Cup-shaped arc grinding wheel spherical surface grinding and error compensation method based on cradle type five-axis machine tool

Abstract

The invention discloses a cup-shaped arc grinding wheel spherical surface grinding and error compensation method based on a cradle type five-axis machine tool, which comprises the following steps of: acquiring various sizes and process parameters required by spherical surface grinding, and acquiring a motion track of a workpiece grinding spherical surface; based on a cradle type five-axis machine tool, according to the motion trail of the workpiece grinding spherical surface, the end face of the to-be-machined workpiece is ground into a spherical workpiece through a cup-shaped arc grinding wheel; after machining is finished, the surface shape precision of the spherical workpiece is detected, and the surface shape error of the spherical workpiece is measured, so that the position error of the cup-shaped arc grinding wheel is calculated, the machining position of the cup-shaped arc grinding wheel is compensated and adjusted, the movement track of the grinding spherical surface of the workpiece is calculated again, and machining is conducted again till the surface shape error of the spherical workpiece is within the allowable range. The spherical surface machining efficiency is improved, the spherical surface radius precision is improved, and the problem that the tool setting abrasion control precision is limited is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of precision machining, and relates to a method for grinding a spherical surface with a cup-shaped arc grinding wheel and compensating for errors based on a cradle-type five-axis 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 error 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 for errors using a cup-shaped arc grinding wheel based on a cradle-type five-axis machine tool, which improves the spherical surface processing efficiency, improves the accuracy of the spherical surface radius and solves the problem of limited tool wear control accuracy.

[0005] The present invention is achieved through the following technical solutions: A method for grinding a spherical surface with a cup-shaped arc grinding wheel and compensating for errors comprises the following steps: S1, obtaining various dimensions and process parameters required for grinding the spherical surface, and obtaining the motion trajectory of the workpiece grinding spherical surface; S2, based on a cradle-type five-axis machine tool, according to the motion trajectory of the workpiece grinding the spherical surface, the workpiece to be processed changes with the swing angle of the cradle axis of the cradle-type five-axis machine tool, and the end surface of the workpiece to be processed is ground into a spherical workpiece by a cup-shaped arc grinding wheel; the processing types of the spherical workpiece include convex spherical surface and concave spherical surface; S3, after the processing is completed, the surface accuracy of the spherical workpiece is detected, and the surface error of the spherical workpiece is measured, so as to calculate the position error of the cup-shaped circular arc grinding wheel; S4, according to the position compensation amount of the cup-shaped arc grinding wheel, compensate and adjust the processing position of the cup-shaped arc grinding wheel, recalculate the motion trajectory of the workpiece grinding the spherical surface, and re-process the spherical workpiece until the surface error of the spherical workpiece is within the allowable range and the processing is completed.

[0006] Preferably, various dimensions and process parameters required for grinding the spherical surface are obtained in S1, specifically including: 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 cradle swing center and the bottom surface of the workpiece to be processed when the workpiece is mounted on a cradle-type five-axis machine tool , the distance between the swing center of the cradle axis and the center of the spherical workpiece to be processed , the speed at which the radius of the spherical workpiece decreases during grinding , the middle diameter of the cup-shaped arc grinding wheel and the small arc radius of the abrasive area .

[0007] Preferably, the motion trajectory of the workpiece grinding spherical surface in S1 is specifically: When machining a convex spherical surface, the motion trajectory formula of the workpiece grinding spherical surface is:

[0008]

[0009] ; Where: The radius of the enveloping sphere formed by the section circle of the end face of the cup-shaped arc grinding wheel rotating at the initial grinding position and the rotation of the workpiece to be processed; f The speed at which the radius of a spherical workpiece decreases during grinding; is the median diameter of the cup-shaped arc grinding wheel, It is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel; For grinding time; is the Y-axis position of the cradle-type five-axis machine tool, is the Z-axis position of the cradle-type five-axis machine tool, It is the A-axis position of the cradle-type five-axis machine tool; is the distance between the swing center of the cradle axis and the center of the spherical workpiece; The radius of the enveloping sphere is for: ; Where: is the spherical radius of the spherical workpiece, is the center thickness of the spherical workpiece, is the diameter of the workpiece to be processed; When machining a concave spherical surface, the motion trajectory formula of the workpiece grinding spherical surface is:

