A method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel

Abstract

The present invention provides a method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel, and belongs to the field of grinding processing. The method comprises simplifying the process of grinding zirconia ceramics, calculating the critical grinding depth, and establishing an equation for the protruding height of abrasive grains; determining the distribution range of the protruding height of abrasive grains under different material removal states, and establishing an effective abrasive grain number model; establishing a corresponding single abrasive grain theoretical grinding force model based on fracture mechanics, determining the proportional relationship between the total volume of workpiece material removed in the contact area and the theoretical total volume of material removed by abrasive grains, and establishing a single abrasive grain actual grinding force model; and establishing a grinding wheel total grinding force model based on the single abrasive grain actual grinding force model and the effective abrasive grain number. The method of the present invention establishes a quantitative relationship between the grinding force and related parameters of zirconia ceramic grinding by considering the actual situation of the grinding wheel surface morphology and combining the surface structuring rate of the structured grinding wheel, thereby providing a theoretical basis for setting actual process parameters.

Description

Technical Field

[0001] The invention relates to the technical field of grinding of hard and brittle materials, and in particular to a method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel. Background Art

[0002] With the development of science and technology, hard and brittle materials have achieved rapid development in emerging fields such as aerospace, electronic information, new energy, marine engineering, and bioengineering, and at the same time, higher and higher requirements have been put forward for the structure and performance of materials. Zirconia ceramics have the characteristics of high strength, high hardness, and good wear resistance, but these characteristics will also lead to poor grindability, resulting in higher grinding forces and grinding temperatures during the grinding process. The unique groove structure of the structured grinding wheel can reduce the contact area between the grinding wheel and the workpiece surface, enhance the storage and transportation capacity of the grinding fluid in the grinding area, reduce the grinding force and grinding temperature, and thus improve the surface integrity of the workpiece. Grinding force is an important indicator for monitoring the quality of workpiece material processing. Higher grinding force is likely to cause workpiece surface / subsurface damage, aggravate grinding wheel wear, and thus affect the surface quality of the workpiece. Therefore, the establishment of a grinding force model for grinding zirconia ceramics with a structured grinding wheel has a huge impact on guiding production practice.

[0003] Lang et al. assumed that the shape of the grinding wheel abrasive grains is conical, and their protrusion height obeys Rayleigh distribution. They all participate in cutting and remove materials during the grinding process. The grinding force is divided into two parts: grinding deformation force and friction force. The calculation expressions of grinding deformation force and friction force are derived respectively. Zhang et al. assumed that the abrasive grains are evenly distributed on the surface of the grinding wheel, have the same size, consistent protrusion height, and all effective abrasive grains participate in the grinding process. They analyzed the formation mechanism of the three grinding stages of toughness grinding stage, toughness-brittle transition grinding stage, and brittle grinding stage, and established a theoretical model of grinding force considering the three grinding stages in laser macro-microstructure grinding. However, in the actual grinding process, the abrasive grains on the grinding wheel surface must take into account the inconsistent protrusion height, and not all abrasive grains participate in the grinding process. Therefore, in the grinding force model of the structured grinding wheel, not only the structure of the grinding wheel surface should be considered, but also the geometric characteristics of the protrusion height of the abrasive grains and the number of effective abrasive grains under different grinding conditions are particularly important. Summary of the invention

[0004] The main purpose of the present invention is to solve the shortcomings of the above-mentioned prior art and provide a method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel. Based on the structured grinding wheel grinding of the zirconia ceramic surface, the grinding forces under different grinding depths and material removal mechanisms (toughness removal and brittle removal) are comprehensively analyzed to establish a grinding force model.

[0005] The purpose of the present invention is to predict the grinding force by establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel, comprising the following steps:

[0006] S1: Simplify the grinding process of zirconia ceramics and calculate the critical grinding depth;

[0007] In the process of establishing the grinding force model of zirconia ceramics, the following assumptions are made: the abrasive grains on the surface of the grinding wheel are truncated cone-shaped diamond grains with a high Rayleigh distribution, and the top cone angle is 60° (the half cone angle θ is 30°); the width of the abrasive grain end is a constant value, and the diamond wear during the processing is not considered. The grinding force on the surface of the grinding wheel structure is analyzed by analytical modeling. The main components of the grinding force are the material toughness removal grinding force below the critical grinding depth and the material toughness-brittleness removal grinding force above the critical grinding depth.

[0008] For zirconia ceramics, the critical grinding depth a at which the removal mechanism changes from plastic removal to brittle fracture is pc The calculation is as follows:

[0009] The formula for the critical grinding thickness from plastic removal to brittle fracture is as follows:

[0010]

[0011] Where: α, η, γ are dimensionless constants. For the Vickers indenter, α = 2 / π, η ≈ 1, γ = 0.2; K is the ratio of the load abrasive area to the abrasive area, 0 ≤ k ≤ 1; ε is the workpiece geometry factor; K ID is the dynamic fracture toughness, K ID =0.3K IC , K IC is the fracture toughness of the workpiece material; H V is the Vickers hardness.

[0012] The maximum undeformed cutting thickness equation is as follows:

[0013]

[0014] Where: D is the diameter of the diamond grinding wheel, v f is the workpiece feed speed, v s is the grinding wheel speed, c is the density of abrasive particles, a p is the grinding depth.

