A quantitative method for cutting heat distribution model considering convection cooling and contact thermal resistance

Abstract

The present invention specifically discloses a method for quantifying a cutting heat distribution model that takes into account convection cooling and contact thermal resistance, and relates to the technical field of metal cutting processing. The method comprises: S1, constructing a coordinate system for the cutting heat source and dividing it into a first deformation zone heat source, a second deformation zone heat source and a convection heat transfer heat sink, and spatially discretizing the second deformation zone heat source; S2, calculating the heat flux of the first deformation zone and the second deformation zone based on a mirror heat source model; S3, constructing a steady-state chip temperature model, calculating the temperature rise generated in the first deformation zone and the second deformation zone in the chip; S4, constructing a steady-state tool temperature model, calculating the total tool temperature rise; S5, establishing a temperature continuity equation based on the tool-chip contact thermal resistance, and solving the potential-variable heat distribution coefficient through fixed point iteration and trust region reflection algorithm. This method couples convection heat transfer with contact state to achieve accurate calculation of the spatial distribution of the heat distribution coefficient, improve cutting thermal management accuracy, and is suitable for metal cutting process optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of metal cutting, and in particular to a cutting heat distribution model quantification method taking into account convection cooling and contact thermal resistance. Background Art

[0002] In the field of metal cutting, the generation and distribution mechanism of cutting heat has a decisive impact on tool life, machining accuracy and energy consumption control. Existing cutting heat calculation models generally have the following technical bottlenecks:

[0003] 1. Rough heat source characterization: The heat source morphology in the first deformation zone (shear zone) and the second deformation zone (tool-chip contact zone) is overly simplified, and the dynamic characteristic differences between the inclined moving heat source and the horizontal moving heat source are ignored, resulting in the heat flux calculation deviating from the actual working conditions.

[0004] 2. Lack of cooling effect: The mathematical model of convective heat transfer in the rake face cooling area has not been established, and the influence of parameters such as cutting fluid injection position and flow rate on the tool temperature field cannot be quantified, which restricts the optimization of the cooling process.

[0005] 3. Neglecting contact thermal resistance: The contact thermal resistance caused by the micro-roughness of the tool-chip contact surface is not considered, resulting in the neglect of the interface temperature jump phenomenon during heat conduction and significant errors in the calculation of the heat distribution coefficient.

[0006] 4. Solidification of heat distribution coefficient: Assuming that the heat distribution coefficient is a global constant value, it cannot reflect the impact of parameter variations such as pressure and sliding speed at different positions in the tool-chip contact area on the heat conduction path, and lacks a detailed description of the spatial distribution.

[0007] The above defects make it difficult for traditional models to accurately predict the thermal behavior during the cutting process. Especially in scenarios such as high-speed cutting and cutting of difficult-to-cut materials, the calculated results deviate greatly from the measured data. There is an urgent need to improve the calculation accuracy through multi-physics field coupling modeling and numerical discretization methods. Summary of the Invention

[0008] The purpose of this invention is to propose a quantitative method for cutting heat distribution model considering convection cooling and contact thermal resistance. By coupling convection heat transfer cooling, tool-chip contact state and heat source discretization, the spatial distribution of the heat distribution coefficient can be accurately solved, providing a theoretical basis for cutting parameter optimization and tool structure design.

[0009] To achieve the above objectives, the present invention proposes a cutting heat distribution model quantification method considering convection cooling and contact thermal resistance, the steps are as follows:

[0010] Step S1, constructing a coordinate system for the cutting heat source and dividing it into a first deformation zone heat source, a second deformation zone heat source, and a convection heat sink, and spatially discretizing the second deformation zone heat source;

[0011] Step S2: calculating the heat fluxes of the first deformation zone and the second deformation zone based on the mirror image heat source model of the first deformation zone and the second deformation zone;

[0012] Step S3: constructing a steady-state chip temperature model to calculate the temperature rise generated in the chips in the first deformation zone and the second deformation zone;

[0013] Step S4: construct a steady-state tool temperature model, incorporate the convective heat transfer effect of the rake face cooling sink, and calculate the total tool temperature rise;

[0014] Step S5: establishing a temperature continuity equation based on the tool-chip contact thermal resistance, and solving the potential-variable heat distribution coefficient through fixed point iteration and trust region reflection algorithm.

[0015] Preferably, in step S1, a coordinate system is constructed for the cutting heat source, specifically by setting the origin of the coordinate system at the intersection of the symmetry axis of the tool-chip contact area and the cutting edge, and extending along the cutting edge direction to be Axis, extending along the symmetry axis of the tool-chip contact area as axis, z The axis is defined as Axis and The directions in which the axes are orthogonal.

