Method and system for calculating instantaneous undeformed chip thickness in rock sawing process

Abstract

This invention belongs to the field of grinding technology, specifically providing a method and system for calculating the instantaneous undeformed chip thickness in rock sawing. The method includes: acquiring geometric parameters of a diamond circular saw blade and constructing a saw tooth surface model; acquiring saw blade motion parameters when the diamond circular saw cuts rock and obtaining the abrasive grain motion trajectory; establishing the undeformed chip morphology based on the adjacent abrasive grain motion trajectories and the saw tooth surface model to obtain the maximum undeformed chip thickness; and obtaining the instantaneous undeformed chip thickness when the diamond circular saw cuts rock based on the abrasive grain rotation angle and the maximum undeformed chip thickness, thereby optimizing grinding parameters. This invention constructs a method for calculating the instantaneous undeformed chip thickness for deep rock cutting, which can accurately calculate the instantaneous undeformed chip thickness under different grinding parameters, thus providing a theoretical basis for predicting grinding forces and optimizing grinding parameters.

Description

Technical Field

[0001] This invention belongs to the field of grinding processing technology, specifically relating to a method and system for calculating the instantaneous undeformed chip thickness in rock sawing. Background Technology

[0002] Currently, deep-cutting techniques (ranging from several millimeters to tens of millimeters) are commonly used in rock processing. In grinding, the undeformed chip thickness (the depth of abrasive grain penetration into the workpiece) is a crucial parameter. Grinding force and grinding heat are important indicators for evaluating and characterizing grinding processes. Instability in grinding force not only leads to tool breakage, undercutting, overcutting, and damage, but also severely damages the surface quality of the workpiece. Accurate and effective grinding force models are essential for optimizing grinding parameters and even improving grinding tools. Instantaneous undeformed chip thickness is a key factor and theoretical basis for predicting time-varying grinding forces; therefore, its calculation indirectly optimizes grinding processes and tools. Current research on grinding force prediction often uses the maximum undeformed chip thickness or equivalent undeformed chip thickness model from conventional grinding. However, in rock sawing, the large depth of cut makes it non-negligible compared to the tool diameter, potentially leading to errors when using traditional methods for calculating chip thickness in conventional grinding. Therefore, it is essential to establish the relationship between the instantaneous undeformed chip thickness and grinding parameters in deep cutting, so as to provide an important foundation for the prediction of grinding force and the optimization of grinding parameters.

[0003] In existing technology, the formula for calculating the maximum undeformed chip thickness in surface grinding is: ,in l The distance between two consecutive abrasive cutting edges. a p For depth of cut, d w The diameter of the grinding wheel. V f For feed rate, V s This represents the linear velocity of the grinding wheel.

[0004] In conventional grinding, the difference between the depth of cut and the wheel diameter is relatively large, and some terms are neglected in the formula derivation. From the perspective of the abrasive grains, the abrasive grain exposure height has a significant impact on the instantaneous undeformed chip morphology. At the same time, in surface grinding, the depth of abrasive grain penetration into the workpiece (i.e., the instantaneous undeformed chip thickness) is time-varying, which is also one of the factors that cause changes in grinding force during the grinding process.

[0005] Therefore, it is necessary to propose a method and system for calculating the instantaneous undeformed chip thickness during the deep rock cutting process, so as to provide a theoretical basis for the accurate prediction of grinding force and other parameters and the optimization of grinding process parameters. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method and system for calculating the instantaneous undeformed chip thickness in rock sawing. This method can calculate the instantaneous undeformed chip thickness under different grinding parameters, thereby providing a theoretical basis for predicting parameters such as grinding force and optimizing grinding process parameters.

[0007] To achieve the above objectives, the present invention provides the following solution: Methods for calculating the instantaneous, undeformed chip thickness in rock sawing include: Obtain geometric parameter information of diamond circular saw blade, including the total number of abrasive grains on the saw tooth surface, abrasive grain position distribution, abrasive grain exposure height and spacing between adjacent abrasive grains, and construct a saw tooth surface model; Obtain the saw blade motion parameters information when a diamond circular saw cuts rock, including saw blade feed speed, linear velocity and depth of cut, and obtain the abrasive particle motion trajectory; Based on the motion trajectory of adjacent abrasive grains and the sawtooth surface model, the morphology of the undeformed chip is established, and the maximum thickness of the undeformed chip is obtained. Based on the abrasive rotation angle and the maximum undeformed chip thickness, the instantaneous undeformed chip thickness during the diamond circular saw cutting of rock is obtained, enabling grinding force prediction and grinding parameter optimization.