[0015] From equations (1) and (2), the critical grinding depth equation can be obtained as shown below:

[0016]

[0017] S2: Establish a mathematical model of the characteristic parameters of the abrasive grain morphology on the grinding wheel surface;

[0018] The equation of abrasive protrusion height based on Rayleigh distribution is established, and the correlation coefficient β is solved according to the actual dressing state of the grinding wheel surface; the grinding depth a p and critical grinding depth a pc By comparison, we get a p <a pc When the abrasive protrusion height range and a p ≥a pc The height range of the abrasive protrusion, and a p ≥a pc There are distribution ranges of abrasive protrusion heights for ductile removal and ductile-brittle removal, and the probability of the number of abrasive particles under each grinding state is calculated.

[0019] S2.1: For Rayleigh distributed wear particles, the probability density formula of the protrusion height is as follows:

[0020]

[0021] Where h is the protruding height of the abrasive particles, and β is a constant coefficient related to the distribution of the protruding height of the abrasive particles. The formula is as follows:

[0022]

[0023] Where h 0 is the maximum protruding height of the abrasive particles, p 0 The protrusion height is less than h 0 The probability of , whose value is 0≤p 0 ≤1.

[0024] S2.2: For Rayleigh distributed abrasive particles, the probability formula for the number of abrasive particles is as follows:

[0025] The probability formula of the number of abrasive particles at different grinding depths is as follows:

[0026]

[0027] where h∈(x 1 , x 2 ) is the protruding height range of the abrasive particles, when a p <a pc When h∈[h 0 -a p ,h 0 ], with probability p d . when a p ≥a pc When h∈[h 0 -a p ,h 0 ] belongs to the protruding height range of the grinding abrasive particles in the contact area of ​​the entire grinding zone, and its probability is p b ; h∈[h 0 -ap ,h 0 -a p +a pc ] belongs to the protrusion height range of tough removal of abrasive particles, and its probability is p b1 ; h∈[h 0 -a p +a pc ,h 0 ] belongs to the protrusion height range of ductile-brittle removal of abrasive particles, and its probability is p b2 .

[0028] S3: Establishing the mathematical model of the grinding wheel-workpiece contact area;

[0029] Firstly, a geometric model of the grinding depth of random abrasives is established according to the geometric relationship, and the average grinding depth under different grinding conditions is calculated by combining the average formula. Secondly, the different average grinding depths are substituted into the contact arc length formula to solve the contact arc length under different grinding conditions. Finally, the probability, contact arc length and structuring rate are combined to calculate the effective number of abrasives under different conditions.

[0030] S3.1: Establish a mathematical model for the average grinding depth of grinding wheel abrasive grains at different grinding depths;

[0031] When the grinding depth a p When the grinding depth of random abrasive is pr The formula is as follows:

[0032] a pr =h-(h 0 -a p ) (7)

[0033] The formula for the average grinding depth of abrasive particles at different grinding depths is as follows:

[0034]

[0035] when a p <a pc When p=p d , the average grinding depth is Δa pd . when a p ≥a pc When h∈[h 0 -a p ,h 0 ],p=p b , the average grinding depth is Δa pb ; h∈[h 0 -a p ,h 0 -a p +a pc ],p=p b1, the average grinding depth is Δa pb1 ; h∈[h 0 -a p +a pc ,h 0 ],p=p b2 , the average grinding depth is Δa pb2 .

[0036] S3.2: Establish a mathematical model of average contact arc length under different grinding conditions:

[0037]

[0038] when a p <a pc When Δa p =Δa pd , average contact arc length l d . when a p ≥a pc When h∈[h 0 -a p ,h 0 ], Δa p =Δa pb , average contact arc length l b ; h∈[h 0 -a p ,h 0 -a p +a pc ],Δa p =Δa pb1 , average contact arc length l b1 ; h∈[h 0 -a p +a pc ,h 0 ], Δa p =Δa pb2 , average contact arc length l b2 .

[0039] Under ductile-brittle grinding, the chip is a pentagonal prism with a similar trapezoidal cross section, and the arc length formula of the ductile part is as follows:

[0040]

[0041] where d mb2 To convert Δa pb2 Substitute the maximum undeformed cutting thickness into equation (2) and replace Δa with pd , Δa pb , Δa pb1 Substituting into equation (2) we can obtain d md ,d mb ,d mb1 .

[0042] Under ductile-brittle grinding, the arc length formula of the brittle removal part of the chip is as follows:

[0043]

[0044] S3.3: Establish a mathematical model for the number of effective abrasive grains in the contact zone under different grinding conditions;

[0045] The effective number of abrasive particles is as follows:

[0046]

[0047] when a p <a pc When h∈[h 0 -a p ,h 0 ],p=p d ,l=l d , then the effective number of abrasive particles is N ed . when a p ≥a pc When h∈[h 0 -a p ,h 0 -a p +a pc ],p=p b1 ,l=l b1 , then the effective number of abrasive particles is N eb1 ; h∈[h 0 -a p +a pc ,h 0 ],p=p b2 ,l=l b2 , then the effective number of abrasive particles is M eb2 . b is the effective grinding width of the workpiece; is the structural rate of the grinding wheel grinding surface, and its formula is as follows:

[0048]

[0049] Where A e is the effective area of ​​the grinding wheel, A T is the area of ​​the grinding wheel surface.

