Online monitoring method of grinding wheel wear based on spindle power

Abstract

The invention discloses an online monitoring method for grinding wheel wear based on spindle power, comprising the following steps: step one: solving the critical condition of abrasive-workpiece contact, and obtaining the critical cutting depths in the plowing stage and the cutting stage; step two: obtaining a scraping force calculation model, a plowing force calculation model and a cutting force calculation model; step three: correcting the critical condition of abrasive-workpiece contact and the grinding force model, and obtaining the corrected critical cutting depths in the plowing stage and the cutting stage as well as a scraping force-grinding wheel wear model, a plowing force-grinding wheel wear model and a cutting force-grinding wheel wear model; step four: constructing a grinding resultant force-grinding wheel wear model based on the scraping force-grinding wheel wear model, the plowing force-grinding wheel wear model and the cutting force-grinding wheel wear model; step five: obtaining the spindle power-grinding wheel wear model based on the relationship between the spindle power and the grinding resultant force; step six: detecting the spindle power in real time, and performing online monitoring on the grinding wheel wear.

Description

Technical Field

[0001] The invention belongs to the technical field of grinding processing, and specifically relates to an online monitoring method for grinding wheel wear based on spindle power. Background Art

[0002] Grinding wheel wear is an important reason affecting grinding quality and a key factor restricting grinding process efficiency and economy. Grinding wheel wear will lead to an increase in abrasive wear area, a decrease in sharpness, an increase in the proportion of scraping and plowing abrasives, and an increase in the energy required to remove material per unit volume of the workpiece, resulting in an increase in cutting force and grinding temperature, which in turn affects the accuracy and surface quality of the cut workpiece, and even causes grinding burns. Therefore, in actual production, the grinding performance of the grinding wheel surface is restored by grinding wheel dressing. In production, it is generally determined by empirical methods or trial and error methods. By observing or testing various phenomena caused by grinding wheel wear, such as self-excited vibration during the grinding process, abnormal increase in grinding noise, grinding burns on the workpiece surface, decreased grinding accuracy, increased grinding surface roughness, and other processing abnormalities, the grinding wheel wear is judged and the grinding wheel dressing time is determined. However, the above methods are generally qualitative judgments, without complete and reliable theoretical support, and the optimal dressing time is often not accurately grasped in actual production. In addition, the surface topography of the grinding wheel can usually only be measured offline. The grinding surface of the double-beveled grinding wheel used in the profile grinding process is a complex curved surface. The surface topography measurement process is cumbersome, and repeated loading and unloading is time-consuming and labor-intensive.

[0003] The grinding wheel rotates at high speed during the machining process, and the grinding area is blocked by gears. The surface morphology of the grinding wheel can usually only be detected offline, and the wear state of the grinding wheel cannot be monitored in real time, which makes it difficult to accurately grasp the optimal grinding wheel dressing time, affecting machining efficiency and quality. Therefore, it is necessary to establish a correlation between grinding wheel wear and other measurable machining process parameters, and realize online monitoring of grinding wheel wear by measuring other machining process parameters. Summary of the invention

[0004] In view of this, an object of the present invention is to provide an online monitoring method for grinding wheel wear based on spindle power, which can realize online monitoring of grinding wheel wear.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for online monitoring of grinding wheel wear based on spindle power comprises the following steps:

[0007] Step 1: Based on the abrasive geometric parameters, solve the critical contact conditions between the abrasive and the workpiece, and obtain the critical cutting depths in the plowing stage and the cutting stage;

[0008] Step 2: construct grinding force models for different grinding stages, and obtain scraping force calculation models, plowing force calculation models and cutting force calculation models respectively;

[0009] Step 3: Based on the influence of grinding wheel wear on the geometric parameters of abrasive grains, correct the critical condition of abrasive grain-workpiece contact and the grinding force model to obtain the corrected critical cutting depths in the plowing stage and cutting stage, as well as the scratch force-grinding wheel wear model, plowing force-grinding wheel wear model, and cutting force-grinding wheel wear model;

[0010] Step 4: Based on the scratch force-grinding wheel wear model, plowing force-grinding wheel wear model, and cutting force-grinding wheel wear model, construct a grinding resultant force-grinding wheel wear model;

[0011] Step 5: Based on the relationship between spindle power and grinding resultant force, obtain the spindle power-grinding wheel wear model;

[0012] Step 6: Real-time detect the spindle power to perform online monitoring of grinding wheel wear.

[0013] Furthermore, in the above Step 3, the influence relationship of the abrasive grain wear rate on the contact surface diameter L2 of the abrasive grain is:

[0014] L2 = L1 + 2 tanαh i ε

[0015] In the formula, L1 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece before wear; L2 represents the diameter of the bottom surface of the abrasive grain in contact with the workpiece after wear; ε represents the abrasive grain wear rate; h i represents the protrusion height of the abrasive grain before wear;

[0016] The diameter of the force-bearing surface of the abrasive grain is:

[0017] L3 = L2 + 2 tanαd i

[0018] In the formula, L3 is the diameter of the force-bearing surface of the abrasive grain.

[0019] Furthermore, in the above Step 1, the abrasive grain-workpiece contact deformation is:

[0020]

[0021] Among them, d is the abrasive grain-workpiece contact deformation; P0 is the average stress in the area; E * is the equivalent elastic modulus; L1 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece; α represents the rake angle of the abrasive grain before grinding;

[0022] The grinding stage where the abrasive grain is located is related to the current contact stress of the abrasive grain: when the average stress P0 < 0.4H, the workpiece material is elastically deformed; when the average stress 0.4H < P0 < H, the workpiece material is elasto-plastically deformed; when the average stress H < P0, the workpiece material is completely plastically deformed;

[0023] According to the critical stress value of the abrasive force surface at different cutting stages, the critical cutting depths of the plowing stage and the cutting stage are obtained respectively:

[0024]

[0025]

[0026] Where, d cp and d cc are the critical cutting depths for plowing and cutting respectively; H is the material hardness.

[0027] In step 3, the diameter L1 of the bottom surface of the abrasive grain in contact with the workpiece before wear is replaced by the diameter L3 of the abrasive grain bearing surface, and the corrected critical cutting depths of the plowing stage and the cutting stage are obtained:

[0028]

[0029]

[0030] Where, d cp ′ and d cc ′ are the critical cutting depths of the modified plowing stage and cutting stage, respectively.

[0031] Further, in step 2, when the abrasive grains penetrate into the depth d <d cp When the abrasive is in the scraping stage, the normal force F nr and the tangential force F tr for:

[0032] F nr =P0S1

[0033] F tr =μ r F nr

[0034] Where S1 is the force-bearing surface area of ​​the abrasive:

[0035]

[0036] Where L2 represents the diameter of the bottom surface in contact with the workpiece after abrasive wear:

[0037] L2=L1+2d tanα

[0038] Then the scratch force calculation model is obtained:

[0039] F nr =E * d(L1+2d tanα)

[0040] F tr =μr E * d(L1+2d tan α)

[0041] In the formula, μ r is the friction coefficient in the scraping stage;

[0042] In step 3, the diameter L1 of the bottom surface of the abrasive grain in contact with the workpiece before wear is replaced by the diameter L3 of the abrasive grain bearing surface to obtain the scraping force-grinding wheel wear model:

[0043] F nr ′=E * d(L1+2d tanα)+2 tanαh i E * dε

[0044] F tr ′=μ r E * d(L1+2d tanα)+2μ r tanαh i E * dε

[0045] In the formula, F nr ′ and F tr ′ are the normal force and tangential force on the abrasive particles in the scratching stage after correction.

