CN108151885A - Non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model - Google Patents
Non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model Download PDFInfo
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- 238000000227 grinding Methods 0.000 title claims abstract description 218
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- 238000009826 distribution Methods 0.000 claims abstract description 27
- 238000011068 loading method Methods 0.000 claims abstract description 24
- 238000004088 simulation Methods 0.000 claims abstract description 19
- 238000000205 computational method Methods 0.000 claims abstract description 6
- 239000000463 material Substances 0.000 claims description 36
- 238000004458 analytical method Methods 0.000 claims description 13
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- 239000007787 solid Substances 0.000 description 2
- 230000003685 thermal hair damage Effects 0.000 description 2
- 241001184547 Agrostis capillaris Species 0.000 description 1
- 206010020843 Hyperthermia Diseases 0.000 description 1
- 125000000174 L-prolyl group Chemical group [H]N1C([H])([H])C([H])([H])C([H])([H])[C@@]1([H])C(*)=O 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J5/00—Radiation pyrometry, e.g. infrared or optical thermometry
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Abstract
The invention discloses a kind of non-circular profile Work piece high-speed grinding temperature Forecasting Methodologies based on variable heat source model, include the following steps：Acquire non-circular profile Work piece high-speed grinding process power and temperature data；Establish non-circular profile grinding variable heat source distributed model；Based on variable heat source distributed model and not rounded curve surface grinding heat source loading method, non-circular profile Work piece high-speed grinding process temperature finite element simulation is carried out；Heat distribution ratio computational methods based on workpiece surface temperature correct heat flow density.The present invention is directed to non-circular profile Work piece high-speed grinding process, establish the variable heat source distributed model suitable for non-circular profile grinding and hot distribution ratio computational methods, it is proposed a kind of heat source loading method suitable for the emulation of non-circular profile grinding temperature, solve the problems, such as that non-round surface heat source loads, the temperature field of each grinding arc area in energy Accurate Prediction non-circular profile Work piece high-speed grinding process.Compared with prior art, this method is easy to operate, strong applicability, and accuracy is high.
Description
Technical field
The present invention relates to a kind of non-circular profile Work piece high-speed grinding temperature Forecasting Methodologies based on variable heat source model.
Background technology
Non-circular profile workpiece has obtained widely as internal combustion engine, the critical component of engine in fields such as ship, automobiles
Using precision, the quality on surface, the degree of burn of processing directly decide the work quality and efficiency of engine.Non-
Amount of heat is often generated in circle contour Work piece high-speed grinding process, major part enters workpiece and sand in the form of thermal energy
Wheel, causes grinding arc area local temperature drastically to increase, and greatly influences the surface integrity and its usability of non-circular profile workpiece
Can or even it cause the thermal damage's (burn, crackle, residual stress including surface etc.) for having ground surface, this will lead to not rounded wheel
The reduction of wide workpiece wear resistance and the decline of anti-fatigue ability, influence its reliability and service life.
Contact length and material removing rate is rapid when non-circular profile workpiece leads to grinding due to its complicated contour shape
Variation and the continuous movement of contact point, the research of existing grinding heat are concentrated mainly on flat surface grinding and cylindricalo grinding, and for
The research of the grinding heat of non-circular profile is deep not enough, the basic grinding model of original chip thickness, grinding energy and temperature
It is poorly suitable in non-circular profile high-speed grinding.Therefore, suitable heat source model is established, rapidly and accurately predicts that grinding temperature is
It rationally designs working process parameter and controls the premise of thermal damage, to further improving non-circular profile Grinding Machining Quality and production
Efficiency realizes high-precision, low cost, high efficiency and the intelligence of its production and processing, has very important significance.
Invention content
In order to solve the above technical problem, the present invention provides it is a kind of it is easy to operate, precision of prediction is high based on variable heat source
The non-circular profile Work piece high-speed grinding temperature Forecasting Methodology of model.
