Methods for Grinding Spherical Surfaces with Grinding Wheels Based on Spindle Oscillating Machine Tools and Error Compensation

Abstract

This invention provides a method for grinding spherical surfaces using a spindle-oscillating machine tool and for error compensation. In machining using a five-axis spindle-oscillating machine tool, the blank on the rotary platform rotates only around its own axis. The cup-shaped arc grinding wheel on the oscillating head forms a truncated circular grinding area on its end face due to rotation. The truncated circular grinding area and the rotational motion of the blank combine to form an envelope spherical grinding area. The motion of the oscillating head is a combination of translation in the XOZ plane and rotation around the B-axis. The combined motion trajectory causes the envelope spherical surface to shrink or expand on the blank. During the grinding process, blank material is continuously removed along the boundary of the envelope spherical surface until the oscillating head swings at a certain angle, and the end face of the original cylindrical blank becomes a spherical surface, thus completing the machining. This improves machining consistency and stability, and enhances accuracy and tool durability.

Description

Technical Field

[0001] This invention belongs to the field of precision machining technology, and relates to a method for grinding spherical surfaces with a grinding wheel based on a spindle oscillating machine tool and for error compensation. Background Technology

[0002] Optical components are an indispensable part of optical imaging systems, widely used in aerospace, defense, medicine, and daily life. Optical components typically require rough grinding, fine grinding, and polishing processes. Grinding primarily removes material and shapes the blank, affecting the workpiece's forming accuracy. Polishing mainly removes damaged layers and reduces surface roughness, but the removal amount is minimal and time-consuming. Therefore, improving grinding accuracy can significantly reduce the time required for the subsequent polishing process. Optical components are usually made of hard and brittle materials, and grinding is generally used to process these materials. However, ordinary machining methods are not very accurate and are prone to subsurface damage. Ultra-precision grinding is a machining method that uses superhard abrasive wheels in conjunction with high-performance machine tools, achieving higher machining accuracy than ordinary grinding. Cup-shaped arc grinding wheels have a special shape and are highly efficient for machining spherical surfaces, thus being widely used in spherical grinding. Furthermore, spherical grinding is also widely used in aspherical surface manufacturing processes due to its ability to quickly remove large amounts of material, and it can also compensate for tool setting errors in spherical grinding.

[0003] Currently, the precision requirements for optical components in fields such as aerospace and advanced instruments are becoming increasingly stringent, but current spherical grinding methods cannot achieve a high-precision and high-efficiency machining process. Existing spherical forming methods have low machining efficiency, and the accuracy of the spherical radius is limited due to factors such as tool setting and tool wear control. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method for grinding spherical surfaces with a grinding wheel based on a spindle oscillating machine tool and for error compensation, which improves machining consistency and stability, as well as accuracy and tool durability.

[0005] This invention is achieved through the following technical solution:

[0006] Methods for grinding spherical surfaces using a spindle-oscillating machine tool and for error compensation, including:

[0007] S1, obtain the various dimensions and process parameters required for grinding the spherical surface, and establish the linkage motion trajectory between the linear axis and the spindle swing axis of the spindle swing machine tool;

[0008] S2, based on the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing machine tool, by controlling the swing angle of the spindle swing axis to continuously change during the grinding process, the workpiece to be processed is ground into a spherical workpiece through the abrasive grain area of ​​the grinding wheel; the processing types of the spherical workpiece include convex spherical surface and concave spherical surface;

[0009] S3. After the machining is completed, the positional 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.

[0010] S4, based on the positional error of the grinding wheel, compensates and adjusts the machining position of the grinding wheel, changes the linkage motion trajectory between the linear axis and the swing axis of the spindle swing machine tool, and re-machines the spherical workpiece, thereby realizing error compensation for the spherical workpiece during the grinding process.

[0011] 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 machined and spherical radius The distance between the center of the spherical workpiece and its bottom surface needs to be machined. The rate at which the radius of a spherical workpiece decreases during grinding. The median diameter of the grinding wheel and length The small radius of the abrasive grain area of ​​the arc grinding wheel The length of the grinding wheel mounting position from the center of the B-axis of the spindle-swivel machine tool .