[0046] Further, in step 2, when the abrasive grains penetrate into the depth d cp <d<d cc When the abrasive grains are in the plowing stage, the plowing force generated by the abrasive grains to resist material deformation acts on the peripheral surface of the abrasive grains. Projecting the force surface onto the cross-sectional plane of the abrasive grains, the normal plowing force F np 1 for:

[0047] F np 1 =p1S2

[0048] Where p1 is the average stress of the cross section that resists material deformation; S2 is the projected cross-sectional area of ​​the abrasive in the direction of movement that resists material deformation:

[0049]

[0050] Where, L1 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece; L2 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece after wear; α is the grinding front angle of the abrasive grain;

[0051] The cross-sectional average stress that resists material deformation can be calculated based on the defined material scratch hardness:

[0052] p1=H s

[0053] In the formula, H s is the scratch hardness of the material;

[0054] The normal force F np and the tangential force F tp received by the abrasive grains in the plowing stage are:

[0055] F np = d(E * + H s )(L1 + d tan α)

[0056] F tp = μ p F nr

[0057] In the formula, μ p is the plowing coefficient:

[0058]

[0059] The plowing force calculation model is obtained;

[0060] In the third step, the diameter L3 of the force-bearing surface of the abrasive grain is used to replace the diameter L1 of the bottom surface in contact with the workpiece before the wear of the abrasive grain, and the plowing force - grinding wheel wear model is obtained:

[0061] F np ′ = E * d(L1 + 2 tanαh i ε + 2d tanα) + H s d(L1 + 2 tanαh i ε + d tanα)

[0062] F tp ′ = μ p F nr

[0063] The corrected plowing coefficient is:

[0064]

[0065] In the formula, F np ′ and F tp ′ are the normal force and the tangential force received by the abrasive grains in the plowing stage after correction, respectively; μ p ′ is the corrected plowing coefficient.

[0066] Furthermore, in the second step, when the cutting depth d cc < d, the material is in the cutting stage, and the instantaneous projected area corresponding to the cutting force is:

[0067] dA = 2rg 2 cos 2 α i dα i

[0068] In the formula, r g is the abrasive particle radius corresponding to the cutting force position; α i is the instantaneous cutting rake angle;

[0069] The force F of the abrasive resisting chip formation during the grinding stage is obtained by integrating the entire abrasive cutting surface. nc 1 :

[0070]

[0071] The normal force F exerted on the abrasive during the cutting stage nc and the tangential force F tc for:

[0072]

[0073]

[0074] In the formula, β α and φ α are the friction angle and shear angle respectively; S1 is the force-bearing surface area of ​​the abrasive; τ is the flow stress in the shear area, and:

[0075]

[0076] Where A, B, C, m, and n are the constitutive parameters of the material, and: A represents the initial yield stress under strain rate and temperature; B represents the strain hardening modulus of the material; C represents the strain rate strengthening parameter of the material; m represents the thermal softening index of the material; n represents the strain hardening index of the material; T r and T m are room temperature and material melting point respectively; ε and They are the equivalent strain and the equivalent strain rate:

[0077]

[0078]

[0079] In the formula, is the cutting speed of the abrasive:

[0080]

[0081] In the formula, R i The radial distance between the abrasive grain and the center of the grinding wheel; d s Indicates the grinding wheel diameter corresponding to the grinding position; vs Indicates the grinding wheel speed;

[0082] The cutting force calculation model is obtained;

[0083] In step 3, the diameter L1 of the bottom surface of the abrasive grain in contact with the workpiece before wear is replaced by the diameter L3 of the abrasive grain bearing surface to obtain the cutting force-grinding wheel wear model:

[0084]

[0085]

[0086] In the formula, F nc ′ and F tc ′ are the normal force and tangential force on the abrasive particles during the cutting stage.

[0087] Further, in the step 4, for the i-th abrasive particle, a local coordinate system of the abrasive particle is established with the normal direction of the abrasive particle as the Y direction and the tangent direction of the involute as the X direction. The conversion relationship between the local coordinate system of the abrasive particle and the global coordinate system of the gear is:

[0088]

[0089] In the formula, and are the expression matrices of the grinding force of the i-th abrasive in the abrasive local coordinate system and the gear global coordinate system, respectively, and:

[0090]

[0091] In the formula, and They represent the normal grinding force and tangential grinding force on the i-th abrasive grain respectively; and They represent the grinding force on the i-th abrasive particle in the XYZ directions respectively;

[0092] is the transformation matrix of the grinding force of the i-th abrasive particle from the local coordinate system of the abrasive particle to the global coordinate system of the gear:

[0093]

[0094] In the formula, represents the angle between the normal direction and the radial direction of the i-th;

[0095] According to the principle of line contact cutting of profile grinding gear, the grinding force can be regarded as the vector sum of the grinding forces of all abrasive particles involved in cutting on the contact line:

[0096]

[0097] In the formula, Ft is the grinding force matrix; N i is the total number of abrasive particles involved in grinding; h i represents the protrusion height of the i-th abrasive particle before wear.

[0098] Further, in step 5, the spindle power P of the machine tool is mainly composed of two parts:

[0099] P=P idle +P cut

[0100] Among them, P idle and P cut They are no-load power and cutting power respectively;

[0101] Cutting power is generated by the cutting force during the cutting process. The cutting power of profile grinding is:

[0102] P cut =F t (v s ±v w )

[0103] In the formula, F t v is the tangential cutting force in gear grinding; s is the grinding wheel speed; v w is the workpiece moving speed.

[0104] The beneficial effects of the present invention are:

[0105] The present invention discloses an online monitoring method for grinding wheel wear based on spindle power. First, according to the quantitative expression method of grinding wheel wear, the residual height of abrasive particles and the geometric parameters of the contact surface of abrasive particles under different wear conditions are calculated. On this basis, the critical conditions of the grinding stage considering grinding wheel wear are calculated, and a dynamic grinding force model based on grinding wheel wear is established, revealing the influence of grinding wheel wear on the grinding stage of abrasive particles and the corresponding grinding force. Then, based on the correlation between grinding force and cutting power, a mapping model of abrasive wear rate to grinding power is established. By measuring the spindle power changes during the machining process online in real time, online monitoring of grinding wheel wear based on the spindle power of the forming gear grinder is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0107] Figure 1 Schematic diagram of the forces at different grinding stages;

[0108] Figure 2 Figure 2 is the contact surface stress and calculation diagram;

[0109] Figure 3Schematic diagram of spherical abrasive cutting;

[0110] Figure 4 The influence of the protruding height of the abrasive grain on the critical cutting depth;

[0111] Figure 5 The influence of the bevel angle of the abrasive cross section on the critical cutting depth;

[0112] Figure 6 The influence of the wear of the bottom surface of the abrasive contact on the critical cutting depth;

[0113] Figure 7 For the force analysis of scratching abrasive particles;

[0114] Figure 8 is the penetration depth of abrasive particles and the scraping force;

[0115] Fig. 9 For the force analysis of plowing abrasive particles;

[0116] Fig.10 It is the cutting depth of abrasive grains and the plowing abrasive grains;

[0117] Fig.11 For the analysis of cutting abrasive forces;

[0118] Fig.12 Schematic diagram of abrasive wear geometric parameters;

[0119] Fig.13 is the abrasive wear rate and cutting depth;

[0120] Fig.14 is the abrasive wear rate and scraping force;

[0121] Fig.15 is the abrasion wear rate and plowing coefficient;

[0122] Fig.16 is the abrasive wear rate and cutting force;

[0123] Fig.17 This is an example of grinding force before and after wear;

[0124] Fig.18 It is a schematic diagram of the local coordinate system of the abrasive particles;

[0125] Fig.19 Schematic diagram of grinding wheel wear and cutting power. DETAILED DESCRIPTION

[0126] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0127] The on-line monitoring method of grinding wheel wear based on spindle power in this embodiment includes the following steps.

