Grinding wheel spherical surface grinding and error compensation method based on spindle swing type machine tool

Abstract

According to the grinding wheel spherical surface grinding and error compensation method based on the spindle swing type machine tool, in the machining process through the spindle swing type five-axis machine tool, a blank on a rotating platform only rotates around the axis of the blank, and a cup-shaped arc grinding wheel on a swing head forms a truncated circle type grinding area on the end face due to rotation; the section circle type grinding area and the autorotation motion of the blank are combined to form an enveloping spherical surface grinding area, the motion of the swing head is synthesized by translation in an XOZ plane and rotation around a B axis, the enveloping spherical surface is shrunk or expanded towards the blank through the synthesized motion trail, the blank material is continuously removed with the enveloping spherical surface as the boundary in the grinding process till the swing head swings by a certain angle, and then the blank is ground. The end face of an original cylindrical blank becomes a spherical surface, machining is completed, machining consistency and stability are improved, and precision and tool durability are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of precision machining, and relates to a method for grinding a spherical surface and compensating an error of a grinding wheel based on a spindle swinging machine tool. Background Art

[0002] Optical components are an indispensable part of optical imaging systems and have been widely used in aerospace, national defense, medical treatment and people's daily life. Optical components usually need to go through rough grinding, fine grinding, polishing and other processes. Among them, grinding mainly plays the role of removing materials and processing the blank into shape, which affects the forming accuracy of the workpiece, while the main function of polishing is to remove the damaged layer and reduce the surface roughness. The removal amount is extremely small and takes a long time. Therefore, improving the grinding accuracy can significantly reduce the time of the next polishing process. Optical components are usually made of hard and brittle materials. Hard and brittle materials are generally processed by grinding, but ordinary processing methods are not accurate and are prone to sub-surface damage. Ultra-precision grinding is a processing method that uses super-hard abrasive grinding wheels with high-performance machine tools for grinding, and the processing accuracy is higher than ordinary grinding. The cup-shaped arc grinding wheel has a special shape and is more efficient when used to process spherical surfaces. Therefore, it is widely used in spherical grinding. In addition, spherical grinding generally plays a role in the process of rapidly removing a large amount of material in the manufacturing process of non-spherical surfaces. It is widely used, and it can also complete the compensation of tool setting errors in spherical grinding.

[0003] At present, the precision requirements for optical components in aerospace and advanced instruments are becoming more and more stringent, but the current spherical grinding method cannot achieve high-precision and high-efficiency processing. The existing spherical forming method has low processing efficiency, and the accuracy of the spherical radius is limited due to the control accuracy of tool setting and tool wear. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a method for grinding a spherical surface and compensating an error of a grinding wheel based on a spindle swinging machine tool, which improves processing consistency and stability, and improves precision and tool durability.

[0005] The present invention is achieved through the following technical solutions: The method of grinding spherical surface and error compensation based on a grinding wheel of a spindle swinging machine tool includes: S1, obtaining various dimensions and process parameters required for grinding the spherical surface, and establishing the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool; S2, based on the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool, by controlling the swing angle of the spindle swing axis to change continuously during the grinding process, the workpiece to be processed is ground into a spherical workpiece through the abrasive area of ​​the grinding wheel; the processing types of the spherical workpiece include convex spherical surface and concave spherical surface; S3, after the processing is completed, the position error of the grinding wheel is calculated by detecting the radius of the ground spherical workpiece and the size of the circular protrusion in the central area of ​​the spherical workpiece; S4, according to the position error of the grinding wheel, compensate and adjust the processing position of the grinding wheel, change the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool, and re-process the spherical workpiece, thereby realizing the error compensation of the spherical workpiece during the grinding process.

[0006] Preferably, the dimensions and process parameters required for grinding the spherical surface in S1 include: the diameter of the workpiece to be processed and height , the center thickness of the spherical workpiece to be processed and the spherical radius , the distance between the center of the spherical workpiece and the bottom surface , the speed at which the radius of the spherical workpiece decreases during grinding , the median diameter of the grinding wheel and length , the small arc radius of the abrasive area of ​​the arc grinding wheel , The length from the grinding wheel installation position to the B-axis center of the spindle swing type machine tool .

