Optimization method for spindle speed and feed speed of spiral bevel gear grinding machine tool

Abstract

The application discloses a spiral bevel gear grinding machine tool spindle speed and feed speed optimization method, the spiral bevel gear grinding machine tool spindle speed and feed speed optimization method includes calculating the first grinding force according to the first feed speed value of the spindle speed and feed speed set; calculating the first vibration signal value according to the first grinding force; when the first grinding force and the first vibration signal value meet the preset constraint condition, the first feed speed value is saved to the preset matching set; by analogy, until whether the kth feed speed value of the spindle speed and feed speed set meets the preset constraint condition, the maximum value of the saved feed speed value is screened based on the preset matching set, and the maximum value is used as the feed speed of the spiral bevel gear to be optimized, the processing quality, processing efficiency and process stability are improved.

Description

Technical Field

[0001] This application relates to the technical field of optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, and in particular to a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine. Background Technology

[0002] Spiral bevel gears, as a core component in the field of mechanical transmission, possess excellent load-bearing capacity, high-efficiency transmission characteristics, and low noise advantages, occupying an important position in high-precision fields such as aerospace, automotive industry, and shipbuilding. However, due to their complex tooth surface geometry and the involvement of intricate spatial curved surface meshing relationships, balancing machining accuracy and efficiency has become a pressing problem for the industry.

[0003] Currently, grinding parameter optimization methods typically optimize only geometric accuracy or grinding force independently, without considering the coupling relationship between grinding geometry, dynamic grinding force, and vibration. Spindle speed and feed rate, among other machining parameters, are usually fixed based on experience manuals, which cannot adapt to dynamic working conditions and fails to meet the high-precision, high-efficiency manufacturing requirements of high-precision spiral bevel gears. Summary of the Invention

[0004] This application aims to at least address the technical problems existing in the prior art. To this end, this application proposes a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, which can improve machining quality, machining efficiency, and process stability.

[0005] The first aspect of this application provides a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, comprising the following steps:

[0006] Obtain the set of spindle speed and feed rate of the spiral bevel gear to be optimized;

[0007] The first grinding force is calculated based on the first feed rate value of the set of spindle speed and feed rate;

[0008] Calculate the first vibration signal value based on the first grinding force;

[0009] When the first grinding force and the first vibration signal value meet the preset constraint conditions, the first feed rate value is saved to the preset matching set;

[0010] A second grinding force is calculated based on the spindle speed and the second feed rate value of the feed rate set, and a second vibration signal value is calculated based on the second grinding force. When the second grinding force and the second vibration signal value meet the preset constraint conditions, the second feed rate value is saved to the preset matching set, and so on, until the k-th grinding force is calculated based on the k-th feed rate value of the spindle speed and the feed rate set, and the k-th vibration signal value is calculated based on the k-th grinding force. When the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set.

[0011] Based on the preset matching set, the maximum value of the saved feed rate is filtered out, and the maximum value is used as the feed rate of the spiral bevel gear to be optimized.

[0012] The control method according to the embodiments of this application has at least the following beneficial effects:

[0013] This method calculates a first grinding force based on the first feed rate value of the set of spindle speed and feed rate, and calculates a first vibration signal value based on the first grinding force. When the first grinding force and the first vibration signal value meet preset constraints, the first feed rate value is saved to a preset matching set. A second grinding force is calculated based on the second feed rate value of the set of spindle speed and feed rate, and a second vibration signal value is calculated based on the second grinding force. When the second grinding force and the second vibration signal value meet preset constraints, the second feed rate value is saved to a preset matching set, and so on, until the kth grinding force is calculated based on the kth feed rate value of the set of spindle speed and feed rate, and the kth vibration signal value is calculated based on the kth grinding force. When the k-th grinding force and the k-th vibration signal value meet the preset constraints, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set. Based on the preset matching set, the maximum value of the saved feed rate values ​​is selected and used as the feed rate of the spiral bevel gear to be optimized, which improves the accuracy of optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine. This application obtains the spindle speed range without chatter through system dynamics analysis, and then adopts an adaptive control strategy to increase the feed rate during low grinding force periods to shorten the machining cycle and decrease the feed rate during high grinding force periods to avoid vibration risks, thereby improving machining quality, machining efficiency and process stability.

[0014] According to some embodiments of this application, the step of calculating the first grinding force based on the first feed rate value of the set of spindle speed and feed rate includes:

[0015] Construct the following coordinate systems: grinding wheel fixed coordinate system, grinding wheel moving coordinate system, workpiece fixed coordinate system, workpiece moving coordinate system, grinding wheel tip angle coordinate system, grinding wheel installation position coordinate system, and grinding wheel cutter rotation angle coordinate system.

[0016] Based on the grinding wheel fixed coordinate system, the grinding wheel motion coordinate system, the workpiece fixed coordinate system, the workpiece motion coordinate system, the grinding wheel inclination angle coordinate system, the grinding wheel installation position coordinate system, and the grinding wheel cutter rotation angle coordinate system, calculate the unit normal vector and the unit tangential velocity vector within the preset rectangle;

[0017] The grinding thickness is calculated using the following formula:

[0018]

[0019]

[0020] Among them, h t For the grinding thickness, N g The number of abrasive grains participating in grinding, l c N is the contact wire length; ydn (l) represents the abrasive particle density per unit area along the contact line, v w v is the speed of the workpiece. s Let a be the speed of the grinding wheel. j Let λ be the cutting depth of the j-th abrasive grain. j Let d be the spacing between adjacent abrasive grains of the j-th abrasive grain. s Let C be the nominal diameter of the grinding wheel, x(t) be the vibration in the x-direction at time t, τ be the grinding time interval between two adjacent abrasive grains, and C be the distance between the grinding grains. d τ represents the wear amount based on the amount removed per unit volume. g Cutting time of a single abrasive grain, b g T is the cutting width of the abrasive grain. g This represents the rotation cycle of the grinding wheel;

[0021] The first grinding force is calculated based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness.

[0022] According to some embodiments of this application, based on the grinding wheel fixed coordinate system, the grinding wheel motion coordinate system, the workpiece fixed coordinate system, the workpiece motion coordinate system, the grinding wheel cutting edge inclination angle coordinate system, the grinding wheel mounting position coordinate system, and the grinding wheel cutter rotation angle coordinate system, the unit normal vector and unit tangential velocity vector within a preset rectangle are calculated, including:

[0023] Obtain all tooth surface contact points within a preset rectangle, and connect each pair of adjacent tooth surface contact points into a segment;

[0024] Obtain the rocker rotation angle, height parameter, and sand profile rotation angle around the axis at any tooth surface contact point of each segment;

[0025] Based on the grinding wheel fixed coordinate system, the grinding wheel motion coordinate system, the workpiece fixed coordinate system, the workpiece motion coordinate system, the grinding wheel inclination angle coordinate system, the grinding wheel mounting position coordinate system, the grinding wheel cutter rotation angle coordinate system, the table rotation angle, the height parameter, and the rotation angle value of the grinding profile around the axis, the unit normal vector and the unit tangential velocity vector are calculated using the following formulas:

[0026]

[0027] r t (h, θ)=h·I+ρ(h)·n(θ), I=[0 0 1] T ;

[0028]

[0029] in, Let M be the rotation angle of the rocking table, h be the height parameter, θ be the rotation angle of the sand profile around the axis, and M be the rotation angle of the sand profile around the axis. wf M is the coordinate transformation matrix from the grinding wheel tip angle coordinate system to the workpiece motion coordinate system. fc M is the coordinate transformation matrix from the grinding wheel mounting position coordinate system to the grinding wheel cutting edge angle coordinate system. cm M is the coordinate transformation matrix from the fixed coordinate system of the grinding wheel to the coordinate system of the grinding wheel installation position. md M is the coordinate transformation matrix from the workpiece fixed coordinate system to the grinding wheel fixed coordinate system. da M is the coordinate transformation matrix from the grinding wheel tool angular coordinate system to the workpiece fixed coordinate system. at This is the coordinate transformation matrix from the grinding wheel motion coordinate system to the grinding wheel cutter rotation coordinate system. M is the coordinate transformation matrix from the grinding wheel's motion coordinate system to the workpiece's motion coordinate system. 11 for The value of the element in the first row and first column, M 12 for The value of the element in the first row and second column, M 13 for The value of the element in the 1st row and 3rd column, M 14 for The value of the element in the 1st row and 4th column, M 21 for The value of the element in the 2nd row and 1st column, M 22 for The value of the element in the second row and second column, M 23 for The value of the element in the 2nd row and 3rd column, M 24for The value of the element in the 2nd row and 4th column, M 31 for The value of the element in the 3rd row and 1st column, M 32 for The value of the element in the 3rd row and 2nd column, M 33 for The value of the element in the 3rd row and 3rd column, M 34 for The element value in the 3rd row and 4th column, where i is the cutting edge inclination angle, j is the tool rotation angle, S is the radial tool position, q is the angular tool position, and E is the angular tool position. n For vertical wheel positions, X c For beds, X hl X is the helix angle correction factor. p For horizontal wheel position, γ n For installation angle, Let m be the wheel blank rotation angle, I be the rolling ratio, I be the axis of symmetry of the grinding wheel profile, ρ(h) be the distance between a point on the grinding wheel surface and the intersection of the normal vector and axis I, n(θ) be the normal vector of a point on the grinding wheel surface, and R be the wheel blank rotation angle. u P is the nominal radius of the grinding wheel. w Where α is the width of the grinding wheel tip, α is the pressure angle, and ± represents the concave and convex surfaces, respectively. For unit normal vector, r is the unit tangential velocity vector. t (h, θ) is the surface expression of the grinding wheel. For the expression of the surface family generated by the grinding wheel, Let be the position of the origin of the fixed coordinate system for the grinding wheel as the rotation angle of the rocking table changes. The position of the axis of the fixed coordinate system of the grinding wheel as the rotation angle of the rocking table changes.

