

[0013] In the formula, represents the normal pressure angle, is the normal modulus, Represents the auxiliary coordinate system Origin to rack tool coordinate system Distance from the origin; According to the normal pressure angle obtained and the calculated distance, the rack tool coordinate system is established To the auxiliary coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0014] The transformation point and the auxiliary coordinate system The line connecting the origins in the rack coordinate system The plane helix angle in is used as the plane helix angle of the gear shaping tool, and the auxiliary coordinate system is established. to the rack coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0015] In the formula, Indicates the plane helix angle of the gear shaping tool. represents the normal pressure angle of the selected point, Represents the rack tool coordinate system To auxiliary coordinate system The coordinate transformation matrix, Represents the auxiliary coordinate system To the rack coordinate system The coordinate transformation matrix.

[0016] 6. Optionally, the step of developing the tooth surface model of the rack by coordinate transformation to obtain the tooth surface model of the shaping gear shaping tool comprises: The rack is developed into a gear shaping tool, and a cylindrical gear coordinate system is established on the developed gear shaping tool. , and obtain the gear shaping tool in the cylindrical gear coordinate system The pitch circle radius in ; According to the tooth profile parameters and the normal pressure angle of the selected point, and the plane helix angle and pitch circle radius of the shaping gear shaping tool, the rotation angle parameters of the shaping gear shaping tool when the rack is developed into the shaping gear shaping tool are calculated, and the function expression of the rotation angle parameters is:

[0017] In the formula, Indicates the rotation angle parameter of the gear shaping tool. Indicates the pitch radius of the gear shaping tool; According to the pitch circle radius of the shaping gear shaping tool and the calculated rotation angle parameter, the transformation point is calculated to be transformed to the cylindrical gear coordinate system when the rack is developed into the shaping gear shaping tool. The translation distance in , the function expression of the translation distance calculation is:

[0018] In the formula, Indicates the transformation of the selected point to the cylindrical gear coordinate system The translation distance in ; According to the pitch circle radius of the shaping gear shaping tool and the calculated rotation angle parameter and translation distance, a coordinate system from the rack is established. To the cylindrical gear coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0019] In the formula, in the formula, Represents the rack coordinate system To cylindrical gear coordinate system The coordinate transformation matrix of According to the tooth surface model of the rack and the coordinate transformation matrix , establish the tooth surface model of the shaping gear shaping tool, and the function expression of the tooth surface model of the shaping gear shaping tool is:

[0020] In the formula, The tooth surface equation of the gear shaping tool is represented by: represents the normal vector of the gear shaping tool, Represents the coordinate transformation matrix The third-order sequential principal minor of .

[0021] Optionally, the tooth surface model of the gear shaping tool is developed by coordinate transformation to obtain the tooth surface model of the worm grinding wheel, including: The gear shaping tool is developed into a worm grinding wheel, and a grinding wheel coordinate system is established on the developed worm grinding wheel. , and obtain the number of teeth and rotational motion parameters of the shaping gear shaping tool and the number of wheel heads and rotational motion parameters of the worm grinding wheel when the shaping gear shaping tool generates the worm grinding wheel, and calculate the transmission ratio of the shaping gear shaping tool and the worm grinding wheel during the generating process. The function expression for calculating the transmission ratio is:

[0022] In the formula, Indicates the transmission ratio between the gear shaping tool and the worm wheel. Indicates the rotational motion parameters of the gear shaping tool, Indicates the number of teeth of the gear shaping tool. represents the rotational motion parameters of the worm wheel, Indicates the number of wheel heads of the worm sand; The pitch circle radius of the worm grinding wheel is obtained, and the angle between the axes of the worm grinding wheel and the shaping gear shaping tool is calculated according to the pitch circle radius of the worm grinding wheel, the pitch circle radius and the plane helix angle of the shaping gear shaping tool, and the calculated transmission ratio. The function expression of the axis angle is:

[0023]

[0024] In the formula, It represents the angle between the worm wheel and the axis of the gear shaping tool. Indicates the pitch radius of the worm grinding wheel, Indicates the number of wheel heads of the worm sand. 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; According to the pitch circle radius of the shaping gear shaping tool and the pitch circle radius of the worm grinding wheel, the distance from the axis of the worm grinding wheel to the axis of the shaping gear shaping tool is calculated, and the calculation formula of the axis distance is:

[0025] In the formula, Indicates the distance from the axis of the worm wheel to the axis of the gear shaping tool; According to the rotational motion parameters of the shaping gear shaping tool and the calculated axis angle and axis distance, a coordinate system of the cylindrical gear is established. To the grinding wheel coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0026]

[0027]

[0028]

[0029] 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.