[0007] Preferably, in S1, the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool is established, specifically: When machining a convex spherical surface, the X-axis position of the spindle swing type machine tool , Z-axis position With B axis position Relative to time The position change relationship is:

[0008]

[0009]

[0010] When machining a concave spherical surface, the X-axis position of the spindle swing type machine tool , Z-axis position With B axis position Relative to time The position change relationship is:

[0011]

[0012]

[0013] Where: The X-axis position of the spindle swing machine tool, The Z-axis position of the spindle swing machine tool, The B-axis swing angle position of the spindle swing type machine tool; is the grinding wheel length, It is the distance from the grinding wheel installation position to the B-axis center of the spindle swing type machine tool; is the radius of the enveloping sphere formed by the section circle of the end face of the grinding wheel rotating at the initial grinding position and the rotation of the workpiece to be processed, is the speed at which the radius of the spherical workpiece decreases during the grinding process, For grinding time, is the median diameter of the grinding wheel, is the small arc radius of the abrasive area of ​​the grinding wheel, Among them, the X-axis and Z-axis are linear axes, and the B-axis is a swing axis.

[0014] Preferably, when machining a convex spherical surface, the radius of the enveloping spherical surface is The specific calculation formula is:

[0015] Where: The distance between the center of the spherical workpiece and the bottom surface to be machined. is the height of the workpiece to be processed, is the diameter of the workpiece to be processed; When machining a concave spherical surface, the radius of the enveloping sphere The specific calculation formula is:

[0016] Where: is the center thickness of the spherical workpiece to be machined, is the spherical radius of the spherical workpiece to be processed, is the height of the workpiece to be processed.

[0017] Preferably, the position error of the grinding wheel is calculated in S3, specifically: For the convex spherical surface, calculate the position error of the grinding wheel. The specific calculation formula is:

[0018]

[0019] For the concave spherical surface, calculate the position error of the grinding wheel. The specific calculation formula is:

[0020]

[0021] Where: is the distance that the arc center of the grinding wheel deviates from the ideal position in the horizontal X direction, The distance that the arc center of the grinding wheel deviates from the ideal position in the vertical Z direction; is the radius of the spherical workpiece after grinding, is the radius of the circular protrusion in the central area of ​​the spherical workpiece; is the small arc radius of the abrasive area of ​​the grinding wheel, is the spherical radius of the spherical workpiece to be machined.

[0022] Preferably, when the spherical workpiece to be machined is a convex spherical surface, the median diameter of the grinding wheel should meet the following conditions: ; When machining a concave spherical workpiece, the median diameter of the grinding wheel should meet the following conditions: ; Where: is the center thickness of the spherical workpiece, is the spherical radius of the spherical workpiece, is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel, It is the angle between the line from the edge of the spherical workpiece to the center of the sphere and the axis. It is the middle diameter of the cup-shaped arc grinding wheel.

[0023] Preferably, when the spherical workpiece is a convex spherical surface, the cup depth of the grinding wheel is Should meet: , ( ) , ( ) Where: is the spherical radius of the spherical workpiece, is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel, It is the angle between the line from the edge of the spherical workpiece to the center of the sphere and the axis. is the median diameter of the cup-shaped arc grinding wheel, It is the spindle swing angle after machining is completed.

[0024] Preferably, at the initial processing position, the axis of the grinding wheel and the axis of the workpiece to be processed are at an angle of , that is, the spindle swing angle is The machining surface of the grinding wheel is in point contact with the end face of the workpiece to be machined; at the end of machining, the workpiece to be machined has been ground into a spherical workpiece, and there is an angle between the axis of the grinding wheel and the axis of the spherical workpiece. , that is, the spindle swing angle is , the machining surface of the grinding wheel and the spherical surface of the spherical workpiece are in line contact.

[0025] Preferably, the grinding wheel is a cup-shaped arc grinding wheel, and the workpiece to be processed is a cylindrical structure.

[0026] A spindle swing type machine tool, a method for grinding a spherical surface and compensating an error based on a grinding wheel of the spindle swing type machine tool, using the spindle swing type machine tool for processing, comprising: The workpiece to be processed is mounted on the rotating platform of the spindle swing machine tool, and the grinding wheel is mounted on the swing head of the spindle swing machine tool. The workpiece to be processed only rotates around its own axis. The grinding wheel forms a cut-circle grinding area on the end face due to the rotation. The cut-circle grinding area is combined with the rotational motion of the workpiece to be processed to form an enveloping spherical grinding area. The motion of the swing head is a synthetic motion trajectory of the translation in the XOZ plane and the rotation around the B axis. The workpiece to be processed is ground to obtain a spherical workpiece.

