CN109858079B - Cup-shaped grinding wheel plane grinding temperature prediction method based on non-uniform heat source model - Google Patents
Cup-shaped grinding wheel plane grinding temperature prediction method based on non-uniform heat source model Download PDFInfo
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Abstract
The invention relates to a cup-shaped grinding wheel plane grinding temperature prediction method based on a non-uniform heat source model, which comprises the following steps: the method comprises the following steps: setting grinding parameters before grinding, and measuring the grinding force of the cup-shaped grinding wheel during plane grinding by using a force sensor; step two: analyzing the research status quo of the grinding force distribution during the plane grinding of the cup-shaped grinding wheel and the characteristics during the material removal, and establishing a non-uniform heat source model which is distributed in different functions in the circumferential direction and the radial direction according to the corresponding relation of force and heat; step three: and establishing an analytical model and/or a numerical model of the temperature field based on the non-uniform heat source model in the second step, and substituting the planar grinding parameters of the cup-shaped grinding wheel to be predicted into the analytical model and/or the numerical analysis model to obtain corresponding predicted temperature. The method is suitable for temperature prediction by utilizing the cup-shaped grinding wheel to perform surface treatment and other grinding, and the predicted result is compared with the image result acquired by the high-definition thermal infrared imager to find that the result is accurate.
Description
Technical Field
The invention relates to the field of grinding in machine manufacturing, in particular to a cup-shaped grinding wheel plane grinding temperature prediction method based on a non-uniform heat source model.
Background
Grinding is an effective method for improving surface quality and has wide application in the field of precision machining. Surface machining with cup-shaped grinding wheels is receiving increasing attention in this field because of its high efficiency and high grinding quality. There are many factors that affect the quality of the surface finish, and grinding temperature is one of them. High grinding temperatures can cause thermal damage to the workpiece surface, including burns and hot cracks. The studies currently made in this regard are:
[1] deng Chaohui, she Shuailong, yi Jun, et al, non-circular profile workpiece high speed grinding temperature prediction method based on variable heat source model CN 10 8151885A.
[2] Zheng Kan, meng Heng, liao Wenhe, etc. the method for predicting the grinding temperature of a brittle material by ultrasonic vibration assisted grinding CN 107133392A, all of which are methods for predicting the temperature of plane grinding of a special workpiece (brittle material, non-circular profile workpiece) by using a parallel grinding wheel, and at present, the method cannot theoretically provide more favorable support only by experimental monitoring aiming at the problems of plane grinding heat damage and the like of a cup-shaped grinding wheel. Therefore, finding an effective grinding temperature prediction method is an important approach to prevent problems such as grinding burn.
Disclosure of Invention
The invention provides a cup-shaped grinding wheel plane grinding temperature prediction method based on a non-uniform heat source model for surface processing by utilizing a cup-shaped grinding wheel, aiming at solving the problems that the instantaneous high temperature causes heat damage to the surface of a workpiece during plane grinding, the temperature is difficult to monitor in real time and the like.
The technical scheme of the invention is as follows:
a cup-shaped grinding wheel plane grinding temperature prediction method based on a non-uniform heat source model comprises the following steps:
the method comprises the following steps: setting grinding parameters before grinding, and measuring the grinding force of the cup-shaped grinding wheel during plane grinding by using a force sensor;
step two: analyzing the research status of the distribution of grinding force during the plane grinding of the cup-shaped grinding wheel and the characteristics during material removal, and establishing a non-uniform heat source model which is distributed in different functions in the circumferential direction and the radial direction according to the corresponding relation between force and heat;
step three: and establishing an analytical model and/or a numerical model of the temperature field based on the non-uniform heat source model in the second step, and substituting the planar grinding parameters of the cup-shaped grinding wheel to be predicted into the analytical model and/or the numerical analysis model to obtain corresponding predicted temperature.