[0030] According to some embodiments of this application, calculating the first grinding force based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness includes:

[0031] Based on the grinding thickness, the first normal grinding force and the first tangential grinding force per unit width of chip formation stage are calculated using the following formulas:

[0032] F′ nc =K nc ∑Q i ;

[0033] V c ∑Q i =fh t ;

[0034] F′ nc =K nc fh t / V c ;

[0035]

[0036] Among them, F′ nc F′ is the first normal grinding force. tc K is the first tangential grinding force. nc Q is the first coefficient. i V is the cross-sectional area of ​​a single abrasive chip. c where f is the linear velocity of the grinding wheel, h is the feed rate, and f is the feed rate. t For grinding thickness; K is the first corresponding coefficient. tc The second coefficient;

[0037] Based on the grinding thickness, the second normal grinding force and the second tangential grinding force per unit width of the plowing stage are calculated using the following formulas:

[0038]

[0039] Among them, F′ np The second normal grinding force, F′ tp K is the second tangential grinding force. np K is the third coefficient. tp The fourth coefficient is a0, the first preset experimental coefficient is b0, the second preset experimental coefficient is c0, the third preset experimental coefficient is d, and the nominal diameter of the grinding wheel is d. e C is the equivalent diameter of the grinding wheel. s The number of abrasive grains per unit area;

[0040] Based on the grinding thickness, the third normal grinding force and the third tangential grinding force during the unit width scribing stage are calculated using the following formulas:

[0041]

[0042] Among them, F′ nr The third normal grinding force, F′ tr K1 is the third tangential grinding force, K2 is the fifth coefficient, K3 is the sixth coefficient, and K4 is the seventh coefficient.

[0043] The first normal grinding force, the second normal grinding force, and the third normal grinding force are summed to obtain the fourth normal grinding force; the first tangential grinding force, the second tangential grinding force, and the third tangential grinding force are summed to obtain the fourth tangential grinding force.

[0044] The first grinding force is calculated based on the fourth normal grinding force, the fourth tangential grinding force, the unit normal vector, and the unit tangential velocity vector.

[0045] According to some embodiments of this application, calculating the first grinding force based on the fourth normal grinding force, the fourth tangential grinding force, the unit normal vector, and the unit tangential velocity vector includes:

[0046] Calculate the corresponding unit tangential velocity vector for each segment connecting the tooth surface contact points based on the unit tangential velocity vector; calculate the corresponding unit normal vector for each segment connecting the tooth surface contact points based on the unit normal vector.

[0047] The first grinding force is calculated using the following formula:

[0048] dF(k,i)=F′ n dl·n i +F′ t dl·v i ;

[0049]

[0050] Where dF(k,i) is the grinding force of the i-th segment formed by the contact points on the tooth surface, and n i Let v be the unit normal vector corresponding to the i-th segment connecting the contact points of the tooth surfaces. i Let F′ be the unit tangential velocity vector corresponding to the i-th segment connecting the tooth surface contact points. n The fourth normal grinding force, F′ t The fourth tangential grinding force is given by k, where k is the discrete position of the wheel's swing angle, m is the number of discrete wheel swing angles, n is the number of discrete segments on a single contact line, and F is the first grinding force.

[0051] According to some embodiments of this application, the step of calculating the first vibration signal value based on the first grinding force includes:

[0052] Calculate the vibration acceleration based on the first grinding force;

[0053] Calculate the vibration velocity based on the first grinding force;

[0054] Based on the first grinding force, the vibration acceleration, and the vibration velocity, the first vibration signal value is calculated using the Runge-Kuta 4th order algorithm according to the following formula:

[0055]

[0056] Among them, c tx Let c be the first modal damping parameter of the grinding wheel. ty k is the second modal damping parameter of the grinding wheel. tx k is the first modal stiffness parameter of the grinding wheel. ty Let m be the second modal stiffness parameter of the grinding wheel. tx Let m be the first modal mass of the grinding wheel.ty The second modal mass of the grinding wheel, Let X be the component of the vibration acceleration in the X direction within the fixed coordinate system of the grinding wheel. Let Y be the component of the vibration acceleration in the Y direction of the fixed coordinate system of the grinding wheel. Let X be the component of the vibration velocity in the X direction within the fixed coordinate system of the grinding wheel. Let x be the component of the vibration velocity in the Y direction in the fixed coordinate system of the grinding wheel. t Let y be the component of the first vibration signal value in the X direction of the grinding wheel fixed coordinate system. t F represents the Y-axis component of the first vibration signal value in the fixed coordinate system of the grinding wheel. tx Let F be the component of the first grinding force in the X direction of the fixed coordinate system of the grinding wheel. ty This represents the component of the first grinding force in the Y direction within the fixed coordinate system of the grinding wheel.

[0057] According to some embodiments of this application, obtaining the set of spindle speed and feed rate of the spiral bevel gear to be optimized includes:

[0058] Based on preset vibration signal values ​​and preset grinding force, the grinding boundary without chatter is calculated using the fully discrete method.

[0059] Based on the grinding boundary, calculate the spindle speed range and feed rate range;

[0060] Based on a preset speed step size, values ​​are taken within the spindle speed range to obtain a set of spindle speeds;

[0061] Take any value from the set of spindle speeds as the spindle speed of the spiral bevel gear to be optimized;

[0062] Based on a preset feed rate step size, values ​​are taken within the feed rate range to obtain the set of feed rates.

[0063] A second aspect of this application provides an optimization system for the spindle speed and feed rate of a spiral bevel gear grinding machine tool. The optimization system for the spindle speed and feed rate of a spiral bevel gear grinding machine tool includes:

[0064] The data acquisition module is used to acquire the set of spindle speed and feed rate of the spiral bevel gear to be optimized;

[0065] The first grinding force calculation module is used to calculate the first grinding force based on the first feed rate value of the spindle speed and the feed rate set.

[0066] The first vibration signal value calculation module is used to calculate the first vibration signal value based on the first grinding force.

[0067] The storage module is used to save the first feed rate value to a preset matching set when the first grinding force and the first vibration signal value meet the preset constraint conditions.

[0068] An iterative module is used to calculate a second grinding force based on the spindle speed and the second feed rate value of the feed rate set, and to calculate a second vibration signal value based on the second grinding force; when the second grinding force and the second vibration signal value meet the preset constraint conditions, the second feed rate value is saved to the preset matching set, and so on, until the k-th grinding force is calculated based on the k-th feed rate value of the spindle speed and the feed rate set, and the k-th vibration signal value is calculated based on the k-th grinding force; when the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set;

[0069] The optimization module is used to filter the maximum value of the saved feed rate values ​​based on the preset matching set, and use the maximum value as the feed rate of the spiral bevel gear to be optimized.

[0070] This system calculates a first grinding force based on the first feed rate value of the set of spindle speed and feed rate; calculates a first vibration signal value based on the first grinding force; when the first grinding force and the first vibration signal value meet preset constraints, the first feed rate value is saved to a preset matching set; calculates a second grinding force based on the second feed rate value of the set of spindle speed and feed rate, and calculates a second vibration signal value based on the second grinding force; when the second grinding force and the second vibration signal value meet preset constraints, the second feed rate value is saved to a preset matching set, and so on, until the kth grinding force is calculated based on the kth feed rate value of the set of spindle speed and feed rate, and the kth vibration signal value is calculated based on the kth grinding force; When the k-th grinding force and the k-th vibration signal value meet the preset constraints, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set. Based on the preset matching set, the maximum value of the saved feed rate values ​​is selected and used as the feed rate of the spiral bevel gear to be optimized, which improves the accuracy of optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine. This application obtains the spindle speed range without chatter through system dynamics analysis, and then adopts an adaptive control strategy to increase the feed rate during low grinding force periods to shorten the machining cycle and decrease the feed rate during high grinding force periods to avoid vibration risks, thereby improving machining quality, machining efficiency and process stability.

