CN109858079A - Cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model - Google Patents
Cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model Download PDFInfo
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Abstract
The present invention is the cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model, method includes the following steps: step 1: setting grinding parameter before grinding, grinding force when using force sensor measuring cup emery wheel flat surface grinding；Step 2: the feature when present Research and material of grinding force distribution when analysis cupuliform Grinding wheel Grinder remove is established according to power relationship corresponding with heat in the circumferential and radial non-homogeneous heat source model in different functions distribution；Step 3: based on the non-homogeneous heat source model in step 2, establishing the analytic modell analytical model and/or numerical model in temperature field, and cup emery wheel flat surface grinding parameter to be predicted is substituted into above-mentioned analytic modell analytical model and/or numerical analysis model and obtains corresponding predicted temperature.This method a kind of grinding progress temperature prediction such as is surface-treated suitable for carrying out using cup emery wheel, and the image result comparison that the result predicted is acquired with high definition thermal imaging system finds that result is accurate.
Description
Technical field
The present invention relates to the grinding fields in machine-building, the specifically cup emery wheel based on non-homogeneous heat source model
Flat surface grinding temperature predicting method.
Background technique
Grinding is a kind of effective ways for improving surface quality, is had a wide range of applications in Precision Machining field.Benefit
It carries out surface processing with cup emery wheel more and more to be paid attention in the field, because its is high-efficient, grinding quality is high.It influences
Suface processing quality it is many because being known as, one of grinding temperature is exactly.Grinding high temperature can cause thermal damage to workpiece surface,
Including burn and fire check.The research done in this regard at present has:
Non-circular profile Work piece high-speed grinding temperature of the such as [1] Deng Chaohui, She Shuailong, Yi Jun based on variable heat source model is pre-
10 8151885 A. of survey method .CN
[2] the prediction technique .CN of Zheng Kan, Meng Heng, Liao Wen and equal supersonic vibration assistant grinding grinding brittle materials temperature
107133392A. or more is the flat surface grinding that parallel grinding wheel is used for special workpiece (fragile material, non-circular profile workpiece)
Temperature predicting method, and the problems such as be directed to cup wheel flat surface grinding thermal damage, relying solely on experimental monitoring at present can not be
More favorable support is theoretically provided.Therefore, seeking a kind of effective grinding temperature prediction technique is to prevent grinding burn etc. from asking
The important channel of topic.
Summary of the invention
TRANSIENT HIGH TEMPERATURE causes heat waste to injure temperature real-time monitoring difficulty etc. workpiece surface to ask when in order to solve flat surface grinding
Topic, the invention proposes utilize the cup emery wheel flat surface grinding based on non-homogeneous heat source model when cup emery wheel progress surface processing
Temperature predicting method.
The technical scheme is that
A kind of cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model, this method includes following step
It is rapid:
Step 1: setting grinding parameter before grinding, mill when using force sensor measuring cup emery wheel flat surface grinding
Cut power；
Step 2: the spy when present Research and material of grinding force distribution when analysis cupuliform Grinding wheel Grinder remove
Sign is established according to power relationship corresponding with heat in the circumferential and radial non-homogeneous heat source model in different functions distribution；
Step 3: based on the non-homogeneous heat source model in step 2, the analytic modell analytical model and/or Numerical-Mode in temperature field are established
Cup emery wheel flat surface grinding parameter to be predicted is substituted into above-mentioned analytic modell analytical model and/or numerical analysis model and obtained accordingly by type
Predicted temperature.