[0016] Preferably, in step S1, the second deformation zone is spatially discretized, and the specific operations are:

[0017] Assume that the size of the second deformation zone is , and along Axis direction is divided into units, each unit is , and along Axis direction is divided into units, each unit has a width of ,in and The calculation formula is as follows:

[0018] ;

[0019] ;

[0020] in, is the length of the second deformation zone, is the width of the second deformation zone, The second deformation zone The number of discrete axes, The second deformation zone The number of discrete axes;

[0021] from Axis direction and The units in the axial direction are arranged from 1 to or The sequence number is formed cells, and the center of each cell is , whose coordinates are , and The calculation formula is as follows:

[0022] ;

[0023] ;

[0024] in, , , are the column number and row number of the discrete unit on the second deformation zone at the discrete unit point, is an integer.

[0025] Preferably, in step S2, the heat flux calculation formula of the first deformation zone is as follows:

[0026] ;

[0027] in, is the heat flux in the first deformation zone, F s is the shear force, is the shear rate, is the shear surface length;

[0028] Shear surface length The calculation formula is as follows:

[0029] ;

[0030] in, is the uncut thickness; is the shear angle, and the calculation formula is as follows:

[0031] ;

[0032] in, is the chip thickness, is the tip angle;

[0033] shear force F s The calculation formula is as follows:

[0034] ;

[0035] in, is the cutting force, is the back force;

[0036] Shear rate The calculation formula is as follows:

[0037] ;

[0038] in, is the cutting speed, α It is the front angle of the knife.

[0039] Preferably, in step S2, the heat flux in the second deformation zone is calculated using the modified Merchant's chip model, and the formula is as follows:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] in, is the heat flux in the second deformation zone, is the friction force, is the chip moving speed, The length of the second deformation zone Spend, is the blunt radius of the cutting edge.

[0047] Preferably, in step S3, assuming that the thermal conductivity and thermal diffusivity of the tool and the chip are constant, and considering the temperature increment caused by the heat sources in the first and second deformation zones, the chip midpoint is obtained based on the superposition obtained by the quasi-steady-state solution. Temperature value at is the sum of the temperature increments generated in the first and second deformation zones, and the formula is as follows:

[0048] ;

[0049] in, is the temperature rise generated in the first deformation zone at the target position, is the temperature rise generated by the second deformation zone at the target position;

[0050] Temperature rise generated in the first deformation zone at the target position The calculation formula is as follows:

[0051] ;

[0052] in, is the temperature increment caused by the inclined heat source under unit heat flux, is the thermal conductivity of the workpiece, is the thermal diffusivity of the workpiece;

[0053] Temperature increment caused by inclined heat source under unit heat flux The calculation formula is as follows:

[0054] ;

[0055] in, is the width of the inclined heat source, is the thermal conductivity, α 0 is the thermal diffusivity, V 0 is the moving speed of the inclined heat source, is the tilt angle of the tilted heat source, K 0(·) is the zero-order second-type modified Bessel function, is the heat source space length scalar, is the infinitesimal length.

[0056] Temperature rise in the second deformation zone , the formula is as follows:

[0057] ;

[0058] in, B (·) is the heat distribution coefficient on the chip side, is the sum of the temperature increments generated by all discrete elements in the second deformation zone on the chip side, and its formula is as follows:

[0059] ;

[0060] in, is the chip thickness, is the source of temperature rise, when The source of temperature rise is the original heat source. p = 1 when the temperature rise comes from the mirror heat source. is the thermal conductivity of the workpiece;

[0061] The moving rectangular heat source has a unit heat flux in the semi-infinite medium with coordinates The temperature increment value generated at the position is calculated as follows:

[0062] ;

[0063] ;

[0064] in, is half the width of the heat source, is half the length of the heat source, To calculate the Euclidean distance between the target position and the point heat source.

[0065] Preferably, in step S4, the tool temperature is only affected by the second deformation zone, and the second deformation zone is a static heat source relative to the tool. At the same time, each discrete unit position in the second deformation zone has its own independent heat distribution coefficient on the tool side. The discrete heat source unit is: , the heat flux from this heat source unit into the tool is Taking into account the heating of the second deformation zone on the rake face and the cooling of other areas, the total temperature rise of the tool is calculated as follows:

[0066] ;

[0067] in, is the total temperature rise of the tool, is the tool temperature increment caused by the second deformation zone, The tool temperature is reduced due to cooling. To sum the range, is the center coordinate of the rectangular cooling heat sink, 、 、 Cooling heat sinks for discrete rectangular shapes;

[0068] Tool temperature increase caused by the second deformation zone The calculation process is as follows:

[0069] ;

[0070] in, The center coordinates of the second deformation zone are The discrete unit of the tool coordinate is The temperature increase generated at The static rectangular discrete unit heat source and its mirror image heat source in the second deformation zone are expressed as The total temperature increment generated at the location is as follows:

[0071] ;

[0072] in, is the thermal conductivity of the tool, when hour, is a mirror image heat source / sink Axis coordinates, when p =0, Is the original heat source / sink Axis coordinates, The calculation formula is as follows:

[0073] ;

[0074] in, Indicates the original heat source / sink Axis coordinates, W is the tool width, d is the distance between the center line of the second deformation zone and one side of the tool;

[0075] is the temperature increment generated by the static rectangular heat source, and is calculated as follows:

[0076] ;

[0077] Tool temperature reduction due to cooling The formula is as follows:

[0078] ;

[0079] in, The coordinates of the center of the heat sink for heat transfer cooling on the rake face are: P o The discrete rectangular unit of the tool coordinate is The temperature reduction produced at

[0080] is the heat flux generated by convective heat transfer, and the formula is as follows:

[0081] ;

[0082] in, is the convective heat transfer coefficient, is the cooling fluid temperature;

[0083] Discrete rectangular heat sinks and their mirror images in the cooling area are denoted by unit heat flux. The resulting total temperature reduction is as follows:

[0084] ;

[0085] in, The rectangular center of the discrete rectangular cooling heat sink x Axis coordinates, is the length of the cooling rectangular heat source, is the width of the cooling rectangular heat source.

[0086] Preferably, in step S5, it is assumed that the contact thermal resistance between the tool and the chip is Rtc , assuming that the chip temperature is higher than the tool temperature, according to , the temperature relationship of the tool-chip contact area can be obtained as follows:

[0087] ;

[0088] in, is the total chip temperature rise, The second deformation zone Rank The coordinates of the discrete units are listed. is the total temperature rise of the tool, is the temperature difference between the chip side and the tool side of the second deformation zone;

[0089] According to the temperature relationship of the tool-chip contact area, a The linear system of equations is as follows:

[0090] ;

[0091] in, is the temperature rise on the chip in the first deformation zone, is the heat distribution coefficient vector to be solved, and represent the total number of heat distribution coefficients to be solved and the total number of discrete units, respectively. is a vector of all 1s, represents the Hadamard product;

[0092] The linear equations are organized into an expression for the heat distribution coefficient, as follows:

[0093] ;

[0094] in, Generating functions for diagonal matrices.

[0095] Preferably, the heat distribution coefficient of each discrete unit is calculated by fixed point iteration combined with a trust region reflection algorithm, and the steps are as follows:

[0096] Step S51, initializing the cooling sink position temperature;

[0097] Step S52: Calculate the heat flux based on the current temperature of the cooling sink position and solve for the heat distribution coefficient;

[0098] Step S53, updating the tool temperature field and cooling sink temperature;

[0099] Step S54: Repeat the iteration until the Euclidean distance between two adjacent cooling sink temperature vectors is less than a preset threshold.

[0100] Therefore, the present invention proposes a cutting heat distribution model quantification method considering convection cooling and contact thermal resistance, which has the following beneficial effects:

[0101] (1) Improved accuracy: Through heat source discretization and the mirror heat source method, adiabatic boundary conditions are accurately simulated, and the spatial variation of the heat distribution coefficient is taken into account. The calculation error is significantly reduced compared with the traditional model.

[0102] (2) Cooling coupling: For the first time, the convection heat transfer cooling area is incorporated into the heat conduction model to quantify the effect of cooling on tool temperature and provide a basis for cutting fluid optimization.

[0103] (3) Engineering adaptation: It supports the input of multiple physical field parameters (such as cutting speed, tool rake angle, and cooling medium parameters), and can achieve fast calculations through Python programming. It is suitable for various cutting processes such as turning and milling.

[0104] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 Schematic diagram of a flow chart of a method for quantifying a cutting heat distribution model taking into account convection cooling and contact thermal resistance according to the present invention;

[0106] Figure 2 Schematic diagram of the distribution of two major heat sources and the cooling sink on the rake face in the cutting process of the present invention;

[0107] Figure 3 This is a schematic diagram of the Merchant's model after modification of the present invention;

[0108] Figure 4 Schematic diagram of the heat source causing the chip temperature rise in the present invention;

[0109] Figure 5 Schematic diagram of the discrete chip side heat source and its mirror image heat source in the second deformation zone of the present invention;

[0110] Figure 6 Schematic diagram of the discrete heat source on the tool side of the second deformation zone, the discrete cooling sink on the rake face and its mirror image heat source and heat sink;

[0111] Figure 7 This is a flow chart for solving the heat distribution coefficient of the present invention. DETAILED DESCRIPTION

[0112] To make the technical solutions, advantages, and objectives of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are part of the embodiments of the present invention, not all of them. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0113] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0114] Example 1

[0115] like Figure 1 FIG. 1 is a flow chart of a method for quantifying a cutting heat distribution model taking into account convection cooling and contact thermal resistance according to the present invention. The steps are as follows:

[0116] S1. Construct a coordinate system for the cutting heat source and divide it into a heat source in the first deformation zone, a heat source in the second deformation zone, and a convection heat sink, and spatially discretize the heat source in the second deformation zone.