[0071] A third aspect of this application provides an electronic device for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, comprising at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enables the at least one control processor to perform the aforementioned method for optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine.

[0072] A fourth aspect of this application provides a computer-readable storage medium storing computer-executable instructions for causing a computer to execute the aforementioned method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine.

[0073] It should be noted that the beneficial effects of the second to fourth aspects of this application with respect to the prior art are the same as the beneficial effects of the aforementioned optimization system for the spindle speed and feed rate of a spiral bevel gear grinding machine tool with respect to the prior art, and will not be described in detail here.

[0074] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0075] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0076] Figure 1 This is a flowchart of a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application;

[0077] Figure 2 This is a schematic diagram of grinding wheel parameters for an optimization method of spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application;

[0078] Figure 3 This is a schematic diagram illustrating the generating process of a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application.

[0079] Figure 4 This is a schematic diagram of the generating grinding kinematic chain of a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0080] Figure 5 This is a schematic diagram of the macroscopic morphological changes of undeformed chips in a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application.

[0081] Figure 6This is a schematic diagram illustrating the macroscopic variation of the undeformed chip volume over time in an optimization method for the spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application.

[0082] Figure 7 This is a schematic diagram of the contact point calculation of the concave surface of a spiral bevel gear, which is an embodiment of the optimization method for the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to this application.

[0083] Figure 8 This is a rotating projection schematic diagram of a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application;

[0084] Figure 9 This is a schematic diagram of the tooth surface contact point of a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0085] Figure 10 This is a schematic diagram of the dynamic modeling of a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0086] Figure 11 This is a schematic diagram of an embodiment of the optimization system for the spindle speed and feed rate of a spiral bevel gear grinding machine provided in this application;

[0087] Figure 12 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application. Detailed Implementation

[0088] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0089] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0090] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0091] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0092] Currently, grinding parameter optimization methods typically optimize only geometric accuracy or grinding force independently, without considering the coupling relationship between grinding geometry, dynamic grinding force, and vibration. Spindle speed and feed rate, among other machining parameters, are usually fixed based on experience manuals, which cannot adapt to dynamic working conditions and fails to meet the high-precision, high-efficiency manufacturing requirements of high-precision spiral bevel gears.

[0093] To address the aforementioned technical deficiencies, this application provides a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine.

[0094] Please see Figure 1 This is a flowchart illustrating a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine according to an embodiment of this application. This method is applied to electronic devices, such as servers. Figure 1 As shown, the optimization methods for the spindle speed and feed rate of this spiral bevel gear grinding machine include:

[0095] Step S101: Obtain the set of spindle speed and feed rate of the spiral bevel gear to be optimized;

[0096] Step S102: Calculate the first grinding force based on the first feed rate value of the set of spindle speed and feed rate;

[0097] Step S103: Calculate the first vibration signal value based on the first grinding force;

[0098] Step S104: When the first grinding force and the first vibration signal value meet the preset constraint conditions, the first feed rate value is saved to the preset matching set.

[0099] Step S105: Calculate the second grinding force based on the second feed rate value of the spindle speed and feed rate set, and calculate the second vibration signal value based on the second grinding force; when the second grinding force and the second vibration signal value meet the preset constraint conditions, save the second feed rate value to the preset matching set, and so on, until the k-th grinding force is calculated based on the k-th feed rate value of the spindle speed and feed rate set, and the k-th vibration signal value is calculated based on the k-th grinding force; when the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, save the k-th feed rate value to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set;

[0100] Step S106: Based on the preset matching set, filter the maximum value of the saved feed rate value, and use the maximum value as the feed rate of the spiral bevel gear to be optimized.

[0101] This method calculates a first grinding force based on the first feed rate value of the set of spindle speed and feed rate; calculates a first vibration signal value based on the first grinding force; when the first grinding force and the first vibration signal value meet preset constraints, the first feed rate value is saved to a preset matching set; calculates a second grinding force based on the second feed rate value of the set of spindle speed and feed rate, and calculates a second vibration signal value based on the second grinding force; when the second grinding force and the second vibration signal value meet preset constraints, the second feed rate value is saved to a preset matching set, and so on, until the kth grinding force is calculated based on the kth feed rate value of the set of spindle speed and feed rate, and the kth vibration signal value is calculated based on the kth grinding force; When the k-th grinding force and the k-th vibration signal value meet the preset constraints, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set. Based on the preset matching set, the maximum value of the saved feed rate values ​​is selected and used as the feed rate of the spiral bevel gear to be optimized, which improves the accuracy of optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine. This application obtains the spindle speed range without chatter through system dynamics analysis, and then adopts an adaptive control strategy to increase the feed rate during low grinding force periods to shorten the machining cycle and decrease the feed rate during high grinding force periods to avoid vibration risks, thereby improving machining quality, machining efficiency and process stability.

[0102] In some embodiments, refer to Figures 2 to 6 In step S102, the first grinding force is calculated based on the first feed rate value of the set of spindle speed and feed rate, including:

[0103] Step S201: Construct the grinding wheel fixed coordinate system, grinding wheel motion coordinate system, workpiece fixed coordinate system, workpiece motion coordinate system, grinding wheel tip angle coordinate system, grinding wheel installation position coordinate system, and grinding wheel cutter rotation angle coordinate system;

[0104] Step S202: Based on the grinding wheel fixed coordinate system, grinding wheel motion coordinate system, workpiece fixed coordinate system, workpiece motion coordinate system, grinding wheel tip angle coordinate system, grinding wheel installation position coordinate system, and grinding wheel cutter rotation angle coordinate system, calculate the unit normal vector and unit tangential velocity vector within the preset rectangle;

[0105] Step S203: Calculate the grinding thickness using the following formula:

[0106]

[0107] Among them, h tFor the grinding thickness, N g The number of abrasive grains participating in grinding, l c N is the contact wire length; ydn (l) represents the abrasive particle density per unit area along the contact line, v w v is the speed of the workpiece. s Let a be the speed of the grinding wheel. j Let λ be the cutting depth of the j-th abrasive grain. j Let d be the spacing between adjacent abrasive grains of the j-th abrasive grain. s Let C be the nominal diameter of the grinding wheel, x(t) be the vibration in the x-direction at time t, τ be the grinding time interval between two adjacent abrasive grains, and C be the distance between the grinding grains. d τ represents the wear amount based on the amount removed per unit volume. g Cutting time of a single abrasive grain, b g T is the cutting width of the abrasive grain. g This represents the rotation cycle of the grinding wheel;

[0108] Step S204: Calculate the first grinding force based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness.

[0109] This application achieves high-precision modeling and analysis of the grinding process by discretizing the contact line into a series of tiny line segments to accurately describe the grinding process, with each segment approximating a plane grinding process. Based on this, the vibration effect between the grinding wheel and the workpiece during grinding is considered, and it is assumed that the wear of the grinding wheel is proportional to the amount of material removed. The chip thickness of each segment is calculated.

[0110] In some embodiments, refer to Figures 7 to 9 In step S202, based on the grinding wheel fixed coordinate system, grinding wheel motion coordinate system, workpiece fixed coordinate system, workpiece motion coordinate system, grinding wheel cutting edge inclination angle coordinate system, grinding wheel installation position coordinate system, and grinding wheel cutter rotation angle coordinate system, the unit normal vector and unit tangential velocity vector within the preset rectangle are calculated, including:

[0111] Step S301: Obtain all tooth surface contact points within the preset rectangle, and connect each pair of adjacent tooth surface contact points into a segment;

[0112] Step S302: Obtain the rocker rotation angle, height parameters, and rotation angle value of the sand profile line around the axis at any tooth surface contact point of each segment;

[0113] Step S303: Based on the grinding wheel fixed coordinate system, grinding wheel motion coordinate system, workpiece fixed coordinate system, workpiece motion coordinate system, grinding wheel tip angle coordinate system, grinding wheel installation position coordinate system, grinding wheel cutter rotation angle coordinate system, table rotation angle, height parameter, and the rotation angle value of the grinding wheel profile around the axis, calculate the unit normal vector and unit tangential velocity vector using the following formulas:

[0114]

[0115] r t (h, θ)=h·I+ρ(h)·n(θ), I=[0 0 1] T ;