[0012] Preferably, in S1, the linear axis and the spindle swing axis of the oscillating machine tool are linked to each other, specifically as follows:

[0013] When machining convex spherical surfaces, the X-axis position of the spindle tilting machine tool Z-axis position Position relative to B-axis Relative to time The positional changes are as follows:

[0014]

[0015]

[0016]

[0017] When machining a concave spherical surface, the X-axis position of the spindle tilting machine tool Z-axis position Position relative to B-axis Relative to time The positional changes are as follows:

[0018]

[0019]

[0020]

[0021] In the formula: The X-axis position of the spindle-type oscillating machine tool. The Z-axis position of the spindle-type oscillating machine tool. The B-axis swing angle position of the spindle swing type machine tool; The length of the grinding wheel. The distance from the grinding wheel mounting position to the center of the B-axis of the spindle-swivel machine tool; Let be the radius of the envelope sphere formed by the truncated circle of the grinding wheel end face rotating at the initial grinding position and the rotation of the workpiece. The rate at which the radius of the spherical workpiece decreases during the grinding process. For grinding time, The median diameter of the grinding wheel. The radius of the small arc in the abrasive zone of the grinding wheel.

[0022] Among them, the X-axis and Z-axis are linear axes, and the B-axis is a oscillating axis.

[0023] Preferably, when machining a convex spherical surface, the radius of the enveloping spherical surface is... The specific calculation formula is as follows:

[0024]

[0025] In the formula: This is the distance between the center of the sphere and the bottom surface of the spherical workpiece that needs to be machined. The height of the workpiece to be processed. The diameter of the workpiece to be processed;

[0026] When machining a concave spherical surface, the radius of the enveloping sphere... The specific calculation formula is as follows:

[0027] In the formula: The center thickness of the spherical workpiece to be machined. Let be the radius of the spherical workpiece to be machined. The height of the workpiece to be processed.

[0028] Preferably, the positional error of the grinding wheel is calculated in S3 as follows:

[0029] For a convex spherical surface, the specific formula for calculating the positional error of the grinding wheel is as follows:

[0030]

[0031]

[0032] For a concave spherical surface, the specific formula for calculating the positional error of the grinding wheel is as follows:

[0033]

[0034]

[0035] In the formula: This represents the distance by which the center of the grinding wheel's arc deviates from its ideal position in the horizontal X direction. This is the distance by which the center of the arc of the grinding wheel deviates from the ideal position in the vertical Z direction; Let be the radius of the spherical workpiece after grinding. The radius of the circular protrusion in the central region of the spherical workpiece; The radius of the small arc in the abrasive zone of the grinding wheel. The radius of the spherical workpiece to be machined is denoted as .

[0036] Preferably, when machining a convex spherical workpiece, the pitch diameter of the grinding wheel should meet the following conditions:

[0037] ;

[0038] When machining a concave spherical workpiece, the pitch diameter of the grinding wheel should meet the following conditions:

[0039] ;

[0040] In the formula: The center thickness of the spherical workpiece Let be the radius of the sphere of the spherical workpiece. The radius of the small arc in the abrasive region of the cup-shaped arc grinding wheel. The angle between the line connecting the edge of the spherical surface to the center of the sphere and the axis. This refers to the median diameter of the cup-shaped arc grinding wheel.

[0041] Preferably, when machining a convex spherical workpiece, the depth of the cup portion of the grinding wheel is [details to be inserted here]. Should meet:

[0042] , ( )

[0043] , ( )

[0044] In the formula: Let be the radius of the sphere of the spherical workpiece. The radius of the small arc in the abrasive region of the cup-shaped arc grinding wheel. The angle between the line connecting the edge of the spherical surface to the center of the sphere and the axis. The median diameter of the cup-shaped arc grinding wheel. This refers to the spindle swing angle after machining is completed.

[0045] Preferably, at the initial machining position, the axis of the grinding wheel is at an angle to the axis of the workpiece to be machined. That is, the main shaft swing angle is The grinding wheel's machining surface makes point contact with the end face of the workpiece; at the end of the machining process, the workpiece has been ground into a spherical surface, and the axis of the grinding wheel is at an angle to the axis of the spherical workpiece. That is, the main shaft swing angle is The machining surface of the grinding wheel is in line contact with the spherical surface of the workpiece.

[0046] Preferably, the grinding wheel is a cup-shaped arc grinding wheel, and the workpiece to be processed is a cylindrical structure.

[0047] A spindle-oscillating machine tool, comprising a method for grinding spherical surfaces using a grinding wheel and for error compensation based on the spindle-oscillating machine tool, including:

[0048] The workpiece to be processed is mounted on the rotary platform of the spindle oscillating machine tool, and the grinding wheel is mounted on the oscillating head of the spindle oscillating machine tool. The workpiece to be processed rotates only around its own axis. The grinding wheel forms a truncated circular grinding area on its end face due to its rotation. The truncated circular grinding area and the rotational motion of the workpiece to be processed combine to form an envelope spherical grinding area. The motion of the oscillating head is a composite motion trajectory of translation in the XOZ plane and rotation around the B axis, which grinds the workpiece to be processed to obtain a spherical workpiece.