[0050] S4: Establish the mathematical model of grinding force of single abrasive grain under different grinding conditions;

[0051] Firstly, the formulas for the volume of material removed by a single abrasive and the equivalent volume are established based on the geometric relationship, and the average grinding thickness is solved by these two formulas. Secondly, the average grinding thickness is substituted into the fracture mechanics formula to solve the corresponding theoretical grinding force of a single abrasive. Then, the actual material removal volume of the brittle part is solved based on the indentation fracture theory, and the proportional relationship between the total volume of workpiece material removed in the contact area and the theoretical total volume of material removed by the abrasive is established. Finally, the actual grinding force model of a single abrasive is established based on the relationship between the proportional coefficient and the theoretical grinding force of a single abrasive.

[0052] S4.1: Mathematical model of average grinding thickness of chips under different grinding conditions;

[0053] S4.1.1: Mathematical model for average grinding thickness of the toughness portion of the chip;

[0054] The formula for the volume of material removed by a single abrasive particle is as follows:

[0055]

[0056] The chip shape is equivalent to a hexahedron with the same trapezoidal cross section. The formula for the equivalent volume of material removed by a single abrasive particle is as follows:

[0057]

[0058] When V 1 =V 2 The effective average thickness of a single abrasive chip can be calculated:

[0059]

[0060] when a p <a pc When l = l d , d m =d md , then the average chip thickness d a is d ad ;when a p ≥a pc When h∈[h 0 -a p ,h 0 ], l = l b , d m =d mb , then the average chip thickness d a is d ab ; h∈[h 0 -a p ,h 0 -a p +a pc ], l = l b1 , d m =dmb1 , then the average chip thickness d a is d ab1 ; h∈[h 0 -a p +a pc ,h 0 ], when grinding with tough-brittle abrasive grains, the toughness of the chip is l = l b2d , d m =d mb2d , then the average chip thickness d a is d ab2d ; w is the average cutting length of the abrasive end.

[0061] S4.1.2: The brittle part of the chip (i.e. when a p ≥a pc When h∈[h 0 -a p +a pc ,h 0 ], mathematical model of average grinding thickness of brittle part of chip when grinding with tough-brittle abrasive;

[0062] The formula for the volume of material removed by a single abrasive particle is as follows:

[0063]

[0064] The formula for the equivalent volume of material removed by a single abrasive particle is as follows:

[0065]

[0066] When V 3 =V 4 When , the average thickness of chips in the brittle area can be calculated;

[0067]

[0068] S4.2: Mathematical model of grinding force of single abrasive grain under different grinding conditions;

[0069] S4.2.1: Mathematical model of theoretical grinding force of a single abrasive particle under different grinding conditions:

[0070]

[0071] when a p <a pc When,d a =d ad , then F l =F ld ;when a p ≥a pc When h∈[h 0 -a p ,h0 -a p +a pc ],d a =d ab1 , then F l =F lb1 ; h∈[h 0 -a p +a pc ,h 0 ], chip toughness removal part d a =d ab2d , then F l =F lb2d ; Chip brittle removal part d a =d ab2b , then F l =F lb2b .

[0072] when a p ≥a pc When h∈[h 0 -a p +a pc ,h 0 ], Grinding force model of single abrasive grain during ductile-brittle abrasive grinding:

[0073]

[0074] S4.2.2: Ratio of the actual volume of workpiece material removed to the theoretical volume of workpiece material removed under different grinding conditions;

[0075] S4.2.2.1: When a p <a pc , the ratio of material removal volume;

[0076] The theoretical total volume of material removed is given by:

[0077]

[0078] The actual total volume of material removed is given by:

[0079]

[0080] The formula for the ratio of the actual material removed by a single abrasive particle to the total volume of theoretically removed material is as follows:

[0081]

[0082] S4.2.2.2: When a p ≥a pc ,Ratio of material removal volume;

[0083] The length of the crack in the chip brittle removal part cl and height c h for:

[0084]

[0085] Where P = F lb2b , where η is a dimensionless constant, E is Young's modulus, and v is Poisson's ratio;

[0086] The formula for material removal volume under brittle removal is as follows:

[0087]

[0088] when a p ≥a pc When h∈[h 0 -a p ,h 0 -a p +a pc ], the total theoretical volume of material removed by abrasive particles:

[0089]

[0090] when a p ≥a pc When h∈[h 0 -a p +a pc ,h 0 ], the total theoretical volume of material removed by abrasive particles;

[0091]

[0092] when a p ≥a pc When the total theoretical volume of abrasive particles removed is:

[0093]

[0094] The actual total volume of material removed is given by:

[0095]

[0096] The formula for the ratio of the actual material removed by a single abrasive particle to the total volume of theoretically removed material is as follows:

[0097]

[0098] S4.2.3: Actual grinding force model for a single abrasive particle:

[0099]

[0100] S5: Mathematical model of total grinding force of grinding wheel under different grinding conditions;

[0101] S5.1: When a p <a pc When, the mathematical model of the total grinding force of the grinding wheel is:

[0102]

[0103] S5.2: When a p ≥a pc When, the mathematical model of the total grinding force of the grinding wheel is:

[0104]

[0105] S5.3: In summary, the mathematical model of the total grinding force of the grinding wheel is:

[0106]

[0107] when a p pc When, k 1 =1,k 2 =0; when a p ≥a pc When, k 1 =0,k 2 =1.