The above-mentioned cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model, the non-homogeneous heat source mould
Type includes cutting heat source model and frictional heat source model,
Assuming that cutting heat is in cosine distribution in grinding wheel front end face, then heat Q is cutcutting·RwIt is indicated with formula (7):
Wherein ε is real area contact coefficient；R1And R2It is the outer diameter and inner diameter of grinding wheel respectively；RwFor workpiece and grinding wheel it
Between heat distribution rate；QcuttingIt is the heat generated by cutting force acting；φ is angle；q0The hot-fluid in section when for angle being 0
Density then obtains q0Are as follows:
So cutting heat is indicated at circumferentially distributed q (φ) with formula (9):
Assuming that cutting heat is radially in chi square distribution in grinding wheel front end face, chi square function f (x) is indicated with formula (10):
Wherein c0For proportionality coefficient, k is freedom degree, takes the chi square function of k=4 by symmetry transformation are as follows:
The area S in the section in φ=0 are as follows:
It is obtained according to pulse area equal principle:
Then c is obtained0:
So cutting heat is indicated in radial distribution q (r) with formula (15):
The circumferential direction of simultaneous cutting heat and radial formula, which obtain cutting heat source model formula (16), to be indicated:
The distribution of the frictional heat source model is related with the distribution of frictional force, in grinding process, abrasive wheel end face and workpiece
The frictional force that contact relative motion generates is uniformly distributed, therefore frictional heat source model is formula (17):
It is superimposed cutting heat source model to obtain non-homogeneous heat source model q (r, φ) with frictional heat source model, with formula (18)
It indicates:
The above-mentioned cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model, the structure of the analytic modell analytical model
The process of building is:
Continue plane heat source temperature field analytic modell analytical model including establishing on infinitely great workpiece are as follows:
Wherein c is the specific heat capacity of workpiece under constant-pressure conditions, J/ (kg DEG C)；ρ is density of material, kg/m3；α is thermal diffusion
Rate, m2/s；Q (r, φ) is heat point source density, W/m2；X, Y, Z are generalized coordinates systems；V is heat source movement speed, m/s；When τ is
Between, unit s；Thermal diffusivity α in formula (19) is indicated with formula (20):
Then the limited big heat carrier temperature field limited by boundary condition is established, imagination is symmetrically deposited in the another side in insulation face
In a mirror image heat source, practical heat source and mirror image heat source use Γ respectivelyiIt indicates, is practical heat source when i=1, when i=2 and 3 is
Mirror image heat source:
Wherein L be the distance between mirror image heat source and practical heat source, then in limited big plane temperature field parsing mould
Type are as follows:
The above-mentioned cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model, the numerical model are built
Vertical process is:
(1) definition unit type, material parameter；
(2) workpiece three-dimensional entity model is established；
(3) grid is generated；
(4) apply convection boundary condition；
(5) load of non-homogeneous heat source model: definition load step number is N, is secondly established under global cartesian coordinate system
Local cylindrical coordinate, and the node of loading area is selected, then apply nonuniform heat flux load in selected region；
The generating mode of nonuniform heat flux load is: using the Functions editor in ANSYS to non-homogeneous heat source mould
Type saves after being edited, and .func extension name must be had by saving filename, then opens the file of preservation and exports generation array
The heat source array of form loads in selected region later；
(6) solve: solution procedure is continuous cyclic process, deletes load after solving once, if solution frequency n <
N, then establishing local cylindrical coordinate in return step (5), end loop is loaded when solving frequency n >=N；
(7) result treatment: check numerical model as a result, if result is correct, temperature prediction will be terminated, otherwise to grid into
Row adjustment or continue to after regenerating the boundary conditions such as convection current and later the step of.
Compared with prior art, the beneficial effects of the present invention are:
(1) prediction about grinding temperature before is based on testing more, this requires immersioning thermocouple in workpiece, process
It is more complicated, while damage can be generated to workpiece, it is not suitable for production practices.The application establishes non-homogeneous heat source model in early period
When need to acquire grinding force and grinding wheel speed, then carry out the prediction of grinding temperature according to step 2 and three.Actual use is originally
It does not need to immersion thermocouple in workpiece when application method, prediction technique is simply accurate.
(2) the present invention is based on the distributions of grinding force when cup emery wheel flat surface grinding and material to remove feature, it is established that in week
To the non-homogeneous heat source model being distributed with radial direction in different functions, reasonably by the shape of heat source in conjunction with the distribution of heat flow density
Together.And temperature field analytic modell analytical model and numerical model when establishing cup emery wheel flat surface grinding based on the heat source model.
(3) when establishing numerical model (finite element model), the loading method of move function heat source is proposed, it is made
In the course of work that can be suitably used for cup emery wheel grinding.
(4) temperature prediction when the existing detection about grinding temperature is for parallel grinding wheel flat surface grinding, does not have also
There is feasible method to predict the temperature field of cup emery wheel flat surface grinding.Using temperature when cup emery wheel flat surface grinding to adding
The influence of working medium amount is more obvious, and present invention is generally directed to the grindings for be surface-treated etc. one kind using cup emery wheel to provide
Effective method, and the image result for the result and the acquisition of high definition thermal imaging system predicted by analytic modell analytical model is compared and is sent out
Existing, the precision of prediction reaches 8% or so.The temperature of the temperature curve of K-type thermocouple acquisition and numerical model prediction is utilized simultaneously
Line of the writing music goodness of fit with higher.