[0008] Preferably, the method for obtaining the abrasive grain position distribution includes: In MATLAB, generate random numbers between (0,1), and combine them with the sawtooth length and width to obtain the center coordinates of the preset abrasive grains projected onto a rectangular plane. If the preset abrasive grain horizontal coordinate is not greater than the abrasive grain radius and less than the difference between the sawtooth length and the abrasive grain radius, and the preset abrasive grain vertical coordinate is greater than the abrasive grain radius and less than the difference between the sawtooth width and the abrasive grain radius, it is judged as overflow, and the center coordinates of the preset abrasive grain are regenerated; if the preset overlap discrimination condition is met, it is not overflow, and the preset overlap discrimination condition is used to determine whether the preset abrasive grain overlaps with the adjacent abrasive grain. If the center distance between the preset abrasive grain and the adjacent abrasive grain is less than the sum of the radius of the preset abrasive grain and the radius of the adjacent abrasive grain, it is determined that there is an overlap between the preset abrasive grain and the adjacent abrasive grain, and the center coordinates of the preset abrasive grain are regenerated; if there is no overlap, the abrasive grain diameter and abrasive grain position distribution are obtained.

[0009] Preferred methods for obtaining the maximum undeformed chip thickness include: Based on the cutting depth considering the exposed height of the i-th abrasive grain and the distance from the tip of the i-th abrasive grain to the center of the saw blade, calculate the rotation angle when the i-th abrasive grain cuts through the rock; Establish the trajectory of the saw blade's center of motion O 1 O2. The undeformed chip morphology ABCD is obtained based on the motion trajectory of two adjacent abrasive grains; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade O Distance of 2 O 2C, the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O 1 distance Saw blade center movement trajectory O 1 O 2. The angle at which the i-th abrasive grain cuts through the rock is obtained using the law of cosines when the saw blade center moves to... At that time, the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A ; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade O Distance of 2 O 2C and the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A To obtain the maximum undeformed chip thickness h max ( i At this point, the angle through which the abrasive grain i rotates is defined as the maximum undeformed chip thickness angle. i hm ( i ), i hm ( i The calculation formula for ) is as follows: , This represents the angle at which the i-th abrasive grain cuts through the rock. This represents the angle at which the (i-1)th abrasive grain cuts through the rock; Among them, the angle at which the abrasive grains are embedded to the deepest point in the stone O 1 AO 2( ψ As a constant, the following is calculated: , This represents the distance from the tip of the i-th abrasive grain to the center of the saw blade. Represents feed rate, Represents the linear velocity of the saw blade. l ( i -1, i () represents adjacent abrasive grains i and( i The interval between -1).

[0010] Preferably, when the abrasive grain angle i ( i () greater than the maximum undeformed chip thickness angle i hm ( i When a diamond circular saw cuts rock, the formulas for obtaining the instantaneous, undeformed chip thickness include: Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade distance And when the rotation angle of the i-th abrasive grain is At that time, the center of the saw blade Distance between the intersection point of the (i-1)th abrasive grain trajectory AD curve and the intersection point of the (i-1)th abrasive grain trajectory AD curve Calculate the instantaneous chip thickness : , In triangle O 1 K 2 O In section 2, according to the Law of Sines, we have: , in, Represents the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O A distance of 1; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade and the rotation angle of the i-th abrasive grain Obtain the instantaneous undeformed chip thickness during diamond circular saw cutting of rock. : , Preferably, when the preset abrasive grain rotation angle is... smaller than the maximum undeformed chip thickness angle gh m( i When a diamond circular saw cuts rock, the formulas for obtaining the instantaneous, undeformed chip thickness include: Instantaneous chip thickness K 1 K 2 is: , O is the center of the saw blade at this moment, within the triangle. OK 2 E middle: , , , Obtain the instantaneous undeformed chip thickness during diamond circular saw cutting of rock. : , In the formula, rs Let be the radius of the saw blade. anp The nominal cutting depth of the saw blade; The final expression for the instantaneous, undeformed chip thickness during diamond circular saw cutting of rock is as follows: .

[0011] This invention also provides a system for calculating the instantaneous undeformed chip thickness in rock sawing, for implementing the method, including: The saw tooth surface model construction module is used to obtain geometric parameter information of diamond circular saw blades, including the total number of abrasive grains on the saw tooth surface, the abrasive grain position distribution, the abrasive grain exposure height and the spacing between adjacent abrasive grains, and to construct the saw tooth surface model. The abrasive motion trajectory acquisition module is used to acquire the saw blade motion parameter information when the diamond circular saw cuts rock, including the saw blade feed speed, linear speed and cutting depth, and to obtain the abrasive motion trajectory. The maximum undeformed chip thickness calculation module is used to establish the undeformed chip morphology and obtain the maximum undeformed chip thickness based on the motion trajectory of adjacent abrasive grains and the sawtooth surface model. The instantaneous undeformed chip thickness calculation module is used to obtain the instantaneous undeformed chip thickness during the diamond circular saw cutting of rocks based on the abrasive grain rotation angle and the maximum undeformed chip thickness, thereby realizing grinding force prediction and grinding parameter optimization.