Technical proposal that the invention solves the above-mentioned problems is：A kind of non-circular profile Work piece high-speed based on variable heat source model
Grinding temperature Forecasting Methodology, includes the following steps：
Step 1：Acquire non-circular profile Work piece high-speed grinding process power and temperature data；
Step 2：Non-circular profile Work piece high-speed grinding geometry motion characteristic and its relationship between grinding heat are analyzed,
Grinding Contact arc length and grinding points linear velocity computation model are established, derives non-circular profile grinding variable heat source distributed model；
Step 3：Based on variable heat source distributed model and not rounded curve surface grinding heat source loading method, non-circular profile work is carried out
Part high-speed grinding process temperature finite element simulation；
Step 4：Heat distribution ratio computational methods based on workpiece surface temperature correct heat flow density.
The above-mentioned non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, in the step 1,
By the non-circular profile clamping workpiece of temperature to be predicted in the grinding temperature measuring device comprising thermal infrared imager, digital power meter
Grinding process experiment is carried out, thermal infrared imager is directed at practical grinding area and acquires not rounded workpiece profile and grinding wheel side surface contact arc
Area's temperature, digital power meter measure grinding wheel spindle system power.
The above-mentioned non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, the step 2 are specific
Step is
Non-circular profile workpiece grinding process is regarded to the superposition of the cylindricalo grinding of countless different curvature radius as, in grinding points
Corner isPosition, geometrical contact arc lengthIt is expressed as：
In formula, vwFor workpiece linear velocity, vsFor grinding speed, apFor grinding depth, rsFor grinding wheel radius,To connect
The radius of curvature of workpiece profile at contact, " ± " are respectively used to inverse mill and down grinding；
Grinding wheel and the mobile linear velocity v at cam ground pointtIt is expressed as：
vt=vw(sin(θ+α)tanθ+cos(θ+α))
In formula, δ represents the corner of non-circular profile workpiece, the lift that s (δ) is workpiece corner when being δ, r0For workpiece basic circle half
Diameter；
Variable heat source distributed model is expressed as：
In formulaFor grinding points polar diameter,
Non-circular profile is ground variable heat source distributed mode with polar angle θi, grinding points cornerChange and change, embody contour curve
With the continually changing feature of Grinding Contact arc length.
The above-mentioned non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model is imitated in the step 3
Really the specific steps are
3-1) setting unit type, material properties；
3-2) establish non-circular profile workpiece threedimensional model；
3-3) grid division；
Transient analysis parameter and boundary condition 3-4) are set；
3-5) transient heat conduction is analyzed；
3-6) moving heat source loads；
3-7) interpretation of result.
The above-mentioned non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, the step 3-5)
In, the heat transfer control differential equation in Grinding Process is：
In formula：Vx, Vy, VzFor medium conduction velocity；ρ is workpiece material density；C is material specific heat capacity；T is workpiece surface
Temperature；K is the thermal conductivity factor of material；Represent being thermally generated for unit volume；
Equivalent integration forms：
In formula, vol is unit volume,hfFor convection transfer rate；TBFor environment temperature；δT
Dummy variables for temperature；S2Application area for heat flux；S3Application area for convection current；{v}TRepresent the movement of moving heat sources
The derivative of rate against temperature；[D] represents material thermal conductivity attribute matrix；q*Represent heat flow density corresponding with elementary solution；
The polynomial expression that unit junction temperature is set as to unknown number is as follows：
T={ N }T{Te}
In formula, { N }TFor unit shape function；{TeIt is cell node temperature arrowhead amount；
The thermal gradient vector sum hot-fluid of each unit：
{ a }={ L }T=[B] { Te}
In formula, { a } is thermal gradient vector；[B]={ L }T[N]；
{ q }=[D] { L }T=[D] [B] { Te}=[D] { a }
In formula, [N] represents cell node interpolating function matrix, and { q } represents hot-fluid；
The energy relations of distribution of contact zone are：
qt=qw+qs
In formula, qtRepresent the total heat flow density value in contact zone；RwsIndicate entry into the heat distribution ratio of workpiece and grinding wheel；qwTable
Show the heat flow density value for flowing into workpiece；qsRepresent the heat flow density value of inflow grinding wheel；βwCoefficient is thermally contacted for workpiece material；kwFor
The thermal conductivity factor of workpiece material；ρwFor workpiece material density；cwSpecific heat capacity for workpiece material；kgAbrasive grain thermal conductivity factor；r0For mill
Grain effective contact radius；B is polishing width；P is grinding power；
The heat flow density applied with the variation of time is also constantly changing, each load applied is walked, often
Load value, time step and the load step type of one step need to define, and each load step is divided into multiple sub-steps, initially
Time step setting is shown below：
ITS=lδ 2/4k
In formula, lδFor the element length along direction of heat flow thermal gradient maximum, k is the thermal conductivity factor of material.