[0010]

[0011]

[0012] Where: is the height of the workpiece to be processed, It is the distance between the swing center of the cradle and the bottom surface of the workpiece to be processed when the workpiece to be processed is mounted on the cradle-type five-axis machine tool; is the Y-axis position of the cradle-type five-axis machine tool, is the Z-axis position of the cradle-type five-axis machine tool, It is the A-axis position of the cradle-type five-axis machine tool; The radius of the enveloping sphere formed by the tangent circle of the end face of the cup-shaped arc grinding wheel and the rotation of the workpiece to be machined at the initial grinding position; The radius of the enveloping sphere is for: ; Where: is the spherical radius of the spherical workpiece, is the center thickness of the spherical workpiece, is the height of the workpiece to be processed.

[0013] Preferably, the specific processing process of S2 is: Based on the cradle-type five-axis machine tool, the workpiece to be processed is mounted on a turntable and a cup-shaped circular arc grinding wheel is mounted on a spindle; according to the motion trajectory of the workpiece grinding the spherical surface, the workpiece to be processed swings with the cradle axis of the cradle-type five-axis machine tool and rotates around its own axis, and the spindle drives the cup-shaped circular arc grinding wheel to rotate to form a truncated circular grinding area. The swing angle of the cradle axis changes continuously during the grinding process, and contacts the workpiece to be processed through the grinding area of ​​the grinding wheel, and grinds the end face of the workpiece to be processed into a spherical workpiece.

[0014] Preferably, during the machining process, the tangent circle of the end face of the cup-shaped arc grinding wheel at the initial grinding position and the rotation of the workpiece to be machined form an enveloping sphere, and the radius of the enveloping sphere is At speed f With grinding time tUniformly decrease or increase. At any time and at any position on the envelope sphere, the material removal method shrinks or expands toward the workpiece to be processed with the envelope sphere as the boundary. In any radial direction, the thickness of the removed material is uniform.

[0015] Preferably, the position error of the cup arc grinding wheel in S3 is specifically calculated as follows: When the spherical workpiece is a convex spherical surface, the position error of the cup-shaped arc grinding wheel is calculated as follows:

[0016]

[0017] When the spherical workpiece is a concave spherical surface, the position error of the cup-shaped arc grinding wheel is calculated as follows:

[0018]

[0019] Where: is the distance that the arc center of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal Y direction, is the distance that the arc center of the cup-shaped arc 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 center area of ​​the spherical workpiece, is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel; L is the distance from the center of the cup mouth of the cup-shaped arc grinding wheel to the center of the enveloping sphere.

[0020] Preferably, in S2, at the initial processing position, there is an angle between the axis of the cup-shaped arc grinding wheel and the axis of the workpiece to be processed. , that is, the cradle axis swing angle The grinding area of ​​the cup-shaped circular grinding wheel is in point contact with the end face of the workpiece to be processed; at the end of processing, there is an angle between the axis of the cup-shaped circular grinding wheel and the axis of the workpiece to be processed. , that is, the swing angle of the cradle axis is The grinding area of ​​the cup-shaped arc grinding wheel is in line contact with the spherical surface of the workpiece to be processed.

[0021] Preferably, when the spherical workpiece to be machined is a convex spherical surface, the median diameter of the cup-shaped arc grinding wheel should meet the following conditions: ; When machining a concave spherical workpiece, the center diameter of the cup-shaped arc 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.

[0022] Preferably, when the spherical workpiece is a convex spherical surface, the cup depth of the cup-shaped arc 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 swing angle of the cradle axis after processing.

[0023] A cradle-type five-axis machine tool is used for processing based on the cup-shaped arc grinding wheel truncation type spherical surface grinding and error compensation method.