[0117] like Figure 2 The figure shows the relative position relationship between the tool and the chip during the cutting process. The figure also marks the positions of the two main heat sources in the cutting process. The specific method of constructing the coordinate system for the cutting heat source is: the coordinate origin is set at the intersection of the symmetry axis of the tool-chip contact area and the cutting edge, and the coordinate system is extended along the cutting edge to Axis, extending along the symmetry axis of the tool-chip contact area as axis, z The axis is defined as Axis and The directions in which the axes are orthogonal.

[0118] The first deformation zone on the chip coincides with the shear plane, and the second deformation zone on the rake face coincides with the tool-chip contact area, both of which are marked with different color shadows. The size of the second deformation zone is , and along Directions are divided into units, each unit is , and along Axis direction is divided into units, each unit has a width of ,in and The calculation formula is as follows:

[0119] (1);

[0120] (2);

[0121] in, is the length of the second deformation zone, is the width of the second deformation zone, The second deformation zone The number of discrete axes, The second deformation zone The number of discrete axes;

[0122] from Axis direction and The units in the axial direction are arranged from 1 to or The sequence number is formed cells, and the center of each cell is , whose coordinates are , and The calculation formula is as follows:

[0123] (3);

[0124] (4);

[0125] in, , , are the column number and row number of the discrete unit on the second deformation zone at the discrete unit point, is an integer.

[0126] Each unit cell in the second deformation zone has its own unique heat distribution coefficient , defines the proportion of the total heat energy generated by the second deformation that enters the chip, and the corresponding proportion that enters the tool is .

[0127] S2. Calculate the heat fluxes of the first deformation zone and the second deformation zone based on the mirror image heat source model of the first deformation zone and the second deformation zone.

[0128] S2.1. Calculation of heat flux in the first deformation zone. The formula is as follows:

[0129] (5);

[0130] in, is the heat flux in the first deformation zone, F s is the shear force, is the shear rate, is the shear surface length;

[0131] Shear surface length The calculation formula is as follows:

[0132] (6);

[0133] in, is the uncut thickness; is the shear angle, and the calculation formula is as follows:

[0134] (7);

[0135] in, is the chip thickness, is the tip angle;

[0136] shear force F s The calculation formula is as follows:

[0137] (8);

[0138] in, is the cutting force, is the back force;

[0139] Shear rate The calculation formula is as follows:

[0140] (9);

[0141] in, is the cutting speed, α It is the front angle of the knife.

[0142] S2.2. Calculation of heat flux in the second deformation zone.

[0143] like Figure 3 As shown in Figure 2, the cutting heat flux in the second deformation zone on the rake face is calculated using the modified Merchant's chip formation model, as follows:

[0144] (10);

[0145] (11);

[0146] (12);

[0147] (13);

[0148] (14);

[0149] (15);

[0150] in, is the heat flux in the second deformation zone, is the friction force, is the chip moving speed, The length of the second deformation zone Spend, is the blunt radius of the cutting edge.

[0151] F R is the radial force and tangential force The combined force, F R is the friction force between the tool and the chip and the tool's support for the chips These forces keep the chip in a state of equilibrium.

[0152] S3. Construct a steady-state chip temperature model and calculate the temperature rise generated in the chips in the first deformation zone and the second deformation zone.

[0153] S3.1. Temperature rise in the chips in the first deformation zone.

[0154] Assuming that the thermal conductivity and thermal diffusivity of the tool and chip are constant, and considering the temperature increment caused by the heat sources in the first and second deformation zones, the chip midpoint is obtained based on the superposition of the quasi-steady-state solution. Temperature value at is the sum of the temperature increments generated in the first and second deformation zones, and the formula is as follows:

[0155] (16);

[0156] In order to calculate the heat distribution coefficient of the separated heat source unit, the temperature values ​​of these units need to be calculated. The physical coordinates of the center of the second deformation zone are A discrete unit of , the chip side temperature value is recorded as , the formula is as follows:

[0157] (17);

[0158] in, is the temperature rise generated by the first deformation zone at the target position, and the formula is as follows:

[0159] (18);

[0160] in, is the temperature increment caused by the inclined heat source under unit heat flux, is the thermal conductivity of the workpiece, is the thermal diffusivity of the workpiece;

[0161] like Figure 4As shown in the figure, the green solid line represents the first deformation zone, which is in an inclined state. Moving right, the heat source in the first deformation zone moves to the left relative to the chip. With the adiabatic boundary Plane A as the symmetry axis, a mirror image heat source of the first deformation zone heat source represented by the green dotted line is constructed on the opposite side. The mirror image heat source is also a tilted moving heat source, and its intensity should be equal to that of the original heat source. Therefore, the heat fluxes corresponding to the mirror image heat source and the original heat source are both q sp .