[0030] Optionally, a method for obtaining the relative speed of the worm grinding wheel and the shaping gear tool includes: Acquire the angular velocity of any point on the tooth surface of the shaping gear shaping tool and the angular velocity of any point on the tooth surface of the worm grinding wheel when the shaping gear shaping tool generates the worm grinding wheel; The relative speed between the worm grinding wheel and the shaping gear shaping tool is calculated based on the acquired angular velocity. The function expression for the relative speed calculation is:

[0031] 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. It represents the angular velocity of any point on the tooth surface of the gear shaping tool. It represents the angular velocity of any point on the tooth surface of the worm wheel. Represents the rack tool coordinate system Origin and grinding wheel coordinate system Origin distance.

[0032] Optionally, the method comprises injecting the casting into the casting cavity, and obtaining a grinding wheel product by cooling, solidifying and sintering: preparing a grinding wheel abrasive and a binder, and fully mixing the grinding wheel abrasive and the binder in a preset ratio to obtain the casting; Injecting the mixed casting material into the casting cavity of the mold under a preset pressure until the casting material fills the casting cavity; The casting filled in the mold is quickly cooled, and after the casting is cooled to a preset temperature, a first treatment temperature is set to be lower than the melting point of the casting, and the grinding wheel blank is heat-treated under the first treatment temperature condition to obtain a solidified grinding wheel blank; A second processing temperature greater than the first processing temperature is set in a vacuum environment, and the grinding wheel blank is sintered in a vacuum environment until a preset sintering time is reached to obtain the grinding wheel finished product.

[0033] The present invention also discloses a casting device, which adopts the above-mentioned method for casting a worm grinding wheel for face gear grinding, and the casting device comprises: A mold unit, the mold unit comprising a mold body, a casting cavity arranged inside the mold body, and a casting cylinder arranged on the top of the mold body, the casting cavity is a cavity structure matching the three-dimensional structure of the target finished grinding wheel, the top of the casting cylinder is provided with a casting port, and the bottom end of the casting cylinder is connected to the casting cavity; A cooling unit, wherein the cooling unit includes a cooling circulation channel, a coolant injection pipe and a coolant outlet pipe, wherein the cooling circulation channel is opened in the mold body, and the cooling circulation channel is spirally structured along a top-to-bottom direction around the outside of the casting cavity, the coolant injection pipe and the coolant outlet pipe are both arranged on the outer side wall of the mold body, and the coolant injection pipe is connected to the channel on one side of the cooling circulation channel, and the coolant outlet pipe is connected to the channel on the other side of the cooling circulation channel.

[0034] Optionally, the mold body includes a first half mold and a second half mold that divide the casting cavity, the pouring cylinder and the cooling circulation channel into two equal parts, and a guide column is provided on the outer wall of the first half mold, and a guide socket corresponding to the guide column is provided on the outer wall of the second half mold.

[0035] Compared with the prior art, the method and device for casting a worm grinding wheel for face gear grinding provided by the embodiment of the present invention have the following beneficial effects: By building a three-dimensional model of the grinding wheel, a casting cavity is machined inside the mold according to the three-dimensional model. The casting material is injected into the casting cavity of the mold according to a preset ratio, and the finished grinding wheel is obtained through cooling, solidification and sintering. By building a three-dimensional model, the casting cavity inside the mold has a higher precision, so that a high-precision finished grinding wheel can be directly obtained through sintering. There is no need for complex mechanical processing, and the mold can be reused. Compared with traditional diamond roller dressing, it greatly improves the casting efficiency of worm grinding wheels and reduces manufacturing costs. 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 block diagram of the steps of a method for casting a worm grinding wheel for face gear grinding provided by an embodiment of the present invention; Figure 2 The embodiment of the present invention provides a point selection on the rack Establish the rack tool coordinate system Schematic diagram of Figure 3 for Figure 2 Select point Transform to rack coordinate system Intermediate transformation point Schematic diagram of coordinate transformation; Figure 4 for Figure 3 Intermediate transformation point Transform the rack into the cylindrical gear coordinate system when generating the gear shaping tool Schematic diagram of coordinate transformation of midpoint P; Figure 5 A schematic diagram of coordinate transformation of a gear shaping tool to generate a worm grinding wheel according to an embodiment of the present invention; Figure 6 A schematic diagram of the overall structure of a casting device provided in an embodiment of the present invention; Figure 7 A schematic structural diagram of a first half mold provided by an embodiment of the present invention; Figure 8 A schematic structural diagram of a second half mold provided in an embodiment of the present invention.

