Peripheral grinding machine circular blade grinding method based on system shaft coupling

Abstract

The invention discloses a peripheral grinding machine circular blade grinding method based on system shaft coupling, and relates to the technical field of grinding machining.The method comprises the steps that a workpiece is clamped through a four-shaft indexable blade peripheral grinding machine and a tip, it is ensured that the workpiece is tangent to a grinding wheel, and the eccentric problem is solved; analyzing the difference between non-eccentric circle processing and eccentric circle processing; an Archimedes screw feeding mode is adopted, uniform feeding is ensured, abrasion caused by eccentricity is avoided, linkage of an X shaft and a B shaft is dynamically adjusted through a system shaft coupling technology, and the eccentricity influence is reduced; eccentric data are measured in real time, the X-axis feed amount is adjusted, and a coupling table is optimized. According to the eccentric circle grinding method based on shaft coupling, the machining precision can be remarkably improved, the roundness of the machined blade is stabilized within 1 micron, the dimensional tolerance zone is guaranteed within 0.004 mm, the surface roughness value Ra is smaller than 0.2 micron, and the high-precision machining requirement is met.

Description

Technical Field

[0001] The invention relates to the technical field of grinding processing, and in particular to a peripheral grinder circular blade grinding method based on system axis coupling. Background Art

[0002] When using an indexable insert peripheral grinder for circular blade grinding, due to the machine tool's own errors or tool placement errors, the actual clamping center of the tip cannot be the center of the circular blade workpiece, that is, eccentricity occurs. The grinding results show that due to the existence of eccentricity, if the usual X-axis and B-axis linkage method is used, the surface quality of the processed circular blade is very poor, and edges will be formed on the arc surface. At this time, if the non-eccentric circle threshold processing method is used, although the processing surface quality meets the requirements, the processed circular blade is different from the target circular blade.

[0003] Due to the existence of eccentricity, the feed amount of the X axis is different each time, and the speed is also different. The Rexroth CNC system MTX Micro itself has a system axis coupling function. Using this system axis coupling function, the X axis and the B axis are system axis coupled, and the B axis is the active axis. The surface finish quality of the processed circular blade can be greatly improved.

[0004] In view of the above problems, the present invention provides a circular blade grinding method of a peripheral grinder based on system axis coupling. Summary of the invention

[0005] In view of the above problems, the present invention provides a method for grinding circular blades of a peripheral grinder based on system axis coupling to solve the problem of unstable machining accuracy caused by machining errors caused by eccentricity in the prior art.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for grinding circular blades of a peripheral grinder based on system axis coupling, comprising the following steps:

[0007] Step S1, using a four-axis indexable insert peripheral grinder to clamp the workpiece through the top to ensure that the workpiece and the grinding wheel are tangent to solve the eccentricity problem;

[0008] In step S1, the following sub-steps are also included:

[0009] S1-1, a four-axis indexable insert peripheral grinder, the workpiece is clamped by a center, the center is located at the rotation center O of the B axis, during the machining process, the workpiece rotates around the B axis, and the grinding wheel reciprocates along the X axis;

[0010] S1-2. In the ideal case, the center of the center point clamping coincides exactly with the center of the workpiece circle. At this time, the distance between the grinding wheel and the center of the B-axis remains constant, the feed rate of the X-axis is zero, and the grinding linear velocity is constant. However, during actual machining, there is an eccentricity between the center of the center point clamping and the center of the workpiece circle. The distance between the grinding wheel and the center of the B-axis will change as the workpiece rotates, resulting in a change in the feed rate of the X-axis. Therefore, it is necessary to adjust the feed rate of the X-axis in real time to maintain the tangency between the grinding wheel and the arc surface of the workpiece.

[0011] Step S2. Analyze the differences between non-eccentric circle machining and eccentric circle machining.

[0012] In step S2, the following sub-steps are further included:

[0013] S2-1. In the case of no eccentricity, the center of the center point clamping coincides exactly with the center of the workpiece circle. At this time, the distance between the end face of the grinding wheel and the center of the B-axis remains unchanged, the grinding linear velocity is constant, and the equation of the circular workpiece is:

[0014] x 2 +z 2 =R 2 (1)

[0015] where R is the radius of the circular blade to be machined, and x and z are the horizontal and vertical distances on the arc surface of the workpiece respectively.