[0128] Step 1: Based on the abrasive geometric parameters, the critical conditions of abrasive-workpiece contact are solved to obtain the critical cutting depths in the plowing stage and the cutting stage.

[0129] (1) Critical conditions of abrasive-workpiece contact

[0130] In the past research on grinding force, the most common calculation methods were based on empirical formulas and experimental results. In the past decade, some scholars have proposed theoretical calculation methods for grinding force, taking into account the influence of abrasive particles at different grinding stages on the calculation results. In the existing grinding force model, in order to facilitate calculation, it is usually assumed that the abrasive particles are spherical, and the calculation results of the sphere and elastic body contact model in the Hertz contact classic model are used. In addition, some studies, even if the abrasive particles are non-spherical particles such as truncated cones, still use the calculation results of spherical abrasive particles when calculating the grinding stage of the abrasive particles, or do not derive relevant results from the abrasive-workpiece contact and force mechanism based on elastic mechanics and contact mechanics, which affects the accuracy of the calculation results. Therefore, it is necessary to start from the abrasive-workpiece contact analysis based on the measured shape of the abrasive particles, and propose a method for judging the grinding stage of the formed grinding teeth and a method for calculating the critical conditions of each stage.

[0131] According to the results of the grinding wheel measurement test, the abrasive grains are approximately in the shape of a truncated cone. In the grinding process, the cutting state of the abrasive grains can be divided into three grinding stages: scraping, plowing and cutting, such as Figure 1 shown.

[0132] When the abrasive grains penetrate into the workpiece to a small enough depth, the abrasive grains are in the scraping stage on the workpiece surface, and the abrasive contact surface is in contact with the workpiece material. In this stage, the workpiece only has elastic deformation, and no material is removed. When the abrasive grain penetration depth increases and the abrasive-workpiece contact stress exceeds the elastic limit, the abrasive grains enter the plowing stage, in which the material is elastic-plastically deformed, but still no chips are produced. When the abrasive grain penetration depth exceeds the critical value, the abrasive grains enter the cutting stage and produce chips. The principles of abrasive force generation in different grinding stages are different, and it is necessary to derive the critical conditions of different grinding stages and the calculation method of grinding force in each stage. For the geometric shape of the grinding wheel abrasive grains established in this article, it is considered to be an extrusion deformation caused by the contact between the cylindrical indenter and the elastic half-space, such as Figure 2 (a) shown.

[0133] Assuming that the contact bottom surface with radius a=L1 / 2 is subjected to normal stress, the expression is:

[0134]

[0135] Where p is the normal stress on the contact bottom surface; r 2 =x2 +y 2 , and x and y are the plane coordinate axes of the contact bottom surface; p0 is the average stress value; L1 is the diameter of the bottom surface in contact with the workpiece before abrasive wear.

[0136] Considering the normal displacement of the contact bottom surface, according to elastic mechanics, when the normal stress is continuously distributed, the normal displacement is:

[0137]

[0138] In the formula, E * is the equivalent elastic modulus; p z is the distribution of stress in the Z direction; r is the distance between the calculation points:

[0139]

[0140] Stress distribution has rotational symmetry, and the normal displacement of any point is only related to its distance from the origin. Therefore, it is only necessary to calculate the displacement of the relevant points on the x-axis. Calculate the displacement of any point P2 on the stress surface to the point P1 on the x-axis, and integrate the entire stress surface based on the calculation results, such as Figure 2 (b) As shown. Due to rotational symmetry, the stress at point P2 is only related to the distance from this point to the origin of the coordinate system. According to the geometric relationship:

[0141] t 2 =r 2 +k 2 +2rk cos θ2

[0142] Combining the above equations, we get the stress expression:

[0143]

[0144] In the formula, k represents the length of the line segment P1 P2; θ2 represents the angle between the straight line P1 P2 and the x-axis; t is the distance between point P2 and the origin of the coordinate system; r represents the distance between point P1 and the origin of the coordinate system, that is, the calculation point distance;

[0145] Rewrite the formula as:

[0146]

[0147] Where C1 and C2 are process parameters:

[0148] C1 2 =a 2 ―r 2

[0149] C2=r cosθ2

[0150] Substituting into the normal displacement expression we get:

[0151]

[0152] In the formula, s is the equation (C1 2 ―k 2 ―2kC2)=0, the integral in dk is:

[0153]

[0154] C2 is a function of angle θ2, so the formula can be written as:

[0155]

[0156] This term is 0 after integration with respect to θ2, so the normal displacement is:

[0157]

[0158] Therefore, the normal displacement generated at this time is a constant, and the normal displacements of all points in the contact bottom surface are equal, so the total force in this area is:

[0159]

[0160] According to the above calculation, for the abrasive force surface with a diameter of L2, the normal force is F, the normal displacement is d, and the relevant contact force and contact deformation are:

[0161] F=πP0L2 2 / 2

[0162] d=πP0L2 / 2E *

[0163] L2=L1+2d tanα

[0164] Where P0 is the average stress in the region; L2 is the diameter of the bottom surface of the abrasive contacting the workpiece after wear; α is the grinding front angle of the abrasive; E * For the model that regards the abrasive grains as rigid bodies, it can be directly calculated by the mechanical parameters of the workpiece gear material. In this embodiment, both the abrasive grains and the workpiece are regarded as elastic bodies, which is closer to the actual situation. The equivalent elastic modulus can be obtained by the material properties of the workpiece and the abrasive grains:

[0165]

[0166] Where E1 and E2 are the elastic moduli of the abrasive and gear materials, respectively; v1 and v2 are the Poisson's ratios of the abrasive and gear materials, respectively.

[0167] Combining the above equations, the abrasive-workpiece contact deformation can be obtained as:

[0168]

[0169] The grinding stage of the abrasive grains is related to the current contact stress of the abrasive grains. When the average stress P0 < 0.4H, the workpiece material is elastically deformed; when the average stress 0.4H < P0 < H, the workpiece material is elasto-plastically deformed; when the average stress H < P0, the workpiece material is completely plastically deformed. According to the critical stress values of the abrasive grain force-bearing surface in different cutting stages, the corresponding critical penetration depth of the abrasive grains is calculated:

[0170]

[0171]

[0172] In the formula, d cp and d cc are the critical cutting depths of ploughing and cutting respectively; H is the material hardness.

[0173] (2) Comparison with the calculation results of the traditional spherical abrasive grain model

[0174] The existing theoretical calculation models of grinding force mainly adopt the calculation method of spherical abrasive grains. According to the contact analysis definition of the sphere and the spatial semi-elastic body in contact mechanics, the cutting of spherical abrasive grains is as Figure 3 shown. As shown in the figure, the diameter of the spherical abrasive grain is equal to the measured protrusion height of the abrasive grain. According to the classical Hertz contact model, the penetration depth and contact stress of the spherical abrasive grain are:

[0175]

[0176]

[0177]

[0178] In the formula, a is the radius of the cross-sectional circle of the spherical abrasive grain cutting into the bottom surface; R is the radius of the abrasive grain; d is the penetration depth of the abrasive grain; p0 is the average stress level.