[0162] Temperature increment caused by inclined heat source under unit heat flux The calculation formula is as follows:

[0163] (19);

[0164] in, is the width of the inclined heat source, is the thermal conductivity, α 0 is the thermal diffusivity, V 0 is the moving speed of the inclined heat source, is the tilt angle of the tilted heat source, K 0(·) is the zero-order second-type modified Bessel function, is the heat source space length scalar, is the infinitesimal length.

[0165] Substituting the width, moving speed, tilt angle, thermal conductivity, thermal diffusivity and other parameters of the original heat source and its mirror image heat source in the first deformation zone into the formula, the formula can be obtained. .

[0166] S3.2. Temperature rise in the chips in the second deformation zone.

[0167] like Figure 4 As shown, the second deformation zone is a horizontal heat source rather than an inclined heat source, that is, z The angle between the axes is 0°. Consider the temperature change caused by the second deformation zone as a horizontal moving heat source. The second deformation zone is regarded as a distribution with heat flux. q tc A rectangular heat source with dimensions of , the moving speed and the chip movement speed The magnitudes are equal and the directions are opposite. The coordinates of the chip caused by the second deformation zone are The temperature increment value at a certain point is calculated as follows:

[0168] (20);

[0169] in, B(·) is the heat distribution coefficient on the chip side;

[0170] In order to estimate the heat distribution coefficient of the second deformation zone, each discrete unit of the chip has its corresponding heat distribution coefficient , then the heat flux from this unit into the chip is Bq tc .

[0171] To satisfy Figure 4 The adiabatic boundary Plane A of the chip top surface is shown, and a mirror image heat source symmetrical to the heat source of the second deformation zone about the chip top adiabatic plane Plane A is assumed. Figure 3 The central heat source and the mirror heat source are represented by red solid lines and red dashed lines, respectively.

[0172] In addition to the outermost insulation surface Plane A, in order to meet the insulation boundaries of the other two side elevations of the chip, the two are respectively related to the second deformation zone. Figure 5 The mirror heat source is assumed to be symmetrical with the adiabatic plane Plane B and the adiabatic plane Plane C shown in FIG. The mirror heat source is also discretized as The heat distribution coefficient of each mirror image heat source is the same as that of the original heat source. The mirror heat source within the plane also needs to be constructed on the opposite side of the adiabatic plane Plane A to ensure the existence of the adiabatic plane Plane A. Therefore, for the chip, each discrete unit in the second deformation zone generates a total of 6 heat sources, including one original heat source and 5 mirror heat sources (not considering discreteness).

[0173] Considering the original heat source and the mirror image heat source at the same time, the unknown in the formula is given by the coordinates of the center point The discrete unit at a certain point on the chip Temperature increase caused by unit heat flux , the formula is as follows:

[0174] (twenty one);

[0175] in, is the chip thickness, is the sum of the temperature increments generated by all discrete elements in the second deformation zone on the chip side, is the source of temperature rise, when The source of temperature rise is the original heat source. p = 1 when the temperature rise comes from the mirror heat source. is the thermal conductivity of the workpiece;

[0176] The moving rectangular heat source of 2a×2b has a unit heat flux in the semi-infinite medium with coordinates of The temperature increment value generated at the position is as follows:

[0177] (twenty two);

[0178] (twenty three);

[0179] in, is half the width of the heat source, is half the length of the heat source, To calculate the Euclidean distance between the target position and the point heat source.

[0180] S4. Construct a steady-state tool temperature model, incorporate the convective heat transfer effect of the rake face cooling sink, and calculate the total tool temperature rise.

[0181] The tool temperature is only affected by the second deformation zone, and the second deformation zone is stationary relative to the tool, so it is a static heat source. Similar to the chip side, each discrete unit position in the second deformation zone also has its own independent heat distribution coefficient on the tool side. For the center coordinate The discrete heat source unit is: , so the heat flux from this heat source unit into the tool is .like Figure 6 As shown, the tool width is W The center line of the second deformation zone is 1 / 4 of the tool side. d , the distance to the other side is W - d .

[0182] Assume that the tool flank area and other sides of the tool that do not participate in cutting are adiabatic boundaries. In order to meet these adiabatic boundary conditions, The mirror image heat source is constructed in the plane. The discrete form of the second deformation zone for the tool is the same as that for the chip. The original heat source unit is along y The axis is symmetrical about the adiabatic boundary Plane D and the adiabatic boundary Plane E to construct a first-order mirror heat source, and all discrete heat sources are also mirrored on the opposite side of the adiabatic boundary Plane F. The adiabatic boundary Plane F is the boundary where the cutting edge is located. The area within this area is a constant heat flux except for the tool-chip contact area (the second deformation zone). Being cooled, the heat flux is negative because the cooling on the front cutting edge will dissipate the heat. Figure 6 As shown, the convection heat transfer cooling area is divided into three rectangular heat sources with sizes of , center point P A , P B ,P C Coordinates They are The three discrete cooling rectangles act as static rectangular heat sinks on the rake face. In order to meet the adiabatic boundary conditions of the tool, it is also necessary to construct a mirror image heat sink of the cooling heat sink; is the cooling zone length, W A 、 W B 、 W C is the width of the cooling rectangular unit, P A 、 P B 、 P C is the center point of the cooling rectangular unit.