[0024] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention proposes a method for grinding a spherical surface by a cup-shaped arc grinding wheel and compensating for an error based on a cradle-type five-axis machine tool. By controlling the motion trajectory of the workpiece and the cup-shaped arc grinding wheel during the machining process, an envelope trajectory is used to remove material from the workpiece. In any radial direction, the amount of material removed is uniform, and the envelope sphere gradually approaches the required sphere with the same center of the sphere, 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.

[0025] Furthermore, based on the established relationship model between machining error and grinding wheel tool setting or wear error, the radius of the circular protrusion in the center area of ​​the spherical workpiece after machining is detected. and the actual spherical radius The grinding wheel position error is calculated and compensated to reduce the error impact and improve machining accuracy.

[0026] 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

[0027] Figure 1It is a schematic diagram 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 the convex spherical workpiece size and installation size; Figure 4 It is a schematic diagram of the initial position of the convex spherical surface processing; Figure 5 It is a schematic diagram of the end position of convex spherical surface processing; Figure 6 It is a schematic diagram of the convex spherical surface enveloping the spherical surface error; Figure 7 It is a schematic diagram of machining error of convex spherical surface; Figure 8 It is a schematic diagram of the concave spherical workpiece size and installation size; Fig. 9 It is a schematic diagram of the initial position of the concave spherical surface processing; Fig.10 It is a schematic diagram of the spherical surface error of the concave spherical surface enveloping the spher Fig.11 It is a schematic diagram of machining error of concave spherical surface; Fig.12 It is a schematic diagram of the minimum tool radius of a convex sphere; Fig.13 This is a schematic diagram of the depth requirements for cup arc grinding wheels; Fig.14 It is a schematic diagram of the minimum tool radius of a concave spherical surface; In the attached drawings, 1. Y-axis moving platform; 2. Z-axis moving platform; 3. spindle; 4. cradle; 5. turntable; 6. workpiece; 7. cup-shaped circular arc grinding wheel; 8. X-axis moving platform. DETAILED DESCRIPTION

[0028] 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.

[0029] 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.

[0030] The present invention discloses a method for grinding a spherical surface with a cup-shaped arc grinding wheel and error compensation based on a cradle-type five-axis machine tool. In one grinding process, the workpiece swings on the YOZ plane, and at the same time, the workpiece rotates around its own axis. The cup-shaped arc grinding wheel is linked with the main shaft in the YOZ plane, and at the same time, the main shaft drives the cup-shaped arc grinding wheel to rotate. The two rotational movements together form an envelope sphere, and the spherical radius is the envelope sphere radius. During the processing, the radius of the envelope sphere is 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 requirements.

[0031] Specifically: Figure 1 to Figure 2 As shown, the present invention adopts a cradle-type five-axis machine tool, and the CNC machine tool can realize XYZ three-way movement, as well as swinging around the X direction and rotating around the Z direction; specifically includes a Y-axis moving platform, a Z-axis moving platform, a spindle, a cradle, a turntable and an X-axis moving platform, and the cradle can swing around the X direction; a turntable is installed on the cradle, and the turntable can rotate around the Z direction; spherical grinding is realized by using a cup-shaped arc grinding wheel according to the linkage trajectory of two linear axes and a cradle axis, a total of three axes, and the uniformity and consistency of material removal are realized by controlling the swing angle of the cradle axis to change continuously during the grinding process, and 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 changing the linkage trajectory to realize grinding error compensation. In the composition of the machine tool, when a person and the machine tool are face to face, the part of the machine tool that moves left and right is the X-axis, the part that moves forward and backward is the Y-axis, and the part that moves up and down is the Z-axis. The cradle axis is also called the A-axis, which is a rotating axis, and the axis is parallel to the X-axis; The specific steps include: 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 cradle swing center and the bottom surface of the cylindrical blank when the cylindrical blank is installed on the machine tool , the distance between the cradle swing center and the center of the spherical workpiece to be processed , the speed at which the radius of the spherical workpiece decreases during grinding , the middle diameter of the cup-shaped arc grinding wheel and the small arc radius of the abrasive area According to 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 position change relationship.