Detailed description of the invention
Fig. 1 operation of the present invention flow chart.
The parameters such as Fig. 2 grinding force and temperature measuring principle figure.
The Matlab of the non-homogeneous heat source model of Fig. 3 is realized.
The analytic modell analytical model of Fig. 4 cup emery wheel Surface Grinding Temperature Field.
Fig. 5 numerical model (finite element analysis) Establishing process figure.
The numerical model of Fig. 6 cup emery wheel Surface Grinding Temperature Field.
The temperature field of Fig. 7 high definition thermal imaging system acquisition.
Fig. 8 numerical model prediction result and the collected particular point temperature curve of thermocouple compare, and wherein Fig. 8 (a) is A point
Temperature changes over time curve；Fig. 8 (b) is that B point temperature changes over time curve；Fig. 8 (c) is that C point temperature changes over time song
Line.
In figure: 1, force snesor；2, cup emery wheel；3, K-type thermocouple；4, workpiece；5, testing stand；6, high definition thermal imagery
Instrument；7, pressure transmitter；8, temperature transmitter；9, data collecting card；10, computer；
Specific embodiment
The present invention is described further with specific embodiment with reference to the accompanying drawing.
The present invention is based on the cup emery wheel flat surface grinding temperature predicting methods of non-homogeneous heat source model, specifically include following step
It is rapid:
Step 1: setting grinding parameter before grinding, mill when using force sensor measuring cup emery wheel flat surface grinding
Cut power.
Step 2: the spy when present Research and material of grinding force distribution when analysis cupuliform Grinding wheel Grinder remove
Sign is established according to power relationship corresponding with heat in circumferential and radial non-homogeneous heat source model (the wherein cup in different functions distribution
Grinding force distribution and material removal when shape Grinding wheel Grinder are characterized in the achievement with reference to 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 3: based on the non-homogeneous heat source model in step 2, the analytic modell analytical model and/or Numerical-Mode in temperature field are established
Cup emery wheel flat surface grinding parameter to be predicted is substituted into above-mentioned analytic modell analytical model and/or numerical analysis model and obtained accordingly by type
Predicted temperature.
Temperature predicting method when the above-mentioned cup emery wheel flat surface grinding based on non-homogeneous heat source model, the step 1 are specific
Are as follows: grinding parameter is set before grinding, is then ground using the force snesor being mounted in mechanical arm tail end executive device
The grinding force in three directions is denoted as F respectively when cuttingn、FtAnd Fv.When carrying out grinding force acquisition used complete equipment (referring to
It Fig. 2) include force snesor 1, cup emery wheel 2, testing stand 5, pressure transmitter 7, computer 10.When cup emery wheel 2 starts grinding admittedly
When the workpiece for measurement 4 being scheduled on testing stand 5, it is mounted on the electricity that force snesor 1 of the cup emery wheel 2 between mechanical arm will measure
Potential difference is transferred to pressure transmitter 7, and potential difference is converted to pressure value and is transferred in computer to reach grinding by pressure transmitter 7
The acquisition of power.
Temperature predicting method when the above-mentioned cup emery wheel flat surface grinding based on non-homogeneous heat source model, the step 2 are specific
Are as follows: the grinding force measured in above-mentioned steps one is divided into cutting force FcWith frictional force Ff, indicated with formula (1) are as follows:
Wherein μ is coefficient of friction, FnFor vertical force, FtFor radial force, instantaneous hair when grinding can be obtained by grinding force
Heat Q is formula (2):
Q=(Fc+Ff)vs=Qcutting+Qfriction (2)
Wherein QcuttingAnd QfrictionIt is the heat generated by cutting force and friction working respectively, between workpiece and grinding wheel
Heat distribution rate RwFormula (3) can be expressed as according to the model of Hahn:
K in formulawAnd kgIt is the thermal coefficient of workpiece and grinding wheel respectively, can be acquired respectively with formula (4) and (5):
kw=Vfλf+(1-Vf)λm (4)
Wherein VfFor the volume fraction of fiber；λf、λmThe respectively thermal coefficient of fiber and epoxy resin；X=λr/λdFor knot
The ratio between mixture thermal coefficient and diamond heat-conducting coefficient；VdFor the volume fraction of grinding wheel abrasive grain.It is available by above formula
Flow into the heat Q of workpiece surfacewAre as follows:
Qw=QRw=(Qcutting+Qfriction)Rw (6)
According to power and hot (power P) relationship, as grinding wheel speed vsWhen certain, grinding heat when cup emery wheel flat surface grinding
It is distributed identical as the distribution of grinding force.Non-homogeneous heat source model includes cutting heat source model and frictional heat source model.
