CN108262648B - Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method - Google Patents
Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method Download PDFInfo
- Publication number
- CN108262648B CN108262648B CN201810088844.4A CN201810088844A CN108262648B CN 108262648 B CN108262648 B CN 108262648B CN 201810088844 A CN201810088844 A CN 201810088844A CN 108262648 B CN108262648 B CN 108262648B
- Authority
- CN
- China
- Prior art keywords
- workpiece
- grinding
- abrasive grain
- point
- value
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 51
- 239000006061 abrasive grain Substances 0.000 claims abstract description 133
- 238000005070 sampling Methods 0.000 claims abstract description 30
- 238000009825 accumulation Methods 0.000 claims abstract description 29
- 230000005489 elastic deformation Effects 0.000 claims abstract description 23
- 239000011159 matrix material Substances 0.000 claims description 30
- 239000000463 material Substances 0.000 claims description 26
- 238000013178 mathematical model Methods 0.000 claims description 21
- 238000004364 calculation method Methods 0.000 claims description 9
- 238000000926 separation method Methods 0.000 claims description 8
- 238000002715 modification method Methods 0.000 claims description 6
- 239000002245 particle Substances 0.000 claims description 5
- 238000005520 cutting process Methods 0.000 claims description 4
- 238000011084 recovery Methods 0.000 claims description 4
- 238000009795 derivation Methods 0.000 claims description 3
- 239000000428 dust Substances 0.000 claims description 3
- 238000005183 dynamical system Methods 0.000 claims description 3
- 239000004576 sand Substances 0.000 claims description 2
- 238000010189 synthetic method Methods 0.000 claims description 2
- 238000012876 topography Methods 0.000 claims description 2
- 238000004088 simulation Methods 0.000 abstract description 8
- 230000003068 static effect Effects 0.000 abstract description 4
- 238000003754 machining Methods 0.000 abstract description 3
- 238000010586 diagram Methods 0.000 description 9
- 238000005259 measurement Methods 0.000 description 9
- 230000008569 process Effects 0.000 description 6
- 238000012360 testing method Methods 0.000 description 6
- 238000005516 engineering process Methods 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 238000012545 processing Methods 0.000 description 3
- 238000012795 verification Methods 0.000 description 3
- 238000009826 distribution Methods 0.000 description 2
- 230000003746 surface roughness Effects 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 229910001651 emery Inorganic materials 0.000 description 1
- 230000002708 enhancing effect Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000035800 maturation Effects 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 238000005498 polishing Methods 0.000 description 1
- 230000008439 repair process Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000004513 sizing Methods 0.000 description 1
- 230000007306 turnover Effects 0.000 description 1
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
- B24B1/04—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes subjecting the grinding or polishing tools, the abrading or polishing medium or work to vibration, e.g. grinding with ultrasonic frequency
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mechanical Engineering (AREA)
- Grinding And Polishing Of Tertiary Curved Surfaces And Surfaces With Complex Shapes (AREA)
Abstract
The present invention relates to a kind of axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method, ultrasonic vibration can be followed dynamically to choose abrasive grain profile sampled point.Grinding groove is established for the characteristics of axial ultrasonic vibration on this basis to broaden model, it is further introduced into grinding elastic deformation model and plastic accumulation model is modified the dynamic outline method of sampling, realize the combination of geometric simulation and physical simulation, workpiece surface appearance prediction model is ultimately generated, and exports result figure.According to the simulation and prediction of workpiece surface appearance as a result, machined parameters can be in optimized selection in advance, to improve Grinding Machining Quality.Existing emulation mode is overcome due to the shortcomings that cannot being emulated when there is axial ultrasonic vibration using Static Sampling method.It has good practical value in grinding field.
Description
Technical field
The present invention relates to a kind of machine-building processing technology, in particular to a kind of axial direction based on dynamic outline sampling method is super
Acoustic vibration assistant grinding workpiece surface appearance simulated prediction method.
Background technique
Supersonic vibration assistant grinding is that the one kind for combining ultrasonic vibrating machining technology and plain grinding processing technology is answered
Close processing technology.The experimental results show that axial ultrasonic vibration-assisted grinding can obtain the workpiece surface of high quality.In order to
Analyse in depth the influence of axial ultrasonic vibration and grinding parameter to workpiece surface appearance wound at process, it is necessary to shake to axial ultrasonic
The workpiece surface appearance of dynamic auxiliary grinding is predicted.
In general, using workpiece topological matrix g in workpiece surface appearance predictionmnTo indicate workpiece surface appearance.I.e. in work
With the direction the x direction separation delta x and y separation delta y grid division on part surface.With the height value z (m, n) at grid lattice point P (m, n)
As workpiece topological matrix gmnIn element, as shown in Figure 1.Workpiece surface appearance emulation is actually to need to transport by mathematics
Calculate and calculates numerous abrasive grain workpiece topological matrixs after grinding on grinding wheel.
Conventional workpiece surface appearance calculation method needs to carry out Configuration of Grinding-wheel Surface static discrete sampling, is opened up with grinding wheel
Flutter matrix hijIt indicates.It is h (i, j) as grinding wheel using the height value of the sampled point H (i, j) on wheel face abrasive grain profile in Fig. 1
Topological matrix hijElement.When calculating the workpiece surface appearance of plain grinding, the sampled point H in grinding wheel topological matrix is successively taken out
(i, j) calculates its track, as shown in figure 1 curve 1.Then find out curve 1 passed through each workpiece topological matrix lattice point P (m,
N) the height value z (m, n) at place.It calculates by every track at lattice point P (m, n), seeking minimum value min (z (m, n)) is to grind
The workpiece surface final residual height of the point after cutting.After having found out the final residual height of each lattice point of workpiece surface
Obtain workpiece surface appearance.
But the workpiece surface appearance that this method is not suitable for axial ultrasonic vibration-assisted grinding calculates.Because of plain grinding
It is different with the grain motion trajectory of axial ultrasonic vibration-assisted grinding.Sampled point H (i, j) in plain grinding on abrasive grain profile
Motion profile (curve 1 in Fig. 1) exist only in one and be parallel in the section of Oxz plane, can all cover workpiece topology
On the lattice point of matrix.However in axial ultrasonic vibration-assisted grinding, the track of sampled point H (i, j) is space three-dimensional curve (figure
Curve 2 in 1), it is projected as curve 3 on plane Oxy, it can be observed that workpiece topological matrix cannot be completely covered in curve 3
Lattice point on, therefore can not at the lattice point P (m, n) of workpiece topological matrix the corresponding height value z (m, n) of calculated curve 2, from
And it is unable to get workpiece surface appearance.This is because indicating that Configuration of Grinding-wheel Surface is substantially preparatory with grinding wheel topological matrix
Ground statically samples abrasive grain profile.In the presence of having axial ultrasonic vibration, sampled point on grinding wheel cannot always with
The lattice point of workpiece surface is aligned, and also can not just carry out surface topography emulation.
In addition, being ground elastic deformation model and plastic accumulation in current grinding workpiece surface appearance emulation mode
Model is established under the conditions of plain grinding, and under axial ultrasonic vibration condition, due to there is grinding groove to broaden effect,
The two models also can be different.