[0049] Compared with the prior art, the present invention has the following beneficial technical effects:

[0050] This invention proposes a method for grinding spherical surfaces with a cup-shaped arc grinding wheel. By controlling the movement trajectory of the workpiece and the cup-shaped arc grinding wheel during the machining process, the material is removed from the workpiece by an envelope trajectory. The amount of material removed is uniform in any radial direction. The envelope spherical surface gradually approaches the desired spherical surface with the same center, so that the force at each contact point is uniform during the machining process, and the workpiece material is removed uniformly, which improves the consistency and stability of machining, and improves the accuracy and tool durability.

[0051] Furthermore, by detecting the radius of the circular protrusion in the central region of the spherical workpiece after processing... and the actual radius of the sphere Calculating and compensating for grinding wheel position errors reduces the impact of errors and improves machining accuracy.

[0052] Furthermore, the method proposed in this invention can process spherical surfaces of various sizes using grinding wheels of various sizes. Attached Figure Description

[0053] Figure 1 This is a front view of the CNC machine tool grinding installation according to the present invention;

[0054] Figure 2 This is a slant view of the CNC machine tool grinding installation according to the present invention;

[0055] Figure 3 This is a schematic diagram of convex spherical surface grinding.

[0056] Figure 4 This is a schematic diagram of the error of the convex sphere enclosing the spherical surface;

[0057] Figure 5 This is a schematic diagram of machining errors for convex spherical surfaces;

[0058] Figure 6 This is a schematic diagram of concave spherical grinding.

[0059] Figure 7 This is a schematic diagram of the error of the concave sphere enclosing the spherical surface;

[0060] Figure 8 This is a schematic diagram of machining errors for a concave spherical surface;

[0061] Figure 9 This is a schematic diagram of the minimum cutting tool radius for a convex spherical surface;

[0062] Figure 10 This is a schematic diagram illustrating the depth requirements of a cup-shaped arc grinding wheel;

[0063] Figure 11 This is a schematic diagram of the minimum cutting tool radius for a concave spherical surface;

[0064] In the attached diagram, 1 is the Y-axis moving platform; 2 is the Z-axis moving platform; 3 is the spindle; 4 is the rotary table base; 5 is the rotary table; 6 is the workpiece; 7 is the cup-shaped arc grinding wheel; and 8 is the X-axis moving platform. Detailed Implementation

[0065] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0066] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0067] A method for grinding spherical surfaces and compensating for errors using a spindle-oscillating machine tool is characterized by using a cup-shaped arc grinding wheel to achieve spherical grinding along a linkage trajectory of three axes: two linear axes and one spindle oscillation axis. The uniformity and consistency of material removal are achieved by continuously controlling the oscillation angle of the spindle oscillation axis during grinding. The positional error of the cup-shaped arc grinding wheel is calculated by detecting the radius of the ground spherical workpiece and the size of the circular protrusion in the central region of the workpiece, and the grinding error is compensated by changing the linkage trajectory. The method specifically includes the following steps:

[0068] Step 1) Before grinding, obtain the required dimensions and process parameters 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 machined and spherical radius The distance between the center of the spherical workpiece to be machined and the bottom surface of the workpiece. The rate at which the radius of a spherical workpiece decreases during grinding. The median diameter of the cup-shaped arc grinding wheel And length (excluding arcs) The radius of the small arc of the abrasive grain area of ​​the cup-shaped arc grinding wheel is... The length of the cup-shaped arc grinding wheel installation position from the center of axis B. Based on the above parameters, the spindle motion trajectory of the oscillating spindle machine tool, i.e., the X-axis position, is derived. Z-axis position Position relative to B-axis Relative to time The positional relationship. In the components of a machine tool, when a person faces the machine tool, the part that moves left and right is the X-axis, the part that moves back and forth 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 the rotation axis and is parallel to the Y-axis.