[0016] During actual grinding, the center of the center point clamping is perpendicular to the end face of the grinding wheel. Therefore, x = R and z = 0. At this time, equation (1) becomes:

[0017] x = R (2)

[0018] S2-2. When there is eccentricity, there is an eccentricity distance between the center of the center point clamping and the center of the workpiece circle. During the grinding process, the distance between the grinding wheel and the center of the B-axis will change as the workpiece rotates, resulting in a change in the grinding linear velocity and thus affecting the surface quality, as shown in equation (3) specifically:

[0019] (x1 - rsinθ) 2 +(z1 - rcosθ) 2 =R 2 (3)

[0020] where x1 is the horizontal distance from the point on the arc surface of the circular workpiece to the center of the circle, and z1 is the vertical distance between the center of the center point clamping and the center of the actual circular workpiece.

[0021] For simplified calculation and analysis, since the actual eccentricity is very small and the angle of the B-axis for each step is very small, z1 << x1 and z1 - rcosθ ≈ 0. That is, equation (3) is approximated as (x1 - rsinθ) 2 =R 2 , and is further simplified to:

[0022] x1=R±rsinθ (4)

[0023] From formula (2), it can be seen that when grinding a circular blade without eccentricity, the grinding linear velocity change rate is:

[0024]

[0025] It can be seen from formula (5) that when grinding a circular blade without eccentricity, the grinding linear speed is a constant value. In the ideal case, when grinding a circular blade, the feed amount of the x-axis is 0 each time, and it is only necessary to rotate the B-axis uniformly;

[0026] From formula (4), it can be seen that when there is eccentric grinding of circular blades, the rate of change of grinding line speed is:

[0027]

[0028] It can be seen from formula (6) that when grinding a circular blade eccentrically, the grinding line speed change rate is proportional to the eccentric distance r, and changes continuously with the cosine law of θ; the larger the eccentric distance r between the center of the center clamping and the center of the actual circular workpiece, the greater the grinding line speed change rate, and the greater the impact on the workpiece during the grinding process; when grinding a circular blade under eccentricity, the feed amount of the x-axis each time is ±rsinθ, which is a continuously changing amount, and it will also cause an impact on the workpiece surface during the grinding process, so the surface quality of the machined surface cannot be guaranteed.

[0029] Step S3, using the Archimedean screw feeding method to ensure uniform feeding and avoid wear caused by eccentricity;

[0030] In step S3, the following sub-steps are also included:

[0031] S3-1, using the Archimedean screw feeding method, that is, the grinding wheel no longer feeds along the concentric circle path, but gradually penetrates into the workpiece surface along the spiral line. The Cartesian coordinate equation of the Archimedean screw is:

[0032]

[0033] In polar coordinates, the equation of the Archimedean screw is:

[0034] r=a+bθ (8)

[0035] Among them, a and b are real numbers. By adjusting these parameters, the shape of the spiral line can be controlled to make the feeding more uniform;

[0036] When θ=0, a is the distance from the starting point to the origin of the polar coordinates. b is the value that increases with each unit increase in the helix angle r;

[0037] When θ>0, a is equivalent to a rotating spiral, and parameter b controls the distance between two adjacent curves;

[0038] Another formula of Archimedean screw, whose constant speed ratio shows its superiority in circular blade grinding, is as follows:

[0039]

[0040] Among them, ρ is the constant speed ratio, ω is the circumferential speed, and v is the linear speed;

[0041] S3-2, by adjusting the spiral parameters α and β, the starting point and density of the spiral line are controlled to ensure the uniformity of each grinding and reduce the impact on the workpiece surface.