[0108] Beneficial technical effects of the present invention: The present invention provides a method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel. When grinding zirconia ceramics with a structured grinding wheel, the geometric morphology of the abrasive grains on the grinding wheel surface and the structural rate of the grinding wheel surface are considered. By analyzing the material removal mechanism under different grinding states, the effective abrasive grain number and material removal ratio model of the grinding contact zone are established, and then the grinding force model of zirconia grinding with a structured grinding wheel is established. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 The present invention is a flowchart of a method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel.

[0110] Figure 2 It is a schematic diagram of grinding wheel grinding according to the present invention.

[0111] Among them, 1-bronze bond diamond grinding wheel; 2-diamond abrasive grains; 3-zirconia workpiece. DETAILED DESCRIPTION

[0112] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0113] In this embodiment, a method for establishing a grinding force model of a structured grinding wheel grinding zirconia ceramics is as follows:​ Figure 1 As shown, the following steps are included:

[0114] S1: Simplify the grinding process of zirconia ceramics and calculate the critical grinding depth;

[0115] In the process of establishing the grinding force model of zirconia ceramics, the following assumptions are made: the abrasive grains on the surface of the grinding wheel are truncated cone-shaped diamond grains with a high Rayleigh distribution, and the top cone angle is 60° (the half cone angle θ is 30°); the width of the abrasive grain end is a constant value, and the diamond wear during the processing is not considered. The grinding force on the surface of the grinding wheel structure is analyzed by analytical modeling. The main components of the grinding force are the material toughness removal grinding force below the critical grinding depth and the material toughness-brittleness removal grinding force above the critical grinding depth.

[0116] For zirconia ceramics, the critical grinding depth a at which the removal mechanism changes from plastic removal to brittle fracture is pc The calculation is as follows:

[0117] The formula for the critical grinding thickness from plastic removal to brittle fracture is as follows:

[0118]

[0119] Where: α, η, γ are dimensionless constants. For the Vickers indenter, α = 2 / π, η ≈ 1, γ = 0.2; K is the ratio of the load abrasive area to the abrasive area, 0 ≤ k ≤ 1; ε is the workpiece geometry factor; K ID is the dynamic fracture toughness, K ID =0.3K IC , K IC is the fracture toughness of the workpiece material; H V is the Vickers hardness.

[0120] The maximum undeformed cutting thickness equation is as follows:

[0121]

[0122] Where: D is the diameter of the diamond grinding wheel, v f is the workpiece feed speed, v s is the grinding wheel speed, c is the density of abrasive particles, a p is the grinding depth.

[0123] From equations (1) and (2), the critical grinding depth equation can be obtained as shown below:

[0124]

[0125] S2: Establish a mathematical model of the characteristic parameters of the abrasive grain morphology on the grinding wheel surface;

[0126] The equation of abrasive protrusion height based on Rayleigh distribution is established, and the correlation coefficient β is solved according to the actual dressing state of the grinding wheel surface; the grinding depth a p and critical grinding depth a pc By comparison, we get a p <a pc When the abrasive protrusion height range and a p ≥a pc The height range of the abrasive protrusion, and a p ≥a pc There is a distribution range of the protrusion height of the abrasive particles in the ductile removal and ductile-brittle removal conditions, and the probability of the number of abrasive particles under each grinding state is calculated. Figure 2 Schematic diagram of grinding wheel grinding workpiece.

[0127] S2.1: For Rayleigh distributed wear particles, the probability density formula of the protrusion height is as follows:

[0128]

[0129] Where h is the protruding height of the abrasive particles, and β is a constant coefficient related to the distribution of the protruding height of the abrasive particles. The formula is as follows:

[0130]

[0131] Where h 0 is the maximum protruding height of the abrasive grain (depending on the dressing of the grinding wheel), p 0 The protrusion height is less than h 0 The probability of , whose value is 0≤p 0 ≤1.

[0132] S2.2: For Rayleigh distributed abrasive particles, the probability formula for the number of abrasive particles is as follows:

[0133] The probability formula of the number of abrasive particles at different grinding depths is as follows:

[0134]

[0135] where h∈(x 1 , x 2 ) is the protruding height range of the abrasive particles, when a p <a pc When h∈[h 0 -a p ,h 0 ], with probability p d . when a p ≥a pc When h∈[h 0 -a p ,h 0 ] belongs to the protrusion height range of the grinding abrasive particles in the entire grinding contact area, and its probability is pb ; h∈[h 0 -a p ,h 0 -a p +a pc ] belongs to the protrusion height range of tough removal of abrasive particles, and its probability is p b1 ; h∈[h 0 -a p +a pc ,h 0 ] belongs to the protrusion height range of ductile-brittle removal of abrasive particles, and its probability is p b2 .

[0136] S3: Establishing the mathematical model of the grinding wheel-workpiece contact area;

[0137] Firstly, a geometric model of the grinding depth of random abrasives is established according to the geometric relationship, and the average grinding depth under different grinding conditions is calculated by combining the average formula. Secondly, the different average grinding depths are substituted into the contact arc length formula to solve the contact arc length under different grinding conditions. Finally, the probability, contact arc length and structuring rate are combined to calculate the effective number of abrasives under different conditions.