The method for predicting the plane grinding temperature of the cup-shaped grinding wheel based on the non-uniform heat source model comprises the steps of providing a cutting heat source model and a friction heat source model,
if the cutting heat is distributed in cosine form on the front end face of the grinding wheel, the cutting heat Q cutting ·R w Expressed by equation (7):
wherein epsilon is the actual area contact coefficient; r is 1 And R 2 The outer diameter and the inner diameter of the grinding wheel are respectively; r w The heat distribution rate between the workpiece and the grinding wheel; q cutting Is the heat generated by the cutting force; phi is an angle; q. q.s 0 Is the heat flux density of the cross section at an angle of 0, thus obtaining q 0 Comprises the following steps:
then the cutting heat distribution q (φ) in the circumferential direction is expressed by the equation (9):
assuming that the cutting heat is distributed radially on the front end face of the grinding wheel in a chi-square manner, a chi-square function f (x) is expressed by the formula (10):
wherein c is 0 Taking a chi-square function with k =4, and symmetrically transforming the chi-square function into the following components:
the area S of the cross section when Φ =0 is:
according to the equal area principle, the method comprises the following steps:
thus obtaining c 0 ：
Then the radial distribution q (r) of the cutting heat is expressed by the formula (15):
the cutting heat source model obtained by simultaneous circumferential and radial cutting heat formulas is expressed by formula (16):
the distribution of the friction heat source model is related to the distribution of friction force, and in the grinding process, the friction force generated by the relative motion of the end face of the grinding wheel and the workpiece in contact is uniformly distributed, so that the friction heat source model is the formula (17):
superposing the cutting heat source model and the friction heat source model to obtain a non-uniform heat source model q (r, phi), and expressing by a formula (18):
according to the method for predicting the plane grinding temperature of the cup-shaped grinding wheel based on the non-uniform heat source model, the construction process of the analytic model is as follows:
the method comprises the following steps of establishing an analytic model of a continuous surface heat source temperature field on an infinite workpiece:
wherein c is the specific heat capacity of the workpiece under the condition of constant pressure, J/(kg DEG C); rho is the material density, kg/m 3 (ii) a α is thermal diffusivity, m 2 S; q (r, phi) is the point heat source density, W/m 2 (ii) a X, Y, Z is a generalized coordinate system; v is the moving speed of the heat source, m/s; τ is time, in units of s; the thermal diffusivity α in equation (19) is expressed by equation (20):
then, a finite large heat conductor temperature field limited by boundary conditions is established, a mirror image heat source is supposed to symmetrically exist on the other side of the heat insulation surface, and the actual heat source and the mirror image heat source are respectively made of gamma i It is indicated that i =1 is an actual heat source, i =2 and 3 are mirror image heat sources:
where L is the distance between the mirror image heat source and the actual heat source, then the analytical model of the temperature field on the finite large plane is:
the cup-shaped grinding wheel plane grinding temperature prediction method based on the non-uniform heat source model comprises the following steps:
(1) Defining unit types and material parameters;
(2) Establishing a three-dimensional solid model of a workpiece;
(3) Generating a grid;
(4) Applying a convection boundary condition;
(5) Loading a non-uniform heat source model: defining the load step number as N, then establishing a local cylindrical coordinate system under a global Cartesian coordinate system, selecting nodes of a loading area, and then applying a non-uniform heat flow density load in the selected area;
the non-uniform heat flow density load is generated in the following way: editing the non-uniform heat source model by using a function editor in ANSYS, then storing, wherein the stored file name must have a func extension, then opening the stored file, exporting a heat source array in an array form, and then loading in the selected area;
(6) Solving: the solving process is a continuous cyclic process, the load is deleted after one solving, if the solving times N is less than N, the local cylindrical coordinate system is established in the step (5), and the cyclic loading is finished until the solving times N is more than or equal to N;
(7) And (4) processing a result: checking the result of the numerical model, if the result is correct, ending the temperature prediction, otherwise, adjusting or regenerating the grid and continuing applying boundary conditions such as convection and the like and the subsequent steps.
Compared with the prior art, the invention has the beneficial effects that:
(1) The previous prediction about the grinding temperature is based on experiments, which requires embedding a thermocouple in a workpiece, and the process is complicated, and damages can be caused to the workpiece, so that the method is not suitable for production practice. According to the method, when the non-uniform heat source model is established in the early stage, the grinding force and the rotating speed of the grinding wheel need to be collected, and then the grinding temperature is predicted according to the second step and the third step. When the method is actually used, a thermocouple does not need to be embedded in the workpiece, and the prediction method is simple and accurate.
(2) Based on the distribution of grinding force and the material removal characteristics during the plane grinding of the cup-shaped grinding wheel, the invention establishes a non-uniform heat source model which is distributed in different functions in the circumferential direction and the radial direction, and reasonably combines the shape of a heat source with the distribution of heat flux density. And a temperature field analytical model and a numerical model during the plane grinding of the cup-shaped grinding wheel are established based on the heat source model.
(3) When a numerical model (finite element model) is established, a loading mode of a moving function heat source is provided, so that the method can be suitable for the working process of grinding the cup-shaped grinding wheel.
(4) The existing detection of the grinding temperature aims at temperature prediction during plane grinding of a parallel grinding wheel, and no feasible method is available for predicting the temperature field of plane grinding of a cup-shaped grinding wheel. The influence of the temperature on the processing quality is more obvious when the cup-shaped grinding wheel is used for plane grinding, the invention mainly provides an effective method for grinding such as surface treatment by using the cup-shaped grinding wheel, and the prediction precision reaches about 8 percent through the comparison of the result predicted by the analytical model and the image result collected by the high-definition thermal infrared imager. Meanwhile, the temperature curve acquired by the K-type thermocouple and the temperature curve predicted by the numerical model have higher goodness of fit.