[0179] By联立 the above equations, the solution can be obtained:

[0180]

[0181] According to the critical values of the average stress in each grinding stage, the critical conditions of the grinding stage based on spherical abrasive grains are obtained:

[0182]

[0183]

[0184] In the formula, d cp * and dcc * They are the plowing and critical cutting depth based on spherical abrasive particles, respectively.

[0185] It can be seen from the formula that for spherical abrasives, only the protruding height of the abrasive is related to the geometric shape of the abrasive in the calculation expression, and the influence of the contact bottom surface of the abrasive and the grinding front angle are ignored. According to the critical conditions of the grinding stage of the truncated cone abrasive and the spherical abrasive, the critical conditions of the grinding stage are compared under the same material parameters. Figure 4-Figure 6 As shown in the figure, the critical cutting depth results of the grinding stage derived from the actual measurement model of the grinding wheel abrasive grains are different from the calculation results of the traditional model.

[0186] Specifically, for the critical cutting depths in the grinding stage with different abrasive protrusion heights: the critical plowing and critical cutting depths of the truncated cone-shaped abrasive are larger than the corresponding depths of the spherical abrasive, and the critical cutting depth is more sensitive to the change of the abrasive protrusion height.

[0187] For different abrasive cross-section bevel angles: In all calculations, the critical cutting depth of the truncated cone abrasive is greater than that of the spherical abrasive, especially the critical plowing depth, which is quite different. In addition, the abrasive cross-section bevel angle parameter is not considered in the calculation of the critical cutting depth of the spherical abrasive, and its change will not affect the calculation results. For different contact bottom surface wear diameters: Similar to the abrasive bevel angle, the influence of this parameter is not considered in the calculation of spherical abrasives, and the settlement results will not change. For truncated cone abrasives, the contact bottom surface becomes larger after the bottom surface is worn, the sharpness of the abrasive decreases, and greater force is required to achieve cutting. The proportion of scraping and plowing abrasives increases, and the critical plowing and critical cutting depths both increase.

[0188] Through the above calculations and analysis, the critical depth of the grinding stage derived in this embodiment based on the measured geometric shape of the abrasive particles more fully considers the geometric parameters of the abrasive particles, and can reflect the relationship between abrasive wear and the critical cutting depth, which is more practical.

[0189] Step 2: Construct grinding force models for different grinding stages, and obtain the scraping force calculation model, plowing force calculation model and cutting force calculation model respectively.

[0190] The contact state between the abrasive and the workpiece is different at different grinding stages, and the mechanism of generating grinding force is different. Therefore, the abrasives at different grinding stages require their own corresponding grinding force calculation methods. The grinding force calculation method for each stage is established by analyzing the force of the abrasive at different grinding stages, and then the influence of the normal vector direction at different positions of the involute tooth surface on the grinding force direction is considered, and the grinding resultant force is calculated based on the line contact principle of the profile grinding process.

[0191] (1) Scraping force calculation model

[0192] When the abrasive grains penetrate into the depth d <d cp When the abrasive is in the scraping stage, the abrasive slides on the workpiece. The contact deformation produced by the abrasive in this stage is elastic deformation, no material is removed, and there is only normal contact force between the abrasive and the workpiece on the force-bearing surface of the abrasive, such as Figure 7 As shown in the figure, the normal force F exerted on the abrasive particles in the scratching stage is nr and the tangential force F tr for:

[0193] F nr =P0S1

[0194] F tr =μ r F nr

[0195] Where S1 is the force-bearing surface area of ​​the abrasive:

[0196]

[0197] Where L2 represents the diameter of the bottom surface in contact with the workpiece after abrasive wear:

[0198] L2=L1+2d tanα

[0199] Then the scratch force calculation model is obtained:

[0200] F nr =E * d(L1+2d tanα)

[0201] F tr =μ r E * d(L1+2d tanα)

[0202] In the formula, μ r is the friction coefficient in the scraping stage. According to research, the friction coefficient of iron materials in the cutting fluid environment is μ r is 0.4.

[0203] According to the above calculation, the scraping force of the abrasive in the scraping stage is related to the abrasive geometry parameters, cutting depth and material parameters. The calculation results of the scraping force at different cutting depths are shown in Figure 8 As shown in the figure, this calculation condition is the calculation condition without considering the wear of the grinding wheel, the critical plowing depth is 0.072μm, and the normal scraping force corresponding to the critical plowing depth is 0.021N, that is, the grinding force on all scraping abrasive particles will not exceed 0.021N.

[0204] (2) Plowing force calculation model

[0205] When the abrasive grains penetrate into the depth d cp <d<dcc When the abrasive is in the plowing stage, the abrasive plows the workpiece. The contact between the abrasive and the workpiece also generates abrasive-workpiece contact force, and its principle is the same as that of the abrasive in the scraping stage. In addition, in the plowing stage, the workpiece material undergoes plastic deformation, and the material accumulates on both sides of the abrasive or on the front cutting edge. Therefore, the abrasive is also subjected to a force generated by resisting material deformation, which is assumed to be F np 1 , then the force analysis of abrasive particles during the plowing stage is as follows Fig. 9 shown.

[0206] As can be seen from the figure, the contact force on the abrasive is the same as that in the scraping stage, and can be solved by this method based on the calculation of the normal force of scraping. The plowing force generated by the abrasive to resist material deformation acts on the peripheral surface of the abrasive. Projecting the force surface onto the cross-sectional plane of the abrasive, this part of the normal plowing force F np 1 for:

[0207] F np 1 =p1S2

[0208] Where p1 is the average stress of the cross section that resists material deformation; S2 is the projected cross-sectional area of ​​the abrasive in the direction of movement that resists material deformation:

[0209]

[0210] Where, L1 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece; L2 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece after wear; α is the grinding front angle of the abrasive grain;

[0211] The cross-sectional average stress that resists material deformation can be calculated based on the defined material scratch hardness:

[0212] p1=H s

[0213] In the formula, H s is the scratch hardness of the material;

[0214] The normal force F on the abrasive particles in the plowing stage is np and the tangential force F tp for:

[0215] F np =d(E * +H s )(L1+d tanα)

[0216] F tp =μ p F nr

[0217] In the formula, μ p is the plowing coefficient:

[0218]

[0219] Obtain the plowing force calculation model. The normal and tangential plowing forces of the abrasive grains in the plowing stage obtained from the force analysis are as Fig.10 shown. It can be seen from the figure that, similar to the calculation condition of the scratching force, the influence brought by the grinding wheel wear is not considered in the calculation of the plowing force. Under this condition, the critical plowing depth is 0.072 μm, the critical cutting depth is 0.182 μm, the normal scratching force corresponding to the critical plowing depth is 0.022 N, and the normal scratching force corresponding to the critical cutting depth is 0.056 N, that is, the grinding force received by all scratching abrasive grains will not be less than 0.022 N and will not exceed 0.56 N.

[0220] In addition, the material scratching coefficient μ p is related to the cutting parameters, and the change of the cutting depth will affect the scratching coefficient. Therefore, the ratio of the tangential plowing force to the normal plowing force is not a fixed value, but a function that changes with the cutting depth of the abrasive grains.