[0183] Considering the heating of the second deformation zone on the rake face and the cooling of other areas, the coordinates on the tool are The temperature value at a point is the sum of the temperature increments generated by all discrete heat source units in the second deformation zone and the three rectangular cooling zones. The formula is as follows:

[0184] (twenty four);

[0185] in, is the total temperature rise of the tool, is the tool temperature increment caused by the second deformation zone, The tool temperature is reduced due to cooling. To sum the range, is the center coordinate of the rectangular cooling heat sink, 、 、 Cooling heat sinks for discrete rectangular shapes;

[0186] (25);

[0187] in, The center coordinates of the second deformation zone are The discrete unit of the tool coordinate is The temperature increase generated at The static rectangular discrete unit heat source and its mirror image heat source in the second deformation zone are expressed as The total temperature increment generated at the location is as follows:

[0188] (26);

[0189] in, is the thermal conductivity of the tool;

[0190] Tool temperature reduction due to cooling The formula is as follows:

[0191] (27);

[0192] in, The coordinates of the center of the heat sink for heat transfer cooling on the rake face are: P o The discrete rectangular unit of the tool coordinate is The temperature reduction produced at

[0193] is the heat flux generated by convective heat transfer, and the formula is as follows:

[0194] (28);

[0195] Among them, in formula (28) P o Refers to the coordinates of the center point of the rectangular cooling heat sink, is the convective heat transfer coefficient, is the cooling fluid temperature;

[0196] Discrete rectangular heat sinks and their mirror images in the cooling area are denoted by unit heat flux. The resulting total temperature reduction is as follows:

[0197] (29);

[0198] in, The rectangular center of the discrete rectangular cooling heat sink x Axis coordinates, is the length of the cooling rectangular heat source, is the width of the cooling rectangular heat source;

[0199] In formula (26) and formula (29), p= {-1,0,1}, indicating that the highest order of the recursive expansion of the mirror image heat source / sink is first order, that is, only two mirror image heat sources / sinks are considered at the two boundaries; when p ≠0, y p is a mirror image heat source / sink y Axis coordinates, when p =0, y p Is the original heat source / sink y Axis coordinates, the formula is as follows:

[0200] (30);

[0201] in, Indicates the original heat source / sink y Axis coordinates. In the formula , in the formula , o = A , B , C .

[0202] In formula (26) and formula (29), U st is the temperature increment generated by the static rectangular heat source, and the formula is as follows:

[0203] (31);

[0204] Formula (31) describes a static rectangular heat source with an area of ​​2a × 2b applied to a half infinite solid surface with a unit heat flux at The temperature increment caused by the position.

[0205] The physical coordinates of the center of the second deformation zone are A discrete unit of , the tool side temperature value is recorded as , can be calculated according to the formula:

[0206] (32);

[0207] S5. Based on the tool-chip contact thermal resistance, the temperature continuity equation is established, and the potential-variable heat distribution coefficient is solved by fixed point iteration and trust region reflection algorithm.

[0208] The total energy generated in the second deformation zone on the rake face is dissipated into the tool and chip respectively, so we only focus on the temperature of the chip side and tool side of the rake face, that is, and Taking into account the roughness of the tool rake face and the chip contact area, the present invention considers the influence of contact thermal resistance on the calculation of the heat distribution coefficient.

[0209] It is known that the total heat flux generated in the second deformation zone is q tc , assuming that the contact thermal resistance between the tool and the chip is R tc , assuming that the chip temperature is higher than the tool temperature, according to , the temperature relationship of the tool-chip contact area can be obtained as follows:

[0210] (33);

[0211] in, is the total chip temperature rise, The second deformation zone Rank The coordinates of the discrete units are listed. is the total temperature rise of the tool, is the temperature difference between the chip side and the tool side of the second deformation zone;

[0212] The coordinates of the chip on the tool-chip contact surface are The temperature value at the location Temperature value at the same coordinate as the tool They can be obtained by formulas and respectively.

[0213] Constructed according to the formula The linear system of equations is as follows:

[0214] (34);

[0215] in, is the temperature rise on the chip in the first deformation zone, is the heat distribution coefficient vector to be solved, and represent the total number of heat distribution coefficients to be solved and the total number of discrete units, respectively. is a vector of all 1s, represents the Hadamard product; in this invention, it is assumed that each discrete unit corresponds to a heat distribution coefficient, and each discrete unit satisfies formula (33), so .