The above-mentioned non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, the step 3-6)
In, non-circular profile face is carried out segment processing by not rounded curve surface grinding heat source loading method according to practical grinding situation, establishes grinding
Region and the correspondence of time when being ground certain section of contoured surface, section grinding arc are replaced with its secant, by heat flow density edge
On secant direction projection to selected coordinate, the corresponding moment is calculated along the load value on the coordinate direction, is loaded；Work as grinding
To subsequent time, the tangential direction for being ground arc changes, and the loading direction of heat flow density also accordingly changes, and projects to coordinate
Specific load value also changes therewith on axis, at this moment according to the ratio of real load value and computational theory value as correction factor,
The load value in the moment reference axis is corrected with this coefficient, and deletes last moment institute's loaded load, then add again by correction value
It carries, to ensure the correct loading of this moment thermal force；Next this step is constantly repeated, carries out the heat in entire non-circular profile face
Source loads, until completing all time steps.
The above-mentioned non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, the tool of the step 4
Body step is
4-1) the non-circular profile grinding process workpiece surface temperature measured by one technological experiment of analytical procedure and in real time grinding
Power calculates the net grinding power P in non-circular profile Work piece high-speed grinding processt：
Pt=PGR-PEM
In formula, PGRFor grinding power, PEMFor grinding machine no-load power, obtained by digital power meter measurement；
4-2) grinding heat derives from grinding power, therefore the heat flow density value q that contact zone is totaltCalculation formula is：
F in formulatFor tangential grinding force；
4-3) heat distribution ratio is carried out according to the theory of distribution model of existing grinding heat it is assumed that and based on variable heat source mould
Type carries out the finite element simulation of grinding temperature, is then compared with observed temperature, when error is less than 6% between the two, really
The fixed corresponding heat distribution ratio into workpiece of non-circular profile corner；
4-4) carried out again based on variable heat source distributed model and not rounded curve surface grinding heat source loading method according to this distribution ratio
Temperature Field Simulation, the temperature in Accurate Prediction non-circular profile Work piece high-speed grinding process contact arc area.
The beneficial effects of the present invention are：The present invention acquires non-circular profile Work piece high-speed grinding process power and temperature first
Data, this process need not treat thermometric workpiece and carry out any specially treated, it is only necessary to carry out several groups of realities according to normal processing technology
It tests, Accurate Prediction is just carried out to the grinding temperature of the model workpiece, it is easy to operate, quick；Then analysis non-circular profile workpiece is high
Speed grinding geometry motion characteristic and its relationship between grinding heat, establish Grinding Contact arc length and grinding points linear velocity calculates
Model derives non-circular profile grinding variable heat source distributed model, establishes a true reflection non-circular profile workpiece grinding arc area
The heat source theoretical model of heat transfer process, improves simulation accuracy；Then it proposes a kind of suitable for the grinding of not rounded curved surface profile
Heat source loading method solves the problems, such as non-round surface heat source loading, can Accurate Prediction non-circular profile Work piece high-speed grinding process
In each grinding arc area temperature field, based on variable heat source distributed model and not rounded curve surface grinding heat source loading method, carry out not rounded
Variable heat source model is accurately substituted into non-circular profile workpiece finite element and imitated by contoured workpiece high-speed grinding process temperature finite element simulation
In true transient state temperature field, the solution of non-circular profile Work piece high-speed grinding process transient state temperature field is realized；It is finally based on workpiece surface
The heat distribution ratio computational methods of temperature correct the heat distribution ratio calculating side of heat flow density, Binding experiment and finite element simulation
Method improves the validity and practicability of simulation result.
Description of the drawings
Fig. 1 is the flow chart of the present invention.