[0032] For a convex spherical surface, the Y-axis position , Z-axis position A-axis position Relative to time The position change relationship is:

[0033]

[0034]

[0035] 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:

[0036] For a concave spherical surface, the Y-axis position , Z-axis position A-axis position Relative to time The position change relationship is:

[0037]

[0038]

[0039] 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:

[0040] Step 2), install the cylindrical blank to be processed on the rotating platform. During the grinding process, the cylindrical blank swings with the cradle axis and rotates around its own axis. The cup-shaped arc grinding wheel is installed on the machine tool spindle, and its rotation forms a truncated circular grinding area. The linear axis and the cradle axis move according to the trajectory in step 1. The swing angle of the cradle 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.

[0041] 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 compensate for 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 Y 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.

[0042] For a convex sphere, and Calculated by the following formula:

[0043]

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

[0045]

[0046] Furthermore, the trajectory model and method of grinding spherical surfaces using a cradle-type five-axis machine tool and a cup-shaped circular arc grinding wheel were derived and calculated. In the grinding using a cradle-type five-axis machine tool, the blank is mounted on the turntable and rotates with the turntable, and the grinding wheel is mounted on the spindle and moves horizontally with the spindle. The blank swings on the YOZ plane, and at the same time, the blank rotates around its own axis. The spindle drives the cup-shaped circular arc grinding wheel to rotate. The cup-shaped circular arc grinding wheel forms a truncated circular grinding area on the end face due to rotation. The truncated circular grinding area and the rotation of the blank form a grinding area of ​​the enveloping sphere. The cup-shaped circular arc grinding wheel and the blank are linked in the YOZ plane to complete the formation of the matching sphere. The linked trajectory makes the enveloping sphere shrink or expand to the blank. During the translation of the cup-shaped circular arc grinding wheel, the workpiece material is continuously removed with the enveloping sphere as the boundary until the workpiece swings a certain angle and the end face of the original cylindrical blank becomes a spherical surface.

[0047] 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 cradle swing angle is The abrasive part of the cup-shaped arc grinding wheel is in point contact with the end face of the cylindrical blank; at the end of the processing, 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 cradle swing angle is The abrasive area of ​​the cup-shaped arc grinding wheel is in line contact with the spherical surface of the workpiece.

[0048] Furthermore, in the cross section through the YOZ plane, the center of the small arc of the abrasive region of the cup-shaped arc grinding wheel is always on the axis of the workpiece.

[0049] 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 is removed in a manner that shrinks or expands 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 excessive grinding force of the grinding wheel or the workpiece, resulting in tool wear or damage to the workpiece.

[0050] 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.

[0051] Furthermore, the spherical surface formed by grinding can be a convex spherical surface or a concave spherical surface.

[0052] Furthermore, for the center thickness after grinding 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 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 cradle-type five-axis machine tool, in which the workpiece swings along the cradle axis and the cup-shaped arc grinding wheel remains vertical and moves horizontally.

[0053] Example 1 The specific steps include: Step 1), such as Figure 1 , Figure 2 As shown in the figure, the cylindrical workpiece to be processed is mounted on the turntable, the cup-shaped arc grinding wheel is mounted on the spindle, the tool is set according to the installation size of the grinding wheel and the installation size of the workpiece, each axis is set to move to the initial position, the turntable speed and the spindle speed are set, and the motion parameters and grinding time of the XYZ axis and the cradle axis are input. t , the spherical surface is processed by the envelope trajectory. After time t, the cradle swings to the angle , the cylindrical workpiece to be processed is processed into a spherical workpiece, and the spherical surface processing is completed.