Summary of the invention
The present invention be directed to existing emulation modes cannot be when there is axial ultrasonic vibration due to using Static Sampling method
The problem of being emulated proposes a kind of axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method, can be with
Abrasive grain profile sampled point is dynamically chosen with ultrasonic vibration.Grinding is established for the characteristics of axial ultrasonic vibration on this basis
Groove broadens model, is further introduced into grinding elastic deformation model and plastic accumulation model repairs the dynamic outline method of sampling
Just, the combination for realizing geometric simulation and physical simulation, ultimately generates workpiece surface appearance prediction model, and export result figure.
According to the simulation and prediction of workpiece surface appearance as a result, machined parameters can be in optimized selection in advance, add to improve grinding
Working medium amount.
The technical solution of the present invention is as follows: a kind of axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method,
Specifically comprise the following steps:
1) grinding parameter is inputted, Configuration of Grinding-wheel Surface mathematical model is imported:
Model indicates with matrix G, the information of one abrasive grain of element representation of every a line in matrix G, for i-th abrasive grain
Information, the coordinate (x ' including it in wheel face coordinate systemi, y 'i, z 'i) and abrasive grain shape simplification be spherical diameter dgi,
N abrasive grain is shared in grinding wheel numerical model, the form of matrix G is N × 4,
2) grain motion trajectory is calculated:
Using workpiece as stationary reference frame, workpiece coordinate system Oxyz is established, wherein x-axis feeds opposite direction along workpiece, and y-axis is along sand
Wheel shaft is to the position of origin O is selected in the workpiece surface highest point before grinding, during axial ultrasonic vibration-assisted grinding, grinds
The movement of grain consists of three parts: around grinding wheel spindle with angular velocity omegasCircular motion, along direction of feed relative to workpiece with linear speed
Spend vwLinear motion, along grinding wheel axially with respect to workpiece with amplitude A, ultrasonic vibration that frequency f is carried out；
T at the time of if grinding starts0=0s, the origin O ' of wheel face coordinate system is located at grinding wheel minimum point and is located at this time
The surface of workpiece coordinate system origin O, ultrasonic vibration initial phase are 0；
Any equation of locus of the abrasive grain i in workpiece coordinate system:
Wherein rsFor grinding wheel radius, t is from t0Moment starts the time of grain motion, LzFor grinding wheel axis to O it is vertical away from
From,
λ=1,2,3...., λ indicate the number of abrasive grain i incision workpiece, αiFor abrasive grain i to grinding wheel
The vertical line and O ' of axis arrive the angle between the vertical line of grinding wheel axis；
3) the dynamic outline method of sampling:
Workpiece topological matrix g is used in workpiece surface appearance predictionmnIndicate workpiece surface appearance, i.e., on the surface of the workpiece
With the direction the x direction separation delta x and y separation delta y grid division, using the height value z (m, n) at grid lattice point P (m, n) as workpiece
Topological matrix gmnIn element,
Firstly, the series of parallel sampled cross-section in plane Oyz is arranged on the surface of the workpiece, these sampled cross-sections cross workpiece
The lattice point of topological matrix is followed successively by 1,2,3 ... along the number of positive direction of the x-axis since O point, when grinding, a certain mill
Grain is in C1Point incision workpiece, in C2Point leaves workpiece, C1The sampled cross-section n on point the right1It is that first sampling interfered is cut
Face, C2The sampled cross-section n on the point left side2It is the last one, abrasive grain has sequentially passed through during being ground workpiece from n1To n2One
Series of samples section, therefore the scallop-height value for calculating each lattice point in these sampled cross-sections can find out abrasive grain grinding
Workpiece surface appearance afterwards, n1And n2Value can be found out by following formula
L in formula1For C1Point arrives the horizontal distance of workpiece coordinate system origin O, l2For C2Point arrives the horizontal distance of O, l1And l2's
Value can use abrasive grain equation of locus in step 2) and find out；
When calculating each lattice point scallop-height value in n-th of sampled cross-section, the sampled cross-section is calculated first and is sat to workpiece
The horizontal distance x of mark system origin On:
xn=(n-1) Δ x
By xnValue substitute into abrasive grain equation of locus that can to find out in sampled cross-section n abrasive grain center former to workpiece coordinate system
The horizontal distance y of point OnWith vertical range zn, then position of the abrasive grain profile in sampled cross-section n is assured that, abrasive grain profile
Equation indicates are as follows:
(y-yn)2+(z-zn)2=(dg/2)2
D in formulagFor abrasive grain diameter, in C1And C2Intermediate C3Point arrives C4Abrasive grain and workpiece interfere between point, C3Point is right
The lattice point P on side1(m1, n) and it is first lattice point interfered, C4The lattice point P on the point left side2(m2, n) and it is the last one, m1And m2
Value can be found out by following formula,
L in formula3For C3Point arrives the horizontal distance of workpiece coordinate system origin O, l4For C4Point arrives the horizontal distance of O point, l3And l4
Value can use abrasive grain profile equation and find out.
Then, from P1To P2A series of lattice points at abrasive grain profile is sampled, wherein a certain sampled point H (m, n) is arrived
The horizontal distance of workpiece coordinate system origin O is lm:
lm=(m-1) Δ y
By y=lmIt substitutes into and obtains following formula in abrasive grain profile equation, the ordinate z (m, n) of sampled point H (m, n) can be found out,
Assuming that the workpiece material interfered is completely removed, then the value of z (m, n) is exactly the workpiece remnants of the point after grinding
Height value.The coordinate value of sampled point H (m, n) is assigned to lattice point P (m, n), completes the update at the lattice point, similarly, updates sampling
From P in the n of section1Point arrives P2All lattice point coordinates of point complete the calculating in sampled cross-section n；When from n1To n2All samplings
After the completion of section all updates, so that it may which the workpiece surface appearance after obtaining single grain grinding is continued thereafter with and adjusted on this basis
It is updated with other abrasive grains, finally obtains complete workpiece surface appearance；
4) to the amendment of the method for sampling: the characteristics of being directed to axial ultrasonic vibration-assisted grinding establishes grinding groove and broadens
Model, and grinding elastic deformation model and plastic accumulation model are introduced on this basis, the dynamic outline method of sampling is repaired
Just.
The grinding groove model modification method that broadens is as follows in the step 4):
Groove contour is ellipse, ellipse short shaft dg, long axis de, the expression of groove contour equation are as follows:
dgAnd deRatio are as follows:
θ is grain motion speed vgWith the angle between sampled cross-section n, at sampled cross-section n, vgIt can be decomposed into along x-axis
Velocity component vxWith the velocity component v along y-axisy, it is obtained according to the synthetic method of movement:
vxAnd vyValue the derivation of time t can be obtained by abrasive grain equation of locus:
T in formulanAt the time of for abrasive grain center movement at sampled cross-section n, vsFor grinding speed, d can be obtainedeValue:
Work as deValue determine after, groove contour equation determines therewith, when there are axial ultrasonic vibration, using groove contour
Equation replaces the abrasive grain profile equation in step 3), and sampled point is chosen on groove contour.