[0012] Preferably, the sawtooth surface model construction module includes an abrasive grain position distribution acquisition unit, which includes: The center coordinate calculation subunit is used to generate random numbers between (0,1) in MATLAB, and combine them with the sawtooth length and width to obtain the center coordinates of the preset abrasive grains projected onto the rectangular plane. The boundary discrimination subunit is used to determine whether the preset abrasive grain overflows the boundary based on the preset boundary discrimination conditions and the center coordinates; if it overflows, the center coordinates of the preset abrasive grain are regenerated; if it does not overflow, the preset overlap discrimination conditions are used to determine whether the preset abrasive grain overlaps with the adjacent abrasive grain. The overlap discrimination subunit is used to regenerate the center coordinates of the preset abrasive grain if the preset abrasive grain overlaps with the adjacent abrasive grain, and to obtain the abrasive grain diameter and abrasive grain position distribution if no overlap occurs.

[0013] Preferably, the maximum undeformed chip thickness calculation module includes: The angle calculation unit is used to calculate the angle when the i-th abrasive grain cuts through the rock, based on the cutting depth considering the exposed height of the i-th abrasive grain and the distance from the tip of the i-th abrasive grain to the center of the saw blade. The motion trajectory acquisition unit is used to establish the motion trajectory of the saw blade's center.O 1 O 2. The undeformed chip morphology ABCD is obtained based on the motion trajectory of two adjacent abrasive grains; The first point spacing calculation unit is used to calculate the distance from the tip of the i-th abrasive grain to the center of the saw blade. O The distance O2C from the (i-1)th abrasive grain tip to the center of the saw blade. O 1 distance Saw blade center movement trajectory O 1 O 2. The angle at which the i-th abrasive grain cuts through the rock is obtained using the law of cosines when the saw blade center moves to... At that time, the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A ; The second point spacing calculation unit is used to calculate the distance from the tip of the i-th abrasive grain to the center of the saw blade. O Distance of 2 O 2C and the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A To obtain the maximum undeformed chip thickness h max ( i At this point, the angle through which the abrasive grain i rotates is defined as the maximum undeformed chip thickness angle. i hm ( i ), i hm ( i The calculation formula for ) is as follows: , This represents the angle at which the i-th abrasive grain cuts through the rock. This represents the angle at which the (i-1)th abrasive grain cuts through the rock; Among them, the angle at which the abrasive grains are embedded to the deepest point in the stone O 1 AO 2( ψ As a constant, the following is calculated: , This represents the distance from the tip of the i-th abrasive grain to the center of the saw blade. Represents feed rate, Represents the linear velocity of the saw blade. l ( i -1, i () represents adjacent abrasive grains i and( i The interval between -1).

[0014] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention constructs the surface morphology of the saw teeth to obtain parameters such as abrasive grain spacing, exposure height, and distribution. Combined with the motion parameters of the saw blade and the rock, it ultimately realizes the calculation of the instantaneous undeformed chip thickness in deep cutting. When obtaining abrasive grain parameter information, this invention comprehensively considers the random distribution characteristics of abrasive grains, eliminating the simplification of using uniform distribution of abrasive grains on the grinding wheel surface in current technologies, which is more consistent with the actual characteristics of abrasive grains on the saw tooth surface. Existing technologies are aimed at calculating the maximum undeformed chip thickness in ordinary grinding. This invention constructs a method for calculating the instantaneous undeformed chip thickness for deep cutting of rocks, which can accurately calculate the instantaneous undeformed chip thickness under different grinding parameters, thereby providing a theoretical basis for predicting grinding force and optimizing grinding parameters. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of abrasive grain layering on the surface of the saw teeth according to an embodiment of the present invention; Figure 2 This is a motion trajectory diagram of the abrasive particles on the sawtooth surface according to an embodiment of the present invention; Figure 3 This is a two-dimensional morphology diagram of the chips according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the first case of the instantaneous undeformed thickness of the chip according to an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the second case of the instantaneous undeformed thickness of the chip according to an embodiment of the present invention; Figure 6 This is a flowchart illustrating the method for calculating the instantaneous, undeformed chip thickness during rock sawing in an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1: like Figure 6 As shown, the method for calculating the instantaneous undeformed chip thickness in rock sawing includes: S1: Obtain geometric parameter information of the diamond circular saw blade, including the total number of abrasive grains on the saw tooth surface, the distribution of abrasive grain positions, the height of abrasive grain exposure, and the spacing between adjacent abrasive grains, and construct a saw tooth surface model.