[0042] Step S4, dynamically adjusting the linkage between the X-axis and the B-axis through the system axis coupling technology to reduce the eccentricity effect;

[0043] In step S4, the following sub-steps are also included:

[0044] S4-1, by adopting the Rexroth MTX CNC system and combining the system axis coupling function, effectively controls the linkage relationship between the X-axis and the B-axis, reducing the processing error caused by eccentricity; under this system, the rotation of the B-axis is no longer controlled only by the system, but is dynamically adjusted according to the coupling table;

[0045] S4-2, the system generates a coupling table to dynamically adjust the nonlinear coupling relationship between the X-axis and the B-axis according to the real-time measured eccentricity data. The coupling table can provide real-time updates in each processing cycle. The coupling relationship formula is:

[0046] XB(1,CYCNUM)=R-@E83031*COS(DB)*COS(E45)+E43(10)

[0047] Among them, CYCNUM is the number of B-axis feeds, R is the workpiece radius, @E83031 is the eccentricity r, DB is the rotation angle of the B-axis relative to the starting coupling position, E45 is the blade back angle, and E43 is the machining offset compensation.

[0048] Step S5, measuring the eccentricity data in real time, adjusting the X-axis feed amount to optimize the coupling table.

[0049] In step S5, the following sub-steps are also included:

[0050] S5-1, by measuring the eccentricity distance and the rotation angle of the B axis in real time, the system dynamically adjusts the X-axis feed according to the eccentricity data to keep the grinding wheel in contact with the workpiece surface at all times;

[0051] S5-2, based on the real-time feedback during the machining process, the system will generate a new coupling table and make adjustments to optimize the feed mode for each machining.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention uses system axis coupling technology to accurately control the linkage between the X-axis and the B-axis, effectively eliminate the influence of eccentricity, and significantly improve the roundness and dimensional accuracy of the circular blade. The roundness of the processed blade is stabilized within 1μm, and the dimensional tolerance band is maintained within 0.004mm.

[0054] The Archimedean screw feeding method adopted in the present invention allows the grinding wheel to gradually penetrate into the workpiece surface along the spiral line, making the grinding process more uniform, thereby effectively avoiding uneven wear and significantly improving the surface finish, with the surface roughness reaching less than 0.2 μm.

[0055] The present invention adopts a real-time eccentricity measurement and compensation system to dynamically adjust the X-axis feed amount to ensure that the grinding wheel and the workpiece always maintain optimal contact. Through this real-time compensation and adjustment function, the eccentricity changes can be responded to instantly during the processing process, avoiding manual intervention or fixed parameter settings in traditional methods, and improving the consistency and accuracy of processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It is understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0057] Figure 1 is a flow chart of the method of the present invention;

[0058] Figure 2 This is a schematic diagram showing the difference between machining without an eccentric circle and machining with an eccentric circle;

[0059] Figure 3 This is the effect diagram of processing with non-eccentric circle method;

[0060] Figure 4 This is the effect diagram of processing by eccentric circle method;

[0061] Figure 5 This is a schematic diagram of the spiral feed method of eccentric circle grinding;

[0062] Figure 6 is the state diagram of the system axis coupling;

[0063] Figure 7 It is a schematic diagram of the calculation of the reference value of the driven shaft using table coupling;

[0064] Figure 8 It is a coupled program flow chart;

[0065] Fig. 9 It is a schematic diagram of the procedure for establishing the coupling relationship;

[0066] Fig.10 It is the coupling diagram of the active axis B axis and the driven axis X axis;

[0067] Fig.11 This is the effect diagram of a circular blade processed by system axis coupling grinding. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions 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 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 making creative work belong to the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but is only for selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0069] Please refer to Figure 1-Figure 11 Schematic diagram of a method for grinding a circular blade of a peripheral grinder based on system axis coupling provided by an embodiment of the present invention, comprising the following steps:

[0070] Step S1, using a four-axis indexable insert peripheral grinder to clamp the workpiece through the top to ensure that the workpiece and the grinding wheel are tangent to solve the eccentricity problem;

[0071] S1-1, a four-axis indexable insert peripheral grinder, the workpiece is clamped by a center, the center is located at the rotation center O of the B axis, during the machining process, the workpiece rotates around the B axis, and the grinding wheel reciprocates along the X axis. Through this design, the workpiece and the grinding wheel are always tangent to ensure grinding accuracy;

