A stability prediction and optimization method for weak stiffness grinding system based on micro-structured surface

Abstract

The application provides a stability prediction and optimization method of a weak stiffness grinding system based on a microstructured surface. The method comprises the following steps: step one, performing statistics on abrasive grain characteristics; step two, obtaining geometric parameters of a grinding wheel, abrasive grain characteristic parameters, microstructured parameters and dressing parameters; establishing a microstructured grinding wheel topography model according to the obtained parameters; step three, establishing a multi-regeneration stability model according to the microstructured grinding wheel topography model; and step four, judging the stability of the grinding system according to the multi-regeneration stability model. The microstructured grinding wheel solves the chatter problem under high speed. The controllability of the microstructured grinding wheel mainly lies in moving the stability boundary along the speed direction, and the speed limit deviation is increased by 12.2% to 54.0%.

Description

Technical Field

[0001] This invention belongs to the field of deep hole precision grinding technology, and in particular relates to a method for stability prediction and optimization of a weak stiffness grinding system based on microstructured surfaces. Background Technology

[0002] Grinding, as a high-precision, high-quality manufacturing technology, is often used as the final step in precision machining. For critical components of some advanced equipment, such as deep-hole structures, aero-engine blades, and hydraulic or pneumatic components, grinding systems with cantilever tool structures have become the preferred machining method. However, the large length-to-diameter ratio grinding bar structure with one end fixed and the other suspended significantly reduces the stiffness of the grinding system, making it highly susceptible to self-excited vibration, i.e., chatter. Chatter accelerates tool wear, leading to a decline in the quality and precision of the machined surface, reducing production efficiency and profitability, and even damaging machine tools. Therefore, predicting and optimizing grinding chatter has become a research hotspot. In this context, establishing an accurate grinding stability boundary prediction model is extremely important, as it can help engineers and researchers gain a deeper understanding of the occurrence mechanism and influencing factors of chatter. By predicting the chatter region and stability domain under different process parameters, reasonable machining strategies can be formulated to avoid potential production problems.

[0003] It should be noted that, unlike other machining processes, grinding requires consideration of the randomness and variability of abrasive grains, and abrasive grain morphology modeling is crucial to the accuracy of the stability model. In addition, grinding vibration is primarily influenced by grinding mechanics, dynamics, and tool wear. Structured grinding wheels, as high-performance tools, have attracted considerable attention over the past few decades and have been proven to optimize grinding mechanics, dynamics, and tool wear. Therefore, it can be inferred that structured grinding wheels hold the promise of optimizing grinding stability.

[0004] In summary, in order to achieve stability prediction and optimization of weak stiffness grinding systems, it is necessary to establish an accurate prediction model for grinding stability based on a microstructure grinding wheel morphology model, and analyze the optimization effect of microstructure parameters on grinding stability. Summary of the Invention

[0005] This invention addresses the grinding chatter problem in deep-hole structures by proposing a stability prediction and optimization method for weak-stiffness grinding systems based on microstructured surfaces.

[0006] This invention is achieved through the following technical solution: This invention proposes a method for stability prediction and optimization of a weak-stiffness grinding system based on a microstructured surface. The method includes the following steps:

[0007] Step 1: Statistical analysis of abrasive grain characteristics;

[0008] Step 2: Obtain the grinding wheel geometry parameters, abrasive grain characteristic parameters, microstructure parameters, and dressing parameters; establish a microstructured grinding wheel morphology model based on the obtained parameters;

[0009] Step 3: Establish a multi-regeneration stability model based on the microstructured grinding wheel morphology model;

[0010] Step 4: Determine the stability of the grinding system based on the multi-regeneration stability model.

[0011] Furthermore, the microstructuring parameters include microstructure width, microstructuring rate, microstructure angle, microstructure region, and microstructure pattern; the microstructure pattern includes linear, oblique, intersecting, and combined types.

[0012] Furthermore, in abrasive particle characteristic statistics,

[0013] Determine the shape type of abrasive grains, identify the ratio of the abrasive grain corner length to the side length as the cutoff ratio, and perform statistical and probability distribution analysis on the cutoff ratio;

[0014] The distance between the centers of adjacent abrasive grains is defined as the abrasive grain spacing, and statistical and probability distribution analysis is performed on the abrasive grain spacing.