[0138] S3.1: Establish a mathematical model for the average grinding depth of grinding wheel abrasive grains at different grinding depths;

[0139] When the grinding depth a p When the grinding depth of random abrasive is pr The formula is as follows:

[0140] a pr =h-(h 0 -a p ) (7)

[0141] The formula for the average grinding depth of abrasive particles at different grinding depths is as follows:

[0142]

[0143] when a p <a pc When p=p d , the average grinding depth is Δa pd . when a p ≥a pc When h∈[h 0 -a p ,h 0 ],p=p b , the average grinding depth is Δa pb ; k∈[h 0 -a p ,h 0 -a p +apc ],p=p b1 , the average grinding depth is Δa pb1 ; h∈[h 0 -a p +a pc ,h 0 ],p=p b2 , the average grinding depth is Δa pb2 .

[0144] S3.2: Establish a mathematical model of average contact arc length under different grinding conditions:

[0145]

[0146] when a p <a pc When Δa p =Δa pd , average contact arc length l d . when a p ≥a pc When h∈[h 0 -a p ,h 0 ], Δa p =Δa pb , average contact arc length l b ; h∈[h 0 -a p ,h 0 -a p +a pc ],Δa p =Δa pb1 , average contact arc length l b1 ; h∈[h 0 -a p +a pc ,h 0 ], Δa p =Δa pb2 , average contact arc length l b2 .

[0147] Under ductile-brittle grinding, the chip is a pentagonal prism with a similar trapezoidal cross section, and the arc length formula of the ductile part is as follows:

[0148]

[0149] where d mb2 To convert Δa pb2 Substitute the maximum undeformed cutting thickness into equation (2) and replace Δa with pd , Δa pb , Δa pb1 Substituting into equation (2) we can obtain d md ,dmb d mb1 .

[0150] Under ductile-brittle grinding, the arc length formula of the brittle removal part of the chip is as follows:

[0151]

[0152] S3.3: Establish a mathematical model for the number of effective abrasive grains in the contact zone under different grinding conditions;

[0153] The effective number of abrasive particles is as follows:

[0154]

[0155] when a p <a pc When h∈[h 0 -a p ,h 0 ],p=p d ,l=l d , then the effective number of abrasive particles is N ed . when a p ≥a pc When h∈[h 0 -a p ,h 0 -a p +a pc ],p=p b1 ,l=l b1 , then the effective number of abrasive particles is N eb1 ; h∈[h 0 -a p +a pc ,h 0 ],p=p b2 ,l=l b2 , then the effective number of abrasive particles is N eb2 . b is the effective grinding width of the workpiece; is the structural rate of the grinding wheel grinding surface, and its formula is as follows:

[0156]

[0157] Where A e is the effective area of ​​the grinding wheel, A T is the area of ​​the grinding wheel surface.

[0158] S4: Establish the mathematical model of grinding force of single abrasive grain under different grinding conditions;

[0159] Firstly, the formulas for the volume of material removed by a single abrasive and the equivalent volume are established based on the geometric relationship, and the average grinding thickness is solved by these two formulas. Secondly, the average grinding thickness is substituted into the fracture mechanics formula to solve the corresponding theoretical grinding force of a single abrasive. Then, the actual material removal volume of the brittle part is solved based on the indentation fracture theory, and the proportional relationship between the total volume of workpiece material removed in the contact area and the theoretical total volume of material removed by the abrasive is established. Finally, the actual grinding force model of a single abrasive is established based on the relationship between the proportional coefficient and the theoretical grinding force of a single abrasive.

[0160] S4.1: Mathematical model of average grinding thickness of chips under different grinding conditions;

[0161] S4.1.1: Mathematical model for average grinding thickness of the toughness portion of the chip;

[0162] The formula for the volume of material removed by a single abrasive particle is as follows:

[0163]

[0164] The chip shape is equivalent to a hexahedron with the same trapezoidal cross section. The formula for the equivalent volume of material removed by a single abrasive particle is as follows:

[0165]

[0166] When V 1 =V 2 The effective average thickness of a single abrasive chip can be calculated:

[0167]

[0168] when a p <a pc When l = l d , d m =d md , then the average chip thickness d a is d ad ;when a p ≥a pc When h∈[h 0 -a p ,h 0 ], l = l b , d m =d mb , then the average chip thickness d a is d ab ; h∈[h 0 -a p ,h 0 -a p +a pc ], l = l b1 , d m =dmb1 , then the average chip thickness d a is d ab1 ; h∈[h 0 -a p +a pc ,h 0 ], when grinding with tough-brittle abrasive grains, the toughness of the chip is l = l b2d , d m =d mb2d , then the average chip thickness d a is d ab2d , w is the average cutting length of the abrasive tip.