[0221] (3) Cutting force calculation model

[0222] When the cutting depth d cc < d, the material is in the cutting stage, the material produces plastic deformation, and chips are formed. For the abrasive grains in the cutting stage, the abrasive grain-workpiece contact forces calculated in the scratching and plowing stages still exist, and at the same time, the abrasive grains will be subjected to the force generated by resisting chip generation. According to the above description, in this plastic deformation stage, the average stress level of the normal force on the force-bearing surface of the abrasive grains is equivalent to the hardness of the workpiece material. On the other hand, the grinding force received by the abrasive grains when cutting the workpiece to produce chips can be obtained through the material shear stress, as Fig.11 shown. It can be seen from the figure that the instantaneous projected area corresponding to the cutting force is:

[0223] dA = 2r g 2 cos 2 α i dα i

[0224] In the formula, r g is the radius of the abrasive grain corresponding to the cutting force position; α i is the instantaneous cutting rake angle;

[0225] Integrate the entire cutting area of the abrasive grain to obtain the force F nc 1 of the abrasive grain resisting chip formation in the grinding stage:

[0226]

[0227] The normal force F exerted on the abrasive during the cutting stage nc and the tangential force F tc for:

[0228]

[0229]

[0230] In the formula, β α and φ α are the friction angle and shear angle respectively; S1 is the force-bearing surface area of ​​the abrasive; τ is the flow stress in the shear area, and:

[0231]

[0232] Where A, B, C, m, and n are the constitutive parameters of the material, and: A represents the initial yield stress under strain rate and temperature; B represents the strain hardening modulus of the material; C represents the strain rate strengthening parameter of the material; m represents the thermal softening index of the material; n represents the strain hardening index of the material; T r and T m are room temperature and material melting point respectively; ε and They are the equivalent strain and the equivalent strain rate:

[0233]

[0234]

[0235] In the formula, is the cutting speed of the abrasive:

[0236]

[0237] In the formula, R i The radial distance between the abrasive grain and the center of the grinding wheel; d s Indicates the grinding wheel diameter corresponding to the grinding position; v s Indicates the grinding wheel speed.

[0238] Step 3: Based on the influence of grinding wheel wear on the geometric parameters of abrasive particles, the critical contact conditions between abrasive particles and workpiece and the grinding force model are modified to obtain the modified critical cutting depths of the plowing stage and the cutting stage, as well as the scraping force-grinding wheel wear model, the plowing force-grinding wheel wear model and the cutting force-grinding wheel wear model.

[0239] The geometric parameters change before and after abrasive wear, and the contact bottom surface becomes larger, such as Fig.12As shown in the figure, the contact bottom diameter L1 before grinding becomes the contact bottom diameter L2 after grinding, and the force surface diameter is L3. According to the forming grinding force model, the relationship between the current cutting depth of the abrasive and the critical cutting depth of each grinding stage determines the grinding stage of the abrasive. After the grinding wheel is worn, the geometric parameters of the abrasive, the critical cutting depth of the grinding stage, the cutting depth of the abrasive, etc. all change. Therefore, the grinding stage of the same abrasive before and after wear and the corresponding grinding force calculation method change, and the model stage and corresponding grinding force of the abrasive after grinding need to be recalculated.

[0240] The grinding force calculation model of profile grinding mainly includes two types of parameters: the material mechanical parameters of the workpiece gear and the grinding wheel, and the cutting geometric parameters determined by the cutting conditions. Grinding wheel wear has no obvious effect on the material mechanical parameters of the gear and the grinding wheel, but has a significant effect on the cutting geometric parameters, as follows:

[0241] For the maximum undeformed chip thickness t imax :The principle and calculation method of the maximum undeformed chip thickness are based on the kinematics of the abrasive particles and the grinding process parameters. Although the grinding wheel wear will affect the geometric shape of the grinding wheel abrasive particles, it does not affect the grinding of the grinding wheel kinematics and the mutual influence and superposition effect of the motion trajectory between the abrasive particles. Therefore, the grinding wheel wear has no obvious effect on the maximum undeformed chip thickness.

[0242] The undeformed chip thickness t for any cutting abrasive i : Despite the maximum undeformed chip thickness t imax The undeformed chip thickness of any cutting abrasive is not affected by the wear of the grinding wheel, but it is affected by the height of the abrasive. Affected by the wear of the grinding wheel, the height distribution of the abrasive changes from the protruding height distribution before wear to the residual height distribution after wear. Therefore, the undeformed chip thickness t of any cutting abrasive is i will also be affected.

[0243] Half-apex cone angle of abrasive grain α g : Although the geometric shape of the abrasive changes after wear, based on the assumption that the geometric characteristics of the unworn part of the abrasive remain unchanged, the semi-apex cone angle of the abrasive remains unchanged and is not affected by abrasive wear.

[0244] For the diameter L2 of the abrasive contact surface: As the grinding wheel wears, the height of the abrasive changes, and the size of the abrasive contact surface also changes. Based on the assumption that the geometric characteristics of the unworn part of the abrasive remain unchanged during wear and the relationship between the geometric parameters of the abrasive, the relationship between the abrasive wear rate and the abrasive contact surface diameter L2 is:

[0245] L2=L1+2tanαh i ε

[0246] Where L1 is the diameter of the bottom surface in contact with the workpiece before abrasive wear; L2 is the diameter of the bottom surface in contact with the workpiece after abrasive wear; ε is the abrasive wear rate; h is i Indicates the protrusion height before abrasive wear;

[0247] Similar to the diameter of the abrasive contact surface, according to the geometric characteristics of the abrasive, the diameter of the abrasive force surface is:

[0248] L3=L2+2tanαd i

[0249] Where L3 is the diameter of the abrasive force surface.

[0250] It can be seen from the formula that the diameter of the abrasive force surface is affected by the contact surface diameter and the thickness of the undeformed chip. Therefore, the size of the abrasive force surface is directly affected by the wear of the grinding wheel. According to the above analysis, abrasive wear will have a greater impact on the chip geometry parameters and affect the calculation results of the grinding force.

[0251] (1) Corrected critical conditions for abrasive-workpiece contact

[0252] For the critical cutting depth of each grinding stage: After abrasive wear, the critical cutting depth corresponding to each grinding stage changes. According to the change of geometric parameters after abrasive wear and the calculation results of critical conditions of abrasive grinding stage, the influence of wear rate on critical cutting depth is solved. The diameter L1 of the bottom surface in contact with the workpiece before abrasive wear is replaced by the diameter L3 of the abrasive force surface, and the corrected critical cutting depth of the plowing stage and cutting stage is obtained:

[0253]

[0254]

[0255] Where, d cp ′ and d cc ′ are the critical cutting depths of the modified plowing stage and cutting stage, respectively.

[0256] It can be seen from the formula that there is a linear relationship between the critical cutting depth and the abrasive wear rate, where the constant value part represents the critical plowing / cutting depth of the abrasive in the absence of wear. The greater the protrusion height of the abrasive when it is not worn, the larger the contact bottom surface diameter of the abrasive when it is not worn, and the greater the critical cutting depth. In addition, the relevant part of the slope of the curve is also related to the mechanical properties of the abrasive, workpiece gear material and the geometric parameters of the abrasive. The relationship between the critical cutting depth and the abrasive wear rate is calculated, as shown in Fig.13 shown.