[0015] The outer circle diameter of the abrasive grain is defined as the abrasive grain diameter, and statistical and probability distribution analysis of the abrasive grain diameter is performed.

[0016] The height difference between the highest point of the abrasive grain and the bond is defined as the abrasive grain protrusion height. Statistical and probability distribution analysis of the abrasive grain protrusion height is then performed.

[0017] It is assumed that the random deflection of abrasive particles follows a random distribution.

[0018] Further, step three specifically involves: establishing differential equations for a weakly stiff grinding system considering mass, stiffness, and damping; transforming the differential equations into state-space equations; using interpolation to perform polynomial fitting on the right side of the equations, thus transforming the delay differential equations into a problem of solving ordinary differential equations; discretizing the grinding time into multiple time intervals to obtain the state matrix of the j-th time interval; and using fourth-order Lagrange interpolation to approximate the state matrix to obtain the transformation matrix.

[0019] Furthermore, in step four, the stability of the grinding system is determined by judging the relationship between the modulus of the transformation matrix eigenvalue and 1; when the modulus of the transformation matrix eigenvalue is less than or equal to 1, the grinding system is stable, and conversely, when the modulus is greater than 1, the grinding system is unstable.

[0020] Furthermore, the stability of the weak stiffness grinding system is affected by two regenerative processes: workpiece regeneration and tool wear regeneration.

[0021] Furthermore, for tool wear regeneration, abrasive wear is manifested in the loss of protrusion height; considering that the wear height of the abrasive is proportional to the cumulative material removal, a wear rate C is introduced. d To characterize the relationship between abrasive height reduction and material removal rate; for any abrasive, each rotational cycle T... g Each of these processes removes a certain volume of workpiece material; therefore, the wear time delay T... g It can be used to represent the height δ(t) of abrasive grains after wear:

[0022] δ(t)=δ(tT g )-C d V w ′(t)

[0023] In the formula, δ(tT) g V represents the height of the abrasive grain in the previous rotation cycle. w Remove volume from the material.

[0024] Furthermore, for workpiece regeneration, assuming no vibration occurs during grinding, the total static undeformed chip thickness h generated by all effective abrasive grains in the grinding zone is... sta,j Represented as:

[0025]

[0026] In the formula, a j-1 and a j d represents the actual grinding depth of the (j-1)th and j-th abrasive grains, respectively. s λ is the diameter of the grinding wheel. j N represents the spacing between adjacent effective abrasive grains. g v represents the number of abrasive grains in the grinding zone. w v is the workpiece feed rate. s This represents the rotational speed of the grinding wheel.

[0027] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the stability prediction and optimization method for a weak stiffness grinding system based on microstructured surfaces.

[0028] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the stability prediction and optimization method for a weak stiffness grinding system based on a microstructured surface.

[0029] The beneficial effects of this invention are:

[0030] (1) The microstructured grinding wheel described in this invention solves the chatter problem at high speeds. The controllability of the microstructured grinding wheel mainly lies in the movement of the stable boundary along the rotational speed direction, which improves the speed limit deviation by 12.2%-54.0%.

[0031] (2) The stability modeling method described in this invention has strong versatility and can be applied to the stability model of any weak stiffness grinding system. Abrasive grain morphology, microstructure parameters, dressing parameters, and grinding process parameters are key issues affecting the stability boundary of the grinding system and are important inputs that cannot be ignored in the stability model.

[0032] (3) This invention discovers that the stable region of a microstructured grinding wheel can be controlled by changing the abrasive grain diameter, abrasive grain surface area, undeformed chip thickness, and effective number of abrasive grains. The combined microstructure can regulate the local mechanical properties of the grinding wheel in the circumferential direction, change the conditions of time lag and regenerative chatter, thereby improving grinding stability.