[0216] Formula (34) is organized into the expression of heat distribution coefficient, which is as follows:

[0217] (35);

[0218] in, Generating functions for diagonal matrices;

[0219] like Figure 7 As shown, due to The solution range of each term in needs to be constrained to be in the range of [0, 1]. The trust region reflective algorithm can be used to solve this linear least squares problem with boundary constraints. Here, Python's scipy.optimize.lsq_linear() function is used to complete the solution. The final heat distribution coefficient matrix is ​​obtained. The specific steps are:

[0220] S51, initializing the cooling sink position temperature;

[0221] S52, calculating the heat flux according to the current temperature of the cooling sink position and solving the heat distribution coefficient;

[0222] S53, updating the tool temperature field and cooling sink temperature;

[0223] S54, repeating the iteration until the Euclidean distance between two adjacent cooling sink temperature vectors is less than a preset threshold.

[0224] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0225] Therefore, the present invention provides a quantification method for the cutting heat distribution model considering convection cooling and contact thermal resistance. By discretizing the cutting heat source, constructing an inclined / horizontally moving heat source model, coupling the convection heat transfer effect of the front cutting edge cooling sink, and introducing a contact thermal resistance model, the spatial distribution of the heat distribution coefficient in the tool-chip contact area is accurately calculated. The fixed point iteration and trust region reflection algorithm are used to solve the linear equation group with boundary constraints to ensure the convergence and accuracy of the calculation.

[0226] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A cutting heat distribution model quantification method considering convection cooling and contact thermal resistance, characterized in that: Here are the steps: Step S1, constructing a coordinate system for the cutting heat source and dividing it into a first deformation zone heat source, a second deformation zone heat source, and a convection heat sink, and spatially discretizing the second deformation zone heat source; Step S2: calculating the heat fluxes of the first deformation zone and the second deformation zone based on the mirror image heat source model of the first deformation zone and the second deformation zone; Step S3: constructing a steady-state chip temperature model to calculate the temperature rise generated in the chips in the first deformation zone and the second deformation zone; Step S4: construct a steady-state tool temperature model, incorporate the convective heat transfer effect of the rake face cooling sink, and calculate the total tool temperature rise; Step S5: establishing a temperature continuity equation based on the tool-chip contact thermal resistance, and solving the potential-variable heat distribution coefficient by fixed point iteration and trust region reflection algorithm; In step S1, the coordinate system of the cutting heat source is constructed by setting the origin of the coordinate system at the intersection of the symmetry axis of the tool-chip contact area and the cutting edge, and extending along the cutting edge to be Axis, extending along the symmetry axis of the tool-chip contact area as axis, The axis is defined as Axis and Axis directions are orthogonal; In step S4, the tool temperature is only affected by the second deformation zone, and the second deformation zone is a static heat source relative to the tool. At the same time, each discrete unit position in the second deformation zone has its own independent heat distribution coefficient on the tool side. For the center coordinate The discrete heat source unit is: , the heat flux from this heat source unit into the tool is Taking into account the heating of the second deformation zone on the rake face and the cooling of other areas, the total temperature rise of the tool is calculated as follows: ； in, is the total temperature rise of the tool, is the tool temperature increment caused by the second deformation zone, The tool temperature is reduced due to cooling. To sum the range, is the center coordinate of the rectangular cooling heat sink, 、 、 Cooling heat sinks for discrete rectangular shapes; Tool temperature increase caused by the second deformation zone The calculation process is as follows: ； in, is the heat flux in the second deformation zone, The center coordinates of the second deformation zone are The discrete unit of the tool coordinate is The temperature increase generated at The static rectangular discrete unit heat source and its mirror image heat source in the second deformation zone are expressed as The total temperature increment generated at the location is as follows: ； in, is the thermal conductivity of the tool, when hour, is a mirror image heat source / sink Axis coordinates, when hour, Is the original heat source / sink Axis coordinates, The calculation formula is as follows: ； in, Indicates the original heat source / sink Axis coordinates, is the tool width, is the distance between the center line of the second deformation zone and one side of the tool; is the temperature increment generated by the static rectangular heat source, and is calculated as follows: ； Tool temperature reduction due to cooling The formula is as follows: ； in, The coordinates of the center of the heat sink for heat transfer cooling on the rake face are: The discrete rectangular unit of the tool coordinate is The temperature reduction produced at is the heat flux generated by convective heat transfer, and the formula is as follows: ； in, is the convective heat transfer coefficient, is the cooling fluid temperature; Discrete rectangular heat sinks and their mirror images in the cooling area are denoted by unit heat flux. The resulting total temperature reduction is as follows: ； in, The rectangular center of the discrete rectangular cooling heat sink Axis coordinates, is the length of the cooling rectangular heat source, is the width of the cooling rectangular heat source.