[0169] S4.1.2: The brittle part of the chip (i.e. when a p ≥a pc When h∈[h 0 -a p +a pc ,h 0 ], mathematical model of average grinding thickness of brittle part of chip when grinding with tough-brittle abrasive;

[0170] The formula for the volume of material removed by a single abrasive particle is as follows:

[0171]

[0172] The formula for the equivalent volume of material removed by a single abrasive particle is as follows:

[0173]

[0174] When V 3 =V 4 When , the average thickness of chips in the brittle area can be calculated;

[0175]

[0176] S4.2: Mathematical model of grinding force of single abrasive grain under different grinding conditions;

[0177] S4.2.1: Mathematical model of theoretical grinding force of a single abrasive particle under different grinding conditions:

[0178]

[0179] when a p <a pc When,d a =d ad , then F l =F ld ;when a p ≥a pc When h∈[h 0 -a p ,h0 -a p +a pc ],d a =d ab1 , then F l =F lb1 ; h∈[h 0 -a p +a pc ,h 0 ], chip toughness removal part d a =d ab2d , then F l =F lb2d ; Chip brittle removal part d a =d ab2b , then F l =F lb2b .

[0180] when a p ≥a pc When h∈[h 0 -a p +a pc ,h 0 ], Grinding force model of single abrasive grain during ductile-brittle abrasive grinding:

[0181]

[0182] S4.2.2: Ratio of the actual volume of workpiece material removed to the theoretical volume of workpiece material removed under different grinding conditions;

[0183] S4.2.2.1: When a p <a pc , the ratio of material removal volume;

[0184] The theoretical total volume of material removed is given by:

[0185]

[0186] The actual total volume of material removed is given by:

[0187]

[0188] The formula for the ratio of the actual material removed by a single abrasive particle to the total volume of theoretically removed material is as follows:

[0189]

[0190] S4.2.2.2: When a p ≥a pc , the ratio of material removal volume;

[0191] The length of the crack in the chip brittle removal part cl and height c h for:

[0192]

[0193] Where P = F lb2b , where η is a dimensionless constant, E is Young's modulus, and v is Poisson's ratio;

[0194] The formula for material removal volume under brittle removal is as follows:

[0195]

[0196] when a p ≥a pc When h∈[h 0 -a p ,h 0 -a p +a pc ], the total theoretical volume of material removed by abrasive particles:

[0197] when a p ≥a pc When h∈[h 0 -a p +a pc ,h 0 ], the total theoretical volume of material removed by abrasive particles:

[0198] when a p ≥a pc When the total theoretical volume of abrasive particles removed is:

[0199]

[0200] The actual total volume of material removed is given by:

[0201]

[0202] The formula for the ratio of the actual material removed by a single abrasive particle to the total volume of theoretically removed material is as follows:

[0203]

[0204] S4.2.3: Actual grinding force model for a single abrasive particle:

[0205]

[0206] S5: Mathematical model of total grinding force of grinding wheel under different grinding conditions;

[0207] S5.1: When a p <a pc When, the mathematical model of the total grinding force of the grinding wheel is:

[0208]

[0209] S5.2: When a p ≥a pc When, the mathematical model of the total grinding force of the grinding wheel is:

[0210]

[0211] S5.3: In summary, the mathematical model of the total grinding force of the grinding wheel is:

[0212] (36)

[0214] when a p pc When, k 1 =1,k 2 =0; when a p ≥a pc When, k 1 =0,k 2 =1.

[0215] In this embodiment, a 120# bronze bond diamond grinding wheel is used on a high-precision CNC horizontal axis rectangular table surface grinder MGK7120×6 / F to grind the zirconia ceramic surface. The surface structure of the grinding wheel is a V-shaped structure with a structural rate of 80%. The worktable feed speed v f , grinding wheel speed v s The grinding depth is 1.5m / min and 30m / s respectively. p Set as variables, test and calculate a respectively p These are the test values ​​and analytical values ​​under 10μm, 15μm, 20μm, and 25μm conditions. The specific parameters of the test workpiece are shown in Table 1.

[0216] Table 1 Specific parameters of experimental workpiece

[0217]

[0218] In this embodiment, the effective number of abrasive grains in the contact area is calculated according to S3 and the actual grinding force of a single abrasive grain is calculated according to S4, and then the total grinding force model of the structured grinding wheel is solved in S5; at the same time, the grinding force is measured in real time using a Kistler dynamometer.

[0219] ​In this embodiment, the theoretical analytical value of the grinding force in the process of grinding zirconia ceramics with a structured grinding wheel calculated by the present invention is compared with the experimental value, and it is found that the grinding force model of the structured grinding wheel grinding zirconia ceramics has a high prediction accuracy for the prediction of the grinding force.

[0220] In summary, in this embodiment, a method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel is provided, which mainly aims at comprehensively considering the geometric morphology of abrasive particles, surface structural parameters of the grinding wheel and grinding state when grinding hard and brittle materials, so as to make the grinding force model more comprehensive and accurate.

[0221] The above embodiments are only for illustrating the technical idea of ​​the present invention, and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention; any technology not involved in the present invention can be realized by existing technologies.