[0033] (4) This invention compares the effects of the presence or absence of microstructure on grinding accuracy. Compared with grinding wheels without microstructure, the wear resistance of microstructure grinding wheels is improved by 44.2%, significantly optimizing the overcutting phenomenon and improving the surface finish of the workpiece. The tooth height, tooth profile angle, and bottom fillet radius of workpieces machined by microstructure grinding wheels are far superior to those of grinding wheels without microstructure. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of the test results for CBN abrasive particles;

[0036] Figure 2 This is a schematic diagram of the statistical results of abrasive particle geometry parameters;

[0037] Figure 3 These are schematic diagrams of different types of microstructure patterns;

[0038] Figure 4 This is a schematic diagram of the outline of an undressed grinding wheel;

[0039] Figure 5 This is a schematic diagram of the dressinged grinding wheel profile;

[0040] Figure 6 This is a schematic diagram of the stability boundary of a microstructure-free grinding wheel;

[0041] Figure 7This is a schematic diagram of the stability boundary of a linear microstructure grinding wheel;

[0042] Figure 8 This is a schematic diagram of the stability boundary of a microstructured grinding wheel with oblique lines;

[0043] Figure 9 This is a schematic diagram of the stability boundary of a cross-shaped microstructure grinding wheel;

[0044] Figure 10 This is a schematic diagram of the stability boundary of a composite microstructure grinding wheel. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Combination Figures 1-10 This invention proposes a method for stability prediction and optimization of a weak stiffness grinding system based on a microstructured surface. The method includes the following steps:

[0047] Step 1: Statistical analysis of abrasive grain characteristics;

[0048] Step 2: Obtain the grinding wheel geometry parameters, abrasive grain characteristic parameters, microstructure parameters, and dressing parameters; establish a microstructured grinding wheel morphology model based on the obtained parameters;

[0049] Step 3: Establish a multi-regeneration stability model based on the microstructured grinding wheel morphology model;

[0050] Step 4: Determine the stability of the grinding system based on the multi-regeneration stability model.

[0051] The microstructure parameters include microstructure width, microstructure rate, microstructure angle, microstructure region, and microstructure pattern; the microstructure pattern includes linear, diagonal, intersecting, and combined types.

[0052] In abrasive particle characteristic statistics

[0053] Determine the shape type of abrasive grains, identify the ratio of the abrasive grain corner length to the side length as the cutoff ratio, and perform statistical and probability distribution analysis on the cutoff ratio;

[0054] The distance between the centers of adjacent abrasive grains is defined as the abrasive grain spacing, and statistical and probability distribution analysis is performed on the abrasive grain spacing.

[0055] The outer circle diameter of the abrasive grain is defined as the abrasive grain diameter, and statistical and probability distribution analysis of the abrasive grain diameter is performed.

[0056] The height difference between the highest point of the abrasive grain and the bond is defined as the abrasive grain protrusion height. Statistical and probability distribution analysis of the abrasive grain protrusion height is then performed.

[0057] It is assumed that the random deflection of abrasive particles follows a random distribution.

[0058] Step three specifically involves: the multi-regenerative stability model of the weak-stiffness grinding system should consider the material removal time delay and the rotation period time delay. By considering the influence of instantaneous grinding vibration on the material removal amount and abrasive wear amount, the dynamic undeformed chip thickness and instantaneous grinding force can be obtained. Based on this, a differential equation for the weak-stiffness grinding system considering mass, stiffness, and damping is established. The differential equation is transformed into a state-space equation, and the right side of the equation is polynomial-fitted using interpolation, transforming the delay differential equation into a problem of solving ordinary differential equations. The grinding time is discretized into multiple time intervals to obtain the state matrix of the j-th time interval. The state matrix is ​​approximated using fourth-order Lagrange interpolation to obtain the transformation matrix.

[0059] In step four, the stability of the weak-stiffness grinding system can be determined using Floquet theory, specifically by assessing the relationship between the modulus of the transformation matrix's eigenvalues ​​and 1. When the modulus of the transformation matrix's eigenvalues ​​is less than or equal to 1, the grinding system is stable; conversely, when the modulus is greater than 1, the grinding system is unstable. Therefore, this relationship can be used to identify the stability boundary of the weak-stiffness grinding system.

[0060] The stability of the low-stiffness grinding system is affected by two regenerative processes: workpiece regeneration and tool wear regeneration.