The distribution of above-mentioned cutting heat source model is related with the distribution of cutting force, material removal master when cup emery wheel flat surface grinding
Occur the front end face in grinding wheel, and in the central area of grinding wheel direction of advance, can generate biggish cutting force, therefore abrasive grain
Load is greater than the left and right end of grinding wheel.It is assumed that cutting heat is in cosine distribution in grinding wheel front end face, then heat Q is cutcutting·Rw
It is indicated with formula (7):
Wherein ε is real area contact coefficient；R1And R2It is the outer diameter and inner diameter of grinding wheel respectively, φ is angle；q0For angle
The heat flow density in section when being 0 then obtains q0Are as follows:
So cutting heat is indicated at circumferentially distributed q (φ) with formula (9):
In the diameter forward edge region of grinding wheel, relatively large cutting force can be generated, and is cut in the back edge region of grinding wheel
It is smaller to cut power.It is assumed that cutting heat is radially in chi square distribution in grinding wheel front end face, chi square function f (x) is indicated with formula (10):
Wherein c0For proportionality coefficient, k is freedom degree.Take the chi square function of k=4 by symmetry transformation are as follows:
The area S in the section in φ=0 are as follows:
It is obtained according to pulse area equal principle:
Then c is obtained0:
So cutting heat is indicated in radial distribution q (r) with formula (15):
The circumferential direction of simultaneous cutting heat and radial formula, which obtain cutting heat source model formula (16), to be indicated:
The distribution of above-mentioned frictional heat source model is related with the distribution of frictional force, in grinding process, abrasive wheel end face and workpiece
The frictional force that contact relative motion generates is uniformly distributed, therefore frictional heat source model is formula (17):
Cutting heat source model is superimposed to obtain non-homogeneous heat source model q (r, φ) formula (18) table with frictional heat source model
Show:
Temperature predicting method when the above-mentioned cup emery wheel flat surface grinding based on non-homogeneous heat source model, the analytic modell analytical model
Building process is:
Continue plane heat source temperature field analytic modell analytical model including establishing are as follows:
Wherein c is the specific heat capacity of workpiece under constant-pressure conditions, J/ (kg DEG C)；ρ is density of material, kg/m3；α is thermal diffusion
Rate, m2/s；Q (r, φ) is heat point source density (i.e. above-mentioned non-homogeneous heat source model), W/m2；X, Y, Z refer to generalized coordinates system,
I.e. at will take on the surface of the workpiece a bit (X, Y, Z) may know that its temperature value；V is heat source movement speed, m/s；τ is the time,
Unit s.
Thermal diffusivity α in formula can be indicated with following formula:
Then the limited big heat carrier temperature field limited by boundary condition is established, above derivation is in infinitely great work
Carried out on part, and actually workpiece is limited, and the aerial workpiece surface of exposure can approximation regard insulation face as.In order to
Solve limited big object heat conduction problem, can imagination insulation face symmetrically there is a mirror image heat sources for another side.It is practical
Heat source and mirror image heat source use Γ respectivelyi(being practical heat source when i=1, be mirror image heat source when i=2 and 3) expression are as follows:
Wherein L be the distance between mirror image heat source and practical heat source, then in limited big plane temperature field parsing mould
Type are as follows:
The establishment process of the numerical model (finite element analysis) is:
(1) definition unit type, material parameter；
(2) workpiece three-dimensional entity model is established；
(3) grid is generated；
(4) apply the boundary conditions such as convection current；
(5) load of non-homogeneous heat source model；
(6) it solves
(7) result treatment.
Above-mentioned finite element establishment process is step (5) compared with technology, relative to existing finite element establishment process feature,
Above-mentioned non-homogeneous heat source model is introduced during this.
Can establish the analytic modell analytical model and numerical model in temperature field in the present invention simultaneously, the two all in the presence of, and utilize number
Value model (numerical model refers to finite element analysis) verifies analytic modell analytical model, the grinding predicted temperature phase that the two obtains
Closely, it can be used as final predicted temperature to use, meet actual production demand.Establishing non-homogeneous heat source model can be in Matlab
Middle calculating；The analytic modell analytical model in built temperature field can in Mathcad calculated result；Built Numerical Model of Temperature Field is in finite element etc.
It can be achieved in computer aided technique.