Grinding elastic deformation model modification method is as follows in the step 4):
Assume to establish grinding elastic deformation theory's model, abrasive grain stress condition based on spherical wear particles and ideal plane grinding
Similar when to test Brinell hardness, abrasive grain is R by normal pressure, and the depth that abrasive grain cuts workpiece is dp, cut when abrasive grain is mobile
When workpiece, the direction of R has turned over angle, θ ', abrasive grain is coefficient of friction, abrasive grain yielding value by frictional force μ a R, μ in bottom
δcWith workpiece elasticity recovery value δwCalculation formula it is as follows:
δc=C [R (cos θ '-μ sin θ ')]2/3
δw=R (cos θ '-μ sin θ ')/k
C is constant in formula, and value range is 0.08~0.25, and average value 0.15, k is workpiece stiffness coefficient；
The calculation formula of θ ' and R is respectively:
R=π b2B
B is the half that abrasive grain cuts workpiece portion chord length in formula, and B is the ball hardness number of workpiece material；
The calculation formula of the available b of geometrical relationship are as follows:
The depth of abrasive grain incision workpiece is d in desired elastic deformation modelpIt is in the hypothesis that workpiece surface is ideal plane
Lower measurement, the case where practical work piece surface is not ideal plane, sampled cross-section n septal fossula channel profiles and practical work piece Surface Interference
Under, practical work piece surface is lower than ideal workpiece surface, from H1(m1, n) and arrive H2(m2, n) series of points really interfere
Sampled point, each sampled point has different penetraction depths, real in grinding although practical work piece surface is not ideal plane
Border workpiece surface be it is very smooth, the difference in height between each neighboring lattice points is little, therefore, it is considered that desired elastic deformation model is still close
Like establishment, the penetraction depth average value d with each sampled point is only neededp' instead of the d in desired elastic deformation modelp,
Z in formulaw(m, n) is the actual height of workpiece surface lattice point P (m, n) before being ground, and z (m, n) is sampled point H (m, n)
Depth, the scallop-height of workpiece surface lattice point P (m, n) is answered after grinding are as follows: z'(m, n)=z (m, n)+δc+δw
When updating workpiece surface appearance model, z is replaced with the value of z 'wValue.
Plastic accumulation model modification method is as follows in the step 4):
When practical grinding, the material that is interfered on workpiece with abrasive grain only some be removed, form abrasive dust, and
The material not being removed then is plastically deformed, and is deposited in groove two sides, and plastic accumulation model is based on spherical wear particles and ideal
Flat surface grinding is it is assumed that the sectional area of removal material is Ag, it is highly h that the profile of material stacking part, which is assumed to be parabola,p, width
For 2wp, sectional area Ap, abrasive grain profile and the inclination angle for accumulating profile intersection tangent line are αp, wpAnd hpValue be respectively as follows:
ApValue determined by grinding efficiency β,
For axial ultrasonic vibration-assisted grinding, it is contemplated that groove broadens phenomenon, should be using the elliptical grooves profile established
Replace the round abrasive grain profile in ideal plasticity Mathematical Model of heaped-up,
The bottom that profile is accumulated in ideal plasticity Mathematical Model of heaped-up assumes that the workpiece surface for ideal plane, but in grinding
Practical work piece surface is not ideal plane, and position is lower than the ideal plane, although practical work piece surface is not ideal plane,
But due in grinding workpiece surface it is very smooth, almost plane is set up, groove therefore, it is considered that ideal plasticity Mathematical Model of heaped-up is still approximate
Profile is from sampled point H1(m1, n) and arrive H2(m2, n) and practical work piece Surface Interference, remove the sectional area A of materialgIt should be according to practical dry
Relate to situation calculating:
In order to establish accumulation profile, with sampled point H1To H2Practical work piece apparent height average value establish one it is equivalent flat
Face replaces the ideal plane in ideal plasticity Mathematical Model of heaped-up, equivalent plane height value zdAre as follows:
It is still h that accumulation profile, which is higher by the height of equivalent plane,p, but it is 2w that width, which increases,p', model is broadened similarly with groove,
The degree that accumulation profile broadens is identical as the degree that groove contour broadens, and can calculate wp' value:
H is being determinedp, wp', zdValue after, the location and shape for accumulating profile just entirely define, accumulation profile cover
The height value that accumulation profile is calculated at each lattice point covered substitutes former lattice dynamical system value, completes in a sampled cross-section more
Newly.
The beneficial effects of the present invention are: axial ultrasonic vibration-assisted grinding workpiece surface appearance simulation and prediction side of the present invention
Method overcomes existing emulation mode due to that cannot have what is emulated when axial ultrasonic vibration to lack using Static Sampling method
Point.Grinding groove is established for the characteristics of axial ultrasonic vibration on this basis to broaden model, is further introduced into grinding elasticity
Distorted pattern and plastic accumulation model are modified the dynamic outline method of sampling, have ultimately generated workpiece surface appearance prediction mould
Type, and prediction result has also obtained verification experimental verification.It has good practical value in grinding field.
Detailed description of the invention
Fig. 1 is workpiece topological matrix schematic diagram in the present invention；
Fig. 2 is Configuration of Grinding-wheel Surface mathematical model three-dimensional figure used in the present invention；
Fig. 3 is axial supersonic vibration assistant grinding schematic diagram in the present invention；
Fig. 4 is sampled cross-section set-up mode schematic diagram in the present invention；
Fig. 5 is the sampled point set-up mode schematic diagram in the present invention in sampled cross-section n；
Fig. 6 is that groove broadens model schematic in the present invention；
Fig. 7 is the groove contour schematic diagram in the present invention in sampled cross-section n；
Fig. 8 is desired elastic deformation model schematic in the present invention；
Fig. 9 is actual elastic distorted pattern schematic diagram in the present invention；
Figure 10 is ideal plasticity Mathematical Model of heaped-up schematic diagram in the present invention；
Figure 11 is practical plastic accumulation model schematic in the present invention；
Figure 12 is workpiece surface appearance Prediction program general flow chart in the present invention；
Figure 13 a is the prediction workpiece surface appearance of plain grinding in the present invention；
Figure 13 b is the prediction workpiece surface appearance of axial supersonic vibration assistant grinding in the present invention；
Figure 14 a is the actual measurement workpiece surface appearance of plain grinding in the present invention；
Figure 14 b is the actual measurement workpiece surface appearance of axial supersonic vibration assistant grinding in the present invention.