[0020] Specifically, rock sawing involves the contact between the abrasive grains on the saw blade surface and the workpiece surface, resulting in material removal. Therefore, understanding the surface morphology and abrasive grain distribution of the saw blade is crucial. This necessitates constructing a saw blade surface model, considering parameters such as the total number of abrasive grains on the saw blade surface, the abrasive grain position distribution (random distribution), the abrasive grain exposure height, the spacing between adjacent abrasive grains, and the saw blade diameter. i The particle size of the abrasive grains is d g ( i The density of abrasive grains on the saw teeth can be obtained by measurement, and then the total number of abrasive grains on the saw tooth surface can be calculated. The exposed height of abrasive grains on the saw tooth surface can be statistically analyzed to obtain the pattern of exposed height, and the spacing between adjacent abrasive grains can be calculated.

[0021] In this embodiment, the shape of the abrasive grains is simplified to spheres, and the size of the abrasive grains follows a Gaussian distribution. d g The diameter of the abrasive grain. d gm The average diameter of the abrasive grains. d gmax The maximum diameter of the abrasive grain. d gmin Let be the minimum diameter of the abrasive grain, and its probability density distribution function be: ; in, s d The standard deviation of the abrasive particle size distribution: ; Abrasive grain diameter information can be simulated and generated in MATLAB. i The particle size of the abrasive grains is d g ( i ).

[0022] The density of abrasive grains on the saw teeth can be obtained by measurement, and then the total number of abrasive grains on the saw teeth surface can be calculated. The exposed height of abrasive grains on the saw teeth surface can be statistically analyzed to obtain the pattern of the exposed height of abrasive grains.

[0023] A further embodiment of the method for obtaining the abrasive grain position distribution includes: In MATLAB, generate random numbers between (0,1), and combine these with the sawtooth length and width to obtain the center coordinates of the projection of the preset abrasive grain (i.e., the i-th abrasive grain) onto the rectangular plane; specifically, as shown... Figure 1 As shown, the length of the saw teeth is a The width of the saw teeth is b Generate random numbers between (0,1) in MATLAB. r x , r y If the coordinates of the center of the projection of the i-th abrasive grain onto the rectangular plane are (), then the coordinates of the center of the projection of the i-th abrasive grain onto the rectangular plane are (). X ( i ), Y ( i )): ; .

[0024] Based on the preset boundary discrimination conditions and the center coordinates, it is determined whether the preset abrasive grains have overflowed the boundary; if they have overflowed, the center coordinates of the preset abrasive grains are regenerated; if they have not overflowed, the preset overlap discrimination conditions are used to determine whether the preset abrasive grains overlap with adjacent abrasive grains.

[0025] If the preset abrasive grain overlaps with an adjacent abrasive grain, the center coordinates of the preset abrasive grain are regenerated. If there is no overlap, the abrasive grain size and abrasive grain position distribution are obtained.

[0026] Specifically, to determine whether abrasive grains have overflowed the boundary, the preset boundary discrimination condition is: ; ; If the conditions are not met, the center coordinates of the abrasive grains are regenerated. If the conditions are met, the system begins to determine whether the i-th abrasive grain overlaps with the j-th abrasive grain. The default overlap determination condition is: ; If the conditions are not met, the center coordinates of the abrasive grains are regenerated; if the conditions are met, the determination of the abrasive grain size and its position distribution is completed.

[0027] Methods for calculating the spacing between adjacent abrasive grains include: To determine the spacing between adjacent abrasive grains, the saw teeth are first divided along the width direction. m A layer can be represented as: ; Abrasive grains are randomly distributed in m If the center coordinates of abrasive grains are located in the same layer, they are considered to be abrasive grains of the same layer. The abrasive grains of the same layer are then sorted according to the magnitude of their horizontal coordinates. k ,i ), which is represented as k The first layer i Abrasive grains, thus obtaining adjacent abrasive grains ( i and i The interval between -1) l k ( i -1, i ).

[0028] .

[0029] in, X k ( i ) indicates the first k The first layer i The abscissa of each abrasive grain. The above describes the construction of the sawtooth surface features. For ease of description, only one layer of abrasive grains will be analyzed and studied below.

[0030] S2: Obtain saw blade motion parameters when a diamond circular saw is cutting rock, including saw blade feed rate, linear velocity, and depth of cut, to obtain the abrasive grain motion trajectory. For example... Figure 2 As shown.

[0031] Specifically, relative to the origin at the abrasive grain exit point The coordinate system (xy coordinate system) is fixed on the workpiece, and the rotation angle of the i-th abrasive grain on the saw blade is... Time position Represented as: ; In the formula, Represents feed rate, Represents the linear velocity of the saw blade. This represents the angle at which the i-th abrasive grain cuts through the rock.