In addition, being also acquired using high definition thermal imaging system temperature field image to be predicted, by the number of experiment acquisition
It is compared according to the prediction result with above-mentioned analytic modell analytical model and numerical model, the result that the application prediction technique obtains and experiment are tied
Fruit is consistent, and further demonstrates the correctness of analytic modell analytical model and numerical model established by the present invention.K-type thermocouple can also be used
Temperature acquisition is carried out to the position for easily occurring burning on workpiece surface, is tested by prediction curve in empirical curve and numerical model
The accuracy of model of a syndrome.When carrying out thermometric experiment device therefor (referring to fig. 2) include K-type thermocouple 3, workpiece 4, testing stand 5,
High definition thermal imaging system 6, temperature transmitter 8, data collecting card 9, computer 10；K-type thermocouple 3 is embedded in workpiece before grinding
In 4 (tri- positions A, B and C in referring to fig. 2), workpiece 4 is fixed on testing stand 5；Simultaneously by high definition thermal imaging system frame in
Beside grinding experiment.During grinding, collected potential difference is transferred in temperature transmitter 8 by K-type thermocouple 3, temperature
Potential difference is converted to temperature signal by degree transmitter 8, and is sent multi way temperature signal collection and computer by data collecting card 9
It is analyzed in 10；Terminate the moment of withdrawing in grinding, the temperature field image of acquisition is transferred in computer 10 by high definition thermal imaging system 6
Analysis.High definition thermal imaging system can collect the entire grinding temperature field of workpiece surface, can be used for verifying the parsing in temperature field
The accuracy of model and numerical model；Thermocouple can obtain particular point temperature versus time curve, pass through prediction curve
Also can verify that the accuracy of model with empirical curve, high definition thermal imaging system temperature collection is somewhat expensive, and it is at high cost, but acquire
Temperature field image is more intuitive, comprehensively；And thermocouple acquisition cost is lower, but the temperature curve of certain point can only be obtained, nothing
Method obtains the distribution of entire grinding temperature field.
Embodiment 1
The present embodiment material processed is composite material, due to the particularity of composite material, is carried out using cup emery wheel
The heat sharply increased when flat surface grinding will form transient heat clustering phenomena, this may make grinding area instant contact point
Maximum temperature reaches workpiece material melting temperature, easily leads to resin softening, strength reduction, drops to the cementitiousness of carbon fiber
It is low, ultimately form surface groove mark.Therefore the problems such as being directed to real time temperature detection difficult in grinding process proposes based on non-homogeneous
The cup emery wheel flat surface grinding temperature predicting method of heat source model.As shown in Figure 1, specifically including following steps.
Step 1: measuring grinding force when 2 flat surface grinding of cup emery wheel using six-dimension force sensor, and acquisition reaches steady
The revolving speed v for the abrasive grinding wheel that timing is waiteds；Workpiece for measurement 4 is fixed on testing stand 5, and force snesor 1 is mounted on mechanical arm tail end simultaneously
It is connect with pressure transmitter 7 and transfers data to computer 10 and analyzed.First grinding parameter is carried out such as before being processed
The following table 1 setting:
The determination of 1 grinding parameter of table
Power when being ground is obtained by force snesor 1 are as follows:
Step 2: the spy when present Research and material of grinding force distribution when analysis cupuliform Grinding wheel Grinder remove
Sign is established according to the relationship of power and heat pair in the circumferential and radial non-homogeneous heat source model in different functions distribution；By above-mentioned step
The grinding force measured in rapid one is divided into cutting force and Frictional force gauge is shown as:
Wherein μ is coefficient of friction.Instantaneous calorific value when grinding can be obtained by grinding force are as follows:
Q=(Fc+Ff)vs=Qcutting+Qfriction
Wherein QcuttingAnd QfrictionIt is the heat generated by cutting force and friction working respectively, between workpiece and grinding wheel
Heat distribution rate RwIt can be expressed as according to the model of Hahn:
K in formulawAnd kgIt is the thermal coefficient of workpiece and grinding wheel respectively, can be acquired with following formula:
kw=Vfλf+(1-Vf)λm
Wherein VfFor the volume fraction of fiber；λf、λmThe respectively thermal coefficient of fiber and epoxy resin；X=λr/λdFor knot
The ratio between mixture thermal coefficient and diamond heat-conducting coefficient；VdFor the volume fraction of grinding wheel abrasive grain.It is available by above formula
Flow into the heat of workpiece surface are as follows:
Qw=QRw=(Qcutting+Qfriction)Rw
According to power and hot (power P) relationship, as grinding wheel speed vsWhen certain, grinding heat when cup emery wheel flat surface grinding
Distribution it is identical as the distribution of grinding force.Non-homogeneous heat source model includes cutting heat source model and frictional heat source model.