Drawings
FIG. 1 is a flow chart of the operation of the present invention.
FIG. 2 is a schematic diagram of grinding force isoparametric and temperature measurement.
Fig. 3 Matlab implementation of a non-uniform heat source model.
FIG. 4 is an analytical model of the planar grinding temperature field of the cup wheel.
FIG. 5 is a flow chart of numerical modeling (finite element analysis).
Figure 6 numerical model of the cup wheel plane grinding temperature field.
FIG. 7 shows the temperature field collected by the high-definition thermal infrared imager.
FIG. 8 is a comparison of the predicted results of the numerical model with the temperature curves collected at specific points by the thermocouples, wherein FIG. 8 (a) is a graph of the temperature at point A versus time; FIG. 8 (B) is a graph showing the temperature at the point B as a function of time; FIG. 8 (C) is a graph showing the temperature change with time at the point C.
In the figure: 1. a force sensor; 2. a cup-shaped grinding wheel; 3. a type K thermocouple; 4. a workpiece; 5. a test bed; 6. a high-definition thermal infrared imager; 7. a pressure transmitter; 8. a temperature transmitter; 9. a data acquisition card; 10. a computer;
Detailed Description
The invention is further described with reference to the following detailed description of embodiments in conjunction with the accompanying drawings.
The invention discloses a cup-shaped grinding wheel plane grinding temperature prediction method based on a non-uniform heat source model, which specifically comprises the following steps of:
the method comprises the following steps: grinding parameters are set before grinding, and a force sensor is utilized to measure the grinding force during the plane grinding of the cup-shaped grinding wheel.
Step two: analyzing the current research situation of the grinding force distribution during the plane grinding of the cup-shaped grinding wheel and the characteristics during the material removal, and establishing a non-uniform heat source model which is distributed in different functions in the circumferential direction and the radial direction according to the corresponding relation between force and heat (wherein the grinding force distribution and the material removal characteristics during the plane grinding of the cup-shaped grinding wheel refer to the results of other researchers, such as:
[1]FUJIWARA T,TSUKAMOTO S,OHASHI K,et al.Study on Grinding Force Distribution on Cup Type Electroplated Diamond Wheel in Face Grinding of Cemented Carbide[J].Advanced Mat-erials Research,2014,1017(2014):9-14.
[2]LI X.Application of self-inhaling internal cooling wheel in vertical surface grinding[J].Chin-ese Journal of Mechanical Engineering,2014,27(1):86-91。
step three: and establishing an analytical model and/or a numerical model of the temperature field based on the non-uniform heat source model in the second step, and substituting the planar grinding parameters of the cup-shaped grinding wheel to be predicted into the analytical model and/or the numerical analysis model to obtain corresponding predicted temperature.
The temperature prediction method during the plane grinding of the cup-shaped grinding wheel based on the non-uniform heat source model comprises the following steps: setting grinding parameters before grinding, and acquiring grinding forces in three directions respectively marked as F by using force sensors arranged on a mechanical arm tail end execution device during grinding n 、F t And F v . The entire system used for the grinding force detection (see fig. 2) includes the forceThe device comprises a sensor 1, a cup-shaped grinding wheel 2, a test bed 5, a pressure transmitter 7 and a computer 10. When the cup wheel 2 starts to grind a workpiece 4 to be measured fixed on the test bed 5, the force sensor 1 installed between the cup wheel 2 and the mechanical arm transmits the measured potential difference to the pressure transmitter 7, and the pressure transmitter 7 converts the potential difference into a pressure value and transmits the pressure value to the computer to acquire the grinding force.
The temperature prediction method during the plane grinding of the cup-shaped grinding wheel based on the non-uniform heat source model comprises the following steps: dividing the grinding force measured in the first step into cutting force F c And frictional force F f Expressed by equation (1):
wherein μ is the coefficient of friction, F n As a vertical force, F t As the radial force, the instantaneous heat generation Q at the time of grinding can be obtained by the grinding force as formula (2):
Q＝(F c +F f )v s ＝Q cutting +Q friction (2)
wherein Q cutting And Q friction The heat generated by the cutting force and friction force, and the heat distribution ratio R between the workpiece and the grinding wheel w Can be expressed as formula (3) according to a model of Hahn:
k in the formula w And k g The thermal conductivity of the workpiece and the grinding wheel, respectively, can be determined using equations (4) and (5), respectively:
k w ＝V f λ f +(1-V f )λ m (4)
wherein V f Is the volume fraction of the fiber; lambda f 、λ m Thermal conductivity of the fiber and the epoxy resin respectively; x = λ r /λ d The ratio of the thermal conductivity of the bonding agent to the thermal conductivity of the diamond; v d Is the volume fraction of the abrasive grains of the grinding wheel. The heat Q flowing into the surface of the workpiece can be obtained by the above formula w Comprises the following steps:
Q w ＝Q·R w ＝(Q cutting +Q friction )R w (6)
according to the relation between force and heat (power P), when the rotating speed v of the grinding wheel is s At a certain time, the distribution of grinding heat is the same as that of grinding force during the plane grinding of the cup-shaped grinding wheel. The non-uniform heat source model comprises a cutting heat source model and a friction heat source model.