[0069] For a convex spherical surface, the X-axis position Z-axis position Position relative to B-axis Relative to time The positional changes are as follows:

[0070]

[0071]

[0072]

[0073] in, and The formula contains The term is for simplifying 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 envelope sphere formed by the rotating truncated circle of the cup-shaped arc grinding wheel end face at the initial grinding position and the rotating cylindrical blank is... , Calculated by the following formula:

[0074]

[0075] For a concave sphere, the X-axis position Z-axis position Position relative to B-axis Relative to time The positional changes are as follows:

[0076]

[0077]

[0078]

[0079] in, and The formula contains The term is for simplifying 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 envelope sphere formed by the rotating truncated circle of the cup-shaped arc grinding wheel end face at the initial grinding position and the rotating cylindrical blank is... , Calculated by the following formula:

[0080]

[0081] Step 2) Mount the cylindrical blank to be processed on a rotary platform. During the grinding process, the cylindrical blank remains horizontal and rotates only around its own axis. Mount the cup-shaped arc grinding wheel on the machine tool spindle with a swivel head. Its rotation forms a truncated circular grinding area. The linear axis and the swivel axis move along the trajectory in Step 1. The swivel angle of the spindle swivel axis changes continuously during the grinding process. The abrasive grain area of ​​the grinding wheel contacts the cylindrical blank, grinding the end face of the cylindrical blank into a spherical surface.

[0082] Step 3) After one machining operation, measure the surface accuracy of the spherical workpiece, including the spherical error, such as the radius of the ground spherical workpiece. The radius of the circular protrusion in the central region of the spherical workpiece Calculate the positional error of the cup-shaped arc grinding wheel. and Each compensation and The linkage trajectory is adjusted, the machining trajectory is recalculated, and machining continues until the surface shape error of the spherical workpiece is within the allowable range, at which point machining is complete. The aforementioned cup-shaped arc grinding wheel position error refers to the distance by which the center of the arc of the cup-shaped arc grinding wheel deviates from its ideal position in both the horizontal X direction and the vertical Z direction. , ,cause and There are many reasons for this, including tool setting error, grinding wheel wear error, and grinding wheel manufacturing error.

[0083] For a convex spherical surface and Calculated by the following formula:

[0084]

[0085]

[0086] For a concave spherical surface and Calculated by the following formula:

[0087]

[0088]

[0089] Furthermore, the trajectory model and method for grinding spherical surfaces using a spindle-oscillating five-axis machine tool and a cup-shaped arc grinding wheel were derived and calculated. In the machining process using a spindle-oscillating five-axis machine tool, the blank on the rotary platform rotates only around its own axis. The cup-shaped arc grinding wheel on the oscillating head forms a truncated circular grinding area on its end face due to its rotation. The truncated circular grinding area and the rotational motion of the blank combine to form an envelope spherical grinding area. The motion of the oscillating head is a combination of translation in the XOZ plane and rotation around the B-axis. The combined motion trajectory causes the envelope spherical surface to shrink or expand on the blank. During the grinding process, the blank material is continuously removed with the envelope spherical surface as the boundary until the oscillating head swings at a certain angle, and the end face of the original cylindrical blank becomes a spherical surface, thus completing the machining.

[0090] Furthermore, at the initial machining position, there is an angle between the axis of the cup-shaped arc grinding wheel and the axis of the cylindrical blank. That is, the main shaft swing angle is The machining surface of the cup-shaped arc grinding wheel makes point contact with the end face of the cylindrical blank; at the end of the machining process, the cylindrical blank has been ground into a spherical workpiece, and the axis of the cup-shaped arc grinding wheel and the axis of the spherical workpiece are at an angle. That is, the main shaft swing angle is The machining surface of the cup-shaped arc grinding wheel is in line contact with the spherical surface of the workpiece.

[0091] Furthermore, in the cross-section through the XOZ plane, the center of the small arc of the cup-shaped arc grinding wheel abrasive grain region is always on the workpiece axis.

[0092] Furthermore, during the processing, the radius of the enveloping sphere decreases or increases uniformly with time at a speed f. At any time and at any position on the enveloping sphere, the material removal method is to shrink or expand towards the workpiece with the enveloping sphere as the boundary. In any radial direction, the thickness of the removed material is uniform, so as to reduce the excessive local grinding force of the grinding wheel or workpiece, which may cause tool wear or workpiece damage.

[0093] Furthermore, based on the established relationship model between spherical error and cup-shaped arc grinding wheel position error, the actual spherical workpiece radius is measured. The radius of the circular protrusion in the central region of the spherical workpiece Calculate position error and And compensation.

[0094] Furthermore, the spherical surface formed by grinding can be a convex spherical surface or a concave spherical surface.