[0037] The symbols in the accompanying drawings are as follows: 1. Mold body; 11. First half mold; 12. Second half mold; 2. Casting cavity; 3. Cooling circulation channel; 4. Casting cylinder; 5. Coolant injection pipe; 6. Coolant outlet pipe; 7. Guide column; 8. Guide socket. 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, a preferred embodiment of the present invention is described in detail.

[0039] The present invention discloses a method for casting a worm grinding wheel for face gear grinding. Figure 1 As shown, including: S1, obtaining the surface coordinates of the target grinding wheel tooth surface, and establishing a three-dimensional model of the grinding wheel according to the obtained surface coordinates; S2, preparing a mold, and processing a casting cavity 2 inside the mold according to the established three-dimensional model; S3, preparing the casting material, and injecting the casting material into the casting cavity 2 of the mold according to a preset proportion until the casting material fills the casting cavity 2; S4, cooling and solidifying the casting in the casting cavity 2 to obtain a grinding wheel blank, and sintering the grinding wheel blank to obtain a finished grinding wheel product after casting.

[0040] By implementing the above-mentioned embodiment of the method for casting a worm wheel for face gear grinding, the surface coordinates of the target grinding wheel tooth surface are obtained and a three-dimensional model of the grinding wheel is established, so that the established three-dimensional model can accurately correspond to the surface coordinates of the target grinding wheel tooth surface. The casting cavity 2 is processed according to the three-dimensional model inside the mold, so that the casting cavity 2 can match the three-dimensional structure of the target grinding wheel with high precision. Therefore, it is only necessary to inject the casting material into the casting cavity 2 of the mold according to a preset proportion, and directly obtain a high-precision grinding wheel product through cooling, solidification and final sintering. There is no need for complex mechanical processing, and the mold can be reused. Compared with the traditional diamond roller dressing, the casting efficiency of the worm grinding wheel is greatly improved and the manufacturing cost is reduced.

[0041] Furthermore, the surface coordinates of the target grinding wheel tooth surface are obtained, including: Establish the tooth surface model of the rack; The tooth surface model of the rack is developed through coordinate transformation to obtain the tooth surface model of the gear shaping tool; The tooth surface model of the gear shaping tool is developed through coordinate transformation to obtain the tooth surface model of the worm grinding wheel. The function expression of the tooth surface model of the worm grinding wheel is:

[0042] In the formula, The tooth surface equation of the worm grinding wheel is: The coordinate transformation matrix representing the gear shaping tool developing into the worm grinding wheel is: 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; The geometric parameters of any point on the target grinding wheel tooth surface are obtained and input into the tooth surface model of the worm grinding wheel, and the surface coordinates of the corresponding point on the target grinding wheel tooth surface are output.

[0043] By implementing the above-mentioned embodiment of the method for casting a worm grinding wheel for face gear grinding, the established rack tooth surface model is used to develop the tooth surface model of the shaping gear shaping tool, and then the tooth surface model of the shaping gear shaping tool is developed to obtain the tooth surface model of the worm grinding wheel, so as to establish the tooth surface equations associated with the shaping gear shaping tool and the worm grinding wheel, so that the geometric parameters at any point on the tooth surface of the target grinding wheel, such as relative speed, tooth profile parameters, tooth direction parameters, rotational motion parameters, etc., can be input into the tooth surface model of the worm grinding wheel to directly solve the coordinates of any point on the tooth surface of the target grinding wheel, and then according to the coordinates of all points on the tooth surface of the target grinding wheel, a three-dimensional model that matches the target grinding wheel with high precision is established, so as to prepare a high-precision mold.

[0044] Furthermore, a tooth surface model of the rack is established, including: Set the rack and select any point on the rack to establish the rack tool coordinate system at the selected point ; Get the selected point in the rack tool coordinate system The tooth profile parameters and the corresponding normal vector in are obtained, and the tooth surface model of the selected point is established according to the obtained tooth profile parameters. The function expression of the tooth surface model of the selected point is:

[0045] In the formula, represents the tooth surface equation of the selected point, represents the tooth profile parameters of the selected points, Indicates the normal vector corresponding to the tooth profile parameters of the selected point; Establish the rack coordinate system on the rack , and establish an auxiliary coordinate system , through the auxiliary coordinate system Transform the selected points to the rack coordinate system In the rack coordinate system, we get the transformation point. Tooth direction parameters in; According to the tooth surface model of the selected point and the tooth direction parameters of the transformation point, the tooth surface model of the rack is established. The function expression of the rack tooth surface model is:

[0046] In the formula, represents the tooth surface equation of the rack, represents the normal vector of the rack, represents the tooth direction parameter of the transformation point, Indicates that from the auxiliary coordinate system To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To auxiliary coordinate system The coordinate transformation matrix, Represents the coordinate transformation matrix The third-order principal minor of Represents the coordinate transformation matrix The third-order sequential principal minor of .