The distribution of above-mentioned cutting heat source model is related with the distribution of cutting force, material removal master when cup emery wheel flat surface grinding
Occur the front end face in grinding wheel, and in the central area of grinding wheel direction of advance, can generate biggish cutting force, therefore abrasive grain
Load is greater than the left and right end of grinding wheel.It is assumed that cutting heat is in cosine distribution in grinding wheel front end face:
Wherein ε is real area contact coefficient；R1And R2It is the outer diameter and inner diameter of grinding wheel respectively, then obtains q0Are as follows:
So cutting heat is circumferentially distributed are as follows:
In the diameter forward edge region of grinding wheel, relatively large cutting force can be generated, and is cut in the back edge region of grinding wheel
It is smaller to cut power.It is assumed that cutting heat is radially in chi square distribution, chi square function in grinding wheel front end face are as follows:
Wherein c0For proportionality coefficient, k is freedom degree.Take the chi square function of k=4 by symmetry transformation are as follows:
The area S in the section in φ=0 are as follows:
It is obtained according to pulse area equal principle:
Then c is obtained0:
So cutting heat is in radial distribution are as follows:
It is as follows that the circumferential direction of simultaneous cutting heat and radial formula obtain model:
The distribution of above-mentioned frictional heat source model is related with the distribution of frictional force, in grinding process, abrasive wheel end face and workpiece
It contacts relative motion and generates friction, then the distributed model of frictional heat source are as follows:
Cutting heat source model is superimposed with frictional heat source model obtain non-homogeneous heat source model as follows:
It consults material and obtains following parameter:
(a) workpiece made of carbon fiber composite
(1) density: ρ=1.572g/cm3
(2) specific heat capacity under constant pressure: c=802.84J/ (kg DEG C)
(3) volume fraction of carbon fiber: Vf=0.6
(4) thermal coefficient of carbon fiber: λf=0.50~1.10W/ (mK)
(5) thermal coefficient of epoxy resin: λm=0.20~0.80W/ (mK)
(b) cup wheel (D75T25H20W10X3) of Type B number
(1) thermal coefficient of resinoid bond: λr=0.9W/ (mK)
(2) thermal coefficient of diamond abrasive grain: λd=146W/ (mK)
(3) volume fraction of diamond: Vd=0.7
(4) friction coefficient: μ=0.3
The above non-homogeneous heat source model is drawn non-homogeneous when realizing cup emery wheel flat surface grinding as shown in Figure 3 in Matlab
Heat source model.
Step 3: based on the non-homogeneous heat source model in step 2, the analytic modell analytical model in temperature field is established, and utilizes numerical value
Model (finite element analysis) verifies the model；
(I) analytic modell analytical model of cup emery wheel flat surface grinding is established；
(II) numerical model (finite element analysis) of cup emery wheel flat surface grinding is established.
Above-mentioned steps three (I) establish the analytic modell analytical model of cup emery wheel flat surface grinding, specifically include foundation and continue plane heat source temperature
Spend field desorptiion model are as follows:
Wherein c is the specific heat capacity of workpiece under constant-pressure conditions, J/ (kg DEG C)；ρ is density of material, kg/m3；α is thermal diffusion
Rate, m2/s；Q (r, φ) is heat point source density, W/m2；V is heat source movement speed, m/s；τ is time, s.Thermal diffusion in formula
Rate α can be indicated with following formula:
Then the limited big heat carrier temperature field limited by boundary condition is established, above derivation is in infinitely great work
Carried out on part, and actually workpiece is limited, and the aerial workpiece surface of exposure can approximation regard insulation face as.In order to
Solve limited big object heat conduction problem, can imagination insulation face symmetrically there is a mirror image heat sources for another side.It is practical
Heat source and mirror image heat source use Γ respectivelyiIt indicates are as follows:
I=1,2,3；Y1=Y, Y2=Y-L, Y3=Y+L；Z=0
The analytic modell analytical model in temperature field so in limited big plane are as follows:
The analytic modell analytical model of temperatures above field calculates in MathCAD obtains thermo parameters method as shown in Figure 4；
Above-mentioned steps three (II) establish the numerical model (finite element analysis) of cup emery wheel flat surface grinding, soft using ANSYS
APDL language in part programs, and detailed process is as shown in Figure 5:
(1) definition unit type, material parameter；
According to the example calculation data of grinding temperature field, Three dimensional transient heat transfer is carried out using the SOLID70 unit in ANSYS
Analysis, material processed is composite material, and material parameter mainly includes density p, thermal coefficient kwWith specific heat under constant-pressure conditions
Hold c, numerical value is subject to material parameter given in step 2.