[0027] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention provides a method for grinding a spherical surface with a cup-shaped arc grinding wheel. By controlling the motion trajectory of the workpiece and the cup-shaped arc grinding wheel during the machining process, an envelope trajectory is implemented to remove material from the workpiece. In any radial direction, the amount of material removed is uniform, and the envelope spherical surface gradually approaches the required spherical surface with the same spherical center, so that each contact position in the machining process is subjected to uniform force and the workpiece material is uniformly removed, thereby improving the machining consistency and stability, and improving the accuracy and tool durability.

[0028] Furthermore, by detecting the radius of the circular protrusion in the center area of ​​the spherical workpiece after machining, and the actual spherical radius The grinding wheel position error is calculated and compensated to reduce the error impact and improve machining accuracy.

[0029] Furthermore, the method proposed by the present invention can use grinding wheels of various size ranges to process spherical surfaces of various size ranges. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a front view of the grinding installation of the CNC machine tool of the present invention; Figure 2 It is an oblique survey drawing of the grinding installation of the numerically controlled machine tool of the present invention; Figure 3 It is a schematic diagram of convex spherical surface grinding process; Figure 4 It is a schematic diagram of the convex spherical surface enveloping the spherical surface error; Figure 5 It is a schematic diagram of machining error of convex spherical surface; Figure 6 It is a schematic diagram of concave spherical surface grinding; Figure 7 It is a schematic diagram of the spherical surface error of the concave spherical surface enveloping the spherical surface; Figure 8 It is a schematic diagram of machining error of concave spherical surface; Fig. 9 It is a schematic diagram of the minimum tool radius of a convex spherical surface; Fig.10 This is a schematic diagram of the depth requirements for cup arc grinding wheels; Fig.11 It is a schematic diagram of the minimum tool radius of a concave spherical surface; In the attached drawings, 1 is the Y-axis moving platform; 2 is the Z-axis moving platform; 3 is the main shaft; 4 is the turntable seat; 5 is the turntable; 6 is the workpiece; 7 is the cup-shaped circular arc grinding wheel; and 8 is the X-axis moving platform. DETAILED DESCRIPTION

[0031] The present invention is further described in detail below in conjunction with specific embodiments, which are intended to explain the present invention rather than to limit it.

[0032] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0033] The method for grinding a spherical surface and compensating an error of a grinding wheel based on a spindle swinging machine tool is characterized in that the spherical surface grinding is realized by using a cup-shaped arc grinding wheel according to the linkage trajectory of two linear axes and a spindle swinging axis, a total of three axes, and the uniformity and consistency of material removal are realized by controlling the swing angle of the spindle swinging axis to change continuously during the grinding process. The position error of the cup-shaped arc grinding wheel is calculated by detecting the radius of the spherical workpiece after grinding and the size of the circular protrusion in the central area of ​​the spherical workpiece, and the linkage trajectory is changed to realize the grinding error compensation. Specifically, the following steps are included: Step 1) Before grinding, obtain the dimensions and process parameters required for grinding the spherical surface, including: the diameter of the cylindrical blank to be processed and height , the center thickness of the spherical workpiece to be processed and the spherical radius , the distance between the center of the spherical workpiece to be processed and the bottom surface of the workpiece , the speed at which the radius of the spherical workpiece decreases during grinding , the middle diameter of the cup-shaped arc grinding wheel and length (excluding arcs) The radius of the small arc in the abrasive area of ​​the cup-shaped arc grinding wheel is , The length of the cup arc grinding wheel installation position from the center of the B axis Based on the above parameters, the spindle motion trajectory of the spindle swing machine tool is derived, that is, the X-axis position , Z-axis position With B axis position Relative to time In the composition of the machine tool, when a person and the machine tool are face to face, the part that moves left and right on the machine tool is the X-axis, the part that moves forward and backward is the Y-axis, the part that moves up and down is the Z-axis, and the spindle swing axis is the B-axis, which is a rotating axis, and its axis is parallel to the Y-axis.