[0095] Furthermore, for the center thickness after processing... The radius of the sphere is The angle between the line connecting the edge of the sphere to the center of the sphere and the axis is . For spherical workpieces, the allowable mean diameter of the cup-shaped arc grinding wheel should meet the following requirements. For convex spherical surfaces, a "+" sign is used, and for concave spherical surfaces, a "-" sign is used. When machining convex spherical surfaces, the allowable depth of the cup-shaped arc grinding wheel should meet the following requirements.

[0096] , ( )

[0097] , ( )

[0098] Furthermore, the grinding process uses a spindle-oscillating five-axis machine tool, where the workpiece does not move, and the cup-shaped arc grinding wheel performs translation and oscillation.

[0099] Example 1

[0100] This invention discloses a method for grinding a spherical surface using a cup-shaped arc grinding wheel with a truncated circular shape. In a single grinding operation, the workpiece rotates around its own axis in the XOZ plane. The cup-shaped arc grinding wheel moves in tandem with the spindle within the XOZ plane, while the spindle simultaneously drives the cup-shaped arc grinding wheel to rotate. These two rotational movements together form an envelope spherical surface. The linkage motion of the B-axis oscillating head causes the envelope spherical surface to shrink towards the center of the sphere. During the grinding process, workpiece material is continuously removed along the boundary of the envelope spherical surface. During the machining process, the radius of the envelope spherical surface increases with velocity. fThe material removal process decreases uniformly over time, with the material removal direction consistently pointing towards the center of the sphere along the radius. The thickness of the removed material is uniform until, after a certain period, the end face of the original cylindrical blank becomes a spherical surface with the required radius. After grinding, the spherical surface error is checked. Based on the established relationship model between the spherical surface error and the positional error of the cup-shaped arc grinding wheel, the actual spherical workpiece radius is measured. The radius of the circular protrusion in the central region of the spherical workpiece Calculate position error and And compensate, then process again using the compensated trajectory until the dimensions meet the requirements;

[0101] like Figures 1 to 2 As shown, the present invention employs a spindle-swinging five-axis CNC machine tool, which can realize three-axis movement in XYZ, as well as swinging around the B-axis in the Y direction and rotating around the Z direction; specifically, it includes a Y-axis moving platform, a Z-axis moving platform, a spindle, a rotary table and an X-axis moving platform, the spindle can swing around the Y direction and the rotary table can rotate around the Z direction.

[0102] Specifically, the steps include:

[0103] Step 1), as Figure 1 , Figure 2 As shown, the cylindrical blank to be machined is mounted on the rotary table, and the cup-shaped arc grinding wheel is mounted on the spindle. Tool setting is performed according to the grinding wheel mounting dimensions and the workpiece mounting dimensions. Each axis is set to its initial position, the rotary table speed and spindle speed are set, and the motion parameters and grinding time for the XYZ and B axes are input. t Spherical machining is achieved through the envelope trajectory. After time t, the B-axis swings to an angle. The cylindrical blank is processed into a spherical workpiece, thus completing the spherical machining.

[0104] The cup-shaped arc grinding wheel has a median diameter of [missing information]. The length (excluding the arc) is The small arc radius of the abrasive region on its end face is Installed in a length of On the main spindle, that is, the distance from the grinding wheel mounting position to the center of axis B is... .

[0105] The cylindrical blank, as described above 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 connecting the edge of the sphere to the center of the sphere and the axis is . , After the blank is mounted on the turntable, the distance between the bottom surface of the blank and the center of the sphere is... ,in:

[0106]

[0107] The initial position is as follows Figure 3 As shown, within the XOZ plane, with the center of the workpiece's bottom surface as the origin, the coordinates of the B-axis center at any given time are: At any given moment, the radius of the envelope sphere formed by the rotation of the cup-shaped arc grinding wheel and the rotation of the blank is... R At the initial position, the radius of the envelope sphere is... It shares a common center with the sphere formed after processing, satisfying:

[0108]

[0109] The B-axis swing angle is: :

[0110]

[0111] The initial coordinates of the B-axis center relative to the center of the bottom surface of the blank are ( ):

[0112]

[0113]

[0114] like Figure 3 As shown, after processing, the radius of the envelope sphere is... The swing angle of the B-axis is ,

[0115]

[0116] During the processing, the radius of the envelope sphere is controlled to decrease uniformly over time, from Reduce to Time Then the rate at which the radius decreases is:

[0117]

[0118] The radius of the envelope sphere at any time t R for:

[0119]

[0120] At any given time, the swing angle of the B-axis satisfy:

[0121]

[0122] Combining equations (4), (5), (8), and (9), the trajectory of the spindle relative to the center of the blank's bottom surface can be obtained as follows:

[0123]

[0124]

[0125]

[0126] Step 2) After one machining operation, measure the surface accuracy of the spherical workpiece, including the spherical error, such as the radius of the ground spherical workpiece. The radius of the circular protrusion in the central region of the spherical workpiece Calculate the positional error of the cup-shaped arc grinding wheel. and Each compensation and The linkage trajectory is adjusted, the processing trajectory is recalculated, and the processing is repeated.