[0047] Through the implementation of the above-mentioned embodiment of the method for casting a worm grinding wheel for face gear grinding, as Figure 2 and Figure 3 As shown, Figure 2 Select any point on the rack , and select the point Establish the rack tool coordinate system , and establish an auxiliary coordinate system in the tooth profile of the rack , through the auxiliary coordinate system Perform coordinate transformation and select the point Transform to Figure 3 Rack coordinate system in The transformation point The coordinate position of .

[0048] Furthermore, through the auxiliary coordinate system Transform the tooth profile parameters and tooth direction parameters of the selected points to the rack coordinate system ,include: Get the selected points and auxiliary coordinate system The line connecting the origins in the auxiliary coordinate system The normal pressure angle in , and the normal modulus of the selected point; The auxiliary coordinate system is calculated based on the normal pressure angle and normal modulus. Origin to rack tool coordinate system The distance from the origin, the function expression of distance calculation is:

[0049] In the formula, represents the normal pressure angle, is the normal modulus, Represents the auxiliary coordinate system Origin to rack tool coordinate system Distance from the origin; According to the normal pressure angle and the calculated distance, the rack tool coordinate system is established. To auxiliary coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0050] Transform the points with the auxiliary coordinate system The line connecting the origins in the rack coordinate system The plane helix angle in the gear shaping tool is used as the plane helix angle of the gear shaping tool, and the auxiliary coordinate system is established. To the rack coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0051] In the formula, Indicates the plane helix angle of the gear shaping tool. represents the normal pressure angle of the selected point, Represents the rack tool coordinate system To auxiliary coordinate system The coordinate transformation matrix, Represents the auxiliary coordinate system To the rack coordinate system The coordinate transformation matrix.

[0052] Furthermore, the tooth surface model of the rack is developed by coordinate transformation to obtain the tooth surface model of the shaping gear shaping tool, including: The rack is developed into a gear shaping tool, and the cylindrical gear coordinate system is established on the developed gear shaping tool. , and obtain the gear shaping tool in the cylindrical gear coordinate system The pitch radius in ; According to the tooth profile parameters, normal pressure angle, plane helix angle and pitch radius of the gear shaping tool, the rotation angle parameters of the gear shaping tool are calculated when the rack is generated into the gear shaping tool. The function expression of the rotation angle parameters is:

[0053] In the formula, Indicates the rotation angle parameter of the gear shaping tool. Indicates the pitch radius of the gear shaping tool; According to the pitch circle radius of the gear shaping tool and the calculated rotation angle parameters, the transformation point is calculated when the rack is developed into the gear shaping tool and transformed to the cylindrical gear coordinate system. The translation distance in the function expression of the translation distance calculation is:

[0054] In the formula, Indicates the transformation of the selected point to the cylindrical gear coordinate system The translation distance in ; According to the pitch circle radius of the gear shaping tool, as well as the calculated rotation angle parameters and translation distance, the rack coordinate system is established. To cylindrical gear coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is:

[0055] In the formula, in the formula, Represents the rack coordinate system To cylindrical gear coordinate system The coordinate transformation matrix of According to the tooth surface model and coordinate transformation matrix of the rack , the tooth surface model of the shaping gear shaping tool is established, and the function expression of the tooth surface model of the shaping gear shaping tool is:

[0056] In the formula, The tooth surface equation of the gear shaping tool is represented by: represents the normal vector of the gear shaping tool, Represents the coordinate transformation matrix The third-order sequential principal minor of .

[0057] As mentioned above, since the derivation of the above formula is based on the principle of rack-to-cylindrical gear development, the tooth surface model of the gear shaping tool is the model of the rack-to-cylindrical gear development, so the cylindrical gear coordinate system is established. To derive the tooth surface model of the gear shaping tool.

[0058] Among them, the principle and coordinate system of the rack forming tool are as follows: Figure 3 and Figure 4 As shown, Figure 3 Intermediate transformation point During the rack forming process, the gear shaping tool is transformed into 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, the translation distance 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 tooth profile parameters, normal pressure angle, and geometric parameters such as the plane helix angle and pitch circle radius of the shaping gear shaping tool can be simply deduced to obtain the calculation formula of the angular parameters of the shaping gear shaping tool.