Fig. 2 is the structure diagram of grinding temperature measuring device of the present invention.
Fig. 3 analyses schematic diagram for non-circular profile geometry motion credit of the present invention.
Fig. 4 is the not rounded curve surface grinding heat source loading schematic diagram of the present invention.
Fig. 5 is the heat distribution ratio calculation flow chart the present invention is based on workpiece surface temperature.
Fig. 6 is present invention emulation and experimental result comparison diagram.
Fig. 7 is the error schematic diagram of measured value and simulation value of the present invention.
Specific embodiment
The present invention is further illustrated with reference to the accompanying drawings and examples.
Test specimen used in this example is the th465 type camshafts in certain automobile engine, and material is chilled cast iron alloy
(HT250GB9439-88), there are 4 cylinder, 8 cams, respectively air inlet and exhaust.The profile molded line of cam is complex, molded line
It is generally made of basic circle section, lift section, peach point, reverse-running section etc., each section of curve is how common bent for polynomial curve, sine and cosine
Line, parabola, compound cycloid etc..Therefore, the grinding of cam is typical non-circular profile complex surface part processing.
It is as shown in the table for the relevant parameter of th465 type camshaft parts.
Table 1
A kind of non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, as shown in Figure 1, including
Following steps：
Step 1：Acquire non-circular profile Work piece high-speed grinding process power and temperature data.
By 4 clamping of th465 types camshaft of temperature to be predicted as shown in Figure 2 comprising grinding machine, thermal infrared imager 1, number
The grinding temperature measurement of power meter, data acquisition and analysis system, centre with endlong movement 2, grinding wheel 3, outer circle dynamometer amplifier, industrial personal computer
Grinding process experiment is carried out in device, thermal infrared imager is directed at practical grinding area and acquires not rounded workpiece profile and grinding wheel side surface
Contact arc area temperature, digital power meter measure grinding wheel spindle system power.
Step 2：Non-circular profile Work piece high-speed grinding geometry motion characteristic and its relationship between grinding heat are analyzed,
Grinding Contact arc length and grinding points linear velocity computation model are established, derives non-circular profile grinding variable heat source distributed model.
Camshaft high-speed numerical control grinding is ground as typical non-circular profile, except basic circle position is ground situation and cylindricalo grinding
It is equally outer, always the grinding condition at other positions constantly changes with cam contour.Due to camshaft wheel profile not connecting into movement
Continuous and its radius of curvature transient change, grinding points linear velocity and Grinding Contact arc length in grinding process are dynamic changes,
Constantly change so as to cause material removal rate, and then cause the discontinuous variation of grinding temperature, grinding area localized hyperthermia phenomenon occur,
Cause Grinding heat injury.Therefore, cam high-speed grinding geometry motion characteristic and its relationship between grinding heat are analyzed, is established
Correlation computations model is the key point of research control camshaft high-speed grinding temperature.
As shown in figure 3, cam lifting curve general expression is s=s (δ), wherein δ represents the corner of cam, and s represents convex
Take turns lift when corner is δ, P is the extended line of the grinding wheel center of circle and contact point line and the intersection point of cam z-axis, C points for grinding wheel with
Cam ground contact point, is represented by with polar coordinatesFor the polar diameter of cam ground point,For grinding points
Corner.
Non-circular profile workpiece grinding process is regarded to the superposition of the cylindricalo grinding of countless different curvature radius as, in grinding points
Corner isPosition, geometrical contact arc lengthIt is expressed as：
In formula, vwFor workpiece linear velocity, vsFor grinding speed, apFor grinding depth, rsFor grinding wheel radius,To connect
The radius of curvature of workpiece profile at contact, " ± " are respectively used to inverse mill and down grinding；
Grinding wheel and the mobile linear velocity v at cam ground pointtIt is expressed as：
vt=vw(sin(θ+α)tanθ+cos(θ+α))
In formula, δ represents the corner of non-circular profile workpiece, the lift that s (δ) is workpiece corner when being δ, r0For workpiece basic circle half
Diameter；
Variable heat source distributed model is expressed as：
In formulaFor grinding points polar diameter,
Non-circular profile is ground variable heat source distributed mode with polar angle θi, grinding points cornerChange and change, embody contour curve
With the continually changing feature of Grinding Contact arc length.