[0257] As can be seen from the figure, the critical penetration depth of the abrasive during the grinding process is positively correlated with the abrasive wear rate, and the larger the abrasive size, the more sensitive the critical penetration depth is to wear. Therefore, for grinding wheels with larger abrasive sizes, more frequent dressing is required to ensure that a sufficient proportion of abrasives are in the cutting stage.

[0258] (2) Scraping force-grinding wheel wear model

[0259] For abrasives at different stages, the corresponding grinding force at each stage will also change. According to the change of geometric parameters after abrasive wear and the calculation method of scraping force, the change law of abrasive scraping force with grinding wheel wear rate can be obtained by joint solution. Specifically, the diameter L1 of the bottom surface of the abrasive contacting the workpiece before wear is replaced by the diameter L3 of the abrasive force surface, and the scraping force-grinding wheel wear model is obtained:

[0260] F nr ′=E * d(L1+2d tanα)+2 tanαh i E * dε

[0261] F tr ′=μ r E * d(L1+2d tanα)+2μ r tanαh i E * dε

[0262] In the formula, F nr ′ and F tr ′ are the normal force and tangential force on the abrasive particles in the scratching stage after correction.

[0263] It can be seen that the scraping force on the abrasive is proportional to the abrasive wear rate. The abrasive size will affect the sensitivity of the grinding force to the abrasive wear rate. The larger the abrasive size, the more sensitive the scraping force is to the wear rate. According to the formula, the relationship between the abrasive scraping force and the abrasive wear rate and the cutting depth is calculated, as shown in Fig.14 shown.

[0264] (3) Plowing force-grinding wheel wear model

[0265] When the abrasive wear rate increases, the critical plowing depth of the abrasive will increase, and the scraping force will also increase at the same cutting depth. The diameter L1 of the bottom surface of the abrasive contacting the workpiece before wear is replaced by the diameter L3 of the abrasive force surface, and the plowing force-grinding wheel wear model is obtained:

[0266] F np ′=E * d(L1+2 tanαh i ε+2d tanα)+H sd(L1+2 tanαh i ε+d tanα)

[0267] F tp ′=μ p F nr

[0268] It should be noted that as the grinding wheel wears, the plowing coefficient μ calculated by the abrasive geometric parameters p will change, that is, the plowing coefficient μ p After correction, the corrected plowing coefficient is:

[0269]

[0270] In the formula, F np ′ and F tp ′ are the normal force and tangential force on the abrasive particles in the plowing stage after correction; μ p ′ is the corrected plowing coefficient.

[0271] The relationship between the plowing coefficient, the abrasive penetration depth and the abrasive wear rate is calculated according to the formula, such as Fig.15 As shown in the figure, the plowing coefficient changes with the cutting depth. The plowing coefficient becomes smaller as the cutting depth increases, and the critical value is 0.2. On the other hand, when the cutting depth is the same, the wear rate has little effect on the plowing coefficient, but the wear rate will affect the critical cutting depth in the plowing stage. Therefore, the wear rate will affect the calculation results by determining the effective range of the plowing coefficient curve.

[0272] (4) Cutting force-grinding wheel wear model

[0273] The cutting force on the abrasive in the cutting stage is divided into two parts: the force against the chips and the contact force between the abrasive and the workpiece. Both forces are related to the geometric shape of the abrasive. Therefore, both forces will be affected by the wear of the grinding wheel. According to the geometric parameters of the abrasive after wear and the calculation results of the grinding force of the abrasive in the cutting stage, the diameter L1 of the bottom surface of the abrasive contacting the workpiece before wear is replaced by the diameter L3 of the abrasive force surface, and the cutting force-grinding wheel wear model is obtained:

[0274]

[0275]

[0276] In the formula, F nc ′ and F tc ′ are the normal force and tangential force on the abrasive particles during the cutting stage.

[0277] Although the geometric shape of the abrasive changes, the flow stress of the material does not change. In addition, under the assumption that the uncut part of the abrasive retains its original geometric characteristics, the cutting angle parameters of the abrasive do not change. Fig.16 shown.

[0278] It can be seen from the figure that the grinding force exerted on the cutting abrasive increases with the increase of the cutting depth, and the abrasive wear rate has a direct impact on the grinding force exerted on the cutting abrasive: the abrasive wear rate affects the critical cutting depth, thereby affecting the number of abrasives in the cutting stage; for abrasives with the same cutting depth, the greater the abrasive wear rate, the greater the normal force it is subjected to, and when the abrasive wear rate is greater, the change in grinding force is more sensitive to the abrasive wear rate.

[0279] Based on the above analysis of the influence of grinding wheel wear rate on the critical grinding depth of abrasive and grinding force at different stages, the grinding force model of abrasive before and after wear is established. Taking the grinding wheel wear rate of 0 and the wear rate of 0.4 as examples, the cutting force calculation results of some numbered abrasives are as follows: Fig.17 shown.

[0280] As can be seen from the figure, when the grinding wheel is not worn, most of the abrasive particles are in the cutting stage. At this time, the material removal efficiency of the grinding process is high, the cutting heat generated by the scraping and plowing of the abrasive particles is small, and the overall grinding quality is high. When the wear rate gradually increases, the number of abrasive particles in the scraping and plowing stage increases significantly, the proportion of abrasive particles in the cutting stage decreases, the processing material removal efficiency decreases, more heat is generated, and the grinding quality is reduced. At the same time, the wear of the grinding wheel causes a significant increase in the grinding force of the abrasive particles in different cutting stages, and the grinding force increases significantly.

[0281] Step 4: Based on the scraping force-grinding wheel wear model, the plowing force-grinding wheel wear model and the cutting force-grinding wheel wear model, the grinding force-grinding wheel wear model is constructed.

[0282] The directions of the normal grinding force and tangential grinding force of the abrasive grains are based on the axial and radial directions of the cone of the abrasive grain cross section and are based on the abrasive grain coordinate system. Due to the special geometric shape of the tooth surface, the normal direction of the abrasive grains at different positions changes with the involute angle of the gear, and the directions of the normal grinding force and tangential grinding force calculated for each abrasive grain are different, such as Fig.18 For the i-th abrasive, the abrasive local coordinate system (LNCS) is established with the normal direction of the abrasive as the Y direction and the involute tangent direction as the X direction. i ).

[0283] For the i-th abrasive grain, the abrasive grain local coordinate system is established with the normal direction of the abrasive grain as the Y direction and the involute tangent direction as the X direction. The transformation relationship between the abrasive grain local coordinate system and the gear global coordinate system is:

[0284]

[0285] In the formula, and are the expression matrices of the grinding force of the i-th abrasive in the abrasive local coordinate system and the gear global coordinate system, respectively, and:

[0286]

[0287] In the formula, and They represent the normal grinding force and tangential grinding force on the i-th abrasive grain respectively; and They represent the grinding force on the i-th abrasive particle in the XYZ directions respectively;

[0288] is the transformation matrix of the grinding force of the i-th abrasive particle from the local coordinate system of the abrasive particle to the global coordinate system of the gear:

[0289]

[0290] In the formula, represents the angle between the normal direction and the radial direction of the i-th;

[0291] According to the principle of line contact cutting of profile grinding gear, the grinding force can be regarded as the vector sum of the grinding forces of all abrasive particles involved in cutting on the contact line:

[0292]

[0293] In the formula, F t is the grinding force matrix; N i is the total number of abrasive particles involved in grinding; h i represents the protrusion height of the i-th abrasive particle before wear.