[0059] Furthermore, the tooth surface model of the gear shaping tool is developed by coordinate transformation to obtain the tooth surface model of the worm grinding wheel, including: The gear shaping tool is developed into a worm grinding wheel, and the grinding wheel coordinate system is established on the developed worm grinding wheel. , and obtain the number of teeth and rotational motion parameters of the gear shaping tool and the number of wheel heads and rotational motion parameters of the worm grinding wheel when the gear shaping tool is used to generate the worm grinding wheel, and calculate the transmission ratio of the gear shaping tool and the worm grinding wheel during the generation process. The function expression for the transmission ratio calculation is:

[0060] In the formula, Indicates the transmission ratio between the gear shaping tool and the worm wheel. Indicates the rotational motion parameters of the gear shaping tool, Indicates the number of teeth of the gear shaping tool. represents the rotational motion parameters of the worm wheel, Indicates the number of wheel heads of the worm sand; The pitch radius of the worm grinding wheel is obtained, and the angle between the axes of the worm grinding wheel and the shaping gear shaping tool is calculated according to the pitch radius of the worm grinding wheel, the pitch radius of the shaping gear shaping tool and the plane helix angle, as well as the calculated transmission ratio. The function expression of the axis angle is:

[0061]

[0062] In the formula, It represents the angle between the worm wheel and the axis of the gear shaping tool. Indicates the pitch radius of the worm grinding wheel, Indicates the number of wheel heads of the worm sand. 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; According to the pitch radius of the gear shaping tool and the pitch radius of the worm grinding wheel, the distance from the axis of the worm grinding wheel to the axis of the gear shaping tool is calculated. The calculation formula of the axis distance is:

[0063] In the formula, Indicates the distance from the axis of the worm wheel to the axis of the gear shaping tool; According to the rotational motion parameters of the gear shaping tool and the calculated 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:

[0064]

[0065]

[0066]

[0067] 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 5 The figure shows the coordinate system transformation diagram of the gear shaping tool to develop the worm grinding wheel.

[0068] Furthermore, a method for obtaining the relative speed of the worm grinding wheel and the gear shaping tool is provided: Obtain the angular velocity of any point on the tooth surface of the gear shaping tool and the angular velocity of any point on the tooth surface of the worm grinding wheel when the gear shaping tool is generated into the worm grinding wheel; The relative speed of the worm grinding wheel and the gear shaping tool is calculated based on the obtained angular velocity. The function expression of the relative speed calculation is:

[0069] 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 worm wheel tooth surface, It represents the angular velocity of any point on the tooth surface of the gear shaping tool. It represents the angular velocity of any point on the tooth surface of the worm wheel. Represents the rack tool coordinate system Origin and grinding wheel coordinate system Origin distance.

[0070] Furthermore, the method includes injecting the casting into the casting cavity, and obtaining the grinding wheel finished product through cooling, solidification and sintering: preparing a grinding wheel abrasive and a binder, and fully mixing the grinding wheel abrasive and the binder in a preset ratio to obtain a casting; Injecting the mixed casting material into the casting cavity 2 of the mold under a preset pressure until the casting material fills the casting cavity 2; The casting filled in the mold is quickly cooled, and after the casting is cooled to a preset temperature, a first treatment temperature is set to be lower than the melting point of the casting, and the grinding wheel blank is heat-treated under the first treatment temperature condition to obtain a solidified grinding wheel blank; A second processing temperature greater than the first processing temperature is set in a vacuum environment, and the grinding wheel blank is sintered in the vacuum environment until a preset sintering time is reached to obtain a finished grinding wheel.

[0071] Through the implementation of the worm grinding wheel casting method for face gear grinding of this embodiment, the grinding wheel abrasive and the binder are mixed in a preset ratio, which helps to ensure the quality of the casting, so as to improve the overall performance of the finished grinding wheel. Rapid cooling of the casting allows the casting to be quickly solidified and formed, and helps to reduce internal stress and prevent the grinding wheel from deforming or cracking in subsequent use. The heat treatment at the first treatment temperature helps to eliminate the residual stress in the casting, so that the grinding wheel maintains a stable size after cooling, and the heat treatment process can improve the organizational structure of the grinding wheel and improve its wear resistance and impact resistance. The vacuum sintering environment can prevent the grinding wheel from contacting with air during the sintering process, reduce oxidation and pollution, thereby improving the quality of the finished grinding wheel, and help to improve the density of the finished grinding wheel, making it more compact, and then improve the hardness and durability of the finished grinding wheel. Therefore, through the above process, the finished grinding wheel cast finally has high durability and service life.