Step 3：Based on variable heat source distributed model and not rounded curve surface grinding heat source loading method, non-circular profile work is carried out
Part high-speed grinding process temperature finite element simulation.The specific steps are
3-1) setting unit type, material properties.
The selection of cell type：In the simulation analysis of non-circular profile grinding temperature, the selection of unit need to consider following several
A factor：(1) what is carried out is threedimensional FEM, therefore selected unit must be 3D solid unit；(2) cell type selected by
It has to that Nonlinear Transient heat analysis can be suitable for.
According to the requirement of more than Unit selection, Three Dimensional Thermal solid element Solid90 is selected, which defines 20 sections
Point, each node is there are one temperature degree of freedom and the temperature shape function comprising coordination, suitable for three-dimensional Nonlinear Transient heat point
Analysis problem is particularly suitable for the boundary of description bending, is suitble to the modeling analysis of non-circular profile part.
Material properties define：By taking camshaft as an example, camshaft material for test is generally chilled cast iron, chilled cast iron material phase
Closing attribute, it is as shown in the table：
Chilled cast iron association attributes
3-2) establish non-circular profile workpiece threedimensional model.
In ANSYS, can finite element model be established by following 3 kinds of methods：GUI (user is interactive), APDL (parametrizations
Modeling) and the importing of the 3rd side's software (such as UG, Pro/E).GUI modes model have the advantages that it is intuitive, convenient, but model when
Operate comparatively laborious, efficiency is low, and modification model is relatively difficult during error；The advantages of 3rd side's lead-in mode is efficient, but is also had
Feature is easily lost during importing, repairing is relatively difficult.So the threedimensional model of non-circular profile is carried out using parametric modeling mode
Foundation.
If the discrete point on known Noncircular profile curve, Noncircular profile curve equation can be obtained using Mathematical Fitting.
According to the characteristics of parametric modeling, on the basis of the fitting of previous non-circular profile lift discrete offset point curve, using joining three times
Number spline curve fitting carries out non-circular profile lift repeatedly cycle fitting, after Noncircular profile curve fitting finishes, to utilize
Line generates face, then stretches adult using face, and generation body is stretched along face, and so far, non-circular profile modeling finishes.
3-3) grid division.
After three-dimensional entity model is created, the division of finite element grid is carried out to physical model.In mesh generation,
The method that (Volume Sweep) is divided using body sweeping.
The number of unit of mesh generation will influence the size of the precision and scale of simulation calculation, so determining number of grid
When should consider following two factors：
On the one hand it is in the grinding process of non-circular profile, non-circular profile skin temperature occurs drastically to become with heat source movement
Change, very big temperature gradient formed along grinding arc area direction, if mesh generation is too much, very big error will be generated,
Even there is the discontinuous situation of a certain regional temperature, this phenomenon of distortion for causing result of calculation is not allow to occur；
On the other hand, though computational accuracy can draw thinner and increase with unit grid, calculating process can be because generating
Excessive unit number, number of nodes and number of degrees of freedom, and become sufficiently complex, higher and operation time are required to computer hardware
Can be longer, and grid is being encrypted to a certain extent, and the raising of precision as a result is not notable.
Simultaneously, it is contemplated that non-circular profile grinding process grinding depth is smaller in itself, in grid division, can grind workpiece
Surface and surface to be ground are regarded as same surface, ignore influence of the grinding depth to grinding temperature.On this basis, pass through comparison
Solution procedure under 0.1,0.05,0.01 three kind of different units size is with as a result, find 0.05 compared with 0.01, simulation result phase
Poor little, simulation time but shortens dramatically.Therefore, cell size is set to 0.05, by non-circular profile physical model grid division
Discrete physical model can be obtained afterwards, and unit sum is 516300, node total number 546444.
Transient analysis parameter and boundary condition 3-4) are set.
3-5) transient heat conduction is analyzed.