2. A cutting heat distribution model quantification method considering convection cooling and contact thermal resistance according to claim 1, characterized in that: In step S1, the second deformation zone is spatially discretized. The specific operations are as follows: Assume that the size of the second deformation zone is , and along Axis direction is divided into units, each unit is , and along Axis direction is divided into units, each unit has a width of ,in and The calculation formula is as follows: ； ； in, is the length of the second deformation zone, is the width of the second deformation zone, The second deformation zone The number of discrete axes, The second deformation zone The number of discrete axes; from Axis direction and The units in the axial direction are arranged from 1 to or The sequence number is formed cells, and the center of each cell is , whose coordinates are , and The calculation formula is as follows: ； ； in, , , are the column number and row number of the discrete unit on the second deformation zone at the discrete unit point, is an integer.

3. The method for quantifying a cutting heat distribution model considering convection cooling and contact thermal resistance according to claim 2, characterized in that: In step S2, the heat flux calculation formula of the first deformation zone is as follows: ； in, is the heat flux in the first deformation zone, is the shear force, is the shear rate, is the shear surface length; Shear surface length The calculation formula is as follows: ； in, is the uncut thickness; is the shear angle, and the calculation formula is as follows: ； in, is the chip thickness, is the tip angle; shear force The calculation formula is as follows: ； in, is the cutting force, is the back force; Shear rate The calculation formula is as follows: ； in, is the cutting speed, It is the front angle of the knife.

4. The method for quantifying a cutting heat distribution model considering convection cooling and contact thermal resistance according to claim 3, characterized in that: In step S2, the heat flux in the second deformation zone is calculated using the modified Merchant's chip model, and the formula is as follows: ； ； ； ； ； ； in, is the heat flux in the second deformation zone, is the friction force, is the chip moving speed, The length of the second deformation zone Spend, is the blunt radius of the cutting edge.

5. The method for quantifying a cutting heat distribution model considering convection cooling and contact thermal resistance according to claim 4, characterized in that: In step S3, assuming that the thermal conductivity and thermal diffusivity of the tool and the chip are constant, and considering the temperature increment caused by the heat sources in the first and second deformation zones, the chip midpoint is obtained based on the superposition of the quasi-steady-state solution. Temperature value at is the sum of the temperature increments generated in the first and second deformation zones, and the formula is as follows: ； in, is the temperature rise generated in the first deformation zone at the target position, is the temperature rise generated by the second deformation zone at the target position; Temperature rise generated in the first deformation zone at the target position The calculation formula is as follows: ； in, is the temperature increment caused by the inclined heat source under unit heat flux, is the thermal conductivity of the workpiece, is the thermal diffusivity of the workpiece; Temperature increment caused by inclined heat source under unit heat flux The calculation formula is as follows: ； in, is the width of the inclined heat source, is the thermal conductivity, is the thermal diffusivity, is the moving speed of the inclined heat source, is the tilt angle of the tilted heat source, is the zero-order second-type modified Bessel function, is the heat source space length scalar, is the length element; Temperature rise in the second deformation zone , the formula is as follows: ； in, is the heat distribution coefficient on the chip side, is the sum of the temperature increments generated by all discrete elements in the second deformation zone on the chip side, and its formula is as follows: ； in, is the chip thickness, is the source of temperature rise, when The source of temperature rise is the original heat source. The source of the temperature rise is the mirror heat source, is the thermal conductivity of the workpiece; The moving rectangular heat source has a unit heat flux in the semi-infinite medium with coordinates The temperature increment value generated at the position is calculated as follows: ； ； in, is half the width of the heat source, is half the length of the heat source, To calculate the Euclidean distance between the target position and the point heat source.

6. The method for quantifying a cutting heat distribution model considering convection cooling and contact thermal resistance according to claim 5, characterized in that: In step S5, it is assumed that the contact thermal resistance between the tool and the chip is , assuming that the chip temperature is higher than the tool temperature, according to , the temperature relationship of the tool-chip contact area can be obtained as follows: ； in, is the total chip temperature rise, The second deformation zone Rank The coordinates of the discrete units are listed. is the total temperature rise of the tool, is the temperature difference between the chip side and the tool side of the second deformation zone; According to the temperature relationship of the tool-chip contact area, a The linear system of equations is as follows: ； in, is the temperature rise on the chip in the first deformation zone, is the heat distribution coefficient vector to be solved, and represent the total number of heat distribution coefficients to be solved and the total number of discrete units, respectively. is a vector of all 1s, represents the Hadamard product; The linear equations are organized into an expression for the heat distribution coefficient, as follows: ； in, Generating functions for diagonal matrices.

7. A cutting heat distribution model quantification method considering convection cooling and contact thermal resistance according to claim 6, characterized in that: The heat distribution coefficient of each discrete element is calculated by fixed point iteration combined with the trust region reflection algorithm. The steps are as follows: Step S51, initializing the cooling sink position temperature; Step S52: Calculate the heat flux based on the current temperature of the cooling sink position and solve for the heat distribution coefficient; Step S53, updating the tool temperature field and cooling sink temperature; Step S54: Repeat the iteration until the Euclidean distance between two adjacent cooling sink temperature vectors is less than a preset threshold.

Images