[0061] Workpiece regeneration: Due to the differences in spacing, diameter, and cutting width between each abrasive grain, the amount of material removed by each grain also varies. Therefore, the grinding surface left by the previous grain will affect the initial conditions of the grinding trajectory of the next grain, thus resulting in workpiece regeneration.

[0062] Tool wear regeneration: In low-stiffness grinding processes, excessively long grinding paths can lead to wheel wear. The instantaneous wear of any abrasive grain is related to the vibration and material removal in the previous rotation cycle. Therefore, tool wear regeneration is also one of the important factors affecting the machining stability of low-stiffness grinding systems.

[0063] The low-stiffness grinding system described in this invention undergoes three stages: stable, slight chatter, and severe chatter. The signals in each stage correspond to different frequencies, with the chatter frequency higher than the spindle rotation frequency. For slight chatter, the chatter frequency is 630.4 Hz, but the amplitude is lower than the spindle rotation frequency. For severe chatter, many chatter frequencies appear, including 623.2 Hz and 779.5 Hz. The amplitudes of these frequencies far exceed the spindle rotation frequency, so they play a major role.

[0064] This invention, based on a microstructured grinding wheel morphology model and a multi-regeneration stability model, investigates the control effect of microstructured grinding wheels on the stability of low-stiffness grinding systems. It demonstrates that microstructured grinding wheels can significantly suppress workpiece regeneration and tool wear regeneration, thereby improving the stability zone and workpiece machining accuracy during high-speed grinding.

[0065] The design and optimization methods of the present invention will now be systematically described with reference to the accompanying drawings in the embodiments of the present invention.

[0066] See Figure 1 The CBN abrasive particles used in this invention are shown in the test results. CBN abrasive particles conform to a tetrahedral truncated cone shape, meaning the four corners of the tetrahedron are truncated at a certain ratio. To quantify the truncation ratio, a truncation coefficient b is introduced. m , can be represented as:

[0067] b m =t m / l m

[0068] In the formula, t m For the cutoff length, l m This represents the edge length of the abrasive grain. Similarly, the circumcircle diameter D of the abrasive grain is determined using measurements taken with an optical microscope. g Statistical analysis is performed. After determining the shape and size of individual abrasive grains, it is necessary to determine the three-dimensional distribution of different abrasive grains, considering both planar and height distributions. In the planar distribution, the abrasive grain spacing S... g This is the primary determining factor. Regarding height distribution, the height h of the abrasive grains needs to be considered. g This includes the protrusion height of the abrasive grains relative to the binder and the geometric height of the grinding wheel tip. In addition to the abrasive grain distribution, each abrasive grain has a different rotation angle, and this invention assumes that the rotation angles of the abrasive grains about the x, y, and z axes conform to a uniform distribution.

[0069] This invention statistically analyzes the geometric parameters of 300 consecutive abrasive grains on a grinding wheel, and the results are as follows: Figure 2 As shown. h g D g b m All of them satisfy a Gaussian distribution, with values ​​of (179.93 μm, 50.34 μm) respectively. 2), (323.06μm, 38.10μm) 2 ), (0.30, 0.08 2 S g The model satisfies a Cauchy distribution, with a position parameter of 377.20 μm and a scale parameter of 43.88 μm. Therefore, the parameter conditions for accurately constructing the multiple random morphology model of the grinding wheel are met. Combining the geometric parameters of the grinding wheel, the Poisson distribution algorithm can be used to model the grinding wheel morphology.

[0070] Based on the grinding wheel morphology model, microstructure parameters are introduced, including microstructure width b, microstructure ratio α, microstructure angle σ, and the scale ε of the structural pattern. This invention considers linear, oblique, intersecting, and combined microstructures, such as... Figure 3 As shown, under the influence of the microstructure, the original abrasive grains are divided into several independent grains, shortening and regularizing the spacing between them. Furthermore, the microstructure also alters the bearing width and diameter of each abrasive grain; these parameter changes are significant factors affecting material removal. Besides the fabrication of the microstructure, due to the size limitation of the large abrasive grains (300 μm diameter), it is necessary to study the precision dressing process of the grinding wheel. For ease of observation, the changes in the grinding wheel profile are viewed from the xz angle. Figure 4 and Figure 5 The images show the profiles of an undressed grinding wheel and a dressed grinding wheel, respectively. For the undressed wheel, the significant difference in abrasive grain size and protrusion height results in an irregular wheel profile, which needs to be avoided. In contrast, the dressed wheel profile forms a regular V-shape, ensuring grinding accuracy. Therefore, the morphology model of the dressed grinding wheel is used as the basis for analyzing grinding stability.