Heat transfer control differential equation in Grinding Process is：
In formula：Vx, Vy, VzFor medium conduction velocity；ρ is workpiece material density；C is material specific heat capacity；T is workpiece surface
Temperature；K is the thermal conductivity factor of material；.Q.. being thermally generated for unit volume is represented；
Equivalent integration forms：
In formula, vol is unit volume,hfFor convection transfer rate；TBFor environment temperature；δT
Dummy variables for temperature；S2Application area for heat flux；S3Application area for convection current；{v}TRepresent the movement of moving heat sources
The derivative of rate against temperature；[D] represents material thermal conductivity attribute matrix；q*Represent heat flow density corresponding with elementary solution；
The polynomial expression that unit junction temperature is set as to unknown number is as follows：
T={ N }T{Te}
In formula, { N }TFor unit shape function；{TeIt is cell node temperature arrowhead amount；
The thermal gradient vector sum hot-fluid of each unit：
{ a }={ L }T=[B] { Te}
In formula, { a } is thermal gradient vector；[B]={ L }T[N]；
{ q }=[D] { L }T=[D] [B] { Te}=[D] { a }
In formula, [N] represents cell node interpolating function matrix, and { q } represents hot-fluid；
The energy relations of distribution of contact zone are：
qt=qw+qs
In formula, qtRepresent the total heat flow density value in contact zone；RwsIndicate entry into the heat distribution ratio of workpiece and grinding wheel；qwTable
Show the heat flow density value for flowing into workpiece；qsRepresent the heat flow density value of inflow grinding wheel；βwCoefficient is thermally contacted for workpiece material；kwFor
The thermal conductivity factor of workpiece material；ρwFor workpiece material density；cwSpecific heat capacity for workpiece material；kgAbrasive grain thermal conductivity factor；r0For mill
Grain effective contact radius；B is polishing width；P is grinding power.
The heat flow density applied with the variation of time is also constantly changing, each load applied is walked, often
Load value, time step and the load step type of one step need to define, and each load step is divided into multiple sub-steps, initially
Time step setting is shown below：
ITS=lδ 2/4k
In formula, lδFor the element length along direction of heat flow thermal gradient maximum, k is the thermal conductivity factor of material.
3-6) moving heat source loads；
During cam ground, heat flow density direction changes with size in the progress with grinding, how to select
Suitable coordinate is taken to realize that the loading of heat source is the key point of Camshaft Grinding temperature simulation.The present invention proposes that one kind is suitable for
Non- round surface moving heat source loading method, schematic diagram are as shown in Figure 4.
Simultaneously because the linkage grinding of camshaft X-C axis is not a continuous grinding process, feelings are ground thus according to practical
Non-circular profile face is carried out segment processing by condition, establishes grinding area and the correspondence of time, will when being ground certain section of contoured surface
Section grinding arc is replaced with its secant, by heat flow density along secant direction projection to selected coordinate, calculates corresponding moment edge
Load value on the coordinate direction, is loaded.
When being ground to subsequent time, the tangential direction for being ground arc changes, and the loading direction of heat flow density also accordingly changes
Become, project to specific load value in reference axis and also change therewith, at this moment according to the ratio of real load value and computational theory value
Value is used as correction factor, corrects the load value in the moment reference axis with this coefficient, and delete last moment institute's loaded load, then
It is reloaded by correction value, to ensure the correct loading of this moment thermal force；Next this step is constantly repeated, is carried out entire
The heat source loading in non-circular profile face, until completing all time steps.
3-7) interpretation of result.
Step 4：Heat distribution ratio computational methods based on workpiece surface temperature correct heat flow density.Heat as shown in Figure 5
Distribution ratio calculation process, the specific steps are：
4-1) the non-circular profile grinding process workpiece surface temperature measured by one technological experiment of analytical procedure and in real time grinding
Power calculates the net grinding power P in non-circular profile Work piece high-speed grinding processt：
Pt=PGR-PEM
In formula, PGRFor grinding power, PEMFor grinding machine no-load power, obtained by digital power meter measurement；
4-2) grinding heat derives from grinding power, therefore the heat flow density value q that contact zone is totaltCalculation formula is：
F in formulatFor tangential grinding force；
4-3) heat distribution ratio is carried out according to the theory of distribution model of existing grinding heat it is assumed that and based on variable heat source mould
Type carry out grinding temperature finite element simulation, then compared with observed temperature (as shown in Figure 6), on the basis of Fig. 6 into
The processing of one step takes the corresponding simulated temperature of every corner of Fig. 6 and the difference divided by observed temperature of observed temperature and then again absolutely
Value, obtains error (as shown in Figure 7) between the two, when error is less than 6% between the two, determines the non-circular profile corner pair
The heat distribution ratio into workpiece answered；
4-4) carried out again based on variable heat source distributed model and not rounded curve surface grinding heat source loading method according to this distribution ratio
Temperature Field Simulation, the temperature in Accurate Prediction non-circular profile Work piece high-speed grinding process contact arc area.