[0127] like Figure 4 As shown, when the cup-shaped arc grinding wheel has a positional error, in the XOZ plane, the center of the arc of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal X direction and the vertical Z direction, respectively. , Deviations in both directions cause changes in the radius of the envelope sphere, ultimately affecting the actual radius of the machined sphere. and There are many reasons for this, including tool setting error, grinding wheel wear error, and grinding wheel manufacturing error.

[0128] Combination Figure 4 The cup-shaped arc grinding wheel has a positional error. , At that time, the radius of the enclosing sphere becomes The angle between the axis of the cup-shaped arc grinding wheel and the line connecting the center of the arc of the cup-shaped arc grinding wheel to the center of the enveloping spherical surface becomes Position error , satisfy:

[0129]

[0130]

[0131] like Figure 5 As shown, the cup-shaped arc grinding wheel has errors. , At this time, a circular bulge will appear at the center of the sphere, and the radius of the circular bulge is... The height of the entire convex spherical workpiece is from Become .

[0132] according to Figure 5 As shown, the radius of the circular protrusion in the central region of the spherical workpiece is obtained. :

[0133]

[0134] Combining equations (13) and (15), we can obtain:

[0135]

[0136] Combining equations (14) and (15), we can obtain:

[0137]

[0138] (Combined with step 2), the actual spherical radius is measured after processing. The radius of the circular protrusion in the central region of the convex spherical workpiece The result can be obtained through equation (16). 1. Obtain by formula (17) ,Will and The machining trajectory shown in formulas (10) and (11) is compensated until the surface shape error of the spherical workpiece is within the allowable range, and the machining is completed.

[0139] For a concave spherical surface, combining steps 1) and 2), similarly, for a cylindrical blank, such as... Figure 6 As shown, the diameter of the cylindrical blank to be processed is The height is The center thickness of the machined spherical workpiece is The radius of the sphere is After the blank is mounted on the turntable, the distance between the bottom surface of the blank and the center of the sphere is... .

[0140] Initial position as Figure 6 As shown, the B-axis swing angle The cup-shaped arc grinding wheel rotates on its end face, creating a circular grinding motion. This circular grinding motion, combined with the workpiece's rotation, forms an enveloping spherical surface with an initial radius of [missing information]. ,satisfy:

[0141]

[0142]

[0143] The initial coordinates of the center of axis B relative to the center point O of the bottom surface of the blank are ( ):

[0144]

[0145]

[0146] After processing, the radius of the envelope sphere is The swing angle of the B-axis is ,

[0147]

[0148] During the processing, the radius of the envelope sphere is controlled from... Increase uniformly over time to The radius increases at a rate of The trajectory of the spindle relative to the center of the blank bottom surface can be obtained as follows:

[0149]

[0150]

[0151]

[0152] like Figure 7 As shown, when the cup-shaped arc grinding wheel has a positional error, in the XOZ plane, the center of the arc of the cup-shaped arc grinding wheel deviates from the ideal position in the horizontal X direction and the vertical Z direction, respectively. , Deviations in both directions cause changes in the radius of the envelope sphere, ultimately affecting the actual radius of the machined sphere. and There are many reasons for this, including tool setting error, grinding wheel wear error, and grinding wheel manufacturing error.

[0153] Combination Figure 7 The cup-shaped arc grinding wheel has a positional error. , At that time, the radius of the enclosing sphere becomes The angle between the axis of the cup-shaped arc grinding wheel and the line connecting the center of the arc of the cup-shaped arc grinding wheel to the center of the enveloping spherical surface becomes ,size , satisfy:

[0154]

[0155]

[0156] like Figure 8 As shown, the cup-shaped arc grinding wheel has a positional error. , After grinding, a circular protrusion will appear at the center of the spherical surface, with a radius of [missing information]. The center thickness of the concave spherical workpiece is determined by Become .