[0072] S1-2, ideally, the center of the top clamping is completely aligned with the center of the workpiece. At this time, the distance between the grinding wheel and the center of the B-axis remains constant, the X-axis feed is zero, and the grinding linear speed is constant, thereby maintaining a stable surface quality. However, in actual processing, there is an eccentricity between the center of the top clamping and the center of the workpiece. The distance between the grinding wheel and the center of the B-axis will change as the workpiece rotates, resulting in a change in the X-axis feed. Therefore, the X-axis feed needs to be adjusted in real time to keep the grinding wheel tangent to the arc surface of the workpiece.

[0073] It should be noted that Figure 2 It is a schematic diagram of the difference between machining without eccentric circle and machining with eccentric circle, showing the difference when the center of the top clamping coincides with the center of the workpiece (i.e. no eccentricity) and when there is eccentricity, intuitively showing the impact of the two situations on machining.

[0074] Step S2, analyzing the difference between machining without eccentric circle and machining with eccentric circle;

[0075] S2-1, in the absence of eccentricity, the center of the top clamping is completely coincident with the center of the workpiece. At this time, the distance between the end face of the grinding wheel and the center of the B axis remains unchanged, the grinding linear speed is constant, and the equation for the circular workpiece is:

[0076] x 2 +z 2 =R 2 (1)

[0077] Where R is the radius of the circular blade to be machined, x and z are the horizontal and vertical distances on the arc surface of the workpiece, respectively;

[0078] In actual grinding, the center of the center clamp is perpendicular to the end face of the grinding wheel, so x = R, z = 0, and equation (1) becomes:

[0079] x=R (2)

[0080] S2-2, when there is eccentricity, there is an eccentric distance between the center of the top clamping and the center of the workpiece. During the grinding process, the distance between the grinding wheel and the center of the B axis will change as the workpiece rotates. This causes the grinding linear speed to change, thus affecting the surface quality, as shown in formula (3):

[0081] (x1-rsinθ) 2 +(z1-rcosθ) 2 =R 2 (3)

[0082] Among them, x1 is the horizontal distance from the point on the arc surface of the circular workpiece to the center of the circle, and z1 is the vertical distance between the center of the top clamping and the center of the actual circular workpiece;

[0083] To simplify the calculation and analysis, since the actual eccentricity is very small and the B-axis angle of each step is very small, z1<<x1, z1-rcosθ≈0, that is, formula (3) can be approximated as (x1-rsinθ) 2 =R 2 , further simplified to:

[0084] x1=R±rsinθ (4)

[0085] From formula (2), it can be seen that when grinding a circular blade without eccentricity, the grinding linear velocity change rate is:

[0086]

[0087] It can be seen from formula (5) that when grinding a circular blade without eccentricity, the grinding linear speed is a constant value. In an ideal situation, when grinding a circular blade, the feed amount of the x-axis is 0 each time, and it is only necessary to rotate the B-axis evenly.

[0088] From formula (4), it can be seen that when there is eccentric grinding of circular blades, the rate of change of grinding line speed is:

[0089]

[0090] It can be seen from formula (6) that when there is eccentric grinding of circular blades, the grinding linear velocity change rate is proportional to the eccentric distance r, and changes continuously with the cosine law of θ; the larger the eccentric distance r between the center of the top clamping and the center of the actual circular workpiece, the larger the grinding linear velocity change rate, and the greater the impact on the workpiece during grinding;

[0091] Moreover, when grinding circular blades under eccentric conditions, the feed amount of the x-axis each time is ±rsinθ, which is a continuously changing amount. The grinding process will also cause impact on the workpiece surface, so the quality of the machined surface cannot be guaranteed.

[0092] It should be noted that Figure 3 This is the effect diagram of the processing using the non-eccentric circle method, showing the surface quality of the circular blade processed without eccentricity; Figure 4 This is the effect diagram of eccentric circle processing, which shows the influence of the change of grinding line speed on the workpiece surface during eccentric processing.