Claims (7)
1. a kind of non-circular profile Work piece high-speed grinding temperature Forecasting Methodology based on variable heat source model, includes the following steps：
Step 1：Acquire non-circular profile Work piece high-speed grinding process power and temperature data；
Step 2：Non-circular profile Work piece high-speed grinding geometry motion characteristic and its relationship between grinding heat are analyzed, is established
Grinding Contact arc length and grinding points linear velocity computation model derive non-circular profile grinding variable heat source distributed model；
Step 3：Based on variable heat source distributed model and not rounded curve surface grinding heat source loading method, it is high to carry out non-circular profile workpiece
Fast grinding process temperature finite element simulation；
Step 4：Heat distribution ratio computational methods based on workpiece surface temperature correct heat flow density.
2. the non-circular profile Work piece high-speed grinding temperature Forecasting Methodology according to claim 1 based on variable heat source model,
It is characterized in that：In the step 1, the non-circular profile clamping workpiece of temperature to be predicted is being included into thermal infrared imager, digital work(
Grinding process experiment is carried out in the grinding temperature measuring device of rate meter, thermal infrared imager is directed at practical grinding area and acquires non-sired results
Part profile and grinding wheel side surface contact arc area temperature, digital power meter measure grinding wheel spindle system power.
3. the non-circular profile Work piece high-speed grinding temperature Forecasting Methodology according to claim 1 based on variable heat source model,
It is characterized in that：The step 2 the specific steps are
Non-circular profile workpiece grinding process is regarded to the superposition of the cylindricalo grinding of countless different curvature radius as, in grinding points corner
ForPosition, geometrical contact arc lengthIt is expressed as：
In formula, vwFor workpiece linear velocity, vsFor grinding speed, apFor grinding depth, rsFor grinding wheel radius,For contact point
Locate the radius of curvature of workpiece profile, " ± " is respectively used to inverse mill and down grinding；
Grinding wheel and the mobile linear velocity v at cam ground pointtIt is expressed as：
vt=vw(sin(θ+α)tanθ+cos(θ+α))
In formula, δ represents the corner of non-circular profile workpiece, the lift that s (δ) is workpiece corner when being δ, r0For workpiece base radius；
Variable heat source distributed model is expressed as：
In formulaFor grinding points polar diameter,
Non-circular profile is ground variable heat source distributed mode with polar angle θi, grinding points cornerChange and change, embody contour curve and mill
Cut the continually changing feature of contact arc length.
4. the non-circular profile Work piece high-speed grinding temperature Forecasting Methodology according to claim 1 based on variable heat source model,
It is characterized in that：Emulated in the step 3 the specific steps are
3-1) setting unit type, material properties；
3-2) establish non-circular profile workpiece threedimensional model；
3-3) grid division；
Transient analysis parameter and boundary condition 3-4) are set；
3-5) transient heat conduction is analyzed；
3-6) moving heat source loads；
3-7) interpretation of result.