[0157] according to Figure 8 As shown, the radius of the circular protrusion in the central region of the spherical workpiece is obtained. :

[0158]

[0159] Combining equations (26) and (28), we can obtain:

[0160]

[0161] Combining equations (27) and (28), we can obtain:

[0162]

[0163] (Combined with step 2), the actual spherical radius is measured after processing. The radius of the circular protrusion in the central region of the convex spherical workpiece The result can be obtained through equation (29). , derive from equation (30) ,Will and The machining trajectory shown in equations (23) and (24) is compensated until the surface shape error of the spherical workpiece is within the allowable range, at which point the machining is completed.

[0164] The proposed method enables the machining of spherical surfaces of various sizes using cup-shaped arc grinding wheels of various sizes, such as... Figure 9 As shown, after machining the convex spherical surface according to the method of the present invention, the smallest permissible diameter cup-shaped arc grinding wheel should satisfy the requirement that its end face grinding surface is exactly in contact with the edge of the spherical surface of the workpiece. It is known that... ,at this time:

[0165]

[0166] After machining the convex spherical surface according to the method of the present invention, the inner diameter of the cup-shaped arc grinding wheel with the largest permissible diameter is exactly equal to that of the spherical surface, and the cup-shaped arc grinding wheel can just accommodate half of the spherical surface. At this time:

[0167]

[0168] like Figure 10 As shown, after machining the convex spherical surface according to the method of the present invention, the depth of the cup-shaped arc grinding wheel should meet the requirements for accommodating the workpiece. Then the bottom of the cup will not touch the workpiece:

[0169]

[0170] like Then the bottom of the cup will not touch the spherical surface:

[0171]

[0172] Similarly, such as Figure 11 As shown, after machining a concave spherical surface according to the method of the present invention, the smallest permissible diameter cup-shaped arc grinding wheel should satisfy the requirement that its end face grinding surface exactly contacts the edge of the spherical surface of the workpiece. It is known that... ,at this time:

[0173]

[0174] After machining the concave spherical surface according to the method of the present invention, the outer diameter of the cup-shaped arc grinding wheel with the largest permissible diameter is exactly equal to that of the spherical surface. At this time:

[0175]

[0176] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Those skilled in the art can readily implement the present invention based on the accompanying drawings and the above description. However, any modifications, alterations, or variations made by those skilled in the art without departing from the scope of the present invention, utilizing the disclosed technical content, are equivalent embodiments of the present invention. Furthermore, any modifications, alterations, or variations made to the above embodiments based on the essential technology of the present invention are still within the protection scope of the present invention.

Claims

1. A method for grinding spherical surfaces using a spindle-oscillating machine tool and for error compensation, characterized in that, include, S1, obtain the various dimensions and process parameters required for grinding the spherical surface, and establish the linkage motion trajectory between the linear axis and the spindle swing axis of the spindle swing machine tool; S2, based on the linkage motion trajectory of the linear axis and the spindle swing axis of the spindle swing machine tool, by controlling the swing angle of the spindle swing axis to continuously change during the grinding process, the workpiece to be processed is ground into a spherical workpiece through the abrasive grain area of ​​the grinding wheel; the processing types of the spherical workpiece include convex spherical surface and concave spherical surface; S3. After the machining is completed, the positional 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. Based on the positional error of the grinding wheel, the machining position of the grinding wheel is compensated and adjusted, and the linkage motion trajectory of the linear axis and the oscillating axis of the spindle swing machine tool is changed to re-machine the spherical workpiece, thereby realizing error compensation for the spherical workpiece during the grinding process. 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 machined and spherical radius The distance between the center of the spherical workpiece and its bottom surface needs to be machined. The rate at which the radius of a spherical workpiece decreases during grinding. The median diameter of the cup-shaped arc grinding wheel and length The small radius of the abrasive grain area of ​​a cup-shaped arc grinding wheel The length of the grinding wheel mounting position from the center of the B-axis of the spindle-swivel machine tool ; In S1, the linkage motion trajectory between the linear axis and the spindle swing axis of the oscillating spindle machine tool is established as follows: When machining convex spherical surfaces, the X-axis position of the spindle tilting machine tool Z-axis position Position relative to B-axis Relative to time The positional changes are as follows: When machining a concave spherical surface, the X-axis position of the spindle tilting machine tool Z-axis position Position relative to B-axis Relative to time The positional changes are as follows: In the formula: The X-axis position of the spindle-type oscillating machine tool. The Z-axis position of the spindle-type oscillating machine tool. The B-axis swing angle position of the spindle swing type machine tool; The length of the grinding wheel. The distance from the grinding wheel mounting position to the center of the B-axis of the spindle-swivel machine tool; Let be the radius of the envelope sphere formed by the truncated circle of the grinding wheel end face rotating at the initial grinding position and the rotation of the workpiece. The rate at which the radius of the spherical workpiece decreases during the grinding process. For grinding time, The median diameter of the cup-shaped arc grinding wheel, The radius of the small arc of the abrasive grain area of ​​the cup-shaped arc grinding wheel; When machining a convex spherical surface, the radius of the envelope spherical surface The specific calculation formula is as follows: ； In the formula: This is the distance between the center of the sphere and the bottom surface of the spherical workpiece that needs to be machined. The height of the workpiece to be processed. 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 as follows: ； In the formula: The center thickness of the spherical workpiece to be machined. Let be the radius of the spherical workpiece to be machined. The height of the workpiece to be processed; The positional error of the grinding wheel is calculated in S3 as follows: For a convex spherical surface, the specific formula for calculating the positional error of the grinding wheel is as follows: ； For a concave spherical surface, the specific formula for calculating the positional error of the grinding wheel is as follows: In the formula: This represents the distance by which the center of the grinding wheel's arc deviates from its ideal position in the horizontal X direction. This is the distance by which the center of the arc of the grinding wheel deviates from the ideal position in the vertical Z direction; Let be the radius of the spherical workpiece after grinding. The radius of the circular protrusion in the central region of the spherical workpiece; The radius of the small arc in the abrasive region of the cup-shaped arc grinding wheel. The radius of the spherical workpiece to be machined is denoted as .