[0116]

[0117] in, Let M be the rotation angle of the rocking table, h be the height parameter, θ be the rotation angle of the sand profile around the axis, and M be the rotation angle of the rocking table. wf M is the coordinate transformation matrix from the grinding wheel tip angle coordinate system to the workpiece motion coordinate system. fc M is the coordinate transformation matrix from the grinding wheel mounting position coordinate system to the grinding wheel cutting edge angle coordinate system. cm M is the coordinate transformation matrix from the fixed coordinate system of the grinding wheel to the coordinate system of the grinding wheel installation position. md M is the coordinate transformation matrix from the workpiece fixed coordinate system to the grinding wheel fixed coordinate system. da M is the coordinate transformation matrix from the grinding wheel tool angular coordinate system to the workpiece fixed coordinate system. at This is the coordinate transformation matrix from the grinding wheel motion coordinate system to the grinding wheel cutter rotation coordinate system. M is the coordinate transformation matrix from the grinding wheel's motion coordinate system to the workpiece's motion coordinate system. 11 for The value of the element in the first row and first column, M 12 for The value of the element in the first row and second column, M 13 for The value of the element in the 1st row and 3rd column, M 14 for The value of the element in the 1st row and 4th column, M 21 for The value of the element in the 2nd row and 1st column, M 22 for The value of the element in the second row and second column, M 23 for The value of the element in the 2nd row and 3rd column, M 24 for The value of the element in the 2nd row and 4th column, M 31 for The value of the element in the 3rd row and 1st column, M 32 for The value of the element in the 3rd row and 2nd column, M 33 for The value of the element in the 3rd row and 3rd column, M 34 for The element value in the 3rd row and 4th column, where i is the cutting edge inclination angle, j is the tool rotation angle, S is the radial tool position, q is the angular tool position, and E is the angular tool position.n For vertical wheel positions, X c For beds, X hl X is the helix angle correction factor. p For horizontal wheel position, γ n For installation angle, Let m be the wheel blank rotation angle, I be the rolling ratio, I be the axis of symmetry of the grinding wheel profile, ρ(h) be the distance between a point on the grinding wheel surface and the intersection of the normal vector and axis I, n(θ) be the normal vector of a point on the grinding wheel surface, and R be the wheel blank rotation angle. u P is the nominal radius of the grinding wheel. w Where α is the width of the grinding wheel tip, α is the pressure angle, and ± represents the concave and convex surfaces, respectively. For unit normal vector, r is the unit tangential velocity vector. t (h, θ) is the surface expression of the grinding wheel. For the expression of the surface family generated by the grinding wheel, Let be the position of the origin of the fixed coordinate system for the grinding wheel as the rotation angle of the rocking table changes. The position of the axis of the fixed coordinate system of the grinding wheel as the rotation angle of the rocking table changes.

[0118] This embodiment improves the accuracy of the data by calculating the unit normal vector and unit tangential velocity vector within a preset rectangle.

[0119] In some embodiments, in step S204, calculating the first grinding force based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness includes:

[0120] Step S401: Based on the grinding thickness, calculate the first normal grinding force and the first tangential grinding force per unit width during the chip formation stage using the following formula:

[0121] F′ nc =K nc ∑Q i ;

[0122] V c ΣQ i =fh t ;

[0123] F′ nc =K nc fh t / V c ;

[0124]

[0125] Among them, F′ nc F′ is the first normal grinding force. tc K is the first tangential grinding force. nc Q is the first coefficient. iV is the cross-sectional area of ​​a single abrasive chip. c where f is the linear velocity of the grinding wheel, h is the feed rate, and f is the feed rate. t For grinding thickness; K is the first corresponding coefficient. tc The second coefficient;

[0126] Step S402: Based on the grinding thickness, calculate the second normal grinding force and the second tangential grinding force per unit width of the plowing stage using the following formulas:

[0127]

[0128] Among them, F′ np The second normal grinding force, F′ tp K is the second tangential grinding force. np K is the third coefficient. tp The fourth coefficient is a0, the first preset experimental coefficient is b0, the second preset experimental coefficient is c0, the third preset experimental coefficient is d, and the nominal diameter of the grinding wheel is d. e C is the equivalent diameter of the grinding wheel. s The number of abrasive grains per unit area;

[0129] Step S403: Based on the grinding thickness, calculate the third normal grinding force and the third tangential grinding force per unit width during the scribing stage using the following formulas:

[0130]

[0131] Among them, F′ nr The third normal grinding force, F′ tr K1 is the third tangential grinding force, K2 is the fifth coefficient, K3 is the sixth coefficient, and K4 is the seventh coefficient.

[0132] Step S404: Summing the first normal grinding force, the second normal grinding force, and the third normal grinding force yields the fourth normal grinding force; summing the first tangential grinding force, the second tangential grinding force, and the third tangential grinding force yields the fourth tangential grinding force.

[0133] Step S405: Calculate the first grinding force based on the fourth normal grinding force, the fourth tangential grinding force, the unit normal vector, and the unit tangential velocity vector.

[0134] In some embodiments, calculating the first grinding force based on the fourth normal grinding force, the fourth tangential grinding force, the unit normal vector, and the unit tangential velocity vector includes:

[0135] Calculate the corresponding unit tangential velocity vector for each segment connecting the tooth surface contact points based on the unit tangential velocity vector; calculate the corresponding unit normal vector for each segment connecting the tooth surface contact points based on the unit normal vector.

[0136] The first grinding force is calculated using the following formula:

[0137] dF(k,i)=F′ n dl·n i +F′ t dl·v i ;

[0138]

[0139] Where dF(k,i) is the grinding force of the i-th segment formed by the contact points on the tooth surface, and n i Let v be the unit normal vector corresponding to the i-th segment connecting the contact points of the tooth surfaces. i Let F′ be the unit tangential velocity vector corresponding to the i-th segment connecting the tooth surface contact points. n The fourth normal grinding force, F′ t The fourth tangential grinding force is given by k, where k is the discrete position of the wheel's swing angle, m is the number of discrete wheel swing angles, n is the number of discrete segments on a single contact line, and F is the first grinding force.

[0140] This application discretizes the spatial curve into a series of infinitesimal line segments during the grinding process of spiral bevel gears, and approximates each line segment as a plane grinding problem. Based on the local contact geometry and material removal rate, the instantaneous grinding force components at each infinitesimal line segment are calculated. Subsequently, through a coordinate transformation matrix, the grinding force at each line segment is transformed to the workpiece's global coordinate system and then vector-superimposed to obtain the spatial distribution characteristics of the overall grinding force, thereby improving the accuracy of grinding force calculation.

[0141] Reference Figure 7 Given the face cone angle, pitch cone angle, root cone angle, outer cone distance, tooth root height, and tooth tip height of a spiral bevel gear, a fixed rotational projection plane can be determined, which is also the cross-section of the blank along the axis.

[0142] Reference Figure 8 The algorithm determines whether the contact point lies on the tooth surface by checking if the corresponding rotational projection point is located on the rotational projection plane. The core idea is to determine the point's position using the dot product of the edge vectors of the matrix and the vector from the point to a vertex of the matrix. The algorithm steps are as follows:

[0143] Define the four vertices ABCD of the rectangle and determine the side vectors. For point P, calculate the vector calculate and The dot product is used to determine whether the dot product of the edge vectors in sequence with the vectors from each vertex to point P is positive or negative, and whether the calculated point P on the tooth surface of the spiral bevel gear is located within its rectangle.

[0144] Reference Figure 9 Connect the calculated adjacent contact points within the defined area into a segment, and select any one of the two points. Value, substitute into From this, we can obtain the unit normal vector n at each segment. i Unit tangential velocity vector v i .

[0145] Specifically, refer to Figure 10 In some embodiments, in step S103, calculating the first vibration signal value based on the first grinding force includes:

[0146] Step S501: Calculate the vibration acceleration based on the first grinding force;

[0147] Step S502: Calculate the vibration velocity based on the first grinding force;

[0148] Step S503: Based on the first grinding force, vibration acceleration, and vibration velocity, calculate the first vibration signal value using the Runge-Kuta 4th order algorithm according to the following formula:

[0149]

[0150] Among them, c tx Let c be the first modal damping parameter of the grinding wheel. ty k is the second modal damping parameter of the grinding wheel. tx k is the first modal stiffness parameter of the grinding wheel. ty Let m be the second modal stiffness parameter of the grinding wheel. tx Let m be the first modal mass of the grinding wheel. ty The second modal mass of the grinding wheel, Let X be the component of the vibration acceleration in the X direction within the fixed coordinate system of the grinding wheel. Let Y be the component of the vibration acceleration in the Y direction of the fixed coordinate system of the grinding wheel. Let X be the component of the vibration velocity in the X direction within the fixed coordinate system of the grinding wheel. Let x be the component of the vibration velocity in the Y direction in the fixed coordinate system of the grinding wheel. t Let y be the component of the first vibration signal value in the X direction of the grinding wheel fixed coordinate system. t F represents the Y-axis component of the first vibration signal value in the fixed coordinate system of the grinding wheel. tx Let F be the component of the first grinding force in the X direction of the fixed coordinate system of the grinding wheel. ty This represents the component of the first grinding force in the Y direction within the fixed coordinate system of the grinding wheel.