The distribution of the cutting heat source model is related to the distribution of the cutting force, and since the material removal mainly occurs at the front end surface of the grinding wheel during the planar grinding of the cup-shaped grinding wheel and a large cutting force is generated in the central region in the advancing direction of the grinding wheel, the load of the abrasive grains is greater than that of the left and right ends of the grinding wheel. Therefore, if the cutting heat is distributed in cosine form on the front end face of the grinding wheel, the cutting heat Q cutting ·R w Expressed by equation (7):
wherein epsilon is the actual area contact coefficient; r is 1 And R 2 The outer diameter and the inner diameter of the grinding wheel are respectively, and phi is an angle; q. q.s 0 Is the heat flux density of the cross section at an angle of 0, thus obtaining q 0 Comprises the following steps:
then the cutting heat distribution q (φ) in the circumferential direction is expressed by the equation (9):
relatively large cutting forces are generated in the region of the radially leading edge of the grinding wheel, whereas relatively small cutting forces are generated in the region of the trailing edge of the grinding wheel. Therefore, assuming that the cutting heat is distributed radially in the front end face of the grinding wheel in a chi-square manner, the chi-square function f (x) is expressed by the formula (10):
wherein c is 0 K is a scale factor and k is a degree of freedom. Taking the k =4 chi-squared function and performing a symmetric transformation:
the area S of the cross section at Φ =0 is:
according to the equal area principle, the method comprises the following steps:
thus obtaining c 0 ：
Then the radial distribution q (r) of the cutting heat is expressed by the formula (15):
the cutting heat source model obtained by simultaneous circumferential and radial cutting heat formulas is expressed by formula (16):
the distribution of the friction heat source model is related to the distribution of the friction force, and the friction force generated by the relative motion of the end face of the grinding wheel and the workpiece in contact is uniformly distributed in the grinding process, so the friction heat source model is the formula (17):
and (3) superposing the cutting heat source model and the friction heat source model to obtain a non-uniform heat source model q (r, phi) which is expressed by a formula (18):
according to the method for predicting the temperature during the plane grinding of the cup-shaped grinding wheel based on the non-uniform heat source model, the construction process of the analytic model is as follows:
the method comprises the following steps of establishing an analytic model of a continuous surface heat source temperature field as follows:
wherein c is the specific heat capacity of the workpiece under the condition of constant pressure, and J/(kg DEG C); rho is the material density, kg/m 3 (ii) a α is thermal diffusivity, m 2 S; q (r, phi) is the point heat source density (i.e. the above-mentioned non-uniform heat source model), W/m 2 (ii) a X, Y, Z is a generalized coordinate system, i.e. the temperature value can be known by randomly taking a point (X, Y, Z) on the surface of the workpiece; v is the moving speed of the heat source, m/s; τ is time, in units of s.
The thermal diffusivity, α, in the equation can be expressed by the following equation:
then establishing a bounded stripThe finite thermal conductor temperature field of the member limits is derived from an infinite workpiece, which is finite in nature, and the surface of the workpiece exposed to air can be approximated as an adiabatic surface. To solve the problem of heat transfer from a large, finite object, it can be assumed that a mirror image heat source is symmetrically present on the other side of the insulating surface. The actual heat source and the mirror image heat source are respectively made of gamma i (i =1 for the actual heat source, i =2 and 3 for the mirror image heat source) is expressed as:
wherein L is the distance between the mirror image heat source and the actual heat source, then the analytical model of the temperature field on the finite large plane is:
the numerical model (finite element analysis) is established by the following steps:
(1) Defining unit types and material parameters;
(2) Establishing a three-dimensional solid model of a workpiece;
(3) Generating a grid;
(4) Applying boundary conditions such as convection;
(5) Loading a non-uniform heat source model;
(6) Solving for
(7) And (6) processing the result.
The above finite element building process is characterized by step (5) compared with the existing finite element building process, in which the above non-uniform heat source model is introduced.