[0071] Because the spacing, diameter, and bearing width between abrasive grains vary, the amount of material removed by each grain also differs. This causes the grinding surface left by the previous grain to affect the initial conditions of the grinding trajectory of the next grain, resulting in workpiece regeneration. In low-stiffness grinding processes, excessively long grinding paths can lead to wheel wear. The instantaneous wear of any abrasive grain is related to the vibration and material removal amount of the previous rotation cycle; therefore, tool wear regeneration is also one of the important reasons affecting the grinding stability of high aspect ratio grinding systems.

[0072] Regarding tool wear regeneration, this invention posits that the wear of CBN abrasive grains primarily manifests as a loss of protrusion height. Considering that the wear height of the abrasive grains is proportional to the cumulative material removal, a wear rate C is introduced. d This is used to characterize the relationship between abrasive grain height reduction and material removal rate. For any abrasive grain, each rotational cycle T... g Each of these processes removes a certain volume of workpiece material. Therefore, the wear time delay T g It can be used to represent the height δ(t) of abrasive grains after wear:

[0073] δ(t)=δ(tT g )-C d V w ′(t)

[0074] In the formula, δ(tT) g V represents the height of the abrasive grain in the previous rotation cycle. w 'To remove volume from the material.'

[0075] For workpiece regeneration, assuming no vibration occurs during grinding, the total static undeformed chip thickness h generated by all effective abrasive grains in the grinding zone is... sta,j It can be represented as:

[0076]

[0077] In the formula, a j-1 and a j d represents the actual grinding depth of the (j-1)th and j-th abrasive grains, respectively. s λ is the diameter of the grinding wheel. j N represents the effective spacing between adjacent abrasive grains. g v represents the number of abrasive grains in the grinding zone. w v is the workpiece feed rate. s This represents the rotational speed of the grinding wheel.

[0078] In low-stiffness grinding systems, the high grinding force generated in the grinding zone causes the abrasive grains to vibrate to varying degrees, easily leading to frequent separation from the workpiece and recutting. The workpiece regeneration effect results in a dynamic undeformed chip thickness h. dyn,j With static undeformed chip thickness h sta,j The difference. Under the action of grinding vibration, h dyn,j It can be represented as:

[0079]

[0080] In the formula, z(t) and z(t-τ) are the instantaneous vibrations at times t and t-τ, respectively.

[0081] Based on the above analysis, the wear time delay T can be obtained. g Under the combined effect of the grinding interval time delay τ, the thickness of the undeformed chip in dynamic wear can be expressed as:

[0082]

[0083] Where, τ g b is the time difference between adjacent abrasive grains. g The material bearing the width of the abrasive grains.

[0084] In both stable and unstable grinding processes, the normal grinding force is often greater than the tangential grinding force and accounts for the majority of the contribution. This invention considers the normal grinding force F... n It can be expressed as the grinding force coefficient K n The product of the total undeformed chip thickness in the grinding zone and the total thickness of the chips in the grinding zone. In the normal direction, the relationship between the grinding force and grinding vibration in a weakly stiff grinding system can be expressed by a differential equation:

[0085]

[0086] Reconstructing the above equation, the state-space equation of the weak stiffness grinding system can be expressed as:

[0087]

[0088] In the formula,

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] To calculate the state-space equations of a weakly stiff grinding system, a polynomial fit is performed on the right-hand side of the equations using interpolation, transforming the delay differential equations into a problem of solving ordinary differential equations. The grinding time T is discretized into r time intervals. The j-th time interval [t] can be represented as... j ,t j The fitted expression for +1]:

[0095]

[0096] The state matrix q is approximated using fourth-order Lagrange interpolation.