Specific embodiment
A kind of axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method based on dynamic outline sampling method,
Specific step is as follows for this method:
Step 1: Configuration of Grinding-wheel Surface mathematical model is imported
Grinding is that multiple-cutting-edge, the cutting of micro- sword are carried out using the abrasive grain of wheel face, the diameter and distribution feelings of wheel face abrasive grain
Condition has vital influence to workpiece surface appearance after grinding.In general, the diameter of abrasive grain is a certain on grinding wheel
It is Gaussian distributed in section, is to obey random distribution in the position of wheel face, in this regard, having there is maturation now
Configuration of Grinding-wheel Surface emulation mode can be used.In order to by Configuration of Grinding-wheel Surface the application of mathematical model in this method, with existing side
The Configuration of Grinding-wheel Surface model that method generates should meet following condition: the model indicates with matrix G, the member of every a line in matrix G
Element indicates the information of an abrasive grain.Coordinate (x ' for the information of i-th abrasive grain, including it in wheel face coordinate systemi,
y’i, z 'i) and abrasive grain shape simplification be spherical diameter dgi.N abrasive grain is shared in grinding wheel numerical model, the form of matrix G is N
×4.Configuration of Grinding-wheel Surface mathematical model three-dimensional figure used as shown in Figure 2 after the model drawing output.
Step 2: grain motion trajectory is calculated
Axial ultrasonic vibration-assisted grinding is axially to apply high frequency simple harmonic oscillation along grinding wheel on the basis of plain grinding
A kind of Combined Machining Technology on to workpiece or grinding wheel.Its grain motion trajectory and plain grinding grain motion trajectory have very very much not
Together, also different to the effect of workpiece surface appearance forming process, it is therefore necessary to give expression to axial ultrasonic vibration with mathematical formulae
The motion profile of the dynamic auxiliary grinding any abrasive grain in medium plain emery wheel surface.Using workpiece as stationary reference frame, to establish workpiece convenient for research
Coordinate system Oxyz, axial ultrasonic vibration-assisted grinding schematic diagram as shown in Figure 3, wherein x-axis feeds opposite direction, y-axis edge along workpiece
Grinding wheel is axial, and the position of origin O is selected in the workpiece surface highest point before grinding.During axial ultrasonic vibration-assisted grinding,
The movement of abrasive grain consists of three parts: around grinding wheel spindle with angular velocity omegasCircular motion, along direction of feed relative to workpiece with line
Speed vwLinear motion, along grinding wheel axially with respect to workpiece with amplitude A, ultrasonic vibration that frequency f is carried out.
T at the time of if grinding starts0=0s, the origin O ' of wheel face coordinate system is located at grinding wheel minimum point and is located at this time
The surface of workpiece coordinate system origin O, ultrasonic vibration initial phase are 0.O ' is easy to get in workpiece by primary condition and kinematic relation
Equation of locus in coordinate system are as follows:
R in formulasFor grinding wheel radius, t is from t0Moment starts the time of grain motion, LzFor grinding wheel axis to O it is vertical away from
From LzIt can be calculated by formula (3):
Lz=rs+hmax-ap (3)
H in formulamaxFor the maximum projecting height of wheel face abrasive grain, apFor grinding depth.Known any abrasive grain i is in grinding wheel
Coordinate in surface coordinate system is (x 'i, y 'i, z 'i).Remember that abrasive grain i arrives the vertical line of grinding wheel axis to the vertical line and O ' of grinding wheel axis
Between angle be αi, it can be calculated by formula (4):
L hereiniWhat is indicated is arc length of i-th of abrasive grain to grinding wheel coordinate origin.
When grinding wheel is from t0Moment starts to turn over angle [alpha]iWhen, abrasive grain i is located exactly at grinding wheel minimum point.One when in view of grinding
Abrasive grain may repeatedly cut workpiece, be α when grinding wheel turns over angleiWhen+2 π (λ -1), it is minimum that abrasive grain i is also located exactly at grinding wheel
Point, λ indicate the number of abrasive grain i incision workpiece.Remember that this moment is ti:
The abrasive grain i known to formula (5), which is moved at the time of grinding wheel minimum point at the time of ratio O ' moves to grinding wheel minimum point, to fall behind
TiSecond, in the y-axis direction, abrasive grain i is y ' relative to the O ' distance deviatedi, on grinding wheel radius direction, abrasive grain i is higher by grinding wheel
The distance on surface is z 'i, any abrasive grain i can be obtained in workpiece coordinate system on the basis of formula (2) according to these relationships
Equation of locus:
Formula (6) is the general formula of Movement Locus Equation of any abrasive grain i of wheel face in workpiece coordinate system.
Step 3: the dynamic outline method of sampling
Workpiece topological matrix g is generallyd use in workpiece surface appearance predictionmnIndicate workpiece surface appearance.I.e. in workpiece table
With the direction the x direction separation delta x and y separation delta y grid division on face.Using the height value z (m, n) at grid lattice point P (m, n) as
Workpiece topological matrix gmnIn element, as shown in Figure 1.
Firstly, the series of parallel sampled cross-section in plane Oyz is arranged on the surface of the workpiece, these sampled cross-sections cross workpiece
The lattice point of topological matrix is followed successively by 1,2,3 ... as shown in Figure 4 along the number of positive direction of the x-axis since O point.Δ x and Δ y
Value determine the sizing grid of workpiece surface topological matrix, also just determine that simulation accuracy, occurrence should be by we
The user of service of method is arranged according to demand.Below embodiment fall into a trap the result of nomogram 13 when the value that uses are as follows: Δ x=Δ y=
0.004mm, dgiAverage value=0.069mm, can be used as reference.
When grinding, a certain abrasive grain is in C1Point incision workpiece, in C2Point leaves workpiece.C1The sampled cross-section n on point the right1
It is first sampled cross-section interfered, C2The sampled cross-section n on the point left side2It is the last one.Process of the abrasive grain in grinding workpiece
In sequentially passed through from n1To n2A series of sampled cross-sections, therefore the remnants for calculating each lattice point in these sampled cross-sections are high
Angle value can find out abrasive grain workpiece surface appearance after grinding.n1And n2Value can be found out by formula (7).
L in formula1For C1Point arrives the horizontal distance of workpiece coordinate system origin O, l2For C2Point arrives the horizontal distance of O, l1And l2's
Value can use abrasive grain equation of locus (6) and find out.
When calculating each lattice point scallop-height value in n-th of sampled cross-section, the sampled cross-section is calculated first and is sat to workpiece
The horizontal distance x of mark system origin On:
xn=(n-1) Δ x (8)
By xnValue substitute into abrasive grain equation of locus (6) abrasive grain center can be found out in sampled cross-section n to workpiece coordinate
It is the horizontal distance y of origin OnWith vertical range zn.Then position of the abrasive grain profile in sampled cross-section n is assured that, is such as schemed
Shown in 5.Abrasive grain profile can be indicated with equation (9).
(y-yn)2+(z-zn)2=(dg/2)2 (9)
D in formulagFor abrasive grain diameter.In Fig. 5, in C3Point arrives C4Abrasive grain and workpiece interfere between point.C3The lattice on point the right
Point P1(m1, n) and it is first lattice point interfered, C4The lattice point P on the point left side2(m2, n) and it is the last one.m1And m2Value can
To be found out by formula (10).
L in formula3For C3Point arrives the horizontal distance of workpiece coordinate system origin O, l4For C4Point arrives the horizontal distance of O point, l3And l4
Value can use abrasive grain profile equation (9) and find out.