[0032] Figure 2 N in e Represents the abrasive grain removal point. This represents the abrasive grain entry point.

[0033] r a ( i Let be the distance from the tip of the i-th abrasive grain to the center of the saw blade, which can be expressed by the following formula: ; in, r s Where is the radius of the saw blade. h p ( i ) represents the exposed height of the i-th abrasive grain.

[0034] S3: Based on the motion trajectory of adjacent abrasive grains and the sawtooth surface model, establish the morphology of undeformed chips and obtain the maximum thickness of undeformed chips. Figure 3 The image shown is a topographic map of the undeformed chip, in a closed region. ABCD This is the two-dimensional morphology of the undeformed chip. It can be seen that the undeformed chip morphology is formed by the i-th abrasive grain and the (...)-th... i -1) The movement trajectory of each abrasive grain.

[0035] A further embodiment of the method for obtaining the maximum undeformed chip thickness includes: Based on the cutting depth considering the exposed height of the i-th abrasive grain and the distance from the tip of the i-th abrasive grain to the center of the saw blade, the rotation angle when the i-th abrasive grain cuts through the rock is calculated. i max ( i ): ; in, a p ( i The depth of cut considering the exposed height of the i-th abrasive grain is expressed by the following formula: ; in, a np The nominal cutting depth of the saw blade.

[0036] Establish the trajectory of the saw blade's center of motion O 1 O 2. The undeformed chip morphology ABCD is obtained based on the motion trajectory of two adjacent abrasive grains; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade O Distance of 2 O 2C, the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O 1 distance Saw blade center movement trajectory O 1 O 2. The angle at which the i-th abrasive grain cuts through the rock is obtained using the law of cosines when the saw blade center moves to... At that time, the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade. O Distance of 2 O 2C and the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A To obtain the maximum undeformed chip thickness h max (i At this point, the angle through which the abrasive grain i rotates is defined as the maximum undeformed chip thickness angle. i hm ( i ).

[0037] Specifically, Figure 3 In the middle, closed area AC Dot spacing (also available) K 1 K The length of (2) represents the maximum undeformed chip thickness. h max ( i The specific calculation formula is as follows: ; ; O 2 A In a triangle, the law of cosines can be used for calculation, as shown in the following formula: ; in: ; ; l ( i -1, i ) is adjacent abrasive grains ( i and i The interval between -1). Therefore, the maximum undeformed chip thickness can be expressed by the following formula: ; In the formula, This represents the distance from the tip of the i-th abrasive grain to the center of the saw blade. This represents the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. It is the cutting depth considering the exposed height of the (i-1)th abrasive grain.

[0038] Specifically, Figure 3 The depth to which medium abrasive grains embed into the stone is equal to the maximum undeformed chip thickness. h max ( i The angle through which the abrasive grains rotate at this point is defined as the maximum undeformed chip thickness angle. i hm . Figure 3 In the middle, E represents the intersection of the workpiece surface and the perpendicular line passing through the center of the saw blade.

[0039] i hm ( i The calculation formula for ) is as follows: ; This represents the angle at which the i-th abrasive grain cuts through the rock. This represents the angle at which the (i-1)th abrasive grain cuts through the rock.

[0040] Due to the angle at which abrasive grains embed deepest into the stone O 1 AO 2( ψ The value is very small and its range of variation is very small. To simplify the calculation of the instantaneous undeformed chip thickness, it is taken as a constant value, while the angle at which the abrasive grain is embedded to its deepest point in the stone is considered. O 1 AO 2( ψ Using this constant value, we can obtain: ; This represents the distance from the tip of the i-th abrasive grain to the center of the saw blade. Represents feed rate, Represents the linear velocity of the saw blade. l ( i -1, i () represents adjacent abrasive grains i and( i The interval between -1).

[0041] S4: Based on the abrasive rotation angle and the maximum undeformed chip thickness, the instantaneous undeformed chip thickness when the diamond circular saw cuts rock is obtained, realizing grinding force prediction and grinding parameter optimization.

[0042] A further implementation method is, in the first case, such as Figure 4 As shown, when the abrasive grain angle i ( i () greater than the maximum undeformed chip thickness angle i hm ( i When a diamond circular saw cuts rock, the formulas for obtaining the instantaneous, undeformed chip thickness include: Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade distance And when the rotation angle of the i-th abrasive grain is At that time, the center of the saw blade Distance between the intersection point of the (i-1)th abrasive grain trajectory AD curve and the intersection point of the (i-1)th abrasive grain trajectory AD curve Calculate the instantaneous chip thickness : ; In triangle O 1 K 2 O In section 2, according to the Law of Sines, we can obtain: ; in, Represents the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O A distance of 1.