[0097]

[0098] The discrete system described above can be defined as follows:

[0099] w i+2 =D i w i+1

[0100] In the formula, w i+2 =[q i+1 ,q i ,…,q i+1-r ].

[0101] The transformation matrix φ of a weak stiffness grinding system over time interval T can be expressed as:

[0102] φ=D0D1…D k-2 D k-1

[0103] The stability of a weakly stiff grinding system can be determined using Floquet theory, specifically by assessing the relationship between the modulus of the transformation matrix's eigenvalues ​​and 1. When the modulus of the transformation matrix's eigenvalues ​​is less than 1, the grinding system is stable; conversely, when the modulus is greater than 1, the grinding system is unstable. Therefore, this relationship can be used to identify the stability boundary of a large aspect ratio grinding system.

[0104] The low-stiffness grinding system described in this invention undergoes three stages: stable, slight chatter, and severe chatter. The signals in each stage correspond to different frequencies, with the chatter frequency higher than the spindle rotation frequency. For slight chatter, the chatter frequency is 630.4 Hz, but the amplitude is lower than the spindle rotation frequency. For severe chatter, many chatter frequencies appear, including 623.2 Hz and 779.5 Hz. The amplitudes of these frequencies far exceed the spindle rotation frequency, so they play a major role.

[0105] To verify the prediction and optimization results of the weak stiffness grinding system, the stability boundaries of no microstructure, linear microstructure, oblique microstructure, cross-type microstructure, and combined microstructure were compared, such as... Figures 6-10 As shown. For high-speed grinding processes, the focus is mainly on the speed range of 10,000-18,000 r / min. It was found that compared to the stability boundary of a grinding wheel without microstructures, microstructures shift the stability limit at high speeds and low grinding depths along the positive direction of the rotational speed, thus improving grinding stability. Linear, oblique, and cross-shaped microstructures shifted the stability limit from 11,274 r / min to 12,647 r / min, 13,493 r / min, and 15,058 r / min, respectively. Different types of microstructures improved the stability limit by 12.2%, 19.7%, and 33.6%, respectively. However, when the spindle speed is 16,000 r / min, changing the pattern type still cannot solve the chatter problem. It can be found that the stability limit of the combined microstructure increases from 11,274 r / min to 17,357 r / min, increasing stability by 54.0%, which can basically solve the chatter problem at high speeds. Therefore, based on the degree of optimization of grinding stability, the microstructure pattern types can be arranged in descending order: combined type, cross type, oblique type and straight type.

[0106] A comparison was made of grinding wheel profiles with and without microstructures. With increasing grinding time, both microstructured and non-microstructured grinding wheels showed varying degrees of wear, particularly at the V-shaped tip. At 80 minutes of grinding, the non-microstructured grinding wheel experienced a total tip wear of 43 μm. In contrast, the microstructured grinding wheel suppressed chatter, with a tip wear of only 24 μm and a 44.2% improvement in wear resistance. The machining profile accuracy of the workpieces with and without microstructures was also compared. The microstructured grinding wheel produced a relatively uniform tooth height with a maximum height variation of 3 μm, a tooth profile angle error of 0.1°, and a bottom fillet radius of 23 μm. In contrast, the non-microstructured grinding wheel produced a maximum height variation of 32 μm, a tooth profile angle error of 1.3°, and a bottom fillet radius of 239 μm. This is because the non-microstructured grinding wheel exhibits severe chatter during grinding, resulting in different vibration states for each tooth profile. Overcutting or separation can lead to inconsistent material removal, thus affecting the tooth height. Microstructure-less grinding wheels severely compromise the workpiece's contour accuracy, and both workpiece regeneration and tool wear regeneration contribute to severe chatter. Microstructured grinding wheels, on the other hand, can disrupt chatter conditions, ensuring excellent grinding stability and guaranteeing the workpiece's machining contour accuracy.

[0107] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the stability prediction and optimization method for a weak stiffness grinding system based on microstructured surfaces.

[0108] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the stability prediction and optimization method for a weak stiffness grinding system based on a microstructured surface.