Then, from P1To P2A series of lattice points at abrasive grain profile is sampled, wherein a certain sampled point H (m, n) is arrived
The horizontal distance of workpiece coordinate system origin O is lm:
lm=(m-1) Δ y (11)
By y=lmIt substitutes into abrasive grain profile equation (9) and obtains formula (12), the ordinate z of sampled point H (m, n) can be found out
(m, n).
Assuming that the workpiece material interfered is completely removed, then the value of z (m, n) is exactly the workpiece remnants of the point after grinding
Height value.The coordinate value of sampled point H (m, n) is assigned to lattice point P (m, n), completes the update at the lattice point.Similarly, sampling is updated
From P in the n of section1Point arrives P2All lattice point coordinates of point complete the calculating in sampled cross-section n.When from n1To n2All samplings
After the completion of section all updates, so that it may which the workpiece surface appearance after obtaining single grain grinding is continued thereafter with and adjusted on this basis
It is updated with other abrasive grains, finally obtains complete workpiece surface appearance.
Due to the presence for thering is axial ultrasonic to vibrate, in different sampled cross-sections, abrasive grain center to workpiece coordinate system origin O
Horizontal distance ynIt is different, therefore sampled point is movement relative to abrasive grain profile, sampled point dative point alignment always, this
It is exactly the dynamic outline method of sampling.Compared with Configuration of Grinding-wheel Surface topologizes method, the dynamic outline method of sampling can be each
Accurately reflect the profile of abrasive grain in sampled cross-section, so that the workpiece surface appearance to axial ultrasonic vibration-assisted grinding measures in advance
To realize.
Step 4: the amendment to the method for sampling
The above-mentioned dynamic outline method of sampling is hypothesis to be completely removed based on material, but in practical grinding, consider
It is not completely removed to the workpiece material interfered, but a series of elastic-plastic deformations has occurred.Therefore, for axial ultrasonic
The characteristics of vibration-assisted grinding, establishes grinding groove and broadens model, and introduce on this basis grinding elastic deformation model and
Plastic accumulation model is modified the dynamic outline method of sampling.
1, grinding groove broadens the foundation of model
Many scholars are found by experiment that, in axial ultrasonic vibration-assisted grinding, due to the axial movement of abrasive grain, along
The grinding groove of grinding wheel axial direction broadens, and interference degrees enhance between the groove of different abrasive grains, improves workpiece surface quality.Usually
In the case of be, the above-mentioned dynamic outline method of sampling axially measured along grinding wheel to workpiece surface roughness value measurement after grinding
The sampled cross-section of middle setting is also parallel to grinding wheel axial direction.Therefore, it in order to keep prediction result truer, needs to consider to be ground
Groove broadens the influence generated to workpiece surface appearance, establishes grinding groove and broadens model, as shown in Figure 6.Fig. 6 is to overlook view
Angle observation grinding groove, sampled cross-section n is actually the abrasive grain space swept into section E-E motion process from section D-D
An oblique section.Since the distance of section D-D to section E-E are very short, grain motion approximate straight line motion, therefore abrasive grain from cut
It is d that face D-D, which can simplify to the swept space section E-E as a diameter,gCylindrical body, with the sampled cross-section n bevel circle
Cylinder, gained profile are one oval, and groove contour as shown in Fig. 7, the ellipse short shaft is dg, long axis de, groove contour can
To be indicated with equation (13).
According to the geometrical relationship in Fig. 7, dgAnd deRatio are as follows:
θ is grain motion speed vgWith the angle between sampled cross-section n.At sampled cross-section n, vgIt can be decomposed into along x-axis
Velocity component vxWith the velocity component v along y-axisy.It is available according to the compositional rule of movement:
vxAnd vyValue the derivation of time t can be obtained by abrasive grain equation of locus (6):
T in formulanAt the time of for abrasive grain center movement at sampled cross-section n, vsFor grinding speed.Formula (16) are substituted into formula
(15), formula (15), which substitutes into formula (14), can obtain deValue:
Work as deValue determine after, groove contour equation (13) has just determined therewith.From figure 7 it can be seen that groove contour produces
Raw groove width w2The groove width w generated than abrasive grain profile1It is wider.When there are axial ultrasonic vibration, it should use groove
Profile equation (13) replaces abrasive grain profile equation (9), and sampled point is chosen on groove contour.The sampling of different location is cut
Face, deValue be different, it means that different groove contour equations is corresponding in different sampled cross-sections, what groove broadened
Degree is also dynamic.
2, it is ground the introducing of elastic deformation model
When grinding, since abrasive grain is flexibly supported by grinding wheel bond, elastic yield can occur for abrasive grain when grinding,
In addition elastic recovery can also occur for workpiece material after being ground.Existing emulation mode is based on spherical wear particles and ideal plane grinding is false
If establishing grinding elastic deformation theory's model, as shown in Figure 8.Abrasive grain stress condition to test Brinell hardness when similar, abrasive grain
It is R by normal pressure, the depth that abrasive grain cuts workpiece is dp.When the mobile cutting workpiece of abrasive grain, the direction of R has turned over angle
θ ', abrasive grain are coefficient of friction by frictional force μ a R, μ in bottom.Abrasive grain yielding value δcWith workpiece elasticity recovery value δwCalculating
Formula is (18) and (19) respectively.
δc=C [R (cos θ '-μ sin θ ')]2/3 (18)
δw=R (cos θ '-μ sin θ ')/k (19)
C is constant in formula, and value range is 0.08~0.25, and average value 0.15, k is workpiece stiffness coefficient.θ's ' and R
Calculation formula is respectively:
R=π b2B (21)
B is the half that abrasive grain cuts workpiece portion chord length in formula, and B is the ball hardness number of workpiece material.By the geometry of Fig. 8
The calculation formula of the available b of relationship are as follows:
The depth of abrasive grain incision workpiece is d in desired elastic deformation model shown in Fig. 8pIt is to be put down in workpiece surface to be ideal
It is measured under the hypothesis in face.Under actual conditions, most abrasive grains are continued on the basis of existing polishing scratch as subsequent abrasive grain
Grinding.Practical work piece surface is not ideal plane, is illustrated in figure 9 sampled cross-section n septal fossula channel profiles and practical work piece surface is dry
The case where relating to, practical work piece surface is lower than ideal workpiece surface, from H1(m1, n) and arrive H2(m2, n) series of points be really to occur
The sampled point of interference, each sampled point have different penetraction depths.
Although practical work piece surface is not ideal plane, practical work piece surface is very smooth in grinding, each adjacent
Difference in height between lattice point is little, sets up, is only needed with each sampled point therefore, it is considered that desired elastic deformation model is still approximate
Penetraction depth average value dp' instead of the d in desired elastic deformation modelp, as shown in formula (23).
Z in formulaw(m, n) is the actual height of workpiece surface lattice point P (m, n) before being ground, and z (m, n) is sampled point H (m, n)
Depth.The scallop-height of workpiece surface lattice point P (m, n) is answered after grinding are as follows: z'(m, n)=z (m, n)+δc+δw (24)
When updating workpiece surface appearance model, z is replaced with the value of z 'wValue.