[0034] For a convex spherical surface, the X-axis position , Z-axis position With B axis position Relative to time The position change relationship is:

[0035]

[0036]

[0037] in, and The formula contains The term is to simplify the formula. It is derived from the dimensions and process parameters obtained above and is used to simplify the formula. The physical meaning is that the radius of the enveloping sphere formed by the self-rotation of the end face of the cup-shaped arc grinding wheel and the self-rotation of the cylindrical blank at the initial grinding position is , Calculated by the following formula:

[0038] For a concave spherical surface, the X-axis position , Z-axis position With B axis position Relative to time The position change relationship is:

[0039]

[0040]

[0041] in, and The formula contains The term is to simplify the formula. It is derived from the dimensions and process parameters obtained above and is used to simplify the formula. The physical meaning is that the radius of the enveloping sphere formed by the self-rotation of the end face of the cup-shaped arc grinding wheel and the self-rotation of the cylindrical blank at the initial grinding position is , Calculated by the following formula:

[0042] Step 2), install the cylindrical blank to be processed on the rotating platform. The cylindrical blank remains horizontal during the grinding process and only rotates around its own axis. The cup-shaped arc grinding wheel is installed on the machine tool spindle with a swing head, and its rotation forms a truncated circular grinding area. The linear axis and the swing axis move according to the trajectory in step 1. The swing angle of the spindle swing axis changes continuously during the grinding process. The abrasive area of ​​the grinding wheel contacts the cylindrical blank, and the end face of the cylindrical blank is ground into a spherical surface.

[0043] Step 3) After one processing is completed, measure the surface accuracy of the spherical workpiece and measure the spherical error, including the radius of the spherical workpiece after grinding. The radius of the circular protrusion in the center area of ​​the spherical workpiece , calculate the position error of the cup arc grinding wheel and , respectively compensated and The linkage trajectory is adjusted, the machining trajectory is recalculated, and the machining is performed again until the surface error of the spherical workpiece is within the allowable range and the machining is completed. The cup-shaped arc grinding wheel position error refers to the distance that the arc center of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal X direction and the vertical Z direction respectively. , ,cause and There are many reasons for this, including tool setting error, grinding wheel wear error, grinding wheel manufacturing error, etc.

[0044] For a convex sphere, and Calculated by the following formula:

[0045]

[0046] For a concave sphere, and Calculated by the following formula:

[0047]

[0048] Furthermore, the trajectory model and method of spherical grinding using a spindle swinging five-axis machine tool and a cup-shaped arc grinding wheel were derived and calculated. In the processing using the spindle swinging five-axis machine tool, the blank on the rotating platform only rotates around its own axis, and the cup-shaped arc grinding wheel on the swing head forms a truncated circular grinding area on the end face due to the rotation. The truncated circular grinding area and the rotational motion of the blank are combined to form an enveloping spherical grinding area. The movement of the swing head is synthesized by the translation in the XOZ plane and the rotation around the B axis. The synthetic motion trajectory causes the enveloping spherical surface to shrink or expand relative to the blank. During the grinding process, the blank material is continuously removed with the enveloping spherical surface as the boundary until the swing head swings a certain angle, and the end face of the original cylindrical blank becomes a spherical surface, and the processing is completed.

[0049] Furthermore, at the initial processing position, the axis of the cup-shaped arc grinding wheel and the axis of the cylindrical blank are at an angle of , that is, the spindle swing angle is The machining surface of the cup-shaped arc grinding wheel is in point contact with the end face of the cylindrical blank; at the end of the machining, the cylindrical blank has been ground into a spherical workpiece, and there is an angle between the axis of the cup-shaped arc grinding wheel and the axis of the spherical workpiece. , that is, the spindle swing angle is The machining surface of the cup-shaped arc grinding wheel is in line contact with the spherical surface of the spherical workpiece.

[0050] Furthermore, in the cross section passing through the XOZ plane, the center of the small arc of the abrasive grain area of ​​the cup-shaped arc grinding wheel is always on the axis of the workpiece.

[0051] Furthermore, during the machining process, the radius of the envelope sphere decreases or increases uniformly with time at a speed f. At any time and at any position on the envelope sphere, the material removal method is to shrink or expand toward the workpiece with the envelope sphere as the boundary. In any radial direction, the thickness of the removed material is uniform, so as to reduce the excessive grinding force of the grinding wheel or the workpiece, which may cause wear on the tool or damage to the workpiece.

[0052] Furthermore, the relationship model between the spherical surface error and the position error of the cup-shaped arc grinding wheel is established, and the actual spherical workpiece radius is detected. and the radius of the circular protrusion in the center area of ​​the spherical workpiece Calculate position error and And compensate.

[0053] Furthermore, the spherical surface formed by grinding can be a convex spherical surface or a concave spherical surface.