[0109] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0110] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0111] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0112] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0113] The stability prediction and optimization method of a low-stiffness grinding system based on microstructured surfaces proposed in this invention has been described in detail above. Specific examples have been used to illustrate the principle and implementation of this invention. The description of the above embodiments is only for the purpose of helping to understand the method and core idea of ​​this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation and application scope based on the idea of ​​this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for stability prediction and optimization of a weak stiffness grinding system based on microstructured surfaces, characterized in that, The method includes the following steps: Step 1: Statistical analysis of abrasive grain characteristics; Step 2: Obtain the grinding wheel geometry parameters, abrasive grain characteristic parameters, microstructure parameters, and dressing parameters; establish a microstructured grinding wheel morphology model based on the obtained parameters; Step 3: Establish a multi-regeneration stability model based on the microstructured grinding wheel morphology model; Step 4: Determine the stability of the grinding system based on the multi-regeneration stability model; The microstructure parameters include microstructure width, microstructure rate, microstructure angle, microstructure region, and microstructure pattern; the microstructure pattern includes linear, diagonal, intersecting, and combined types. Step three specifically involves: establishing differential equations for a weakly stiff grinding system considering mass, stiffness, and damping; transforming these differential equations into state-space equations; and using interpolation to perform polynomial fitting on the right-hand side of the equations, thus transforming the delay differential equations into a problem of solving ordinary differential equations. The grinding time is then discretized into multiple time intervals to obtain the... j The state matrix for each time period is approximated using fourth-order Lagrange interpolation to obtain the transformation matrix; In step four, the stability of the grinding system is determined by judging the relationship between the modulus of the eigenvalues ​​of the transformation matrix and 1; when the modulus of the eigenvalues ​​of the transformation matrix is ​​less than or equal to 1, the grinding system is stable, and conversely, when the modulus is greater than 1, the grinding system is unstable. The stability of the low-stiffness grinding system is affected by two regenerative processes: workpiece regeneration and tool wear regeneration. Workpiece regeneration: The grinding surface left by the previous abrasive grain will affect the initial conditions of the grinding trajectory of the next abrasive grain, thus forming the workpiece regeneration phenomenon. Tool wear regeneration: For low-rigidity grinding processes, excessively long grinding paths can lead to grinding wheel wear; the instantaneous wear of any abrasive grain is related to the vibration and material removal of the previous rotation cycle.

2. The method according to claim 1, characterized in that, In abrasive particle characteristic statistics Determine the shape type of abrasive grains, identify the ratio of the abrasive grain corner length to the side length as the cutoff ratio, and perform statistical and probability distribution analysis on the cutoff ratio; The distance between the centers of adjacent abrasive grains is defined as the abrasive grain spacing, and statistical and probability distribution analysis is performed on the abrasive grain spacing. The outer circle diameter of the abrasive grain is defined as the abrasive grain diameter, and statistical and probability distribution analysis of the abrasive grain diameter is performed. The height difference between the highest point of the abrasive grain and the bond is defined as the abrasive grain protrusion height. Statistical and probability distribution analysis of the abrasive grain protrusion height is then performed. It is assumed that the random deflection of abrasive particles follows a random distribution.

3. The method according to claim 2, characterized in that, For tool wear regeneration, abrasive wear is manifested in the loss of protrusion height; considering that the wear height of abrasive particles is proportional to the cumulative material removal, a wear rate is introduced. C d This characterizes the relationship between abrasive height reduction and material removal; for any abrasive, each rotation cycle... T g Each of these processes removes a certain volume of workpiece material, thus delaying the wear time. T g It can be used to indicate the height of abrasive grains after wear. δ ( t ): In the formula, δ ( t - T g () represents the height of the abrasive grain in the previous rotation cycle. V w ' Remove volume from the material.

4. The method according to claim 3, characterized in that, For workpiece regeneration, assuming no vibration occurs during grinding, the total static undeformed chip thickness generated by all effective abrasive grains in the grinding zone is... h sta,j Represented as: In the formula, a j-1 and a j The first j -1 and the j The actual grinding depth of each abrasive grain. d s The diameter of the grinding wheel. λ j The effective spacing between adjacent abrasive grains. N g This refers to the number of abrasive grains in the grinding zone. For workpiece feed rate, This represents the rotational speed of the grinding wheel.

5. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-4.

6. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-4.

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