According to the invention, an analytic model and a numerical model of the temperature field can be simultaneously established, when both exist, the analytic model is verified by using the numerical model (the numerical model refers to finite element analysis), and grinding predicted temperatures obtained by the two are similar and can be used as final predicted temperatures to meet actual production requirements. The built non-uniform heat source model can be calculated in Matlab; the analytical model of the established temperature field can calculate the result in Mathcad; the established temperature field numerical model can be realized in computer-aided technologies such as finite elements.
In addition, a temperature field image to be predicted of the high-definition thermal infrared imager can be acquired, data acquired through experiments are compared with the prediction results of the analytic model and the numerical model, the result obtained by the prediction method is consistent with the experiment result, and the correctness of the analytic model and the numerical model established by the method is further verified. And a K-type thermocouple can be used for collecting the temperature of a position on the surface of the workpiece, which is easy to burn, and the accuracy of the model is verified through an experimental curve and a prediction curve in a numerical model. The device (see figure 2) used in the temperature measurement experiment comprises a K-type thermocouple 3, a workpiece 4, a test bed 5, a high-definition thermal infrared imager 6, a temperature transmitter 8, a data acquisition card 9 and a computer 10; embedding a K-type thermocouple 3 in a workpiece 4 before grinding (see A, B and C positions in FIG. 2), and fixing the workpiece 4 on a test bench 5; and simultaneously, the high-definition thermal infrared imager is arranged beside the grinding experiment. In the grinding process, the K-type thermocouple 3 transmits the collected potential difference to the temperature transmitter 8, the temperature transmitter 8 converts the potential difference into a temperature signal, and the temperature signal is collected and sent to a computer 10 for analysis through a data acquisition card 9; and at the moment of finishing the grinding and retracting, the high-definition thermal infrared imager 6 transmits the acquired temperature field image to the computer 10 for analysis. The high-definition thermal infrared imager can acquire the whole grinding temperature field of the surface of the workpiece and can be used for verifying the accuracy of an analytical model and a numerical model of the temperature field; the thermocouple can obtain a change curve of the temperature of a special point along with time, the accuracy of the model can be verified through a prediction curve and an experimental curve, the high-definition thermal infrared imager is expensive in temperature collection and high in cost, and the collected temperature field image is visual and comprehensive; the thermocouple acquisition cost is low, but only a temperature curve of a certain point can be obtained, and the distribution of the whole grinding temperature field cannot be obtained.
Example 1
The material processed by the embodiment is a composite material, and due to the particularity of the composite material, instantaneous heat aggregation phenomenon can be formed by the heat which is sharply increased when the cup-shaped grinding wheel is used for plane grinding, so that the highest temperature of an instantaneous contact point in a grinding area can reach the melting point temperature of a workpiece material, resin softening and strength reduction are easily caused, the bonding capability to carbon fibers is reduced, and surface groove marks are finally formed. Therefore, the cup-shaped grinding wheel plane grinding temperature prediction method based on the non-uniform heat source model is provided for solving the problems of difficulty in real-time temperature detection and the like in the grinding process. As shown in fig. 1, the method specifically includes the following steps.
The method comprises the following steps: measuring the grinding force of the cup-shaped grinding wheel 2 during plane grinding by using a six-dimensional force sensor, and collecting the rotating speed v of the grinding wheel when the grinding wheel is stable s (ii) a The workpiece 4 to be tested is fixed on the test bed 5, and the force sensor 1 is installed at the tail end of the mechanical arm and connected with the pressure transmitter 7 to transmit data to the computer 10 for analysis. The following table 1 sets the grinding parameters prior to machining:
TABLE 1 determination of grinding parameters
The force during grinding is obtained by the force sensor 1 as follows:
step two: analyzing the research status quo of the grinding force distribution during the plane grinding of the cup-shaped grinding wheel and the characteristics during the material removal, and establishing a non-uniform heat source model which is distributed in different functions in the circumferential direction and the radial direction according to the relationship between force and heat pair; dividing the grinding force measured in the first step into a cutting force and a friction force, and expressing the cutting force and the friction force as follows:
where μ is the coefficient of friction. The instantaneous heating value during grinding can be obtained by the grinding force as follows:
Q＝(F c +F f )v s ＝Q cutting +Q friction
wherein Q cutting And Q friction The heat generated by the cutting force and friction force, and the heat distribution ratio R between the workpiece and the grinding wheel w The model according to Hahn can be expressed as:
k in the formula w And k g The thermal conductivity coefficients of the workpiece and the grinding wheel are obtained by the following formula:
k w ＝V f λ f +(1-V f )λ m
wherein V f Is the volume fraction of the fiber; lambda [ alpha ] f 、λ m Thermal conductivity of the fiber and the epoxy resin respectively; x = λ r /λ d The ratio of the thermal conductivity of the binding agent to the thermal conductivity of the diamond; v d Is the volume fraction of the abrasive grains of the grinding wheel. The heat flowing into the surface of the workpiece can be obtained by the following formula:
Q w ＝Q·R w ＝(Q cutting +Q friction )R w
according to the relation between force and heat (power P), when the rotating speed v of the grinding wheel is s At a certain time, the distribution of grinding heat is the same as that of grinding force during the plane grinding of the cup-shaped grinding wheel. The non-uniform heat source model comprises a cutting heat source model and a friction heat source model.