[0054] Furthermore, for the center thickness after processing The radius of the sphere is , the angle between the line from the edge of the sphere to the center of the sphere and the axis is For spherical workpieces, the allowable cup-shaped arc grinding wheel should have a mean diameter that meets , where the convex spherical surface is "+" and the concave spherical surface is "-"; when machining the convex spherical surface, the cup depth of the cup-shaped arc grinding wheel allowed to be used should meet , ( ) , ( ) Furthermore, the grinding process uses a five-axis machine tool with a swinging spindle, in which the workpiece does not move and the cup-shaped arc grinding wheel performs translation and swing.

[0055] Example 1 The present invention discloses a method for grinding a spherical surface with a cup-shaped arc grinding wheel in a circular section. In one grinding process, the workpiece rotates around its own axis on the XOZ plane, and the cup-shaped arc grinding wheel is linked with the main shaft in the XOZ plane. At the same time, the main shaft drives the cup-shaped arc grinding wheel to rotate. The two rotational movements together form an envelope spherical surface. The linkage movement of the B-axis swing head causes the envelope spherical surface to shrink toward the center of the sphere. During the grinding process, the workpiece material is continuously removed with the envelope spherical surface as the boundary. During the processing, the radius of the envelope spherical surface is controlled by the speed. f The material removal direction decreases evenly over time, and the material removal direction points to the center of the sphere along the radius direction. The thickness of the material removal is uniform until a certain period of time later, the end face of the original cylindrical blank becomes a spherical surface, and the spherical surface radius is the required radius. After the grinding process is completed, the spherical surface error is detected. According to the established relationship model between the spherical surface error and the position error of the cup-shaped arc grinding wheel, the actual spherical workpiece radius is detected. and the radius of the circular protrusion in the center area of ​​the spherical workpiece Calculate position error and And compensate, and process again with the compensated trajectory until the size meets the requirement; like Figure 1 to Figure 2 As shown, the present invention adopts a spindle swinging five-axis CNC machine tool, which can realize XYZ three-way movement, as well as B-axis swing around the Y direction and rotation around the Z direction; specifically, it includes a Y-axis moving platform, a Z-axis moving platform, a spindle, a turntable and an X-axis moving platform, the spindle can swing around the Y direction, and the turntable can rotate around the Z direction.

[0056] The specific steps include: Step 1), such as Figure 1 , Figure 2 As shown in the figure, the cylindrical blank to be processed is installed on the turntable, the cup-shaped arc grinding wheel is installed on the spindle, and the tool is set according to the installation size of the grinding wheel and the installation size of the workpiece. Set each axis to move to the initial position, set the turntable speed and spindle speed, and enter the motion parameters and grinding time of the XYZ axis and B axis. t, the spherical surface is processed by the envelope trajectory. After time t, the B axis swings to an angle , the cylindrical blank is processed into a spherical workpiece, completing the spherical surface processing.

[0057] The cup-shaped arc grinding wheel has a median diameter of , the length (excluding arc) is , the small arc radius of the end surface abrasive area is , installed at a length of The grinding wheel installation position is on the spindle of the B axis. .

[0058] The cylindrical blank is as follows Figure 3 As shown, the diameter of the cylindrical blank to be processed is , the height is The center thickness of the convex spherical workpiece to be machined is The radius of the sphere is , the angle between the line from the edge of the sphere to the center of the sphere and the axis is , After the blank is installed on the turntable, the distance between the bottom surface of the blank and the center of the ball is ,in:

[0059] The initial position is as follows Figure 3 As shown, in the XOZ plane, with the center of the bottom of the workpiece as the origin, the center coordinate of the B axis at any time is At any time, the radius of the envelope sphere formed by the rotation of the cup-shaped arc grinding wheel and the blank is R At the initial position, the radius of the envelope sphere is , and the spherical surface formed after processing has the same center, satisfying:

[0060] The swing angle of B axis is :

[0061] Relative to the center of the bottom surface of the blank, the initial coordinate of the B-axis center is ( ):

[0062]

[0063] like Figure 3 As shown in the figure, after the processing is completed, the radius of the envelope sphere is , the swing angle of B axis is ,

[0064] During the machining process, the radius of the envelope sphere is controlled to decrease uniformly over time. Reduce to Time , then the speed at which the radius decreases is:

[0065] The radius of the enveloping sphere at any time t R for:

[0066] At any time, the B-axis swing angle satisfy:

[0067] Combining equations (4), (5), (8), and (9), we can obtain the motion trajectory of the spindle relative to the center of the bottom surface of the blank as follows:

[0068]

[0069]

[0070] Step 2) After one processing is completed, measure the surface accuracy of the spherical workpiece and measure the spherical error, including the radius of the spherical workpiece after grinding. The radius of the circular protrusion in the center area of ​​the spherical workpiece , calculate the position error of the cup arc grinding wheel and , respectively compensated and And adjust the linkage trajectory, recalculate the processing trajectory and process again. like Figure 4 As shown in Figure 2, when there is a position error in the cup-shaped arc grinding wheel, the arc center of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal X direction and the vertical Z direction in the XOZ plane. , Deviations in both directions lead to changes in the radius of the envelope sphere, which ultimately affects the actual radius of the processed sphere. and There are many reasons for this, including tool setting error, grinding wheel wear error, grinding wheel manufacturing error, etc.

[0071] Combination Figure 4 , the cup-shaped arc grinding wheel has position error , When , the radius of the enveloping sphere becomes The angle between the axis of the cup-shaped arc grinding wheel and the line connecting the center of the cup-shaped arc grinding wheel to the center of the enveloping sphere becomes , position error , satisfy:

[0072]

[0073] like Figure 5 As shown, the cup-shaped arc grinding wheel has an error , When , a circular protrusion will appear in the center of the sphere, and the radius of the circular protrusion is The height of the entire convex spherical workpiece is becomes .

[0074] according to Figure 5 As shown, the radius of the circular protrusion in the center area of ​​the spherical workpiece is :

[0075] Combining equation (13) and equation (15), we can get:

[0076] Combining equation (14) and equation (15), we can get:

[0077] Combined with step 2), detect the actual spherical radius after processing and the radius of the circular protrusion in the center area of ​​the convex spherical workpiece , calculated by formula (16) , calculated by formula (17) ,Will and The machining trajectory shown in equations (10) and (11) is compensated until the surface error of the spherical workpiece is within the allowable range and the machining is completed.

[0078] For the concave spherical surface, combine step 1) and step 2), similarly, the cylindrical blank is as follows Figure 6 As shown, the diameter of the cylindrical blank to be processed is , the height is , the center thickness of the spherical workpiece after processing is The radius of the sphere is After the blank is installed on the turntable, the distance between the bottom surface of the blank and the center of the ball is .

[0079] The initial position is Figure 6 As shown, the B-axis swing angle The cup-shaped arc grinding wheel forms a circular grinding motion on the end face due to its rotation. The circular grinding motion and the rotation motion of the workpiece form an enveloping sphere. The initial enveloping sphere radius is ,satisfy:

[0080]

[0081] Relative to the center point O of the bottom surface of the blank, the initial coordinates of the center of the B axis are ( ):

[0082]

[0083] After processing, the radius of the envelope sphere is , the swing angle of B axis is ,

[0084] During the processing, the radius of the envelope sphere is controlled from Increases uniformly over time The speed at which the radius increases is , we can get the motion trajectory of the spindle relative to the center of the bottom surface of the blank as:

[0085]

[0086]

[0087] like Figure 7 As shown in Figure 2, when there is a position error in the cup-shaped arc grinding wheel, the arc center of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal X direction and the vertical Z direction in the XOZ plane. , Deviations in both directions lead to changes in the radius of the envelope sphere, which ultimately affects the actual radius of the processed sphere. and There are many reasons for this, including tool setting error, grinding wheel wear error, grinding wheel manufacturing error, etc.

[0088] Combination Figure 7 , the cup-shaped arc grinding wheel has position error , When , the radius of the enveloping sphere becomes The angle between the axis of the cup-shaped arc grinding wheel and the line connecting the center of the cup-shaped arc grinding wheel to the center of the enveloping sphere becomes ,size , satisfy:

[0089]

[0090] like Figure 8 As shown, the cup-shaped arc grinding wheel has position error , When grinding, a circular protrusion will appear in the center of the spherical surface, and the radius of the circular protrusion is , the center thickness of the concave spherical workpiece is becomes .

[0091] according to Figure 8 As shown, the radius of the circular protrusion in the center area of ​​the spherical workpiece is :

[0092] Combining equation (26) and equation (28), we can get:

[0093] Combining equation (27) and equation (28), we can get:

[0094] Combined with step 2), detect the actual spherical radius after processing and the radius of the circular protrusion in the center area of ​​the convex spherical workpiece , calculated by formula (29) , calculated by formula (30) ,Will and Compensate the machining trajectory shown in equations (23) and (24) until the surface error of the spherical workpiece is within the allowable range and the machining is completed.