(2) workpiece three-dimensional entity model is established；
Workpiece shapes are simple in this example, simple using parametric modeling, quick, efficient.Workpiece size be respectively (it is long ×
It is wide × high): 0.3m × 0.15m × 0.015m
(3) grid is generated；
The division of grid will have a direct impact on the accuracy of emulation in Three dimensional transient model.Size of mesh opening is too small to lead
Cause simulation time too long or even collapse, and the excessive result precision that will cause of size of mesh opening reduces.For optimization Simulation process, remote
Side from grinding skin uses the grid of larger size, and the side grid far from grinding surface is set as 0.5mm in this modeling；And
Grinding Contact surface uses the higher grid of precision, and contact surface grids are set as 0.2mm in this modeling.
(4) apply the boundary conditions such as convection current；
Figure specifically includes that initial temperature and the cross-ventilation coefficient of heat transfer to boundary condition in this experiment.
Setting initial temperature value is T0=20 DEG C, the cross-ventilation coefficient of heat transfer is h=20W/ (m2·K)。
(5) load of non-homogeneous heat source model；
The load of non-homogeneous heat source model specifically includes, and starts to start recursive subroutine (i.e. loading procedure), first in son
It is N that load step number is defined in program, local cylindrical coordinate is secondly established under global cartesian coordinate system, and select loading area
Node, then apply nonuniform heat flux load, and the generation of nonuniform heat flux load in selected region
Mode is as follows: saving after being edited using the Functions editor in ANSYS to non-homogeneous heat source model, it is necessary to save filename
There is .func extension name, then open the file of preservation and export the heat source array for generating array form, later in selected region
Load.Specific loading method is as shown in Figure 5.
(6) it solves；
Solution procedure is continuous cyclic process, deletes load after solving once, if solving frequency n < N, then heavy
Established in multiple step (5) local cylindrical coordinate and its later the step of, end loop subprogram when solving frequency n >=N.
(7) result treatment.
Numerical model result is checked using post-processing module.If result is correct, temperature prediction will be terminated, otherwise to grid
Be adjusted after regenerating continue to the boundary conditions such as convection current and later the step of.
The modeling of numerical model is carried out using APDL Parametric Language.The numerical model in the present embodiment temperature field such as Fig. 6 institute
Show.
Temperature field image is acquired using high definition thermal imaging system, is compared.High definition thermal imaging system 6 in described Fig. 1
The analytic modell analytical model in temperature field when collected models for temperature field is transferred to analysis verifying cup emery wheel flat surface grinding in computer 10
With the accuracy of numerical model, the purpose of grinding temperature prediction is finally reached.Thermal imaging system acquisition temperature field as shown in fig. 7,
The measured value of four mark points in Fig. 7 is as shown in table 2 compared with Fig. 4 analytic modell analytical model predicted value, the precision of prediction of grinding temperature
Reach 8% or so.
The comparison of table 2 predicted value and experiment value
Three positions A, B and C using K-type thermocouple 3 on 4 surface of workpiece carry out temperature acquisition as shown in fig. 6, and will adopt
The data of collection are transferred to analysis in computer 10 by temperature transmitter 8 and data collecting card 9 and obtain: the result of numerical model prediction
There is the preferable goodness of fit with the temperature curve of experimental result, as shown in Figure 8.
The present invention does not address place and is suitable for the prior art.
Claims (4)
1. a kind of cup emery wheel flat surface grinding temperature predicting method based on non-homogeneous heat source model, this method includes following step
It is rapid:
Step 1: setting grinding parameter before grinding, grinding force when using force sensor measuring cup emery wheel flat surface grinding；
Step 2: the feature when present Research and material of grinding force distribution when analysis cupuliform Grinding wheel Grinder remove, root
According to power relationship corresponding with heat, establish in the circumferential and radial non-homogeneous heat source model in different functions distribution；
Step 3: based on the non-homogeneous heat source model in step 2, establishing the analytic modell analytical model and/or numerical model in temperature field,
Cup emery wheel flat surface grinding parameter to be predicted is substituted into above-mentioned analytic modell analytical model and/or numerical analysis model to obtain accordingly in advance
Testing temperature.