The distribution of the cutting heat source model is related to the distribution of the cutting force, and since the material removal mainly occurs at the front end surface of the grinding wheel during the planar grinding of the cup-shaped grinding wheel and a large cutting force is generated in the central region in the advancing direction of the grinding wheel, the load of the abrasive grains is greater than that of the left and right ends of the grinding wheel. Therefore, the cutting heat is assumed to be distributed in a cosine form on the front end face of the grinding wheel:
wherein epsilon is the actual area contact coefficient; r 1 And R 2 Respectively the outer diameter and the inner diameter of the grinding wheel, thus obtaining q 0 Comprises the following steps:
the cutting heat is then distributed circumferentially as:
relatively large cutting forces are generated in the region of the radially leading edge of the grinding wheel, whereas relatively small cutting forces are generated in the region of the trailing edge of the grinding wheel. Therefore, assuming that the cutting heat is radially distributed in a chi-square manner on the front end surface of the grinding wheel, the chi-square function is as follows:
wherein c is 0 Is the proportionality coefficient and k is the degree of freedom. Taking a chi-square function with k =4, the symmetric transformation is:
the area S of the cross section when Φ =0 is:
according to the equal area principle, the method comprises the following steps:
thus obtaining c 0 ：
The cutting heat is then distributed in the radial direction:
the circumferential and radial equations of simultaneous cutting heat are modeled as follows:
the distribution of the friction heat source model is related to the distribution of the friction force, and in the grinding process, the contact relative motion of the end face of the grinding wheel and the workpiece generates friction, so that the distribution model of the friction heat source is as follows:
superposing the cutting heat source model and the friction heat source model to obtain a non-uniform heat source model as follows:
the reference material yields the following parameters:
(a) Carbon fiber composite material workpiece
(1) Density: ρ =1.572g/cm 3
(2) Specific heat capacity at constant pressure: c = 802.84J/(kg. Degree. C)
(3) Volume fraction of carbon fiber: v f ＝0.6
(4) Thermal conductivity of carbon fiber: lambda f ＝0.50～1.10W/(m·K)
(5) Thermal conductivity of epoxy resin: lambda [ alpha ] m ＝0.20～0.80W/(m·K)
(b) Type B cup grinding wheel (D75T 25H20W10X 3)
(1) Thermal conductivity of resin binder: lambda [ alpha ] r ＝0.9W/(m·K)
(2) Thermal conductivity of diamond abrasive grains: lambda d ＝146W/(m·K)
(3) Volume fraction of diamond: v d ＝0.7
(4) Coefficient of friction: μ =0.3
The non-uniform heat source model is drawn in Matlab, and when the cup-shaped grinding wheel plane grinding is realized, the non-uniform heat source model is shown in FIG. 3.
Step three: establishing an analytical model of the temperature field based on the non-uniform heat source model in the step two, and verifying the model by using a numerical model (finite element analysis);
establishing an analytical model for plane grinding of a cup-shaped grinding wheel;
and (II) establishing a numerical model (finite element analysis) of the cup-shaped grinding wheel plane grinding.
Establishing an analytical model of cup-shaped grinding wheel plane grinding in the third step (I), specifically comprising the following steps of establishing an analytical model of a continuous surface heat source temperature field:
wherein c is the specific heat capacity of the workpiece under the condition of constant pressure, J/(kg DEG C); rho is the material density, kg/m 3 (ii) a α is thermal diffusivity, m 2 S; q (r, phi) is the point heat source density, W/m 2 (ii) a v is the moving speed of the heat source, m/s; τ is time, s. The thermal diffusivity, α, in the equation can be expressed by the following equation:
then, a finite thermal conductor temperature field limited by the boundary conditions is established, the above derivation being carried out on an infinite workpiece, whereas in practice the workpiece is finite and the surface of the workpiece exposed to air can be approximately seen as the adiabatic surface. To solve the problem of heat transfer from a large, finite object, it can be assumed that a mirror image heat source is symmetrically present on the other side of the insulating surface. The actual heat source and the mirror image heat source are respectively made of gamma i Expressed as:
i＝1,2,3；Y 1 ＝Y,Y 2 ＝Y-L,Y 3 ＝Y+L；Z＝0
the analytical model of the temperature field over a finite large plane is then:
the analytical model of the temperature field is calculated in MathCAD to obtain the temperature field distribution shown in figure 4;
establishing a numerical model (finite element analysis) of the cup-shaped grinding wheel plane grinding in the step three (II), programming by using an APDL language in ANSYS software, and specifically, the flow is shown in FIG. 5:
(1) Defining unit types and material parameters;
according to example calculation data of a grinding temperature field, three-dimensional transient heat transfer analysis is carried out by using SOLID70 unit in ANSYS, the processed material is a composite material, and material parameters mainly comprise density rho and heat conductivity coefficient k w And the specific heat capacity c under the constant pressure condition, wherein the numerical value of the specific heat capacity c is based on the material parameters given in the second step.