[0054] 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 cradle swing center and the bottom surface of the cylindrical blank when the cylindrical blank is installed on the machine tool , the distance between the cradle swing center and the center of the spherical workpiece to be processed , the speed at which the radius of the spherical workpiece decreases during grinding , the middle diameter of the cup-shaped arc grinding wheel and the small arc radius of the abrasive area Based on the above parameters, the spindle motion trajectory of the cradle-type five-axis machine tool is derived, that is, the Y-axis position , Z-axis position A-axis position Relative to time The position change relationship is: The cup-shaped arc grinding wheel has a median diameter of The arc radius of the end surface grinding part is .

[0055] The cylindrical workpiece to be processed is as follows: Figure 3 As shown, the diameter of the cylindrical workpiece to be processed is , the height is , the thickness of the convex spherical workpiece to be processed 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 swing center of the cradle is , the distance between the cradle swing center and the ball center is .in: The cup-shaped arc grinding wheel has a median diameter of The arc radius of the end surface grinding part is .

[0056] The cylindrical workpiece to be processed is as follows Figure 3 As shown, the diameter of the cylindrical workpiece to be processed is , the height is , the thickness of the convex spherical workpiece to be processed 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 swing center of the cradle is , the distance between the cradle swing center and the ball center is .in:

[0057] The initial position is as follows Figure 4 As shown, in the YOZ plane, with the swing center of the cradle as the origin, the coordinates of the center of the cup-shaped arc grinding wheel at any time are 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:

[0058] The swing angle of the cradle is :

[0059] Relative to the swing center of the cradle, the initial coordinates of the arc center of the cup-shaped arc grinding wheel contact segment are ( ):

[0060]

[0061] like Figure 5 As shown in the figure, after the processing is completed, the radius of the envelope sphere is , the cradle swing angle is ,

[0062] During the processing, the radius of the control envelope surface decreases uniformly over time. Reduce to Time , then the speed at which the radius decreases is:

[0063] The radius of the enveloping sphere at any time t R for:

[0064] At any time, the cradle swing angle satisfy:

[0065] Combining equations (4), (5), (8), and (9), we can obtain the motion trajectory of the arc center of the cup-shaped arc grinding wheel contact segment relative to the cradle swing center:

[0066]

[0067]

[0068] 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.

[0069] like Figure 6 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 Y direction and the vertical Z direction in the YOZ 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.

[0070] Combination Figure 5 Ideally, after machining, the Z-direction distance between the center of the mid-diameter circle of the cup-shaped arc grinding wheel end face and the center of the enveloping sphere is L:

[0071] Combination Figure 6 , the cup-shaped arc grinding wheel has errors , When the machining is completed, the Z-direction distance between the center of the cup-shaped arc grinding wheel and the center of the enveloping sphere becomes , the radius of the enveloping sphere becomes ,

[0072] The angle between the axis of the cup-shaped arc grinding wheel and the line from the center of the cup-shaped arc grinding wheel to the center of the enveloping sphere becomes :

[0073]

[0074] like Figure 7 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 .

[0075] according to Figure 7 As shown, the radius of the circular protrusion in the center area of ​​the spherical workpiece is :

[0076] Combining equation (15) and equation (17), we can get:

[0077] Combining equation (16) and equation (17), we can get:

[0078] 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 (18) , calculated by formula (19) ,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.

[0079] For the concave spherical surface, combine step 1) and step 2), similarly, the cylindrical workpiece to be processed is as follows Fig. 9 As shown, the diameter of the cylindrical workpiece to be processed is , the height is , the thickness of the spherical workpiece after machining 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 swing center of the cradle is .

[0080] The initial position is Fig. 9 As shown, the cradle 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:

[0081]

[0082] Relative to the cradle swing center, the initial coordinates of the arc center of the contact segment of the cup-shaped arc grinding wheel are ( ):

[0083]

[0084] After processing, the radius of the envelope sphere is , the cradle swing angle is ,

[0085] 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 arc center of the cup-shaped arc grinding wheel contact segment relative to the cradle swing center:

[0086]

[0087]

[0088] like Fig.10As 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 Y direction and the vertical Z direction in the YOZ 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.