[0043] Obtain the instantaneous undeformed chip thickness during diamond circular saw cutting of rock. : ; The angle representing the deepest point the abrasive grains embed in the rock. , This represents the angle at which the i-th abrasive grain cuts through the rock.

[0044] A further implementation method is the second case, such as Figure 5 As shown, when the preset abrasive grain rotation angle smaller than the maximum undeformed chip thickness angle gh m( i When a diamond circular saw cuts rock, the formulas for obtaining the instantaneous, undeformed chip thickness include: Instantaneous chip thickness K 1 K 2 is: ; O is the center of the saw blade at this moment, within the triangle. OK 2 E middle: ; ; ; Therefore, one can seek appropriateness. i ( i )< gh m( i At that time, the instantaneous undeformed chip thickness during the diamond circular saw cutting of rock is: ; In the formula, rs Let be the radius of the saw blade. anp The nominal cutting depth of the saw blade.

[0045] The final expression for the instantaneous, undeformed chip thickness during diamond circular saw cutting of rock is as follows: .

[0046] Example 2: This invention also provides a system for calculating the instantaneous undeformed chip thickness in rock sawing, for implementing the method described in Embodiment 1, including: The saw tooth surface model construction module is used to obtain the geometric parameter information of the diamond circular saw blade, including the total number of abrasive grains on the saw tooth surface, the distribution of abrasive grain positions, the exposure height of abrasive grains, and the spacing between adjacent abrasive grains, and to construct the saw tooth surface model.

[0047] The abrasive motion trajectory acquisition module is used to acquire the saw blade motion parameter information when the diamond circular saw cuts rock, including the saw blade feed speed, linear speed and cutting depth, and obtain the abrasive motion trajectory.

[0048] The maximum undeformed chip thickness calculation module is used to establish the undeformed chip morphology based on the motion trajectory of adjacent abrasive grains and the sawtooth surface model, and obtain the maximum undeformed chip thickness.

[0049] The instantaneous undeformed chip thickness calculation module is used to obtain the instantaneous undeformed chip thickness during the diamond circular saw cutting of rocks based on the abrasive grain rotation angle and the maximum undeformed chip thickness, thereby realizing grinding force prediction and grinding parameter optimization.

[0050] A further implementation method includes a sawtooth surface model construction module comprising an abrasive grain position distribution acquisition unit, the abrasive grain position distribution acquisition unit comprising: The center coordinate calculation subunit is used to generate random numbers between (0,1) in MATLAB, and combine them with the sawtooth length and width to obtain the center coordinates of the preset abrasive grains projected onto the rectangular plane.

[0051] The boundary discrimination subunit is used to determine whether the preset abrasive grains have overflowed the boundary based on the preset boundary discrimination conditions and the center coordinates. If they overflow, the center coordinates of the preset abrasive grains are regenerated. If they do not overflow, the preset overlap discrimination conditions are used to determine whether the preset abrasive grains overlap with adjacent abrasive grains.

[0052] The overlap discrimination subunit is used to regenerate the center coordinates of the preset abrasive grain if the preset abrasive grain overlaps with the adjacent abrasive grain, and to obtain the abrasive grain diameter and abrasive grain position distribution if no overlap occurs.

[0053] A further implementation method includes a maximum undeformed chip thickness calculation module comprising: The angle calculation unit is used to calculate the angle when the i-th abrasive grain cuts through the rock, based on the cutting depth considering the exposed height of the i-th abrasive grain and the distance from the tip of the i-th abrasive grain to the center of the saw blade.

[0054] The motion trajectory acquisition unit is used to establish the motion trajectory of the saw blade's center. O 1 O 2. The undeformed chip morphology ABCD is obtained based on the motion trajectory of two adjacent abrasive grains.

[0055] The first point spacing calculation unit is used to calculate the distance from the tip of the i-th abrasive grain to the center of the saw blade. ODistance of 2 O 2C, the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O 1 distance Saw blade center movement trajectory O 1 O 2. The angle at which the i-th abrasive grain cuts through the rock is obtained using the law of cosines when the saw blade center moves to... At that time, the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A .

[0056] The second point spacing calculation unit is used to calculate the distance from the tip of the i-th abrasive grain to the center of the saw blade. O Distance of 2 O 2C and the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A To obtain the maximum undeformed chip thickness h max( i At this point, the angle through which the abrasive grain i rotates is defined as the maximum undeformed chip thickness angle. gh m( i ).

[0057] i hm ( i The calculation formula for ) is as follows: ; and This represents the angle at which the i-th abrasive grain and the (i-1)-th abrasive grain cut through the rock.