[0151] In some embodiments, in step S101, obtaining the set of spindle speed and feed rate of the spiral bevel gear to be optimized includes:

[0152] Step S601: Based on the preset vibration signal value and preset grinding force, the grinding boundary without chatter is calculated by the fully discrete method;

[0153] Step S602: Based on the grinding boundary, calculate the spindle speed range and feed rate range;

[0154] Step S603: Based on the preset speed step size, take values ​​within the spindle speed range to obtain the spindle speed set;

[0155] Step S604: Take any value from the set of spindle speeds as the spindle speed of the spiral bevel gear to be optimized;

[0156] Step S605: Based on the preset feed rate step size, take values ​​within the feed rate range to obtain a set of feed rates.

[0157] Specifically, the correlation between the vibration signal generated by grinding force and surface roughness is analyzed. Through experimental design, the vibration signal information corresponding to the optimal surface roughness is analyzed, and this information is pre-set as the component x in the X direction of the reference vibration value of the vibration signal. t，base and the component in the Y direction y t，base At the same time, the pre-designed reference grinding force component F in the X direction can also be obtained. tx，base and the component F in the Y direction ty，base .

[0158] The characteristic matrix of the state-space equations is solved using a fully discrete method, thereby obtaining a stable grinding boundary that does not exhibit chatter. The range of the grinding wheel speed N and the range of the feed rate f are then set based on this stable grinding boundary.

[0159] N min ≤N≤N max

[0160] f min ≤f≤f max

[0161] Where, N min The minimum set grinding wheel speed, N max f is the maximum set grinding wheel speed. min f is the set minimum feed rate. max This is the maximum set feed rate.

[0162] From N min To N max The grinding wheel speed is uniformly divided, and the grinding wheel speed of the i-th segment is N. i From f min to f max The feed rate is uniformly divided, and the spindle speed of the u-th segment is f. u .

[0163] The spindle speed is iterated from its minimum to its maximum value. By calculating the grinding force and vibration amplitude, it is ensured that the set constraints for the grinding force fluctuation range and vibration amplitude fluctuation range are met, respectively. Based on this, the maximum feed rate that satisfies the constraints is optimized and sought. The process is as follows:

[0164] The rotational speed at position i is N. i traverse f u From f min to f max Calculate the corresponding grinding force F x，i，u F y，i，u The value, and the corresponding vibration signal x are calculated. i，u y i，u .

[0165] Through constraint expressions Calculate the maximum feed rate that satisfies the constraints. Where ΔF x ΔF is the set range of grinding force fluctuation in the X direction. y For the set grinding force fluctuation range in the Y direction, Δx t Δy is the range of vibration magnitude fluctuation in the X direction. t The range of vibration magnitude fluctuations in the Y direction is set.

[0166] Determine N i+1 By repeating the above calculations, a line can be obtained for each grinding wheel speed N. i The corresponding f u The curve; when the spindle speed is selected, a curve of the feed rate changing with time can be obtained.

[0167] This application, through system dynamics analysis based on the time-varying characteristics of chip volume and grinding force during generating grinding, obtains the spindle speed range where chatter does not occur. Secondly, it employs an adaptive control strategy: increasing the feed rate during low grinding force periods to shorten the machining cycle, and decreasing the feed rate during high grinding force periods to avoid vibration risks. This application significantly improves machining quality, efficiency, and process stability, while reducing production costs, thus promoting the intelligent and adaptive upgrading of spiral bevel gear machining.

[0168] Specifically, for the convenience of those skilled in the art, a set of preferred embodiments is provided below:

[0169] I. Data Acquisition:

[0170] Obtain the set of spindle speed and feed rate of the spiral bevel gear to be optimized, specifically:

[0171] Based on preset vibration signal values ​​and preset grinding force, the grinding boundary without chatter is calculated using the fully discrete method.

[0172] Based on the grinding boundary, calculate the spindle speed range and feed rate range;

[0173] Based on a preset speed step size, values ​​are taken within the spindle speed range to obtain a set of spindle speeds;

[0174] Use any value from the set of spindle speeds as the spindle speed of the spiral bevel gear to be optimized;

[0175] Based on the preset feed rate step size, values ​​are taken within the feed rate range to obtain a set of feed rates.

[0176] II. Calculation of the first grinding force:

[0177] The first grinding force is calculated based on the first feed rate value from the set of spindle speed and feed rate, specifically:

[0178] Construct the following coordinate systems: grinding wheel fixed coordinate system, grinding wheel moving coordinate system, workpiece fixed coordinate system, workpiece moving coordinate system, grinding wheel tip angle coordinate system, grinding wheel installation position coordinate system, and grinding wheel cutter rotation angle coordinate system.

[0179] Based on the coordinate systems of the grinding wheel fixed coordinate system, grinding wheel motion coordinate system, workpiece fixed coordinate system, workpiece motion coordinate system, grinding wheel tip angle coordinate system, grinding wheel mounting position coordinate system, and grinding wheel cutter rotation angle coordinate system, the unit normal vector and unit tangential velocity vector within the preset rectangle are calculated as follows:

[0180] Obtain all tooth surface contact points within a preset rectangle, and connect every two adjacent tooth surface contact points into a segment;

[0181] Obtain the rocker rotation angle, height parameter, and sand profile rotation angle around the axis at any tooth surface contact point of each segment;

[0182] Based on the fixed coordinate system of the grinding wheel, the moving coordinate system of the grinding wheel, the fixed coordinate system of the workpiece, the moving coordinate system of the workpiece, the coordinate system of the grinding wheel inclination angle, the coordinate system of the grinding wheel installation position, the coordinate system of the grinding wheel cutter rotation angle, the rotation angle of the rocking table, the height parameter, and the rotation angle value of the grinding wheel profile around the axis, the unit normal vector and the unit tangential velocity vector are calculated using the following formulas:

[0183]

[0184] r t (h, θ)=h·I+ρ(h)·n(θ), I=[0 0 1] T ;

[0185]

[0186] in, Let M be the rotation angle of the rocking table, h be the height parameter, θ be the rotation angle of the sand profile around the axis, and M be the rotation angle of the sand profile around the axis. wf M is the coordinate transformation matrix from the grinding wheel tip angle coordinate system to the workpiece motion coordinate system. fc M is the coordinate transformation matrix from the grinding wheel mounting position coordinate system to the grinding wheel cutting edge angle coordinate system. cm M is the coordinate transformation matrix from the fixed coordinate system of the grinding wheel to the coordinate system of the grinding wheel installation position. md M is the coordinate transformation matrix from the workpiece fixed coordinate system to the grinding wheel fixed coordinate system. da M is the coordinate transformation matrix from the grinding wheel tool angular coordinate system to the workpiece fixed coordinate system. at This is the coordinate transformation matrix from the grinding wheel motion coordinate system to the grinding wheel cutter rotation coordinate system. M is the coordinate transformation matrix from the grinding wheel's motion coordinate system to the workpiece's motion coordinate system. 11 for The value of the element in the first row and first column, M 12 for The value of the element in the first row and second column, M 13 for The value of the element in the 1st row and 3rd column, M 14 for The value of the element in the 1st row and 4th column, M 21 for The value of the element in the 2nd row and 1st column, M 22 for The value of the element in the second row and second column, M 23 for The value of the element in the 2nd row and 3rd column, M 24 for The value of the element in the 2nd row and 4th column, M 31 for The value of the element in the 3rd row and 1st column, M 32 for The value of the element in the 3rd row and 2nd column, M 33 for The value of the element in the 3rd row and 3rd column, M 34 for The element value in the 3rd row and 4th column, where i is the cutting edge inclination angle, j is the tool rotation angle, S is the radial tool position, q is the angular tool position, and E is the angular tool position. n For vertical wheel positions, X c For beds, X hl X is the helix angle correction factor. p For horizontal wheel position, γ n For installation angle, Let m be the wheel blank rotation angle, I be the rolling ratio, I be the axis of symmetry of the grinding wheel profile, ρ(h) be the distance between a point on the grinding wheel surface and the intersection of the normal vector and axis I, n(θ) be the normal vector of a point on the grinding wheel surface, and R be the wheel blank rotation angle. u P is the nominal radius of the grinding wheel. w Where α is the width of the grinding wheel tip, α is the pressure angle, and ± represents the concave and convex surfaces, respectively. For unit normal vector, r is the unit tangential velocity vector. t (h, θ) is the surface expression of the grinding wheel. For the expression of the surface family generated by the grinding wheel, Let be the position of the origin of the fixed coordinate system for the grinding wheel as the rotation angle of the rocking table changes. The position of the axis of the fixed coordinate system of the grinding wheel as the rotation angle of the rocking table changes.