[0093] Step S3, using the Archimedean screw feeding method to ensure uniform feeding and avoid wear caused by eccentricity;

[0094] S3-1, using the Archimedean screw feeding method, that is, the grinding wheel no longer feeds along the concentric circle path, but gradually penetrates into the workpiece surface along the spiral line. The Cartesian coordinate equation of the Archimedean screw is:

[0095]

[0096] In polar coordinates, the equation of the Archimedean screw is:

[0097] r=a+bθ (8)

[0098] Among them, a and b are real numbers. By adjusting these parameters, the shape of the spiral can be controlled to make the feeding more uniform;

[0099] When θ=0, a is the distance from the starting point to the origin of the polar coordinates. b is the value that increases with each unit increase in the helix angle r;

[0100] When θ>0, a is equivalent to a rotating spiral, and parameter b controls the distance between two adjacent curves;

[0101] Another formula of Archimedean screw, whose constant speed ratio shows its superiority in circular blade grinding, is as follows:

[0102]

[0103] Among them, ρ is the constant speed ratio, ω is the circumferential speed, and v is the linear speed;

[0104] According to this formula, when the circumferential speed ω and the linear speed v increase or decrease by the same multiple at the same time, the shape of the Archimedean spiral will not change. Therefore, when using the Archimedean spiral for machining, the circumferential speed ω and the linear speed v can be adjusted according to the performance that the peripheral grinder can achieve to improve the machining efficiency. It is sufficient to ensure that the proportional relationship remains unchanged.

[0105] S3-2, optimization of the feed path. By adjusting the spiral parameters α and β, the starting point and density of the spiral line can be controlled to ensure the uniformity of each grinding, thereby reducing the impact on the workpiece surface and improving the processing accuracy.

[0106] It should be noted that the traditional circular blade grinding method usually adopts layer-by-layer grinding, where the workpiece is fed gradually from the outer ring to the inner ring to ensure stable surface quality when there is no eccentricity. However, when there is eccentricity, layer-by-layer grinding will lead to uneven wear and produce obvious processing marks.

[0107] Figure 5 This is a schematic diagram of the spiral feed method for eccentric circle grinding, which shows the path of the Archimedean screw feed and its application in eccentric circle grinding. The Archimedean screw feed avoids the fixed force on the fixture and the center at the fixed feed position, reduces wear; reduces the idle stroke of the X-axis, improves grinding efficiency; and improves the surface finish and uniformity of the workpiece, especially in the eccentric case.

[0108] Step S4, dynamically adjusting the linkage between the X-axis and the B-axis through the system axis coupling technology to reduce the eccentricity effect;

[0109] S4-1, by adopting the Rexroth MTX CNC system and combining the system axis coupling function, can effectively control the linkage relationship between the X-axis and the B-axis, reducing the processing error caused by eccentricity; under this system, the rotation of the B-axis is no longer controlled only by the system, but is dynamically adjusted according to the coupling table;

[0110] S4-2, the system generates a coupling table to dynamically adjust the nonlinear coupling relationship between the X-axis and the B-axis according to the real-time measured eccentricity data. In each processing cycle, the coupling table can provide real-time updates to ensure that each feed can optimize the processing quality. The coupling relationship formula is:

[0111] XB(1,CYCNUM)=R-@E83031*COS(DB)*COS(E45)+E43(10)

[0112] Among them, CYCNUM is the number of B-axis feeds, R is the workpiece radius, @E83031 is the eccentricity r, DB is the rotation angle of the B-axis relative to the starting coupling position, E45 is the blade back angle, and E43 is the machining offset compensation;

[0113] It should be noted that Figure 6 The state diagram of the system axis coupling shows the state changes during system startup, coupling activation and adjustment; Figure 7 In order to calculate the reference value of the driven axis using table coupling, it is demonstrated how to calculate and apply table coupling data to optimize the relationship between the B-axis and the X-axis; there are two types of system axis coupling: formula coupling and table coupling. Table coupling can show the nonlinear coupling relationship between the active axis and the driven axis.