[0072] The present invention also discloses a casting device, which adopts the above-mentioned method for casting a worm grinding wheel for face gear grinding, such as Figure 6-Figure 8 As shown, the casting device comprises: A mold unit, the mold unit includes a mold body 1, a casting cavity 2 arranged inside the mold body 1, and a casting tube 4 arranged on the top of the mold body 1, the casting cavity 2 is a cavity structure matching the three-dimensional structure of the target finished grinding wheel, a casting port is arranged on the top of the casting tube 4, and the bottom end of the casting tube 4 is connected to the casting cavity 2; The cooling unit includes a cooling circulation channel 3, a coolant injection pipe 5 and a coolant outlet pipe 6. The cooling circulation channel 3 is opened in the mold body 1, and the cooling circulation channel 3 is spirally structured along the top-to-bottom direction around the outside of the casting cavity 2. The coolant injection pipe 5 and the coolant outlet pipe 6 are both arranged on the outer side wall of the mold body 1, and the coolant injection pipe 5 is connected to the channel on one side of the cooling circulation channel 3, and the coolant outlet pipe 6 is connected to the channel on the other side of the cooling circulation channel 3.

[0073] Furthermore, the mold body 1 includes a first half mold 11 and a second half mold 12 that divide the casting cavity 2, the pouring tube 4 and the cooling circulation channel 3 into two equal parts. A guide column 7 is provided on the outer wall of the first half mold 11, and a guide socket 8 corresponding to the guide column 7 is provided on the outer wall of the second half mold 12.

[0074] Through the implementation of the casting device of this embodiment, the casting cavity 2 set inside the mold body 1 is used to match the cavity structure of the three-dimensional structure of the target finished grinding wheel to ensure that the final cast grinding wheel product has high precision. Before casting the grinding wheel, first clean the casting cavity 2 to ensure that it is clean and free of foreign matter, then connect the external water source and the coolant injection pipe 5, and connect the drain pipe and the coolant outlet pipe 6 to ensure the circulation of the coolant. Turn on the water source so that the coolant enters the cooling circulation channel 3 for circulation to ensure that the heat dissipation effect of the casting cavity 2 is good. The grinding wheel abrasive and the binder are fully mixed according to the proportion, and then poured into the mold through the casting tube 4 until the casting cavity 2 is filled. The coolant in the cooling circulation channel 3 then quickly takes away the heat of the grinding wheel mixture, so that the mixture is cooled and solidified.

[0075] In addition, by using the first half mold 11 and the second half mold 12 that divide the casting cavity 2, the pouring tube 4 and the cooling circulation channel 3 into two, the first half mold 11 and the second half mold 12 can be assembled into a complete mold body 1 and fixed by docking the guide column 7 on the first half mold 11 with the guide socket 8 on the second half mold 12, and then the casting and cooling and solidification operations are performed. Similarly, after cooling and solidifying to obtain the grinding wheel blank, it is only necessary to separate the first half mold 11 and the second half mold 12 to take out the grinding wheel blank. Then the grinding wheel blank is moved to a vacuum sintering environment for sintering to obtain a high-precision worm grinding wheel finished product for face gear grinding. No complicated machining is required, and the mold can be reused. Compared with the traditional diamond roller dressing, the casting efficiency of the worm grinding wheel is greatly improved and the manufacturing cost is reduced.

[0076] 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 casting a worm grinding wheel for face gear grinding, characterized in that: The method for casting a worm grinding wheel for face gear grinding comprises: Acquire the surface coordinates of the target grinding wheel tooth surface, and establish a three-dimensional model of the grinding wheel according to the acquired surface coordinates; Preparing a mold, and machining a casting cavity inside the mold according to the established three-dimensional model; Preparing a casting material, and injecting the casting material into the casting cavity of the mold according to a preset proportion until the casting material fills the casting cavity; The casting in the casting cavity is cooled and solidified to obtain a grinding wheel blank, and the grinding wheel blank is sintered to obtain a cast grinding wheel finished product.

2. The method for casting a worm grinding wheel for face gear grinding according to claim 1, characterized in that: The step of obtaining the surface coordinates of the target grinding wheel tooth surface comprises: Establish the tooth surface model of the rack; The tooth surface model of the rack is developed by coordinate transformation to obtain the tooth surface model of the shaping gear shaping tool; The tooth surface model of the gear shaping tool is developed by coordinate transformation to obtain the tooth surface model of the worm grinding wheel. The function expression of the tooth surface model of the worm grinding wheel is: In the formula, The tooth surface equation of the worm wheel is: The coordinate transformation matrix representing the gear shaping tool developing into the worm grinding wheel is: 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; The geometric parameters of any point on the tooth surface of the target grinding wheel are obtained and input into the tooth surface model of the worm grinding wheel, and the surface coordinates of the corresponding point on the tooth surface of the target grinding wheel are obtained as output.