(2) Establishing a three-dimensional solid model of a workpiece;
in the embodiment, the shape of the workpiece is simple, and the parameterized modeling is simple, quick and efficient. The workpiece dimensions were (length × width × height): 0.3 m.times.0.15 m.times.0.015 m
(3) Generating a grid;
the division of the mesh in the three-dimensional transient model directly affects the accuracy of the simulation. Too small a mesh size may result in too long a simulation time and even a breakdown, while too large a mesh size may result in reduced accuracy of the results. In order to optimize the simulation process, a grid with a larger size is adopted on one side far away from the grinding surface, and the grid on one side far away from the grinding surface in the modeling is set to be 0.5mm; and the grinding contact surface adopts a grid with higher precision, and the grid of the contact surface in the modeling is set to be 0.2mm.
(4) Applying boundary conditions such as convection;
the boundary conditions in this experiment are mainly illustrated by: initial temperature and convective heat transfer coefficient of air.
Setting the initial temperature value as T 0 =20 ℃, and the convective heat transfer coefficient of air is h = 20W/(m) 2 ·K)。
(5) Loading a non-uniform heat source model;
the loading of the non-uniform heat source model specifically comprises the steps of starting a starting cycle subroutine (namely a loading procedure), firstly defining the load step number as N in the subroutine, secondly establishing a local cylindrical coordinate system under a global Cartesian coordinate system, selecting nodes of a loading area, and then applying a non-uniform heat flow density load in the selected area, wherein the non-uniform heat flow density load is generated in the following mode: and editing and storing the non-uniform heat source model by using a function editor in ANSYS, wherein the stored file name must have a func extension, opening the stored file, exporting a heat source array in an array form, and then loading in the selected area. The specific loading method is shown in fig. 5.
(6) Solving;
and (4) the solving process is a continuous cyclic process, the load is deleted after one solving, if the solving times N is less than N, the steps of establishing the local cylindrical coordinate system and the subsequent steps in the step (5) are repeated until the solving times N is more than or equal to N, and the cyclic subprogram is ended.
(7) And (6) processing the result.
The numerical model results are examined using a post-processing module. If the result is correct, the temperature prediction is finished, otherwise, boundary conditions such as convection and the like and the following steps are continuously applied after the grid is adjusted and regenerated.
And (3) utilizing an APDL (android package) parameterized language to model a numerical model. The numerical model of the temperature field of this example is shown in fig. 6.
And acquiring and comparing the temperature field image by using a high-definition thermal infrared imager. And the high-definition thermal infrared imager 6 in the figure 1 transmits the collected temperature field model to a computer 10 for analyzing and verifying the accuracy of the analytical model and the numerical model of the temperature field during the planar grinding of the cup-shaped grinding wheel, and finally the aim of predicting the grinding temperature is fulfilled. The temperature field collected by the thermal imager is shown in fig. 7, the measured values of the four marked points in fig. 7 are compared with the predicted value of the analytical model in fig. 4, and the prediction accuracy of the grinding temperature reaches about 8 percent as shown in table 2.
TABLE 2 comparison of predicted values with Experimental values
Temperature acquisition is carried out at three positions A, B and C on the surface of the workpiece 4 by using the K-type thermocouple 3 as shown in FIG. 6, and the acquired data is transmitted to a computer 10 through a temperature transmitter 8 and a data acquisition card 9 to be analyzed: the result predicted by the numerical model has better goodness of fit with the temperature curve of the experimental result, as shown in fig. 8.
Nothing in this specification is said to apply to the prior art.