2. the cup emery wheel flat surface grinding temperature predicting method according to claim 1 based on non-homogeneous heat source model, institute
Stating non-homogeneous heat source model includes cutting heat source model and frictional heat source model,
Assuming that cutting heat is in cosine distribution in grinding wheel front end face, then heat Q is cutcutting·RwIt is indicated with formula (7):
Wherein ε is real area contact coefficient；R1And R2It is the outer diameter and inner diameter of grinding wheel respectively；RwBetween workpiece and grinding wheel
Heat distribution rate；QcuttingIt is the heat generated by cutting force acting；φ is angle；q0The hot-fluid in section is close when for angle being 0
Degree then obtains q0Are as follows:
So cutting heat is indicated at circumferentially distributed q (φ) with formula (9):
Assuming that cutting heat is radially in chi square distribution in grinding wheel front end face, chi square function f (x) is indicated with formula (10):
Wherein c0For proportionality coefficient, k is freedom degree, takes the chi square function of k=4 by symmetry transformation are as follows:
The area S in the section in φ=0 are as follows:
It is obtained according to pulse area equal principle:
Then c is obtained0:
So cutting heat is indicated in radial distribution q (r) with formula (15):
The circumferential direction of simultaneous cutting heat and radial formula, which obtain cutting heat source model formula (16), to be indicated:
The distribution of the frictional heat source model is related with the distribution of frictional force, and in grinding process, abrasive wheel end face is contacted with workpiece
The frictional force that relative motion generates is uniformly distributed, therefore frictional heat source model is formula (17):
It is superimposed cutting heat source model to obtain non-homogeneous heat source model q (r, φ) with frictional heat source model, be indicated with formula (18):
3. the cup emery wheel flat surface grinding temperature predicting method according to claim 2 based on non-homogeneous heat source model,
It is characterized in that, the building process of the analytic modell analytical model is:
Continue plane heat source temperature field analytic modell analytical model including establishing on infinitely great workpiece are as follows:
Wherein c is the specific heat capacity of workpiece under constant-pressure conditions, J/ (kg DEG C)；ρ is density of material, kg/m3；α is thermal diffusivity, m2/
s；Q (r, φ) is heat point source density, W/m2；X, Y, Z are generalized coordinates systems；V is heat source movement speed, m/s；τ is time, unit
s；Thermal diffusivity α in formula is indicated with formula (20):
Then establish the limited big heat carrier temperature field limited by boundary condition, imagination insulation face another side symmetrically there is
One mirror image heat source, practical heat source and mirror image heat source use Γ respectivelyiIt indicates, is practical heat source when i=1, be mirror image when i=2 and 3
Heat source:
Wherein L be the distance between mirror image heat source and practical heat source, then in limited big plane temperature field analytic modell analytical model are as follows:
4. the cup emery wheel flat surface grinding temperature predicting method according to claim 2 based on non-homogeneous heat source model,
It is characterized in that, the establishment process of the numerical model is:
(1) definition unit type, material parameter；
(2) workpiece three-dimensional entity model is established；
(3) grid is generated；
(4) apply convection boundary condition；
(5) load of non-homogeneous heat source model: definition load step number is N, and part is secondly established under global cartesian coordinate system
Cylindrical coordinate, and the node of loading area is selected, then apply nonuniform heat flux load in selected region；
The generating mode of nonuniform heat flux load is: using the Functions editor in ANSYS to non-homogeneous heat source model into
It is saved after edlin .func extension name must be had by saving filename, then opened the file of preservation and exported generation array form
Heat source array, later selected region load；
(6) solve: solution procedure is continuous cyclic process, deletes load after solving once, if solving frequency n < N, that
Local cylindrical coordinate is established in return step (5), end loop loads when solving frequency n >=N；
(7) result treatment: check that numerical model as a result, if result is correct, will terminate temperature prediction, otherwise adjust to grid
It is whole or continue to after regenerating convection boundary condition and later the step of.
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| CN112861337A (en) * | 2021-02-01 | 2021-05-28 | 中国科学院宁波材料技术与工程研究所 | Surface temperature prediction method for heated carbon fiber heating wire |
| CN112861337B (en) * | 2021-02-01 | 2024-04-30 | 中国科学院宁波材料技术与工程研究所 | Surface temperature prediction method for heated carbon fiber heating wire |
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