[0187] The grinding thickness is calculated using the following formula:

[0188]

[0189] Among them, h t For the grinding thickness, N g The number of abrasive grains participating in grinding, l c N is the contact wire length; ydn (l) represents the abrasive particle density per unit area along the contact line, v w v is the speed of the workpiece. s Let a be the speed of the grinding wheel. j Let λ be the cutting depth of the j-th abrasive grain. j Let d be the spacing between adjacent abrasive grains of the j-th abrasive grain. s Let C be the nominal diameter of the grinding wheel, x(t) be the vibration in the x-direction at time t, τ be the grinding time interval between two adjacent abrasive grains, and C be the distance between the grinding wheels. d τ represents the wear amount based on the amount removed per unit volume. g Cutting time of a single abrasive grain, b g T is the cutting width of the abrasive grain. g This refers to the rotation cycle of the grinding wheel;

[0190] The first grinding force is calculated based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness, specifically as follows:

[0191] Based on the grinding thickness, the first normal grinding force and the first tangential grinding force per unit width during the chip formation stage are calculated using the following formulas:

[0192] F′ nc =K nc ΣQ i ;

[0193]

[0194] F′ nc =K nc fh t / V c ;

[0195]

[0196] Among them, F′ nc F′ is the first normal grinding force. tc K is the first tangential grinding force. nc Q is the first coefficient. i V is the cross-sectional area of ​​a single abrasive chip. c where f is the linear velocity of the grinding wheel, h is the feed rate, and f is the feed rate. t For grinding thickness; K is the first corresponding coefficient. tc The second coefficient;

[0197] Based on the grinding thickness, the second normal grinding force and the second tangential grinding force per unit width of the plowing stage are calculated using the following formulas:

[0198]

[0199] Among them, F′ np The second normal grinding force, F′ tp K is the second tangential grinding force. np K is the third coefficient. tp The fourth coefficient is a0, the first preset experimental coefficient is b0, the second preset experimental coefficient is c0, the third preset experimental coefficient is d, and the nominal diameter of the grinding wheel is d. e C is the equivalent diameter of the grinding wheel. s The number of abrasive grains per unit area;

[0200] Based on the grinding thickness, the third normal grinding force and the third tangential grinding force during the unit width scribing stage are calculated using the following formulas:

[0201]

[0202] Among them, F′ nr The third normal grinding force, F′ tr K1 is the third tangential grinding force, K2 is the fifth coefficient, K3 is the sixth coefficient, and K4 is the seventh coefficient.

[0203] The fourth normal grinding force is obtained by summing the first normal grinding force, the second normal grinding force, and the third normal grinding force; the fourth tangential grinding force is obtained by summing the first tangential grinding force, the second tangential grinding force, and the third tangential grinding force.

[0204] Calculate the corresponding unit tangential velocity vector for each segment connecting the tooth surface contact points based on the unit tangential velocity vector; calculate the corresponding unit normal vector for each segment connecting the tooth surface contact points based on the unit normal vector.

[0205] The first grinding force is calculated using the following formula:

[0206] dF(k,i)=F′ n dl·n i +F′ t dl·v i ;

[0207]

[0208] Where dF(k,i) is the grinding force of the i-th segment formed by the contact points on the tooth surface, and n i Let v be the unit normal vector corresponding to the i-th segment connecting the contact points of the tooth surfaces. i Let F′ be the unit tangential velocity vector corresponding to the i-th segment connecting the tooth surface contact points. n The fourth normal grinding force, F′ t The fourth tangential grinding force is given by k, where k is the discrete position of the wheel's swing angle, m is the number of discrete wheel swing angles, n is the number of discrete segments on a single contact line, and F is the first grinding force.

[0209] III. Calculation of the first vibration signal value:

[0210] The first vibration signal value is calculated based on the first grinding force, specifically as follows:

[0211] Calculate the vibration acceleration based on the first grinding force;

[0212] Calculate the vibration velocity based on the first grinding force;

[0213] Based on the first grinding force, vibration acceleration, and vibration velocity, the first vibration signal value is calculated using the Runge-Kuta 4th order algorithm according to the following formula:

[0214]

[0215] Among them, c tx Let c be the first modal damping parameter of the grinding wheel. ty k is the second modal damping parameter of the grinding wheel. tx k is the first modal stiffness parameter of the grinding wheel. ty Let m be the second modal stiffness parameter of the grinding wheel. tx Let m be the first modal mass of the grinding wheel. ty The second modal mass of the grinding wheel, Let X be the component of the vibration acceleration in the X direction within the fixed coordinate system of the grinding wheel. Let Y be the component of the vibration acceleration in the Y direction of the fixed coordinate system of the grinding wheel. Let X be the component of the vibration velocity in the X direction within the fixed coordinate system of the grinding wheel. Let x be the component of the vibration velocity in the Y direction in the fixed coordinate system of the grinding wheel. t Let y be the component of the first vibration signal value in the X direction of the grinding wheel fixed coordinate system. t F represents the Y-axis component of the first vibration signal value in the fixed coordinate system of the grinding wheel. tx Let F be the component of the first grinding force in the X direction of the fixed coordinate system of the grinding wheel. ty This represents the component of the first grinding force in the Y direction within the fixed coordinate system of the grinding wheel.

[0216] IV. Feed rate optimization:

[0217] When the first grinding force and the first vibration signal value meet the preset constraint conditions, the first feed rate value is saved to the preset matching set;

[0218] The second grinding force is calculated based on the second feed rate value from the set of spindle speed and feed rate, and the second vibration signal value is calculated based on the second grinding force. When the second grinding force and the second vibration signal value meet the preset constraint conditions, the second feed rate value is saved to the preset matching set. This process continues until the k-th grinding force is calculated based on the k-th feed rate value from the set of spindle speed and feed rate, and the k-th vibration signal value is calculated based on the k-th grinding force. When the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set.

[0219] Based on a preset matching set, the maximum value of the saved feed rate is filtered and used as the feed rate of the spiral bevel gear to be optimized.

[0220] Additionally, refer to Figure 11 One embodiment of this application provides an optimization system for the spindle speed and feed rate of a spiral bevel gear grinding machine, including a data acquisition module 1100, a first grinding force calculation module 1200, a first vibration signal value calculation module 1300, a storage module 1400, an iteration module 1500, and an optimization module 1600, wherein:

[0221] The data acquisition module 1100 is used to acquire the set of spindle speed and feed rate of the spiral bevel gear to be optimized;

[0222] The first grinding force calculation module 1200 is used to calculate the first grinding force based on the first feed rate value of the set of spindle speed and feed rate;

[0223] The first vibration signal value calculation module 1300 is used to calculate the first vibration signal value based on the first grinding force;

[0224] The storage module 1400 is used to save the first feed rate value to a preset matching set when the first grinding force and the first vibration signal value meet the preset constraint conditions.

[0225] The iteration module 1500 is used to calculate the second grinding force based on the second feed rate value of the spindle speed and feed rate set, and to calculate the second vibration signal value based on the second grinding force. When the second grinding force and the second vibration signal value meet the preset constraint conditions, the second feed rate value is saved to the preset matching set, and so on, until the k-th grinding force is calculated based on the k-th feed rate value of the spindle speed and feed rate set, and the k-th vibration signal value is calculated based on the k-th grinding force. When the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set.

[0226] The optimization module 1600 is used to filter the maximum value of the saved feed rate values ​​based on a preset matching set, and use the maximum value as the feed rate of the spiral bevel gear to be optimized.

[0227] This system calculates a first grinding force based on the first feed rate value of the set of spindle speed and feed rate; calculates a first vibration signal value based on the first grinding force; when the first grinding force and the first vibration signal value meet preset constraints, the first feed rate value is saved to a preset matching set; calculates a second grinding force based on the second feed rate value of the set of spindle speed and feed rate, and calculates a second vibration signal value based on the second grinding force; when the second grinding force and the second vibration signal value meet preset constraints, the second feed rate value is saved to a preset matching set, and so on, until the kth grinding force is calculated based on the kth feed rate value of the set of spindle speed and feed rate, and the kth vibration signal value is calculated based on the kth grinding force; When the k-th grinding force and the k-th vibration signal value meet the preset constraints, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set. Based on the preset matching set, the maximum value of the saved feed rate values ​​is selected and used as the feed rate of the spiral bevel gear to be optimized, which improves the accuracy of optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine. This application obtains the spindle speed range without chatter through system dynamics analysis, and then adopts an adaptive control strategy to increase the feed rate during low grinding force periods to shorten the machining cycle and decrease the feed rate during high grinding force periods to avoid vibration risks, thereby improving machining quality, machining efficiency and process stability.