[0294] The total number of grinding grains can be calculated by the grinding contact line length and the number of grinding grains per unit length:

[0295]

[0296] Where, C is the number of abrasive grains per unit area of ​​the grinding wheel; L ai is the effective involute length.

[0297] Step 5: Based on the relationship between spindle power and grinding force, the spindle power-grinding wheel wear model is obtained.

[0298] During the process of forming gear grinding, the C-axis of the workbench has periodic indexing motion, but the measuring equipment installed on the workbench is wired transmission mode, and the signal line will be entangled as the indexing motion proceeds. Therefore, the grinding force of the single tooth groove processing process is measured, and the processing is stopped after the single tooth groove cutting is completed to avoid the rotation of the workbench. In addition, single-sided grinding is achieved during the grinding process by deflecting the grinding wheel to avoid the mutual cancellation of grinding forces in double-sided grinding. The equipment installation problem in the actual measurement process is solved, the forming gear grinding force measurement is completed, and the proposed forming gear grinding force model is verified. This experiment is aimed at the fine grinding process in forming gear grinding, and the selection of process parameters refers to the parameter range used in actual production.

[0299] The spindle power P of the machine tool is mainly composed of two parts:

[0300] P=P idle +P cut

[0301] Among them, P idle and P cut They are no-load power and cutting power respectively.

[0302] During the no-load motion of the grinding wheel in the profile grinding process, the grinding wheel continues to rotate at a high speed, and the feed speed of the tool holder in the gear axis is very small compared to the grinding wheel speed, and its influence on the spindle axis feed motor is small. Therefore, the no-load power of the spindle of the profile grinding machine can be regarded as a single factor function of the grinding wheel speed.

[0303] In the form gear grinding process, the spindle speed, as a processing parameter, does not change during the entire processing cycle. Therefore, the power consumption of the machine tool spindle caused by factors such as electric heat and friction is regarded as a constant during the entire grinding process and is obtained by measuring the spindle power in the air-cut state.

[0304] Cutting power is generated by the cutting force during the cutting process. According to the basic definition of power and the motion principle of profile grinding, the cutting power of profile grinding can be obtained as:

[0305] P cut =F t (v s ±v w )

[0306] In the formula, F t v is the tangential cutting force in gear grinding; s is the grinding wheel speed; v w It is the workpiece moving speed, which corresponds to the axial feed speed of the tool holder in form grinding. The positive and negative signs represent the reverse grinding and forward grinding of the grinding wheel respectively.

[0307] The rotation speed of the grinding wheel in gear forming processing is usually 500-1000 times its axial feed speed. The influence of the axial feed speed of the grinding wheel can be ignored, that is, the influence of forward grinding and reverse grinding on cutting power can be ignored.

[0308] Before the gear grinding process, the gear will be heat treated to obtain better mechanical properties of the tooth surface. During the heat treatment, the gear will release its internal residual stress, resulting in large deformation of the gear tooth surface after heat treatment. The residual stress at different positions of the same gear tooth is unevenly distributed, resulting in uneven deformation of the tooth surface after heat treatment. Therefore, in order to ensure the accuracy and tooth surface quality of the gear after processing, the gear should be ground to ensure that the last cutting depth is uniform on the entire tooth profile, and the grinding depth of each previous cutting is reversed.

[0309] In addition, the deformation between different gear teeth of the same workpiece gear is also very different, and the grinding allowances of different tooth grooves of the same gear after heat treatment are quite different. Therefore, during the first cut, the cutting depth of different gear teeth is uneven and unknown, resulting in large changes in the grinding force of the grinding wheel when cutting different tooth grooves, and large fluctuations in the spindle grinding power. In contrast, during the tail cut, the grinding allowances at all positions on the gear tooth surface are uniform, the grinding allowances between each gear tooth are the same, and the difference in spindle power is small. Therefore, the average value of the spindle power of the tail cutter represents the cutting power of the grinding wheel under this working condition.

[0310] Step 6: Detect the spindle power in real time and monitor the grinding wheel wear online.

[0311] Due to the limitations of the gear profile grinding processing principle and measuring equipment, it is impossible to achieve real-time measurement of the grinding force during the entire gear processing process. Therefore, considering the correlation between cutting force and machine tool spindle power, the wear of the grinding wheel is further monitored by real-time measurement of the machine tool spindle power.

[0312] In the processing of a single tooth groove, the grinding wheel and the workpiece gear always maintain line contact during the processing, and the contact line extends from the initial point of the effective involute to the end point of the effective involute. Therefore, the non-stable cutting process such as cutting in and cutting out of the grinding wheel in the profile grinding is extremely short, and the entire grinding process of a single tooth groove can be regarded as a cutting process of full cutting in. Therefore, the influence of non-full cutting in is not considered when calculating the grinding force and grinding power.

[0313] According to the grinding wheel wear to cutting force mapping relationship model proposed in this embodiment, the variation law of the tangential force and spindle cutting power of the gear grinding process with the grinding wheel wear is calculated. Considering the random characteristics of the grinding wheel and the construction process of the abrasive height sequence, the same method is used for multiple calculations and the average value is obtained to reduce the influence of random number generation. The calculation results are as follows: Fig.19 shown.

[0314] As can be seen from the figure, cutting power increases with the increase of abrasive wear rate, and when the abrasive wear rate is higher, the growth rate of cutting power becomes faster. In addition, the larger the average diameter of the abrasive particles, the greater the cutting power, and the faster the rate of increase with abrasive wear rate.