[0058] Among them, the angle at which the abrasive grains are embedded to the deepest point in the stone O 1 AO 2( ψ As a constant, the following is calculated: .

[0059] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the instantaneous, undeformed chip thickness in rock sawing, characterized in that, include: Obtain geometric parameter information of diamond circular saw blade, including the total number of abrasive grains on the saw tooth surface, abrasive grain position distribution, abrasive grain exposure height and spacing between adjacent abrasive grains, and construct a saw tooth surface model; Obtain the saw blade motion parameters information when a diamond circular saw cuts rock, including saw blade feed speed, linear velocity and depth of cut, and obtain the abrasive particle motion trajectory; Based on the motion trajectory of adjacent abrasive grains and the sawtooth surface model, the morphology of the undeformed chip is established, and the maximum thickness of the undeformed chip is obtained. Based on the abrasive rotation angle and the maximum undeformed chip thickness, the instantaneous undeformed chip thickness during the diamond circular saw cutting of rock is obtained, enabling grinding force prediction and grinding parameter optimization.

2. The method according to claim 1, characterized in that, Methods for obtaining abrasive grain position distribution include: In MATLAB, generate random numbers between (0,1), and combine them with the sawtooth length and width to obtain the center coordinates of the preset abrasive grains projected onto a rectangular plane. If the preset abrasive grain horizontal coordinate is not greater than the abrasive grain radius and less than the difference between the sawtooth length and the abrasive grain radius, and the preset abrasive grain vertical coordinate is greater than the abrasive grain radius and less than the difference between the sawtooth width and the abrasive grain radius, it is judged as overflow, and the center coordinates of the preset abrasive grain are regenerated; if the preset overlap discrimination condition is met, it is not overflow, and the preset overlap discrimination condition is used to determine whether the preset abrasive grain overlaps with the adjacent abrasive grain. If the center distance between the preset abrasive grain and the adjacent abrasive grain is less than the sum of the radius of the preset abrasive grain and the radius of the adjacent abrasive grain, it is determined that there is an overlap between the preset abrasive grain and the adjacent abrasive grain, and the center coordinates of the preset abrasive grain are regenerated; if there is no overlap, the abrasive grain diameter and abrasive grain position distribution are obtained.

3. The method according to claim 1, characterized in that, Methods for obtaining the maximum undeformed chip thickness include: Based on the cutting depth considering the exposed height of the i-th abrasive grain and the distance from the tip of the i-th abrasive grain to the center of the saw blade, calculate the rotation angle when the i-th abrasive grain cuts through the rock; Establish the trajectory of the saw blade's center of motion O 1 O 2. The undeformed chip morphology ABCD is obtained based on the motion trajectory of two adjacent abrasive grains; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade O Distance of 2 O 2C, the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O Distance of 1 Saw blade center movement trajectory O 1 O 2. The angle at which the i-th abrasive grain cuts through the rock is obtained using the law of cosines when the saw blade center moves to... At that time, the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A ; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade O Distance of 2 O 2C and the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A To obtain the maximum undeformed chip thickness h max ( i At this point, the angle through which the abrasive grain i rotates is defined as the maximum undeformed chip thickness angle. θ hm ( i ); θ hm ( i The calculation formula for ) is as follows: ， This represents the angle at which the i-th abrasive grain cuts through the rock. This represents the angle at which the (i-1)th abrasive grain cuts through the rock; Among them, the angle at which the abrasive grains are embedded to the deepest point in the stone O 1 AO 2( ψ As a constant, the following is calculated: ， This represents the distance from the tip of the i-th abrasive grain to the center of the saw blade. Represents feed rate, Represents the linear velocity of the saw blade. λ ( i -1, i () represents adjacent abrasive grains i and( i The interval between -1).