[0114] The coupling program includes the circular blade eccentricity algorithm and coupling table data generation subroutine, coupling table loading subroutine, coupling opening subroutine, coupling release subroutine, etc. The coupling program flow chart is as follows: Figure 8 shown.

[0115] Step S5, real-time measurement of eccentricity data, adjustment of X-axis feed rate, and optimization of coupling table.

[0116] S5-1, by measuring the eccentric distance and the rotation angle of the B axis in real time, the system dynamically adjusts the X-axis feed according to the eccentricity data to ensure that the grinding wheel always maintains the best contact with the workpiece surface;

[0117] S5-2, based on real-time feedback during the machining process, the system generates a new coupling table and makes adjustments to optimize the feed mode for each machining process to ensure continuous machining accuracy and surface quality.

[0118] It should be noted that Figure 8 It is the flow chart of coupling procedure, showing how to carry out eccentricity algorithm and generate coupling table in coupling process; Fig. 9 The establishment procedure of coupling relationship is shown, and how to control coupling relationship through program; Fig.10 This is the coupling table of the active axis B and the driven axis X, showing how the system adjusts the coupling relationship based on real-time feedback; Fig.11 This is the effect diagram of a circular blade processed by system axis coupling grinding, showing the final high-precision blade effect.

[0119] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention has various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for grinding circular blades of a peripheral grinder based on system axis coupling, characterized in that: The following steps are involved: Step S1, using a four-axis indexable insert peripheral grinder to clamp the workpiece through the top to ensure that the workpiece and the grinding wheel are tangent to solve the eccentricity problem; Step S2, analyzing the difference between machining without eccentric circle and machining with eccentric circle; Step S3, using the Archimedean screw feeding method to ensure uniform feeding and avoid wear caused by eccentricity; Step S4, dynamically adjusting the linkage between the X-axis and the B-axis through the system axis coupling technology to reduce the eccentricity effect; Step S5, measuring the eccentricity data in real time, adjusting the X-axis feed amount to optimize the coupling table.

2. The method for grinding circular blades of a peripheral grinder based on system axis coupling according to claim 1, characterized in that: In step S1, the following sub-steps are also included: S1-1, a four-axis indexable insert peripheral grinder, the workpiece is clamped by a center, the center is located at the rotation center O of the B axis, during the machining process, the workpiece rotates around the B axis, and the grinding wheel reciprocates along the X axis; S1-2, ideally, the center of the top clamping is completely aligned with the center of the workpiece, at which point the distance between the grinding wheel and the center of the B-axis remains constant, the X-axis feed is zero, and the grinding linear speed is constant; however, in actual machining, there is an eccentricity between the center of the top clamping and the center of the workpiece, and the distance between the grinding wheel and the center of the B-axis changes as the workpiece rotates, causing the X-axis feed to change. Therefore, the X-axis feed needs to be adjusted in real time to keep the grinding wheel tangent to the arc surface of the workpiece.