[0095] The method proposed in this paper can use cup-shaped arc grinding wheels of various size ranges to machine spherical surfaces of various size ranges, such as Fig. 9 As shown, after the convex spherical surface is processed according to the method of the present invention, the cup-shaped arc grinding wheel with the smallest allowable diameter should satisfy that its end grinding surface just contacts the spherical edge of the workpiece. ,at this time:

[0096] After the convex spherical surface is processed according to the method of the present invention, the inner diameter of the cup-shaped arc grinding wheel with the largest allowable diameter is exactly equal to the spherical surface, and the cup-shaped arc grinding wheel can just accommodate half of the spherical surface. At this time:

[0097] like Fig.10 As shown, after the convex spherical surface is processed according to the method of the present invention, the depth of the cup-shaped arc grinding wheel should meet the requirements of accommodating the workpiece. , then the bottom of the cup does not touch the workpiece:

[0098] like , then the bottom of the cup does not touch the sphere:

[0099] Similar, such as Fig.11 As shown, after the concave spherical surface is processed according to the method of the present invention, the cup-shaped arc grinding wheel with the smallest allowable diameter should satisfy that its end grinding surface just contacts the spherical edge of the workpiece. ,at this time:

[0100] After the concave spherical surface is processed according to the method of the present invention, the outer diameter of the cup-shaped arc grinding wheel with the largest allowable diameter is exactly equal to the spherical surface. At this time:

[0101] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any ordinary technician in the industry can smoothly implement the present invention as shown in the drawings and described above. However, any equivalent changes, modifications and evolutions made by technicians familiar with the profession without departing from the scope of the technical solution of the present invention using the technical content disclosed above are all equivalent embodiments of the present invention. At the same time, any equivalent changes, modifications and evolutions made to the above embodiments based on the essential technology of the present invention are still within the protection scope of the technical solution of the present invention.

Claims

1. A method for grinding a spherical surface and compensating an error of a grinding wheel based on a spindle swinging machine tool, characterized in that: include, S1, obtaining various dimensions and process parameters required for grinding the spherical surface, and establishing the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool; S2, based on the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool, by controlling the swing angle of the spindle swing axis to change continuously during the grinding process, the workpiece to be processed is ground into a spherical workpiece through the abrasive area of ​​the grinding wheel; the processing types of the spherical workpiece include convex spherical surface and concave spherical surface; S3, after the processing is completed, the position error of the grinding wheel is calculated by detecting the radius of the ground spherical workpiece and the size of the circular protrusion in the central area of ​​the spherical workpiece; S4, according to the position error of the grinding wheel, compensate and adjust the processing position of the grinding wheel, change the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing type machine tool, and re-process the spherical workpiece, thereby realizing the error compensation of the spherical workpiece during the grinding process.

2. The method for grinding a spherical surface and compensating an error by a grinding wheel based on a spindle swinging machine tool according to claim 1, characterized in that: The dimensions and process parameters required for grinding the spherical surface in S1 include: the diameter of the workpiece to be processed and height , the center thickness of the spherical workpiece to be processed and the spherical radius , the distance between the center of the spherical workpiece and the bottom surface , the speed at which the radius of the spherical workpiece decreases during grinding , the median diameter of the grinding wheel and length , the small arc radius of the abrasive area of ​​the arc grinding wheel , The length from the grinding wheel installation position to the B-axis center of the spindle swing type machine tool .

3. The method for grinding a spherical surface and compensating an error by a grinding wheel based on a spindle swinging machine tool according to claim 1, characterized in that: In S1, the linear axis and the spindle swing axis linkage motion trajectory of the spindle swing type machine tool are established, specifically: When machining a convex spherical surface, the X-axis position of the spindle swing type machine tool , Z-axis position With B axis position Relative to time The position change relationship is: When machining a concave spherical surface, the X-axis position of the spindle swing type machine tool , Z-axis position With B axis position Relative to time The position change relationship is: Where: The X-axis position of the spindle swing machine tool, The Z-axis position of the spindle swing machine tool, The B-axis swing angle position of the spindle swing type machine tool; is the grinding wheel length, It is the distance from the grinding wheel installation position to the B-axis center of the spindle swing type machine tool; is the radius of the enveloping sphere formed by the section circle of the end face of the grinding wheel rotating at the initial grinding position and the rotation of the workpiece to be processed, is the speed at which the radius of the spherical workpiece decreases during the grinding process, For grinding time, is the median diameter of the grinding wheel, It is the small arc radius of the abrasive area of ​​the grinding wheel.