[0315] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. An online monitoring method for grinding wheel wear based on spindle power, characterized in that: It includes the following steps: Step 1: Based on the geometric parameters of the abrasive grains, solve the critical conditions of abrasive grain-workpiece contact to obtain the critical cutting depths in the plowing stage and the cutting stage; Step 2: Construct grinding force models for different grinding stages, and obtain the scratch force calculation model, the plowing force calculation model, and the cutting force calculation model respectively; Step 3: Based on the influence of wheel wear on the geometric parameters of the abrasive grains, correct the critical conditions of abrasive grain-workpiece contact and the grinding force models to obtain the corrected critical cutting depths in the plowing stage and the cutting stage, as well as the scratch force-wheel wear model, the plowing force-wheel wear model, and the cutting force-wheel wear model; Step 4: Based on the scratch force-wheel wear model, the plowing force-wheel wear model, and the cutting force-wheel wear model, construct the grinding resultant force-wheel wear model; Step 5: Based on the relationship between the spindle power and the grinding resultant force, obtain the spindle power-wheel wear model; Step 6: Real-time detect the spindle power to perform online monitoring of wheel wear; In the said Step 3, the influence relationship of the abrasive grain wear rate on the contact surface diameter L2 of the abrasive grain is: <h2 style=";text-align:left;direction:ltr">L2 = L1 + 2tanαh<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> ε Where L1 is the diameter of the bottom surface in contact with the workpiece before abrasive wear; L2 is the diameter of the bottom surface in contact with the workpiece after abrasive wear; ε is the abrasive wear rate; h is i Indicates the protrusion height before abrasive wear; The diameter of the force-bearing surface of the abrasive grain is: <h2 style=";text-align:left;direction:ltr">L3 = L2 + 2tanαd<h2 style=";text-align:left;direction:ltr"> i In the formula, L3 is the diameter of the force-bearing surface of the abrasive grain; In the said Step 1, the abrasive grain-workpiece contact deformation is: Where d is the contact deformation between the abrasive particle and the workpiece; P0 is the average stress in the region; E * is the equivalent elastic modulus; L1 is the diameter of the bottom surface of the abrasive grain in contact with the workpiece; α is the grinding front angle of the abrasive grain; The grinding stage where the abrasive grain is located is related to the current contact stress of the abrasive grain: when the average stress P0 < 0.4H, the workpiece material is elastically deformed; when the average stress 0.4H < P0 < H, the workpiece material is elasto-plastically deformed; when the average stress H < P0, the workpiece material is completely plastically deformed; According to the critical stress values of the force-bearing surface of the abrasive grain in different cutting stages, obtain the critical cutting depths in the plowing stage and the cutting stage respectively: Where, d cp and d cc are the critical cutting depths for plowing and cutting, respectively; H is the material hardness; In the said Step 3, replace the diameter L1 of the bottom surface of the contact between the abrasive grain and the workpiece before wear with the diameter L3 of the force-bearing surface of the abrasive grain to obtain the corrected critical cutting depths in the plowing stage and the cutting stage: Where, d cp ′ and d cc ′ are the modified critical cutting depths of the plowing stage and cutting stage, respectively; In step 2, when the abrasive grains penetrate into the depth d <d cp When the abrasive is in the scraping stage, the normal force F nr and the tangential force F tr for: F nr =P0S1 F tr =μ r F nr In the formula, S1 is the area of the force-bearing surface of the abrasive grain: In the formula, L2 represents the diameter of the bottom surface of the contact between the worn abrasive grain and the workpiece: L2 = L1 + 2d tanα Then obtain the scratch force calculation model: F nr =E * d(L1+2d tanα) F tr =μ r AND * d(L1+2d tanα) In the formula, μ r is the friction coefficient in the scraping stage; In the said Step 3, replace the diameter L1 of the bottom surface of the contact between the abrasive grain and the workpiece before wear with the diameter L3 of the force-bearing surface of the abrasive grain to obtain the scratch force-wheel wear model: F nr ′=And * d(L1+2d tanα)+2tanαh i AND * of F tr ′=μ r And * d(L1+2d tanα)+2μ r tanαh i And * dε In the formula, F nr ′ and F tr ′ are the normal force and tangential force on the abrasive particles in the scraping stage after correction; In step 2, when the abrasive grains penetrate into the depth d cp <d<d cc When the abrasive grains are in the plowing stage, the plowing force generated by the abrasive grains to resist material deformation acts on the peripheral surface of the abrasive grains. Projecting the force surface onto the cross-sectional plane of the abrasive grains, the normal plowing force F np 1 for: F np 1 =p1S2 In the formula, p1 is the cross-sectional average stress for resisting material deformation; S2 is the projected cross-sectional area of the abrasive grain in the movement direction for resisting material deformation: In the formula, L1 is the diameter of the bottom surface of the contact between the abrasive grain and the workpiece; L2 represents the diameter of the bottom surface of the contact between the worn abrasive grain and the workpiece; α represents the grinding rake angle of the abrasive grain; The cross-sectional average stress for resisting material deformation can be calculated according to the defined scratch hardness of the material: p1=H s In the formula, H s is the scratch hardness of the material; The normal force R on the abrasive particles in the plowing stage is np and the tangential force F tp for: R np =d(E * +H s )(L1+d tanα) F tp =μ p F nr In the formula, μ p is the plowing coefficient: Obtain the plowing force calculation model; In the said Step 3, replace the diameter L1 of the bottom surface of the contact between the abrasive grain and the workpiece before wear with the diameter L3 of the force-bearing surface of the abrasive grain to obtain the plowing force-wheel wear model: F np ′=E * d(L1+2landαh i ε+2d tanα)+H s d(L1+2landαh i ε+d tanα) F tp ′=μ p F nr The corrected plowing coefficient is: In the formula, F np ′ and F tp ′ are the normal force and tangential force on the abrasive particles in the plowing stage after correction; μ p ′ is the corrected plowing coefficient; In the second step, when the cutting depth d of the abrasive grains cc < d, the material is in the cutting stage, and the instantaneous projected area corresponding to the cutting force is: dA=2r g 2 cos 2 a i dα i In the formula, r g is the abrasive particle radius corresponding to the cutting force position; α i is the instantaneous cutting rake angle; The force F of the abrasive resisting chip formation during the grinding stage is obtained by integrating the entire abrasive cutting surface. nc 1 : The normal force F exerted on the abrasive during the cutting stage nc and the tangential force F tc for: In the formula, β α and φ α are the friction angle and shear angle respectively; S1 is the force-bearing surface area of ​​the abrasive; τ is the flow stress in the shear area, and: Where A, B, C, m, and n are the constitutive parameters of the material, and: A represents the initial yield stress under strain rate and temperature; B represents the strain hardening modulus of the material; C represents the strain rate strengthening parameter of the material; m represents the thermal softening index of the material; n represents the strain hardening index of the material; T r and T m are room temperature and material melting point respectively; ε and They are the equivalent strain and the equivalent strain rate: In the formula, is the cutting speed of the abrasive: In the formula, R i The radial distance between the abrasive grain and the center of the grinding wheel; d s Indicates the grinding wheel diameter corresponding to the grinding position; v s Indicates the grinding wheel speed; Obtain the cutting force calculation model; In the said Step 3, replace the diameter L1 of the bottom surface of the contact between the abrasive grain and the workpiece before wear with the diameter L3 of the force-bearing surface of the abrasive grain to obtain the cutting force-wheel wear model: In the formula, F nc ′ and F tc ′ are the normal force and tangential force on the abrasive particles during the cutting stage.

2. The method for online monitoring of grinding wheel wear based on spindle power according to claim 1, characterized in that: In the step 4, for the i-th abrasive particle, a local coordinate system of the abrasive particle is established with the normal direction of the abrasive particle as the Y direction and the tangent direction of the involute as the X direction. The conversion relationship between the local coordinate system of the abrasive particle and the global coordinate system of the gear is: In the formula, and are the expression matrices of the grinding force of the i-th abrasive in the abrasive local coordinate system and the gear global coordinate system, respectively, and: In the formula, and They represent the normal grinding force and tangential grinding force on the i-th abrasive grain respectively; and They represent the grinding force on the i-th abrasive particle in the XYZ directions respectively; is the transformation matrix of the grinding force of the i-th abrasive particle from the local coordinate system of the abrasive particle to the global coordinate system of the gear: In the formula, represents the angle between the normal direction and the radial direction of the i-th; According to the principle of line contact cutting of profile grinding gear, the grinding force is regarded as the vector sum of the grinding forces of all abrasive particles involved in cutting on the contact line: In the formula, F t is the grinding force matrix; N i is the total number of abrasive particles involved in grinding; h i represents the protrusion height of the i-th abrasive particle before wear.

3. The method for online monitoring of grinding wheel wear based on spindle power according to claim 1, characterized in that: In step 5, the spindle power P of the machine tool is mainly composed of two parts: P=P idle +P cut Among them, P idle and P cut They are no-load power and cutting power respectively; Cutting power is generated by the cutting force during the cutting process. The cutting power of profile grinding is: P cut =F t (v s ±v w ) In the formula, F t v is the tangential cutting force in gear grinding; s is the grinding wheel speed; v w is the workpiece moving speed.

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