3. The method for casting a worm grinding wheel for face gear grinding according to claim 2, characterized in that: The step of establishing the tooth surface model of the rack includes: Set the rack, select any point on the rack, and establish the rack tool coordinate system at the selected point ; Get the selected point in the rack tool coordinate system The tooth profile parameters and the corresponding normal vector in are obtained, and the tooth surface model of the selected point is established according to the obtained tooth profile parameters. The function expression of the tooth surface model of the selected point is: In the formula, represents the tooth surface equation of the selected point, represents the tooth profile parameters of the selected points, Indicates the normal vector corresponding to the tooth profile parameters of the selected point; Establish a rack coordinate system on the rack , and establish an auxiliary coordinate system , through the auxiliary coordinate system Transform the selected point to the rack coordinate system In the rack coordinate system, the transformation point is obtained. Tooth direction parameters in; According to the tooth surface model of the selected point and the tooth direction parameter of the transformation point, the tooth surface model of the rack is established, and the function expression of the rack tooth surface model is: In the formula, represents the tooth surface equation of the rack, represents the normal vector of the rack, represents the tooth direction parameter of the transformation point, Indicates that from the auxiliary coordinate system To the rack coordinate system The coordinate transformation matrix, Represents the coordinate system from the rack tool To auxiliary coordinate system The coordinate transformation matrix, Represents the coordinate transformation matrix The third-order principal minor of Represents the coordinate transformation matrix The third-order sequential principal minor of .

4. The method for casting a worm grinding wheel for face gear grinding according to claim 3, characterized in that: The auxiliary coordinate system Transform the tooth profile parameters and tooth direction parameters of the selected point to the rack coordinate system ,include: Get the selected point and the auxiliary coordinate system The line connecting the origins in the auxiliary coordinate system The normal pressure angle in , and the normal modulus of the selected point; The auxiliary coordinate system is obtained by calculating the normal pressure angle and the normal modulus. Origin to the rack-tool coordinate system The distance from the origin, the function expression of distance calculation is: In the formula, represents the normal pressure angle, is the normal modulus, Represents the auxiliary coordinate system Origin to rack tool coordinate system Distance from the origin; According to the normal pressure angle obtained and the calculated distance, the rack tool coordinate system is established To the auxiliary coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: The transformation point and the auxiliary coordinate system The line connecting the origins in the rack coordinate system The plane helix angle in is used as the plane helix angle of the gear shaping tool, and the auxiliary coordinate system is established. to the rack coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: In the formula, Indicates the plane helix angle of the gear shaping tool. represents the normal pressure angle of the selected point, Represents the rack tool coordinate system To auxiliary coordinate system The coordinate transformation matrix, Represents the auxiliary coordinate system To the rack coordinate system The coordinate transformation matrix.

5. The method for casting a worm grinding wheel for face gear grinding according to claim 4, characterized in that: The tooth surface model of the rack is developed by coordinate transformation to obtain the tooth surface model of the shaping gear shaping tool, including: The rack is developed into a gear shaping tool, and a cylindrical gear coordinate system is established on the developed gear shaping tool. , and obtain the gear shaping tool in the cylindrical gear coordinate system The pitch radius in ; According to the tooth profile parameters and the normal pressure angle of the selected point, and the plane helix angle and pitch circle radius of the shaping gear shaping tool, the rotation angle parameters of the shaping gear shaping tool when the rack is developed into the shaping gear shaping tool are calculated, and the function expression of the rotation angle parameters is: In the formula, Indicates the rotation angle parameter of the gear shaping tool. Indicates the pitch radius of the gear shaping tool; According to the pitch circle radius of the shaping gear shaping tool and the calculated rotation angle parameter, the transformation point is calculated to be transformed to the cylindrical gear coordinate system when the rack is developed into the shaping gear shaping tool. The translation distance in , the function expression of the translation distance calculation is: In the formula, Indicates the transformation of the selected point to the cylindrical gear coordinate system The translation distance in ; According to the pitch circle radius of the shaping gear shaping tool and the calculated rotation angle parameter and translation distance, a coordinate system from the rack is established. To the cylindrical gear coordinate system The coordinate transformation matrix , coordinate transformation matrix The expression is: In the formula, in the formula, Represents the rack coordinate system To cylindrical gear coordinate system The coordinate transformation matrix of According to the tooth surface model of the rack and the coordinate transformation matrix , establish the tooth surface model of the shaping gear shaping tool, and the function expression of the tooth surface model of the shaping gear shaping tool is: In the formula, The tooth surface equation of the gear shaping tool is represented by: represents the normal vector of the gear shaping tool, Represents the coordinate transformation matrix The third-order sequential principal minor of .