4. The method according to claim 3, characterized in that, When the abrasive grains rotate θ ( i () greater than the maximum undeformed chip thickness angle θ hm ( i When a diamond circular saw cuts rock, the formulas for obtaining the instantaneous, undeformed chip thickness include: Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade distance And when the rotation angle of the i-th abrasive grain is At that time, the center of the saw blade Distance between the intersection point of the (i-1)th abrasive grain trajectory AD curve and the intersection point of the (i-1)th abrasive grain trajectory AD curve Calculate the instantaneous chip thickness : ， In triangle O 1 K 2 O In section 2, according to the Law of Sines, we have: ， in, Represents the distance from the tip of the (i-1)th abrasive grain to the center of the saw blade. O A distance of 1; Based on the distance from the tip of the i-th abrasive grain to the center of the saw blade and the rotation angle of the i-th abrasive grain Obtain the instantaneous undeformed chip thickness during diamond circular saw cutting of rock. : 。 5. The method according to claim 4, characterized in that, When the preset abrasive rotation angle smaller than the maximum undeformed chip thickness angle θh m( i When ), the formula for obtaining the instantaneous undeformed chip thickness during the diamond circular saw cutting of rock is... include: Instantaneous chip thickness K 1 K 2 is: ， O is the center of the saw blade at this moment, within the triangle. OK 2 E middle: ， ， ， Obtain the instantaneous undeformed chip thickness during diamond circular saw cutting of rock. : ， In the formula, rs Let be the radius of the saw blade. anp The nominal cutting depth of the saw blade; The final expression for the instantaneous, undeformed chip thickness during diamond circular saw cutting of rock is as follows: 。 6. A system for calculating the instantaneous, undeformed chip thickness in rock sawing, used to implement the method described in any one of claims 1-5, characterized in that, include: The saw tooth surface model construction module is used to obtain geometric parameter information of diamond circular saw blades, including the total number of abrasive grains on the saw tooth surface, the abrasive grain position distribution, the abrasive grain exposure height and the spacing between adjacent abrasive grains, and to construct the saw tooth surface model. The abrasive motion trajectory acquisition module is used to acquire the saw blade motion parameter information when the diamond circular saw cuts rock, including the saw blade feed speed, linear speed and cutting depth, and to obtain the abrasive motion trajectory. The maximum undeformed chip thickness calculation module is used to establish the undeformed chip morphology and obtain the maximum undeformed chip thickness based on the motion trajectory of adjacent abrasive grains and the sawtooth surface model. The instantaneous undeformed chip thickness calculation module is used to obtain the instantaneous undeformed chip thickness during the diamond circular saw cutting of rocks based on the abrasive grain rotation angle and the maximum undeformed chip thickness, thereby realizing grinding force prediction and grinding parameter optimization.

7. The system according to claim 6, characterized in that, The sawtooth surface model construction module includes an abrasive grain position distribution acquisition unit, which includes: The center coordinate calculation subunit is used to generate random numbers between (0,1) in MATLAB, and combine them with the sawtooth length and width to obtain the center coordinates of the preset abrasive grains projected onto the rectangular plane. The boundary discrimination subunit is used to determine whether the preset abrasive grain overflows the boundary based on the preset boundary discrimination conditions and the center coordinates; if it overflows, the center coordinates of the preset abrasive grain are regenerated; if it does not overflow, the preset overlap discrimination conditions are used to determine whether the preset abrasive grain overlaps with the adjacent abrasive grain. The overlap discrimination subunit is used to regenerate the center coordinates of the preset abrasive grain if the preset abrasive grain overlaps with the adjacent abrasive grain, and to obtain the abrasive grain diameter and abrasive grain position distribution if no overlap occurs.

8. The system according to claim 7, characterized in that, The maximum undeformed chip thickness calculation module includes: The angle calculation unit is used to calculate the angle when the i-th abrasive grain cuts through the rock, based on the cutting depth considering the exposed height of the i-th abrasive grain and the distance from the tip of the i-th abrasive grain to the center of the saw blade. The motion trajectory acquisition unit is used to establish the motion trajectory of the saw blade's center. O 1 O 2. The undeformed chip morphology ABCD is obtained based on the motion trajectory of two adjacent abrasive grains; The first point spacing calculation unit is used to calculate the distance from the tip of the i-th abrasive grain to the center of the saw blade. O The distance O2C from the (i-1)th abrasive grain tip to the center of the saw blade. O Distance of 1 Saw blade center movement trajectory O 1 O 2. The angle at which the i-th abrasive grain cuts through the rock is obtained using the law of cosines when the saw blade center moves to... At that time, the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A ; The second point spacing calculation unit is used to calculate the distance from the tip of the i-th abrasive grain to the center of the saw blade. O Distance of 2 O 2C and the center of the saw blade The distance to the point where the tip of the (i-1)th abrasive grain just penetrates the rock O 2 A To obtain the maximum undeformed chip thickness h max ( i At this point, the angle through which the abrasive grain i rotates is defined as the maximum undeformed chip thickness angle. θ hm ( i ); θ hm ( i The calculation formula for ) is as follows: ， This represents the angle at which the i-th abrasive grain cuts through the rock. This represents the angle at which the (i-1)th abrasive grain cuts through the rock; Among them, the angle at which the abrasive grains are embedded to the deepest point in the stone O 1 AO 2( ψ As a constant, the following is calculated: ， This represents the distance from the tip of the i-th abrasive grain to the center of the saw blade. Represents feed rate, Represents the linear velocity of the saw blade. λ ( i -1, i () represents adjacent abrasive grains i and( i The interval between -1).

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