[0089] The cup-shaped arc grinding wheel has position error , When the machining is completed, the Z-direction distance between the center of the mid-diameter circle of the cup-shaped arc grinding wheel end face and the center of the enveloping sphere becomes , the radius of the enveloping sphere becomes ,

[0090] The angle between the axis of the cup-shaped arc grinding wheel and the line from the center of the arc of the contact segment of the cup-shaped arc grinding wheel to the center of the enveloping sphere becomes :

[0091]

[0092] like Fig.11 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 .

[0093] according to Fig.10 , Fig.11 As shown, the radius of the circular protrusion in the center area of ​​the spherical workpiece is :

[0094] Combining equation (29) and equation (31), we can get:

[0095] Combining equation (30) and equation (31), we can get:

[0096] Combined with step 2), detect the actual spherical radius after processing and the radius of the circular protrusion in the center area of ​​the spherical workpiece , calculated by formula (32) , calculated by formula (33) ,Will and The machining trajectory shown in equations (25) and (26) is compensated until the surface error of the spherical workpiece is within the allowable range and the machining is completed.

[0097] 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.12 As shown, according to the method of the present invention, the convex spherical surface machining is completed, and the cup-shaped arc grinding wheel with the smallest allowable diameter should satisfy that its end grinding surface just contacts with the spherical edge of the workpiece. ,at this time:

[0098] 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:

[0099] like Fig.13 As shown, for the selected radius The cup-shaped arc grinding wheel has a cup depth that matches the radius to accommodate the workpiece. , then the bottom of the cup does not touch the workpiece:

[0100] like , then the bottom of the cup does not touch the sphere:

[0101] Similar, such as Fig.14 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:

[0102] 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:

[0103] 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 with a cup-shaped arc grinding wheel and compensating for errors, characterized in that: The following steps are involved: S1, obtaining various dimensions and process parameters required for grinding the spherical surface, and obtaining the motion trajectory of the workpiece grinding spherical surface; S2, based on a cradle-type five-axis machine tool, according to the motion trajectory of the workpiece grinding the spherical surface, the workpiece to be processed changes with the swing angle of the cradle axis of the cradle-type five-axis machine tool, and the end surface of the workpiece to be processed is ground into a spherical workpiece by a cup-shaped arc grinding wheel; the processing types of the spherical workpiece include convex spherical surface and concave spherical surface; S3, after the processing is completed, the surface accuracy of the spherical workpiece is detected, and the surface error of the spherical workpiece is measured, so as to calculate the position error of the cup-shaped circular arc grinding wheel; S4, according to the position compensation amount of the cup-shaped arc grinding wheel, compensate and adjust the processing position of the cup-shaped arc grinding wheel, recalculate the motion trajectory of the workpiece grinding the spherical surface, and re-process the spherical workpiece until the surface error of the spherical workpiece is within the allowable range and the processing is completed.

2. 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: S1 obtains the dimensions and process parameters required for grinding the spherical surface, including: 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 cradle swing center and the bottom surface of the workpiece to be processed when the workpiece is mounted on a cradle-type five-axis machine tool , the distance between the swing center of the cradle axis and the center of the spherical workpiece to be processed , the speed at which the radius of the spherical workpiece decreases during grinding , the middle diameter of the cup-shaped arc grinding wheel and the small arc radius of the abrasive area .