Claims (3)
1. A cup-shaped grinding wheel plane grinding temperature prediction method based on a non-uniform heat source model comprises the following steps:
the method comprises the following steps: setting grinding parameters before grinding, and measuring the grinding force of the cup-shaped grinding wheel during plane grinding by using a force sensor;
step two: analyzing the research status quo of the grinding force distribution during the plane grinding of the cup-shaped grinding wheel and the characteristics during the material removal, and establishing a non-uniform heat source model which is distributed in different functions in the circumferential direction and the radial direction according to the corresponding relation of force and heat;
step three: establishing an analytical model and/or a numerical model of a temperature field based on the non-uniform heat source model in the second step, and substituting the planar grinding parameters of the cup-shaped grinding wheel to be predicted into the analytical model and/or the numerical analysis model to obtain corresponding predicted temperature;
the non-uniform heat source model comprises a cutting heat source model and a friction heat source model,
if the cutting heat is distributed in cosine form on the front end face of the grinding wheel, the cutting heat Q cutting ·R w Expressed by equation (7):
wherein epsilon is the actual area contact coefficient; r is 1 And R 2 The outer diameter and the inner diameter of the grinding wheel are respectively; r w The heat distribution rate between the workpiece and the grinding wheel; q cutting Is the heat generated by the cutting force; is more than an angle; q. q.s 0 Is the heat flux density of the cross section at an angle of 0, thus obtaining q 0 Comprises the following steps:
then the cutting heat distribution q (φ) in the circumferential direction is expressed by the equation (9):
assuming that the cutting heat is distributed radially on the front end face of the grinding wheel in a chi-square manner, a chi-square function f (x) is expressed by the formula (10):
wherein c is 0 Taking a chi-square function of k =4 as a proportionality coefficient and k is a degree of freedomThe symmetry transformation is:
the area S of the cross section at Φ =0 is:
according to the equal area principle, the method comprises the following steps:
thus obtaining c 0 ：
Then the radial distribution q (r) of the cutting heat is expressed by the formula (15):
the simultaneous circumferential and radial cutting heat equations to obtain the cutting heat source model are expressed by equation (16):
the distribution of the friction heat source model is related to the distribution of friction force, and in the grinding process, the friction force generated by the relative motion of the end face of the grinding wheel and the workpiece in contact is uniformly distributed, so that the friction heat source model is the formula (17):
wherein Q is friction Heat generated by friction work;
and (3) superposing the cutting heat source model and the friction heat source model to obtain a non-uniform heat source model q (r, phi), and expressing by a formula (18):
2. the method for predicting the plane grinding temperature of the cup-shaped grinding wheel based on the non-uniform heat source model according to claim 1, wherein the analytical model is constructed by the following steps:
the method comprises the following steps of establishing an analytic model of a continuous surface heat source temperature field on an infinite workpiece:
wherein c is the specific heat capacity of the workpiece under the condition of constant pressure, J/(kg DEG C); rho is the material density, kg/m 3 (ii) a α is thermal diffusivity, m 2 S; q (r, phi) is the point heat source density, W/m 2 (ii) a X, Y, Z is a generalized coordinate system; v is the moving speed of the heat source, m/s; τ is time, in units of s; the thermal diffusivity in the formula is represented by formula (20):
then, a finite large heat conductor temperature field limited by boundary conditions is established, a mirror image heat source is supposed to symmetrically exist on the other side of the heat insulation surface, and the actual heat source and the mirror image heat source are respectively made of gamma i Indicating that i =1 is the actual heat source, i =2 and 3 are mirror image heat sources:
where L is the distance between the mirror image heat source and the actual heat source, then the analytical model of the temperature field on the finite large plane is:
3. the method for predicting the plane grinding temperature of the cup-shaped grinding wheel based on the non-uniform heat source model as claimed in claim 1, wherein the numerical model is established by the following steps:
(1) Defining unit types and material parameters;
(2) Establishing a three-dimensional solid model of a workpiece;
(3) Generating a grid;
(4) Applying a convection boundary condition;
(5) Loading a non-uniform heat source model: defining the load step number as N, then establishing a local cylindrical coordinate system under a global Cartesian coordinate system, selecting nodes of a loading area, and then applying a non-uniform heat flow density load in the selected area;
the non-uniform heat flow density load is generated in the following way: the method comprises the steps that a function editor in ANSYS is used for editing and storing a non-uniform heat source model, a stored file name must have a func extension, then a stored file is opened, a heat source array in an array form is exported and generated, and then the heat source array is loaded in a selected area;
(6) Solving: the solving process is a continuous cyclic process, the load is deleted after one solving, if the solving times N is less than N, the local cylindrical coordinate system is established in the step (5), and the cyclic loading is finished until the solving times N is more than or equal to N;
(7) And (4) processing results: checking the numerical model result, if the result is correct, ending the temperature prediction, otherwise, adjusting or regenerating the grid and continuing to apply the convection boundary condition and the subsequent steps.
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| CN108151885A (en) * | 2017-12-15 | 2018-06-12 | 湖南科技大学 | Non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model |
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