2. The method for grinding spherical surfaces and error compensation using a spindle-oscillating machine tool according to claim 1, characterized in that, When machining a convex spherical workpiece, the pitch diameter of the grinding wheel should meet the following conditions: ； When machining a concave spherical workpiece, the pitch diameter of the grinding wheel should meet the following conditions: ； In the formula: The center thickness of the spherical workpiece Let be the radius of the sphere of the spherical workpiece. The radius of the small arc in the abrasive region of the cup-shaped arc grinding wheel. The angle between the line connecting the edge of the spherical surface to the center of the sphere and the axis. This refers to the median diameter of the cup-shaped arc grinding wheel.

3. The method for grinding spherical surfaces and error compensation based on a spindle-oscillating machine tool according to claim 1, characterized in that, When machining a convex spherical workpiece, the depth of the cup of the grinding wheel. Should meet: ，( ) ，( )； In the formula: Let be the radius of the sphere of the spherical workpiece. The radius of the small arc in the abrasive region of the cup-shaped arc grinding wheel. The angle between the line connecting the edge of the spherical surface to the center of the sphere and the axis. The median diameter of the cup-shaped arc grinding wheel, This refers to the spindle swing angle after machining is completed.

4. The method for grinding spherical surfaces and error compensation based on a spindle-oscillating machine tool according to claim 1, characterized in that, At the initial machining position, there is an angle between the axis of the grinding wheel and the axis of the workpiece to be machined. That is, the main shaft swing angle is The grinding wheel's machining surface makes point contact with the end face of the workpiece; at the end of the machining process, the workpiece has been ground into a spherical surface, and the axis of the grinding wheel is at an angle to the axis of the spherical workpiece. That is, the main shaft swing angle is The machining surface of the grinding wheel is in line contact with the spherical surface of the workpiece.

5. The method for grinding spherical surfaces and error compensation based on a spindle-oscillating machine tool according to claim 1, characterized in that, The grinding wheel is a cup-shaped arc grinding wheel, and the workpiece to be processed is a cylindrical structure.

6. A spindle-oscillating machine tool, based on the method for grinding spherical surfaces and error compensation using a spindle-oscillating machine tool according to any one of claims 1-5, characterized in that, include, The workpiece to be processed is mounted on the rotary platform of the spindle oscillating machine tool, and the grinding wheel is mounted on the oscillating head of the spindle oscillating machine tool. The workpiece to be processed rotates only around its own axis. The grinding wheel forms a truncated circular grinding area on its end face due to its rotation. The truncated circular grinding area and the rotational motion of the workpiece to be processed combine to form an envelope spherical grinding area. The motion of the oscillating head is a composite motion trajectory of translation in the XOZ plane and rotation around the B axis, which grinds the workpiece to be processed to obtain a spherical workpiece.

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