3. The method for grinding circular blades of a peripheral grinder based on system axis coupling according to claim 1, characterized in that: In step S2, the following sub-steps are also included: S2-1, in the absence of eccentricity, the center of the top clamping is completely coincident with the center of the workpiece. At this time, the distance between the end face of the grinding wheel and the center of the B axis remains unchanged, the grinding linear speed is constant, and the equation for the circular workpiece is: x 2 +z 2 =R 2 (1) Where R is the radius of the circular blade to be machined, x and z are the horizontal and vertical distances on the arc surface of the workpiece, respectively; In actual grinding, the center of the center clamp is perpendicular to the end face of the grinding wheel, so x = R, z = 0, and equation (1) becomes: x=R (2) S2-2, when there is eccentricity, there is an eccentric distance between the center of the top clamping and the center of the workpiece. During the grinding process, the distance between the grinding wheel and the center of the B axis will change with the rotation of the workpiece, resulting in a change in the grinding linear speed, thereby affecting the surface quality, as shown in formula (3): (x1-rsinθ) 2 +(z1-rcosθ) 2 =R 2 (3) Among them, x1 is the horizontal distance from the point on the arc surface of the circular workpiece to the center of the circle, and z1 is the vertical distance between the center of the top clamping and the center of the actual circular workpiece; For simplifying the calculation and analysis, since the actual eccentricity is very small and the angle of the B-axis for each step is very small, so z1 << x1 and z1 - rcosθ ≈ 0, that is, equation (3) is approximated as (x1 - rsinθ) 2 = R 2 , which is further simplified to: x1=R±rsinθ (4) From formula (2), it can be seen that when grinding a circular blade without eccentricity, the grinding linear velocity change rate is: It can be seen from formula (5) that when grinding a circular blade without eccentricity, the grinding linear speed is a constant value. In the ideal case, when grinding a circular blade, the feed amount of the x-axis is 0 each time, and it is only necessary to rotate the B-axis uniformly; From formula (4), it can be seen that when there is eccentric grinding of circular blades, the rate of change of grinding line speed is: It can be seen from formula (6) that when grinding a circular blade eccentrically, the grinding line speed change rate is proportional to the eccentric distance r, and changes continuously with the cosine law of θ; the larger the eccentric distance r between the center of the center clamping and the center of the actual circular workpiece, the greater the grinding line speed change rate, and the greater the impact on the workpiece during the grinding process; when grinding a circular blade under eccentricity, the feed amount of the x-axis each time is ±rsinθ, which is a continuously changing amount, and it will also cause an impact on the workpiece surface during the grinding process, so the surface quality of the machined surface cannot be guaranteed.

4. The method for grinding circular blades of a peripheral grinder based on system axis coupling according to claim 1, characterized in that: In step S3, the following sub-steps are also included: S3-1, using the Archimedean screw feeding method, that is, the grinding wheel no longer feeds along the concentric circle path, but gradually penetrates into the workpiece surface along the spiral line. The Cartesian coordinate equation of the Archimedean screw is: In polar coordinates, the equation of the Archimedean screw is: r=a+bθ (8) Among them, a and b are real numbers. By adjusting these parameters, the shape of the spiral line can be controlled to make the feeding more uniform; When θ=0, a is the distance from the starting point to the origin of the polar coordinates. b is the value that increases with each unit increase in the helix angle r; When θ>0, a is equivalent to a rotating spiral, and parameter b controls the distance between two adjacent curves; Another formula of Archimedean screw, whose constant speed ratio shows its superiority in circular blade grinding, is as follows: Among them, ρ is the constant speed ratio, ω is the circumferential speed, and v is the linear speed; S3-2, by adjusting the spiral parameters α and β, the starting point and density of the spiral line are controlled to ensure the uniformity of each grinding and reduce the impact on the workpiece surface.

5. The method for grinding circular blades of a peripheral grinder based on system axis coupling according to claim 1, characterized in that: In step S4, the following sub-steps are also included: S4-1, by adopting the Rexroth MTX CNC system and combining the system axis coupling function, effectively controls the linkage relationship between the X-axis and the B-axis, reducing the processing error caused by eccentricity; under this system, the rotation of the B-axis is no longer controlled only by the system, but is dynamically adjusted according to the coupling table; S4-2, the system generates a coupling table to dynamically adjust the nonlinear coupling relationship between the X-axis and the B-axis according to the real-time measured eccentricity data. The coupling table can provide real-time updates in each processing cycle. The coupling relationship formula is: XB(1,CYCNUM)=R-@E83031*COS(DB)*COS(E45)+E43(10) Among them, CYCNUM is the number of B-axis feeds, R is the workpiece radius, @E83031 is the eccentricity r, DB is the rotation angle of the B-axis relative to the starting coupling position, E45 is the blade back angle, and E43 is the machining offset compensation.

6. The method for grinding circular blades of a peripheral grinder based on system axis coupling according to claim 1, characterized in that: In step S5, the following sub-steps are also included: S5-1, by measuring the eccentricity distance and the rotation angle of the B axis in real time, the system dynamically adjusts the X-axis feed according to the eccentricity data to keep the grinding wheel in contact with the workpiece surface at all times; S5-2, based on the real-time feedback during the machining process, the system will generate a new coupling table and make adjustments to optimize the feed mode for each machining.

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