4. The method for grinding a spherical surface and compensating an error by a grinding wheel based on a spindle swinging machine tool according to claim 3, characterized in that: When machining a convex spherical surface, the radius of the enveloping spherical surface The specific calculation formula is: ； Where: The distance between the center of the spherical workpiece and the bottom surface to be machined. is the height of the workpiece to be processed, is the diameter of the workpiece to be processed; When machining a concave spherical surface, the radius of the enveloping sphere The specific calculation formula is: ； Where: is the center thickness of the spherical workpiece to be machined, is the spherical radius of the spherical workpiece to be processed, is the height of the workpiece to be processed.

5. The method for grinding a spherical surface and compensating an error by a grinding wheel based on a spindle swinging machine tool according to claim 1, characterized in that: The position error of the grinding wheel is calculated in S3, specifically: For the convex spherical surface, calculate the position error of the grinding wheel. The specific calculation formula is: ； For the concave spherical surface, calculate the position error of the grinding wheel. The specific calculation formula is: Where: is the distance that the arc center of the grinding wheel deviates from the ideal position in the horizontal X direction, The distance that the arc center of the grinding wheel deviates from the ideal position in the vertical Z direction; is the radius of the spherical workpiece after grinding, is the radius of the circular protrusion in the central area of ​​the spherical workpiece; is the small arc radius of the abrasive area of ​​the grinding wheel, is the spherical radius of the spherical workpiece to be machined.

6. The method for grinding a spherical surface with a cup-shaped arc grinding wheel and compensating for errors according to claim 1, characterized in that: When machining a convex spherical workpiece, the median diameter of the grinding wheel should meet the following conditions: ； When machining a concave spherical workpiece, the median diameter of the grinding wheel should meet the following conditions: ； Where: is the center thickness of the spherical workpiece, is the spherical radius of the spherical workpiece, is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel, It is the angle between the line from the edge of the spherical workpiece to the center of the sphere and the axis. It is the middle diameter of the cup-shaped arc grinding wheel.

7. The method for grinding a spherical surface with a cup-shaped arc grinding wheel and compensating for errors according to claim 1, characterized in that: When machining a convex spherical workpiece, the cup depth of the grinding wheel Should meet: ，( ) ，( )； Where: is the spherical radius of the spherical workpiece, is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel, It is the angle between the line from the edge of the spherical workpiece to the center of the sphere and the axis. is the median diameter of the cup-shaped arc grinding wheel, It is the spindle swing angle after machining is completed.

8. The method for grinding a spherical surface and compensating an error by a grinding wheel based on a spindle swinging machine tool according to claim 1, characterized in that: At the initial processing position, there is an angle between the axis of the grinding wheel and the axis of the workpiece to be processed. , that is, the spindle swing angle is The machining surface of the grinding wheel is in point contact with the end face of the workpiece to be machined; at the end of machining, the workpiece to be machined has been ground into a spherical workpiece, and there is an angle between the axis of the grinding wheel and the axis of the spherical workpiece. , that is, the spindle swing angle is , the machining surface of the grinding wheel and the spherical surface of the spherical workpiece are in line contact.

9. The method for grinding a spherical surface and compensating an error by a grinding wheel based on a spindle swinging machine tool according to claim 1, characterized in that: The grinding wheel is a cup-shaped circular arc grinding wheel, and the workpiece to be processed is a cylindrical structure.

10. A spindle swing type machine tool, based on the method for grinding a spherical surface and compensating an error of a grinding wheel based on a spindle swing type machine tool according to any one of claims 1 to 9, characterized in that: include, The workpiece to be processed is mounted on the rotating platform of the spindle swing machine tool, and the grinding wheel is mounted on the swing head of the spindle swing machine tool. The workpiece to be processed only rotates around its own axis. The grinding wheel forms a cut-circle grinding area on the end face due to the rotation. The cut-circle grinding area is combined with the rotational motion of the workpiece to be processed to form an enveloping spherical grinding area. The motion of the swing head is a synthetic motion trajectory of the translation in the XOZ plane and the rotation around the B axis. The workpiece to be processed is ground to obtain a spherical workpiece.

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