3, it is ground the introducing of plastic accumulation model
When practical grinding, the material that is interfered on workpiece with abrasive grain only some be removed, form abrasive dust, and
The material not being removed then is plastically deformed, and is deposited in groove two sides.In order to consider the workpiece material plasticity of groove two sides
Situation is accumulated, the plain grinding plastic accumulation model that existing emulation mode is established is introduced.As shown in Figure 10, which is based on spherical shape
Abrasive grain and ideal plane grinding are assumed.The sectional area for removing material is Ag, the profile of material stacking part is assumed to be parabola, high
Degree is hp, width 2wp, sectional area Ap.The inclination angle of abrasive grain profile and accumulation profile intersection tangent line is αp。wpAnd hpValue
It is respectively as follows:
ApValue determined by grinding efficiency β.
Ideal plasticity Mathematical Model of heaped-up shown in Fig. 10 is processed for plain grinding and is established, and axial ultrasonic is vibrated auxiliary
Grinding aid is cut, it is contemplated that groove broadens phenomenon, and the elliptical grooves profile that Ying Caiyong has just been established replaces ideal plasticity Mathematical Model of heaped-up
In round abrasive grain profile.In addition, the bottom for accumulating profile in ideal plasticity Mathematical Model of heaped-up assumes that the workpiece for ideal plane
Surface, but practical work piece surface is not ideal plane in grinding, and position is lower than the ideal plane, as shown in figure 11:
Although practical work piece surface is not ideal plane, since workpiece surface is very smooth in grinding, almost plane, because
This thinks that ideal plasticity Mathematical Model of heaped-up is still approximate and sets up.Groove contour is from sampled point H1(m1, n) and arrive H2(m2, n) and practical work piece
Surface Interference removes the sectional area A of materialgIt should be calculated according to practical interference situation:
In order to establish accumulation profile, with sampled point H1To H2Practical work piece apparent height average value establish one it is equivalent flat
Face replaces the ideal plane in ideal plasticity Mathematical Model of heaped-up, equivalent plane height value zdAre as follows:
It is still h that accumulation profile, which is higher by the height of equivalent plane,p, but it is 2w that width, which increases,p'.Model is broadened similarly with groove,
The degree that accumulation profile broadens is identical as the degree that groove contour broadens, and can calculate w referring to formula (17)p' value:
H is being determinedp, wp', zdValue after, the location and shape for accumulating profile just entirely define.It is covered in accumulation profile
The height value that accumulation profile is calculated at each lattice point covered substitutes former lattice dynamical system value, completes in a sampled cross-section more
Newly.
Workpiece surface appearance Prediction program flow chart as shown in figure 12, the pre- flow gauge after designing according to the above method, by this
Process can carry out workpiece surface appearance prediction.
According to the pre- flow gauge of this method, to plain grinding and axial ultrasonic vibration auxiliary under typical process Parameter Conditions
The workpiece surface appearance of grinding is predicted, using parameter: grinding wheel outer diameter 300mm, ultrasonic vibration frequency f=20.45KHz,
Amplitude A=15 μm, grinding wheel speed vs=20m/s, feed-speed vw=1m/min, grinding depth ap=4 μm.Prediction obtains
Result as shown in Figure 13 a, 13b.In order to verify the accuracy of above-mentioned prediction technique, corresponding verification test has been carried out.Figure
14a, 14b are the workpiece surface appearance of test actual measurement.
The prediction result and Figure 14 a of comparison diagram 13a, 13b, the measured result of 14b are can be found that: the common mill in Figure 13 a
It is narrow, straight to cut groove, there are obvious protuberance in keeping parallelism between adjacent trenches, groove two sides, and residual altitude is higher, with Figure 14 a
In actual measurement workpiece surface appearance feature it is similar.The groove width of axial supersonic vibration assistant grinding is wider in Figure 13 b, and groove is walked
To slight curving, there is obvious interference between adjacent trenches, the protuberance of groove two sides is mutually cut off by adjacent trenches, residual altitude compared with
It is low.Actual measurement workpiece surface appearance feature in Figure 14 b is similar.
Further comparison prediction and actual measurement workpiece surface roughness value Ra: 0.88 μm of plain grinding predicted value, plain grinding
0.91 μm of measured value, 0.76 μm of ultrasonic grinding predicted value, 0.82 μm of ultrasonic grinding measured value.Mean error is 5.3%, prediction with
Test result is close.The result of prediction and test actual measurement all shows the resulting workpiece surface matter of axial ultrasonic vibration-assisted grinding
Amount is better than plain grinding.The reason is that abrasive grain track becomes more complicated under the action of axial ultrasonic vibration, lead to groove width
It broadens, effect enhancing is interfered between groove, so that remaining material and protuberance are removed originally for groove two sides, reduce work
The microfluctuation on part surface, to obtain higher-quality surface.
The above results demonstrate the feasibility and accuracy of prediction technique.Dynamic outline sampling method can be accurately by groove
Profile is mapped on workpiece surface appearance model, and is introduced groove with can be convenient broadened model, elastic deformation model and modeling
Property Mathematical Model of heaped-up improves precision of prediction, reaches good prediction effect.