3. 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: The motion trajectory of the workpiece grinding spherical surface in S1 is specifically: When machining a convex spherical surface, the motion trajectory formula of the workpiece grinding spherical surface is: ； Where: The radius of the enveloping sphere formed by the section circle of the end face of the cup-shaped arc grinding wheel rotating at the initial grinding position and the rotation of the workpiece to be processed; f The speed at which the radius of a spherical workpiece decreases during grinding; is the median diameter of the cup-shaped arc grinding wheel, It is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel; For grinding time; is the Y-axis position of the cradle-type five-axis machine tool, is the Z-axis position of the cradle-type five-axis machine tool, It is the A-axis position of the cradle-type five-axis machine tool; is the distance between the swing center of the cradle axis and the center of the spherical workpiece; The radius of the enveloping sphere is for: ； Where: is the spherical radius of the spherical workpiece, is the center thickness of the spherical workpiece, is the diameter of the workpiece to be processed; When machining a concave spherical surface, the motion trajectory formula of the workpiece grinding spherical surface is: Where: is the height of the workpiece to be processed, It is the distance between the swing center of the cradle and the bottom surface of the workpiece to be processed when the workpiece to be processed is mounted on the cradle-type five-axis machine tool; is the Y-axis position of the cradle-type five-axis machine tool, is the Z-axis position of the cradle-type five-axis machine tool, It is the A-axis position of the cradle-type five-axis machine tool; The radius of the enveloping sphere formed by the tangent circle of the end face of the cup-shaped arc grinding wheel and the rotation of the workpiece to be machined at the initial grinding position; The radius of the enveloping sphere is for: ； Where: is the spherical radius of the spherical workpiece, is the center thickness of the spherical workpiece, is the height of the workpiece to be processed.

4. 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: The specific processing process of S2 is: Based on the cradle-type five-axis machine tool, the workpiece to be processed is mounted on a turntable and a cup-shaped circular arc grinding wheel is mounted on a spindle; according to the motion trajectory of the workpiece grinding the spherical surface, the workpiece to be processed swings with the cradle axis of the cradle-type five-axis machine tool and rotates around its own axis, and the spindle drives the cup-shaped circular arc grinding wheel to rotate to form a truncated circular grinding area. The swing angle of the cradle axis changes continuously during the grinding process, and contacts the workpiece to be processed through the grinding area of ​​the grinding wheel, and grinds the end face of the workpiece to be processed into a spherical workpiece.

5. The method for grinding a spherical surface with a cup-shaped arc grinding wheel and compensating for errors according to claim 4, characterized in that: During the machining process, the section circle of the end face rotation of the cup-shaped arc grinding wheel at the initial grinding position and the rotation of the workpiece to be machined form an enveloping sphere. The radius of the enveloping sphere is At speed f With grinding time t Uniformly decrease or increase. At any time and at any position on the envelope sphere, the material removal method shrinks or expands toward the workpiece to be processed with the envelope sphere as the boundary. In any radial direction, the thickness of the removed material is uniform.

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: The position error of the cup-shaped arc grinding wheel in S3 is calculated as follows: When the spherical workpiece is a convex spherical surface, the position error of the cup-shaped arc grinding wheel is calculated as follows: When the spherical workpiece is a concave spherical surface, the position error of the cup-shaped arc grinding wheel is calculated as follows: Where: is the distance that the arc center of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal Y direction, is the distance that the arc center of the cup-shaped arc 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 center area of ​​the spherical workpiece, is the small arc radius of the abrasive area of ​​the cup-shaped arc grinding wheel; L is the distance from the center of the cup mouth of the cup-shaped arc grinding wheel to the center of the enveloping sphere.

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: In S2, at the initial machining position, there is an angle between the axis of the cup-shaped arc grinding wheel and the axis of the workpiece to be machined. , that is, the cradle axis swing angle The grinding area of ​​the cup-shaped circular arc grinding wheel is in point contact with the end face of the workpiece to be processed; at the end of processing, there is an angle between the axis of the cup-shaped circular arc grinding wheel and the axis of the workpiece to be processed. , that is, the swing angle of the cradle axis is The grinding area of ​​the cup-shaped arc grinding wheel is in line contact with the spherical surface of the workpiece to be processed.

8. 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 center diameter of the cup-shaped arc grinding wheel should meet the following conditions: ； When machining a concave spherical workpiece, the center diameter of the cup-shaped arc 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.

9. 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 cup-shaped arc 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 swing angle of the cradle axis after processing.

10. A cradle-type five-axis machine tool, characterized in that: The method for grinding a spherical surface by a cup-shaped arc grinding wheel and compensating for errors described in any one of claims 1 to 9 is processed using the cradle-type five-axis machine tool.

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