6. The method for casting a worm grinding wheel for face gear grinding according to claim 5, characterized in that: The tooth surface model of the gear shaping tool is developed by coordinate transformation to obtain the tooth surface model of the worm grinding wheel, including: The gear shaping tool is developed into a worm grinding wheel, and a grinding wheel coordinate system is established on the developed worm grinding wheel. , and obtain the number of teeth and rotational motion parameters of the shaping gear shaping tool and the number of wheel heads and rotational motion parameters of the worm grinding wheel when the shaping gear shaping tool generates the worm grinding wheel, and calculate the transmission ratio of the shaping gear shaping tool and the worm grinding wheel during the generating process. The function expression for calculating the transmission ratio is: In the formula, Indicates the transmission ratio between the gear shaping tool and the worm wheel. Indicates the rotational motion parameters of the gear shaping tool, Indicates the number of teeth of the gear shaping tool. represents the rotational motion parameters of the worm wheel, Indicates the number of wheel heads of the worm sand; The pitch circle radius of the worm grinding wheel is obtained, and the angle between the axes of the worm grinding wheel and the shaping gear shaping tool is calculated according to the pitch circle radius of the worm grinding wheel, the pitch circle radius and the plane helix angle of the shaping gear shaping tool, and the calculated transmission ratio. The function expression of the axis angle is: In the formula, It represents the angle between the worm wheel and the axis of the gear shaping tool. Indicates the pitch radius of the worm grinding wheel, Indicates the number of wheel heads of the worm sand. 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; According to the pitch circle radius of the shaping gear shaping tool and the pitch circle radius of the worm grinding wheel, the distance from the axis of the worm grinding wheel to the axis of the shaping gear shaping tool is calculated, and the calculation formula of 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; According to the rotational motion parameters of the shaping gear shaping tool and the calculated axis angle and axis distance, a coordinate system of the cylindrical gear 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.

7. The method for casting a worm grinding wheel for face gear grinding according to claim 2, characterized in that: Including the method of obtaining the relative speed of the worm grinding wheel and the gear shaping tool: Acquire the angular velocity of any point on the tooth surface of the shaping gear shaping tool and the angular velocity of any point on the tooth surface of the worm grinding wheel when the shaping gear shaping tool generates the worm grinding wheel; The relative speed between the worm grinding wheel and the shaping gear shaping tool is calculated based on the acquired angular velocity. The function expression for the relative speed calculation 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 worm wheel tooth surface, It represents the angular velocity of any point on the tooth surface of the gear shaping tool. It represents the angular velocity of any point on the tooth surface of the worm wheel. Represents the rack tool coordinate system Origin and grinding wheel coordinate system Origin distance.

8. The method for casting a worm grinding wheel for face gear grinding according to claim 1, characterized in that: The method comprises injecting the casting into the casting cavity, and obtaining a grinding wheel product through cooling, solidification and sintering: preparing a grinding wheel abrasive and a binder, and fully mixing the grinding wheel abrasive and the binder in a preset ratio to obtain the casting; Injecting the mixed casting material into the casting cavity of the mold under a preset pressure until the casting material fills the casting cavity; The casting filled in the mold is quickly cooled, and after the casting is cooled to a preset temperature, a first treatment temperature is set to be lower than the melting point of the casting, and the grinding wheel blank is heat-treated under the first treatment temperature condition to obtain a solidified grinding wheel blank; A second processing temperature greater than the first processing temperature is set in a vacuum environment, and the grinding wheel blank is sintered in a vacuum environment until a preset sintering time is reached to obtain the grinding wheel finished product.

9. A casting device, characterized in that: The method for casting a worm grinding wheel for face gear grinding according to any one of claims 1 to 8 is adopted, wherein the casting device comprises: A mold unit, the mold unit comprising a mold body, a casting cavity arranged inside the mold body, and a casting cylinder arranged on the top of the mold body, the casting cavity is a cavity structure matching the three-dimensional structure of the target finished grinding wheel, the top of the casting cylinder is provided with a casting port, and the bottom end of the casting cylinder is connected to the casting cavity; A cooling unit, wherein the cooling unit includes a cooling circulation channel, a coolant injection pipe and a coolant outlet pipe, wherein the cooling circulation channel is opened in the mold body, and the cooling circulation channel is spirally structured along a top-to-bottom direction around the outside of the casting cavity, the coolant injection pipe and the coolant outlet pipe are both arranged on the outer side wall of the mold body, and the coolant injection pipe is connected to the channel on one side of the cooling circulation channel, and the coolant outlet pipe is connected to the channel on the other side of the cooling circulation channel.

10. The casting device according to claim 9, characterized in that: The mold body includes a first half mold and a second half mold that divide the casting cavity, the pouring cylinder and the cooling circulation channel into two parts. The outer wall of the first half mold is provided with a guide column, and the outer wall of the second half mold is provided with a guide socket corresponding to the guide column.

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