[0228] It should be noted that the system embodiments described above are based on the same inventive concept as the method embodiments described above. Therefore, the relevant content of the method embodiments described above is also applicable to the system embodiments described above, and will not be repeated here.

[0229] Figure 12 This paper illustrates a schematic diagram of the optimized hardware structure for the spindle speed and feed rate of a spiral bevel gear grinding machine tool provided in an embodiment of this application.

[0230] The device for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine may include a processor 301 and a memory 302 storing computer program instructions.

[0231] Specifically, the processor 301 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0232] Memory 302 may include mass storage for data or instructions. For example, and not limitingly, memory 302 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 302 may include removable or non-removable (or fixed) media. Where appropriate, memory 302 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 302 is non-volatile solid-state memory.

[0233] In some embodiments, memory 302 may include read-only memory (ROM), random access memory (RAM), disk storage media device, optical storage media device, flash memory device, electrical, optical, or other physical / tangible memory storage device. Thus, generally, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to one aspect of this disclosure.

[0234] The processor 301 reads and executes computer program instructions stored in the memory 302 to implement any of the methods for optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine tool in the above embodiments.

[0235] In one example, the device for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine may also include a communication interface 303 and a bus 310. Wherein, such as Figure 12 As shown, the processor 301, memory 302, and communication interface 303 are connected through bus 310 and complete communication with each other.

[0236] The communication interface 303 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0237] Bus 310 includes hardware, software, or both, that couples components of an optimization device for the spindle speed and feed rate of a spiral bevel gear grinding machine to each other. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 310 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0238] The device for optimizing the spindle speed and feed rate of the spiral bevel gear grinding machine tool can execute the optimization method for the spindle speed and feed rate of the spiral bevel gear grinding machine tool in this application embodiment based on a three-dimensional design model, thereby achieving a combination of... Figure 1 and Figure 11 The invention describes a method and system for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine.

[0239] Furthermore, in conjunction with the optimization methods for the spindle speed and feed rate of the spiral bevel gear grinding machine tool in the above embodiments, this application embodiment can provide a computer storage medium for implementation. This computer storage medium stores computer program instructions; when these computer program instructions are executed by a processor, they implement any of the optimization methods for the spindle speed and feed rate of the spiral bevel gear grinding machine tool in the above embodiments.

[0240] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0241] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0242] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0243] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0244] The above description is merely a specific implementation of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, characterized in that, The optimization methods for the spindle speed and feed rate of the spiral bevel gear grinding machine tool include: Obtain the set of spindle speed and feed rate of the spiral bevel gear to be optimized; The first grinding force is calculated based on the first feed rate value of the set of spindle speed and feed rate; Calculate the first vibration signal value based on the first grinding force; When the first grinding force and the first vibration signal value meet the preset constraint conditions, the first feed rate value is saved to the preset matching set, specifically: from to The grinding wheel speed is evenly divided, and its first The grinding wheel speed of the section is ,from to Uniformly divide the feed rate, its first The spindle speed of the section is ,in, This is the set minimum grinding wheel speed. This is the maximum set grinding wheel speed. The minimum set feed rate, This is the maximum set feed rate; The expression for the preset constraint is: ； in, For the first The grinding wheel speed of the first segment, the first The spindle speed of the segment corresponds to the set first grinding force in the X direction. For the first The grinding wheel speed of the first segment, the first The first grinding force in the Y direction corresponding to the spindle speed of the segment. The set range of grinding force fluctuation in the X direction. The set range of grinding force fluctuation in the Y direction. The range of vibration magnitude fluctuation in the X direction is set. The set range of vibration magnitude fluctuation in the Y direction. The component of the pre-designed reference grinding force in the X direction, obtained through experimental design analysis, The Y-direction component of the pre-designed reference grinding force obtained through experimental design analysis. The component of the reference vibration value in the X direction obtained through experimental design analysis is the vibration signal reference value. The component of the reference vibration value in the Y direction of the vibration signal obtained through experimental design analysis; A second grinding force is calculated based on the spindle speed and the second feed rate value of the feed rate set, and a second vibration signal value is calculated based on the second grinding force. When the second grinding force and the second vibration signal value meet the preset constraint conditions, the second feed rate value is saved to the preset matching set, and so on, until the k-th grinding force is calculated based on the k-th feed rate value of the spindle speed and the feed rate set, and the k-th vibration signal value is calculated based on the k-th grinding force. When the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set. Based on the preset matching set, the maximum value of the saved feed rate is filtered out, and the maximum value is used as the feed rate of the spiral bevel gear to be optimized.

2. The method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to claim 1, characterized in that, The calculation of the first grinding force based on the first feed rate value of the set of spindle speed and feed rate includes: Construct the following coordinate systems: grinding wheel fixed coordinate system, grinding wheel moving coordinate system, workpiece fixed coordinate system, workpiece moving coordinate system, grinding wheel tip angle coordinate system, grinding wheel installation position coordinate system, and grinding wheel cutter rotation angle coordinate system. Based on the grinding wheel fixed coordinate system, the grinding wheel motion coordinate system, the workpiece fixed coordinate system, the workpiece motion coordinate system, the grinding wheel inclination angle coordinate system, the grinding wheel installation position coordinate system, and the grinding wheel cutter rotation angle coordinate system, calculate the unit normal vector and the unit tangential velocity vector within the preset rectangle; The grinding thickness is calculated using the following formula: ； in, For grinding thickness, The number of abrasive grains involved in the grinding process. This refers to the length of the contact wire; The abrasive density per unit area along the contact line. For the speed of the workpiece, For grinding wheel speed, For the first The cutting depth of each abrasive grain. For the first The spacing between adjacent abrasive grains. The nominal diameter of the grinding wheel. for Moment The amount of vibration in the direction, This refers to the grinding time interval between two adjacent abrasive grains. This refers to the amount of wear removed per unit volume. Cutting time of a single abrasive grain This represents the cutting width of the abrasive grain. This represents the rotation cycle of the grinding wheel; The first grinding force is calculated based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness.

3. The method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to claim 2, characterized in that, Based on the grinding wheel fixed coordinate system, the grinding wheel motion coordinate system, the workpiece fixed coordinate system, the workpiece motion coordinate system, the grinding wheel cutting edge inclination angle coordinate system, the grinding wheel mounting position coordinate system, and the grinding wheel cutter rotation angle coordinate system, the unit normal vector and unit tangential velocity vector within the preset rectangle are calculated, including: Obtain all tooth surface contact points within a preset rectangle, and connect each pair of adjacent tooth surface contact points into a segment; Obtain the rocker rotation angle, height parameter, and sand profile rotation angle around the axis at any tooth surface contact point of each segment; Based on the grinding wheel fixed coordinate system, the grinding wheel motion coordinate system, the workpiece fixed coordinate system, the workpiece motion coordinate system, the grinding wheel inclination angle coordinate system, the grinding wheel mounting position coordinate system, the grinding wheel cutter rotation angle coordinate system, the table rotation angle, the height parameter, and the rotation angle value of the grinding profile around the axis, the unit normal vector and the unit tangential velocity vector are calculated using the following formulas: ； ； ； ； ； ； ； ； ； ； ； ； ； in, The angle of the rocking table, For the height parameter, Let be the angle value of the sand profile around the axis. This is the coordinate transformation matrix from the grinding wheel tip angle coordinate system to the workpiece motion coordinate system. This is the coordinate transformation matrix from the grinding wheel installation position coordinate system to the grinding wheel cutting edge angle coordinate system. This is the coordinate transformation matrix from the fixed coordinate system of the grinding wheel to the coordinate system of the grinding wheel installation position. This is the coordinate transformation matrix from the workpiece fixed coordinate system to the grinding wheel fixed coordinate system. This is the coordinate transformation matrix from the grinding wheel tool angular coordinate system to the workpiece fixed coordinate system. This is the coordinate transformation matrix from the grinding wheel motion coordinate system to the grinding wheel cutter rotation coordinate system. This is the coordinate transformation matrix from the grinding wheel's motion coordinate system to the workpiece's motion coordinate system. for The value of the element in the first row and first column. for The value of the element in the first row and second column. for The value of the element in the 1st row and 3rd column. for The value of the element in the 1st row and 4th column. for The value of the element in the second row and first column. for The value of the element in the second row and second column. for The value of the element in the 2nd row and 3rd column. for The value of the element in the 2nd row and 4th column. for The value of the element in the 3rd row and 1st column. for The value of the element in the 3rd row and 2nd column. for The value of the element in the 3rd row and 3rd column. for The value of the element in the 3rd row and 4th column. For the blade inclination angle, For the knife to turn the corner, For radial tool position, For angular tool position, For vertical wheel positions, For beds, This is the helix angle correction factor. For horizontal wheel positions, For installation angle, For the wheel blank rotation angle, For rolling ratio, The axis of symmetry of the sand profile. Let a point on the surface of the grinding wheel be along the direction of the normal vector and the axis. Distance between intersections Let be the normal vector of a point on the surface of the grinding wheel. Where is the nominal radius of the grinding wheel. The width of the grinding wheel tip. For pressure angle, It has concave and convex surfaces. For unit normal vector, The unit tangential velocity vector, The surface expression of the grinding wheel, For the expression of the surface family generated by the grinding wheel, Let be the position of the origin of the fixed coordinate system for the grinding wheel as the rotation angle of the rocking table changes. The position of the axis of the fixed coordinate system of the grinding wheel as the rotation angle of the rocking table changes.