5. the non-circular profile Work piece high-speed grinding temperature Forecasting Methodology according to claim 4 based on variable heat source model,
It is characterized in that：The step 3-5) in, the heat transfer control differential equation in Grinding Process is：
In formula：Vx, Vy, VzFor medium conduction velocity；ρ is workpiece material density；C is material specific heat capacity；T is workpiece surface temperature；
K is the thermal conductivity factor of material；Represent being thermally generated for unit volume；
Equivalent integration forms：
In formula, vol is unit volume,hfFor convection transfer rate；TBFor environment temperature；δ T are temperature
Dummy variables；S2Application area for heat flux；S3Application area for convection current；{v}TRepresent the rate travel pair of moving heat sources
The derivative of temperature；[D] represents material thermal conductivity attribute matrix；q*Represent heat flow density corresponding with elementary solution；
The polynomial expression that unit junction temperature is set as to unknown number is as follows：
T={ N }T{Te}
In formula, { N }TFor unit shape function；{TeIt is cell node temperature arrowhead amount；
The thermal gradient vector sum hot-fluid of each unit：
{ a }={ L }T=[B] { Te}
In formula, { a } is thermal gradient vector；[B]={ L }T[N]；
{ q }=[D] { L }T=[D] [B] { Te}=[D] { a }
In formula, [N] represents cell node interpolating function matrix, and { q } represents hot-fluid；
The energy relations of distribution of contact zone are：
qt=qw+qs
In formula, qtRepresent the total heat flow density value in contact zone；RwsIndicate entry into the heat distribution ratio of workpiece and grinding wheel；qwRepresent stream
Enter the heat flow density value of workpiece；qsRepresent the heat flow density value of inflow grinding wheel；βwCoefficient is thermally contacted for workpiece material；kwFor workpiece
The thermal conductivity factor of material；ρwFor workpiece material density；cwSpecific heat capacity for workpiece material；kgAbrasive grain thermal conductivity factor；r0Have for abrasive grain
Imitate contact radius；B is polishing width；P is grinding power；
The heat flow density applied with the variation of time is also constantly changing, each load applied is walked, Mei Yibu
Load value, time step and load step type need to define, and by each load step be divided into multiple sub-steps, initial time
Step-length setting is shown below：
ITS=lδ 2/4k
In formula, lδFor the element length along direction of heat flow thermal gradient maximum, k is the thermal conductivity factor of material.
6. the non-circular profile Work piece high-speed grinding temperature Forecasting Methodology according to claim 4 based on variable heat source model,
It is characterized in that：The step 3-6) in, not rounded curve surface grinding heat source loading method is according to the practical situation that is ground by non-circular profile
Face carries out segment processing, establishes grinding area and the correspondence of time, and when being ground certain section of contoured surface, section grinding arc is used
Its secant replaces, and by heat flow density along secant direction projection to selected coordinate, calculates the corresponding moment along the coordinate direction
Load value, loaded；When being ground to subsequent time, the tangential direction for being ground arc changes, the loading direction of heat flow density
It accordingly changes, projects to specific load value in reference axis and also change therewith, at this moment according to real load value with calculating
The ratio of theoretical value corrects the load value in the moment reference axis, and delete last moment institute as correction factor with this coefficient
Loaded load, then reloaded by correction value, to ensure the correct loading of this moment thermal force；Next this step is constantly repeated
Suddenly, the heat source loading in entire non-circular profile face is carried out, until completing all time steps.
7. the non-circular profile Work piece high-speed grinding temperature Forecasting Methodology according to claim 4 based on variable heat source model,
It is characterized in that：The step 4 the specific steps are
4-1) the non-circular profile grinding process workpiece surface temperature measured by one technological experiment of analytical procedure and real-time grinding power,
Calculate the net grinding power P in non-circular profile Work piece high-speed grinding processt：
Pt=PGR-PEM
In formula, PGRFor grinding power, PEMFor grinding machine no-load power, obtained by digital power meter measurement；
4-2) grinding heat derives from grinding power, therefore the heat flow density value q that contact zone is totaltCalculation formula is：
F in formulatFor tangential grinding force；
4-3) according to the theory of distribution model of existing grinding heat to heat distribution ratio carry out it is assumed that and based on variable heat source model into
The finite element simulation of row grinding temperature, is then compared with observed temperature, and when error is less than 6% between the two, determining should
The corresponding heat distribution ratio into workpiece of non-circular profile corner；
4-4) carry out the temperature based on variable heat source distributed model and not rounded curve surface grinding heat source loading method again according to this distribution ratio
Spend field emulation, the temperature in Accurate Prediction non-circular profile Work piece high-speed grinding process contact arc area.
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