Claims

1. A method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel, characterized in that: The following steps are involved: S1: Simplify the grinding process of zirconia ceramics and calculate the critical grinding depth. In other words, make the following assumptions in the process of establishing the grinding force model of zirconia ceramics: the abrasive grains on the surface of the grinding wheel are truncated cone-shaped diamond grains with a high Rayleigh distribution, and the top semi-cone angle θ is 30°; the width of the abrasive grain end is a constant value, and the diamond wear during the processing is not considered; the grinding force on the surface of the grinding wheel structure is analyzed by the analytical modeling method. The main components of the grinding force are the material toughness removal grinding force below the critical grinding depth and the material toughness-brittleness removal grinding force above the critical grinding depth; S2: Establish a mathematical model of the characteristic parameters of the abrasive morphology on the grinding wheel surface, that is, establish an equation for the protruding height of the abrasive based on the Rayleigh distribution, and solve the correlation coefficient β according to the actual dressing state of the grinding wheel surface; p and critical grinding depth a pc By comparison, we get a p <a pc When the abrasive protrusion height range and a p ≥a pc The height range of the abrasive protrusion, and a p ≥a pc There are distribution ranges of abrasive protrusion heights in ductile removal and ductile-brittle removal, and the probability of the number of abrasive particles under each grinding state is calculated; S3: Establish a mathematical model of the grinding wheel-workpiece contact area, that is, firstly establish a geometric model of the random abrasive grinding depth based on the geometric relationship, and combine the average formula to calculate the average grinding depth under different grinding conditions; secondly, substitute the different average grinding depths into the contact arc length formula to solve the contact arc length under different grinding conditions; finally, combine the obtained probability, contact arc length and structuring rate to calculate the effective number of abrasives under different conditions; S4: Establish a mathematical model of the grinding force of a single abrasive under different grinding conditions. First, the volume and equivalent volume formula of material removed by a single abrasive are established based on the geometric relationship. The average grinding thickness is solved by these two formulas. Secondly, the fracture mechanics formula is used to substitute the average grinding thickness into the formula to solve the corresponding theoretical grinding force of a single abrasive. Then, the theoretical actual material removal volume of the brittle part is solved according to the indentation fracture theory, and the proportional relationship between the total volume of workpiece material removed in the contact area and the theoretical total volume of material removed by abrasive particles is established; finally, the actual grinding force model of a single abrasive particle is established based on the relationship between the proportional coefficient and the theoretical grinding force of a single abrasive particle; S5: Under different grinding conditions, a mathematical model of the total grinding force of the grinding wheel is established, that is, the number of effective abrasive grains under different grinding conditions and the actual grinding force model of a single abrasive grain are combined to establish the total grinding force model of the grinding wheel.

2. The method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel according to claim 1, characterized in that: For zirconia ceramics, the critical grinding depth a at which the removal mechanism changes from plastic removal to brittle fracture is pc The calculation is as follows: The formula for the critical grinding thickness from plastic removal to brittle fracture is as follows: Where: α, η, γ are dimensionless constants. For the Vickers indenter, α = 2 / π, η ≈ 1, γ = 0.2, K is the ratio of the load abrasive area to the abrasive area, 0 ≤ K ≤ 1, ε is the workpiece geometry factor, K ID is the dynamic fracture toughness, K ID =0.3K IC , K IC is the fracture toughness of the workpiece material, H V is the Vickers hardness, The maximum undeformed cutting thickness equation is as follows: Where: D is the diameter of the diamond grinding wheel, v f is the workpiece feed speed, v s is the grinding wheel speed, c is the density of abrasive particles, a p is the grinding depth, From equations (1) and (2), the critical grinding depth equation can be obtained as shown below:

3. The method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel according to claim 2, characterized in that: The specific method of step 2 is: S2.1: For Rayleigh distributed abrasive particles, the formula for the protrusion height of the abrasive particles is as follows: Where h is the protruding height of the abrasive particles, and β is a constant coefficient related to the distribution of the protruding height of the abrasive particles. The formula is as follows: Where h0 is the highest protrusion height of the abrasive, p0 is the probability that the protrusion height is less than h0, and its value is 0≤p0≤1; S2.2: For Rayleigh distributed abrasive particles, the probability formula for the number of abrasive particles is as follows: The probability formula of the number of abrasive particles at different grinding depths is as follows: Where h∈(x1, x2) is the protruding height range of the abrasive particles. p <a pc When, h∈[h0-a p ,h0], with a probability of p d ;when a p ≥a pc When, h∈[h0-a p ,h0] belongs to the protruding height range of the grinding abrasive particles in the contact area of ​​the entire grinding zone, and its probability is p b ; h∈[h0-a p ,h0-a p +a pc ] belongs to the protrusion height range of tough removal of abrasive particles, and its probability is p b1 ; h∈[h0-a p +a pc ,h0] belongs to the protrusion height range of ductile-brittle removal of abrasive particles, and its probability is p b2。 4. The method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel according to claim 3, characterized in that: The specific method of step 3 is: S3.1: Establish a mathematical model for the average grinding depth of grinding wheel abrasive grains at different grinding depths; When the grinding depth a p When the grinding depth of random abrasive is pr The formula is as follows: a pr =h-(h0-a p ) (7), The formula for the average grinding depth of abrasive particles at different grinding depths is as follows: when a p <a pc When p=p d , the average grinding depth is Δa pd ;when a p ≥a pc When, h∈[h0-a p ,h0],p=p b , the average grinding depth is Δa pb ; h∈[h0-a p ,h0-a p +a pc ],p=p b1 , the average grinding depth is Δa pb1 ; h∈[h0-a p +a pc ,h0],p=p b2 , the average grinding depth is Δa pb2 ; Where Φ function is the standard normal distribution function; S3.2: Establish a mathematical model of average contact arc length under different grinding conditions: when a p <a pc When Δa p =Δa pd , average contact arc length l d ;when a p ≥a pc When, h∈[h0-a p ,h0],Δa p =Δa pb , average contact arc length l b ; h∈[h0-a p ,h0-a p +a pc ],Δa p =Δa pb1 , average contact arc length l b1 ; h∈[h0-a p +a pc ,h0],Δa p =Δa pb2 , average contact arc length l b2 ; Under ductile-brittle grinding, the chip is a pentagonal prism with a similar trapezoidal cross section, and the arc length formula of the ductile part is as follows: where d mb2 To convert Δa pb2 Substitute the maximum undeformed cutting thickness into equation (2) and replace Δa with pd , Δa pb , Δa pb1 Substituting into equation (2) we can obtain d md d mb d mb1 , Under ductile-brittle grinding, the arc length formula of the brittle removal part of the chip is as follows: S3.3: Establish a mathematical model for the number of effective abrasive grains in the contact zone under different grinding conditions; The effective number of abrasive particles is as follows: when a p <a pc When, h∈[h0-a p ,h0],p=p d ,l=l d , then the effective number of abrasive particles is N ed ;when a p ≥a pc When, h∈[h0-a p ,h0-a p +a pc ], p =p b1 ,l=l b1 , then the effective number of abrasive particles is N eb1 ; h∈[h0-a p +a pc ,h0],p=p b2 ,l=l b2 , then the effective number of abrasive particles is N eb2 ; b is the effective grinding width of the workpiece, is the structural rate of the grinding wheel grinding surface, and its formula is as follows: Where A e is the effective area of ​​the grinding wheel, A T is the area of ​​the grinding wheel surface.