4. The method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to claim 3, characterized in that, The calculation of the first grinding force based on the unit normal vector, the unit tangential velocity vector, and the grinding thickness includes: Based on the grinding thickness, the first normal grinding force and the first tangential grinding force per unit width of chip formation stage are calculated using the following formulas: ； ； ； ； in, The first normal grinding force, The first tangential grinding force, As the first coefficient, The cross-sectional area of ​​a single abrasive chip. The linear velocity of the grinding wheel. For feed rate, For grinding thickness; The first corresponding coefficient, The second coefficient; Based on the grinding thickness, the second normal grinding force and the second tangential grinding force per unit width of the plowing stage are calculated using the following formulas: ； ； in, The second normal grinding force, This is the second tangential grinding force. The third coefficient, It is the fourth coefficient. The first preset experimental coefficient, This is the second preset experimental coefficient. This is the third preset experimental coefficient. The nominal diameter of the grinding wheel. Let be the equivalent diameter of the grinding wheel. The number of abrasive grains per unit area; Based on the grinding thickness, the third normal grinding force and the third tangential grinding force during the unit width scribing stage are calculated using the following formulas: ； ； in, The third normal grinding force, This is the third tangential grinding force. It is the fifth coefficient. It is the sixth coefficient. It is the seventh coefficient; The first normal grinding force, the second normal grinding force, and the third normal grinding force are summed to obtain the fourth normal grinding force; the first tangential grinding force, the second tangential grinding force, and the third tangential grinding force are summed to obtain the fourth tangential grinding force. The first grinding force is calculated based on the fourth normal grinding force, the fourth tangential grinding force, the unit normal vector, and the unit tangential velocity vector.

5. The method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to claim 4, characterized in that, The calculation of the first grinding force based on the fourth normal grinding force, the fourth tangential grinding force, the unit normal vector, and the unit tangential velocity vector includes: Calculate the corresponding unit tangential velocity vector for each segment connecting the tooth surface contact points based on the unit tangential velocity vector; calculate the corresponding unit normal vector for each segment connecting the tooth surface contact points based on the unit normal vector. The first grinding force is calculated using the following formula: ； ； in, The first point formed by connecting the contact points of the tooth surfaces Grinding force of segment, The first point formed by connecting the contact points of the tooth surfaces The corresponding unit normal vector of the segment. The first point formed by connecting the contact points of the tooth surfaces The corresponding unit tangential velocity vector of the segment. The fourth normal grinding force, This is the fourth tangential grinding force. The discrete positions of the grinding wheel's swing angle are given. The number of discrete points in the grinding wheel's swing angle. This represents the number of discrete segments on a single contact line. This is the first grinding force.

6. The method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to claim 2, characterized in that, The calculation of the first vibration signal value based on the first grinding force includes: Calculate the vibration acceleration based on the first grinding force; Calculate the vibration velocity based on the first grinding force; Based on the first grinding force, the vibration acceleration, and the vibration velocity, the first vibration signal value is calculated using the Runge-Kuta 4th order algorithm according to the following formula: in, The first modal damping parameter of the grinding wheel is... The second modal damping parameter of the grinding wheel, The first modal stiffness parameter of the grinding wheel is... This refers to the second modal stiffness parameter of the grinding wheel. The first modal mass of the grinding wheel, The second modal mass of the grinding wheel, Let X be the component of the vibration acceleration in the X direction within the fixed coordinate system of the grinding wheel. Let Y be the component of the vibration acceleration in the Y direction of the fixed coordinate system of the grinding wheel. Let X be the component of the vibration velocity in the X direction within the fixed coordinate system of the grinding wheel. Let Y be the component of the vibration velocity in the Y direction of the grinding wheel's fixed coordinate system. Let X be the component of the first vibration signal value in the X direction of the grinding wheel fixed coordinate system. Let Y be the component of the first vibration signal value in the fixed coordinate system of the grinding wheel. Let X be the component of the first grinding force in the X direction within the fixed coordinate system of the grinding wheel. This represents the component of the first grinding force in the Y direction within the fixed coordinate system of the grinding wheel.

7. The method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine tool according to claim 1, characterized in that, The process of obtaining the set of spindle speed and feed rate of the spiral bevel gear to be optimized includes: Based on preset vibration signal values ​​and preset grinding force, the grinding boundary without chatter is calculated using the fully discrete method. Based on the grinding boundary, calculate the spindle speed range and feed rate range; Based on a preset speed step size, values ​​are taken within the spindle speed range to obtain a set of spindle speeds; Take any value from the set of spindle speeds as the spindle speed of the spiral bevel gear to be optimized; Based on a preset feed rate step size, values ​​are taken within the feed rate range to obtain the set of feed rates.

8. A system for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, characterized in that, The optimization system for the spindle speed and feed rate of the spiral bevel gear grinding machine tool includes: The data acquisition module is used to acquire the set of spindle speed and feed rate of the spiral bevel gear to be optimized; The first grinding force calculation module is used to calculate the first grinding force based on the first feed rate value of the spindle speed and the feed rate set. The first vibration signal value calculation module is used to calculate the first vibration signal value based on the first grinding force. The storage module is used to save the first feed rate value to a preset matching set when the first grinding force and the first vibration signal value meet preset constraints. Specifically: from to The grinding wheel speed is evenly divided, and its first The grinding wheel speed of the section is ,from to Uniformly divide the feed rate, its first The spindle speed of the section is ,in, This is the set minimum grinding wheel speed. This is the maximum set grinding wheel speed. The minimum set feed rate, This is the maximum set feed rate; The expression for the preset constraint is: ； in, For the first The grinding wheel speed of the first segment, the first The spindle speed of the segment corresponds to the set first grinding force in the X direction. For the first The grinding wheel speed of the first segment, the first The first grinding force in the Y direction corresponding to the spindle speed of the segment. The set range of grinding force fluctuation in the X direction. The set range of grinding force fluctuation in the Y direction. The range of vibration magnitude fluctuation in the X direction is set. The set range of vibration magnitude fluctuation in the Y direction. The component of the pre-designed reference grinding force in the X direction, obtained through experimental design analysis, The Y-direction component of the pre-designed reference grinding force obtained through experimental design analysis. The component of the reference vibration value in the X direction obtained through experimental design analysis is the vibration signal reference value. The component of the reference vibration value in the Y direction of the vibration signal obtained through experimental design analysis; An iterative module is used to calculate a second grinding force based on the spindle speed and the second feed rate value of the feed rate set, and to calculate a second vibration signal value based on the second grinding force; when the second grinding force and the second vibration signal value meet the preset constraint conditions, the second feed rate value is saved to the preset matching set, and so on, until the k-th grinding force is calculated based on the k-th feed rate value of the spindle speed and the feed rate set, and the k-th vibration signal value is calculated based on the k-th grinding force; when the k-th grinding force and the k-th vibration signal value meet the preset constraint conditions, the k-th feed rate value is saved to the preset matching set, where k is the total number of feed rate values ​​in the feed rate set; The optimization module is used to filter the maximum value of the saved feed rate values ​​based on the preset matching set, and use the maximum value as the feed rate of the spiral bevel gear to be optimized.

9. A device for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine, characterized in that, It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enables the at least one control processor to perform a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions for causing a computer to perform a method for optimizing the spindle speed and feed rate of a spiral bevel gear grinding machine as described in any one of claims 1 to 7.

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