5. The method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel according to claim 4, characterized in that: The specific method of step 4 is: S4.1: Mathematical model of average grinding thickness of chips under different grinding conditions; S4.1.1: Mathematical model for average grinding thickness of the toughness portion of the chip; The formula for the volume of material removed by a single abrasive particle is as follows: The chip shape is equivalent to a hexahedron with the same trapezoidal cross section. The formula for the equivalent volume of material removed by a single abrasive particle is as follows: When V1=V2, the effective average thickness of a single abrasive chip can be calculated: when a p <a pc When l = l d , d m =d md , then the average chip thickness d a is d ad ;when a p ≥a pc When, h∈[h0-a p ,h0],l=l b , d m =d mb , then the average chip thickness d a is d ab ; h∈[h0-a p ,h0-a p +a pc ], l = l b1 , d m =d mb1 , then the average chip thickness d a is d ab1 ; h∈[h0-a p +a pc ,h0], when grinding with tough-brittle abrasive grains, the tough chip part has l=l b2d , d m =d mb2d , then the average chip thickness d a is d ab2d ; w is the average cutting length of the abrasive tip; S4.1.2: Mathematical model for average grinding thickness of brittle part of chip; The formula for the volume of material removed by a single abrasive particle is as follows: The formula for the equivalent volume of material removed by a single abrasive particle is as follows: When V3=V4, the average thickness of chips in the brittle area can be calculated: S4.2: Mathematical model of grinding force of single abrasive grain under different grinding conditions; S4.2.1: Mathematical model of theoretical grinding force of a single abrasive particle under different grinding conditions: when a p <a pc When,d a =d ad , then F l =F ld ;when a p ≥a pc When, h∈[h0-a p ,h0-a p +a pc ],d a =d ab1 , then F l =F lb1 ; h∈[h0-a p +a pc ,h0], chip toughness removal part d a =d ab2d , then F l =F lb2d ; Chip brittle removal part d a =d ab2b , then F l =F lb2b , when a p ≥a pc When, h∈[h0-a p +a pc ,h0], Grinding force model of single abrasive grain during ductile-brittle abrasive grinding: S4.2.2: Ratio of the actual volume of workpiece material removed to the theoretical volume of workpiece material removed under different grinding conditions; S4.2.2.1: When a p <a pc When the material removal volume ratio is The theoretical total volume of material removed is given by: The actual total volume of material removed is given by: The formula for the ratio of the actual material removed by a single abrasive particle to the total volume of theoretically removed material is as follows: S4.2.2.2: When a p ≥a pc , the ratio of material removal volume; The length of the crack in the chip brittle removal part c l and height c h for: Where P = F lb2b , where η is a dimensionless constant, E is Young's modulus, and v is Poisson's ratio. The formula for material removal volume under brittle removal is as follows: when a p ≥a pc When, h∈[h0-a p ,h0-a p +a pc ], the total theoretical volume of material removed by abrasive particles, when a p ≥a pc When, h∈[h0-a p +a pc ,h0], the total theoretical volume of material removed by abrasive particles, when a p ≥a pc When the total theoretical volume of abrasive particles removed is: The actual total volume of material removed is given by the following formula; The formula for the ratio of the actual material removed by a single abrasive particle to the total volume of theoretically removed material is as follows: S4.2.3: Actual grinding force model for a single abrasive particle:

6. The method for establishing a grinding force model for grinding zirconia ceramics with a structured grinding wheel according to claim 5, characterized in that: The specific method of step 5 is: S5.1: When a p <a pc When the total grinding force of the grinding wheel is: S5.2: When a p ≥a pc When, the mathematical model of the total grinding force of the grinding wheel is: S5.3: In summary, the mathematical model of the total grinding force of the grinding wheel is: when a p pc When k1=1, k2=0; when a p ≥a pc , k1=0, k2=1.​

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