Claims (4)
1. a kind of axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method, which is characterized in that specifically include as
Lower step:
1) grinding parameter is inputted, Configuration of Grinding-wheel Surface mathematical model is imported:
Model indicates with matrix G, the information of one abrasive grain of element representation of every a line in matrix G, for the letter of i-th abrasive grain
Breath, the coordinate (x ' including it in wheel face coordinate systemi, y 'i, z 'i) and abrasive grain shape simplification be spherical diameter dgi, sand
It takes turns and shares N abrasive grain in numerical model, the form of matrix G is N × 4,
2) grain motion trajectory is calculated:
Using workpiece as stationary reference frame, workpiece coordinate system Oxyz is established, wherein x-axis feeds opposite direction along workpiece, and y-axis is along grinding wheel spindle
To the position of origin O is selected in the workpiece surface highest point before grinding, during axial ultrasonic vibration-assisted grinding, abrasive grain
Movement consists of three parts: around grinding wheel spindle with angular velocity omegasCircular motion, along direction of feed relative to workpiece with linear velocity vw
Linear motion, along grinding wheel axially with respect to workpiece with amplitude A, ultrasonic vibration that frequency f is carried out；
T at the time of if grinding starts0=0s, the origin O ' of wheel face coordinate system is located at grinding wheel minimum point and is located at workpiece at this time
The surface of coordinate origin O, ultrasonic vibration initial phase are 0；
Any equation of locus of the abrasive grain i in workpiece coordinate system:
Wherein rsFor grinding wheel radius, t is from t0Moment starts the time of grain motion, LzFor the vertical range of grinding wheel axis to O,
λ indicates the number of abrasive grain i incision workpiece, αiFor abrasive grain i to grinding wheel
The vertical line and O ' of axis arrive the angle between the vertical line of grinding wheel axis；
3) the dynamic outline method of sampling:
Workpiece topological matrix g is used in workpiece surface appearance predictionmnIndicate workpiece surface appearance, i.e., on the surface of the workpiece with x
The direction direction separation delta x and y separation delta y grid division, is opened up using the height value z (m, n) at grid lattice point P (m, n) as workpiece
Flutter matrix gmnIn element,
Firstly, the series of parallel sampled cross-section in plane Oyz is arranged on the surface of the workpiece, these sampled cross-sections cross workpiece topology
The lattice point of matrix is followed successively by 1,2,3 ... along the number of positive direction of the x-axis since O point, and when grinding, a certain abrasive grain exists
C1Point incision workpiece, in C2Point leaves workpiece, C1The sampled cross-section n on point the right1It is first sampled cross-section interfered, C2Point
The sampled cross-section n on the left side2It is the last one, abrasive grain has sequentially passed through during being ground workpiece from n1To n2A series of adopt
Sample section, therefore the scallop-height value for calculating each lattice point in these sampled cross-sections can find out abrasive grain work after grinding
Part surface topography, n1And n2Value can be found out by following formula
L in formula1For C1Point arrives the horizontal distance of workpiece coordinate system origin O, l2For C2Point arrives the horizontal distance of O, l1And l2Value can
To be found out using abrasive grain equation of locus in step 2)；
When calculating each lattice point scallop-height value in n-th of sampled cross-section, the sampled cross-section is calculated first to workpiece coordinate system
The horizontal distance x of origin On:
xn=(n-1) Δ x
By xnValue substitute into abrasive grain equation of locus and can find out in sampled cross-section n abrasive grain center to workpiece coordinate system origin O's
Horizontal distance ynWith vertical range zn, then position of the abrasive grain profile in sampled cross-section n is assured that, abrasive grain profile equation
It indicates are as follows:
(y-yn)2+(z-zn)2=(dg/2)2
D in formulagFor abrasive grain diameter, in C1And C2Intermediate C3Point arrives C4Abrasive grain and workpiece interfere between point, C3Point the right
Lattice point P1(m1, n) and it is first lattice point interfered, C4The lattice point P on the point left side2(m2, n) and it is the last one, m1And m2Value
It can be found out by following formula,
L in formula3For C3Point arrives the horizontal distance of workpiece coordinate system origin O, l4For C4Point arrives the horizontal distance of O point, l3And l4Value
It can use abrasive grain profile equation to find out；Then, from P1To P2A series of lattice points at abrasive grain profile is sampled, wherein
The horizontal distance of a certain sampled point H (m, n) to workpiece coordinate system origin O are lm:
lm=(m-1) Δ y
By y=lmIt substitutes into and obtains following formula in abrasive grain profile equation, the ordinate z (m, n) of sampled point H (m, n) can be found out,
Assuming that the workpiece material interfered is completely removed, then the value of z (m, n) is exactly the workpiece scallop-height of the point after grinding
Value, is assigned to lattice point P (m, n) for the coordinate value of sampled point H (m, n), completes the update at the lattice point, similarly, updates sampled cross-section n
It is interior from P1Point arrives P2All lattice point coordinates of point complete the calculating in sampled cross-section n；When from n1To n2All sampled cross-sections
After the completion of all updating, so that it may which the workpiece surface appearance after obtaining single grain grinding continues thereafter with and calls it on this basis
He is updated abrasive grain, finally obtains complete workpiece surface appearance；
4) to the amendment of the method for sampling: the characteristics of being directed to axial ultrasonic vibration-assisted grinding establishes grinding groove and broadens model,
And grinding elastic deformation model and plastic accumulation model are introduced on this basis, the dynamic outline method of sampling is modified.
2. axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method, feature exist according to claim 1
The grinding groove model modification method that broadens is as follows in, the step 4):
Groove contour is ellipse, ellipse short shaft dg, long axis de, the expression of groove contour equation are as follows:
dgAnd deRatio are as follows:
θ is grain motion speed vgWith the angle between sampled cross-section n, at sampled cross-section n, vgThe speed along x-axis can be decomposed into
Spend component vxWith the velocity component v along y-axisy, it is obtained according to the synthetic method of movement:
vxAnd vyValue the derivation of time t can be obtained by abrasive grain equation of locus:
T in formulanAt the time of for abrasive grain center movement at sampled cross-section n, vsFor grinding speed, d can be obtainedeValue:
Work as deValue determine after, groove contour equation determines therewith, when there are axial ultrasonic vibration, using groove contour equation
Instead of the abrasive grain profile equation in step 3), sampled point is chosen on groove contour.
3. axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method, feature exist according to claim 2
In grinding elastic deformation model modification method is as follows in the step 4):
Assume to establish grinding elastic deformation theory's model, abrasive grain stress condition and survey based on spherical wear particles and ideal plane grinding
Similar when examination Brinell hardness, abrasive grain is R by normal pressure, and the depth that abrasive grain cuts workpiece is dp, when the mobile cutting workpiece of abrasive grain
When, the direction of R has turned over angle, θ ', abrasive grain is coefficient of friction, abrasive grain yielding value δ by frictional force μ a R, μ in bottomcWith
Workpiece elasticity recovery value δwCalculation formula it is as follows:
δc=C [R (cos θ '-μ sin θ ')]2/3
δw=R (cos θ '-μ sin θ ')/k
C is constant in formula, and value range is 0.08~0.25, and average value 0.15, k is workpiece stiffness coefficient；
The calculation formula of θ ' and R is respectively:
R=π b2B
B is the half that abrasive grain cuts workpiece portion chord length in formula, and B is the ball hardness number of workpiece material；
The calculation formula of the available b of geometrical relationship are as follows:
The depth of abrasive grain incision workpiece is d in desired elastic deformation modelpIt is to be measured in the case where workpiece surface is the hypothesis of ideal plane
, practical work piece surface is not ideal plane, real in the case where sampled cross-section n septal fossula channel profiles and practical work piece Surface Interference
Border workpiece surface is lower than ideal workpiece surface, from H1(m1, n) and arrive H2(m2, n) series of points be the sampling really interfered
Point, each sampled point have different penetraction depths,
Although practical work piece surface is not ideal plane, practical work piece surface is very smooth, each neighboring lattice points in grinding
Between difference in height it is little, set up therefore, it is considered that desired elastic deformation model is still approximate, only need the incision with each sampled point
Depth-averaged value dp' instead of the d in desired elastic deformation modelp,
Z in formulaw(m, n) is the actual height of workpiece surface lattice point P (m, n) before being ground, and z (m, n) is the depth of sampled point H (m, n)
Degree, the scallop-height of workpiece surface lattice point P (m, n) is answered after grinding are as follows: z'(m, n)=z (m, n)+δc+δw
When updating workpiece surface appearance model, z is replaced with the value of z 'wValue.
4. axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method, feature exist according to claim 2
In plastic accumulation model modification method is as follows in the step 4):
When practical grinding, the material that is interfered on workpiece with abrasive grain only some be removed, form abrasive dust, without
The material being removed then is plastically deformed, and is deposited in groove two sides, and plastic accumulation model is based on spherical wear particles and ideal plane
Grinding is it is assumed that the sectional area of removal material is Ag, it is highly h that the profile of material stacking part, which is assumed to be parabola,p, width is
2wp, sectional area Ap, abrasive grain profile and the inclination angle for accumulating profile intersection tangent line are αp, wpAnd hpValue be respectively as follows:
ApValue determined by grinding efficiency β,
For axial ultrasonic vibration-assisted grinding, it is contemplated that groove broadens phenomenon, should be using the elliptical grooves profile established come generation
For the round abrasive grain profile in ideal plasticity Mathematical Model of heaped-up,
The bottom that profile is accumulated in ideal plasticity Mathematical Model of heaped-up assumes that the workpiece surface for ideal plane, but practical in grinding
Workpiece surface is not ideal plane, and position is lower than the ideal plane, although practical work piece surface is not ideal plane,
Since workpiece surface is very smooth in grinding, almost plane is set up, groove contour therefore, it is considered that ideal plasticity Mathematical Model of heaped-up is still approximate
From sampled point H1(m1, n) and arrive H2(m2, n) and practical work piece Surface Interference, remove the sectional area A of materialgFeelings should be interfered according to practical
Condition calculates:
In order to establish accumulation profile, with sampled point H1To H2Practical work piece apparent height average value establish an equivalent plane generation
For the ideal plane in ideal plasticity Mathematical Model of heaped-up, equivalent plane height value zdAre as follows:
It is still h that accumulation profile, which is higher by the height of equivalent plane,p, but it is 2w that width, which increases,p', model is broadened similarly with groove, is accumulated
The degree that profile broadens is identical as the degree that groove contour broadens, and can calculate wp' value:
H is being determinedp, wp', zdValue after, the location and shape for accumulating profile just entirely define, accumulation profile cover
Each lattice point at calculate the height value of accumulation profile, substitute former lattice dynamical system value, complete the update in a sampled cross-section.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810088844.4A CN108262648B (en) | 2018-01-30 | 2018-01-30 | Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810088844.4A CN108262648B (en) | 2018-01-30 | 2018-01-30 | Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108262648A CN108262648A (en) | 2018-07-10 |
| CN108262648B true CN108262648B (en) | 2019-10-29 |
Family
ID=62777044
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810088844.4A Expired - Fee Related CN108262648B (en) | 2018-01-30 | 2018-01-30 | Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108262648B (en) |
Families Citing this family (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109271711B (en) * | 2018-09-25 | 2023-03-28 | 重庆大学 | Finite element modeling method for carburizing and hardening gear considering uneven characteristics |
| CN109614657A (en) * | 2018-11-15 | 2019-04-12 | 天津大学 | A kind of three-dimensional parameterized Geometric Modeling Method of side abrasive grinding wheel based on ABAQUS software and python language |
| CN109614727A (en) * | 2018-12-17 | 2019-04-12 | 天津大学 | Ultrasonic wave added aperture drilling grinding wheel parametric modeling method based on ABAQUS software |
| CN110328575B (en) * | 2019-05-09 | 2020-07-28 | 东北大学 | Prediction method for polished surface morphology of optical hard and brittle material |
| CN112276683B (en) * | 2020-10-28 | 2022-04-01 | 沈阳工业大学 | Method for predicting surface appearance of abrasive belt grinding screw curved surface |
| CN113042823B (en) * | 2021-03-22 | 2022-04-01 | 吉林大学 | Prediction method for residual height of cutting along straight line under condition of multiple process parameters |
| CN113094841B (en) * | 2021-04-28 | 2023-08-15 | 苏州科技大学 | Simulation method for ultrasonic vibration assisted grinding surface |
| CN113486552B (en) * | 2021-07-01 | 2023-11-17 | 江苏科技大学 | Method for predicting bending stiffness of unidirectional composite material |
| CN113732369B (en) * | 2021-09-07 | 2022-09-13 | 大连理工大学 | Method for acquiring ultrasonic milling amplitude in load state based on morphology simulation |
| CN114161240B (en) * | 2021-12-15 | 2023-03-24 | 清华大学 | Grinding surface shape prediction method, grinding system and terminal equipment |
| CN114239188A (en) * | 2021-12-31 | 2022-03-25 | 华侨大学 | Cut-in grinding theoretical model simulation prediction method |
| CN114444297A (en) * | 2022-01-21 | 2022-05-06 | 安徽理工大学 | Method for predicting surface topography of threaded workpiece in cyclone milling |
| CN115609770A (en) * | 2022-10-11 | 2023-01-17 | 上海理工大学 | Ultrasonic cavitation auxiliary fretsaw cutting device and method |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE112004002942T5 (en) * | 2004-08-26 | 2007-08-09 | Agency For Science, Technology And Research | Apparatus for ultrasonic assisted machining |
| CN103753357B (en) * | 2014-01-23 | 2015-12-02 | 南京理工大学 | The axial cutting force Forecasting Methodology of fragile material supersonic vibration assistant grinding |
| CN104889829B (en) * | 2015-05-27 | 2017-03-29 | 上海理工大学 | A kind of oscillation trajectory tracking and controlling method of two-dimensional ultrasound assistant grinding |
| CN107480339B (en) * | 2017-07-20 | 2018-08-21 | 中南大学 | Ultrasonic grinding workpiece surface three-dimensional appearance emulation mode and its system |
-
2018
- 2018-01-30 CN CN201810088844.4A patent/CN108262648B/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| CN108262648A (en) | 2018-07-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108262648B (en) | Axial ultrasonic vibration-assisted grinding workpiece surface appearance simulated prediction method | |
| CN107480339B (en) | Ultrasonic grinding workpiece surface three-dimensional appearance emulation mode and its system | |
| CN106228606B (en) | Three-dimensional elliptical vibration assisted cutting micro-texture morphology modeling method | |
| CN107562013B (en) | The curved surface subregion of equal scallop-heights becomes tool sharpening method for planning track | |
| CN102490081B (en) | Workpiece three-dimensional surface topography simulating method based on ball head milling | |
| CN110500969B (en) | High-gradient complex curved surface in-situ measurement planning method | |
| Hlaváč et al. | Shape distortion reduction method for abrasive water jet (AWJ) cutting | |
| CN107335847B (en) | A kind of processing method of cutting efficiency constraint cutter-orientation | |
| CN105643394A (en) | High-efficiency and high-precision advanced manufacturing technology process for medium or large caliber aspherical optical element | |
| CN104741994A (en) | Precise curved-surface grinding method for grinding wheel with any curved surface | |
| CN106897501A (en) | The positioning and optimizing method based on blade parts deformation towards in adaptive machining | |
| CN106271429B (en) | A kind of compensation method of blisk blade profile anti-deformation | |
| CN109590523B (en) | Reverse correction method for torsion and bending deformation of blisk blade | |
| CN102357666A (en) | Three-coordinate end milling method for blade with freeform surface by using flat-bottomed cutter | |
| CN111931338B (en) | Algorithm for determining machinable geometric structure of ultrasonic elliptical vibration cutting technology | |
| CN113704928B (en) | Inclined milling surface morphology generation method based on machining physical process | |
| CN117390794B (en) | Ultrasonic vibration turning surface micro-texture morphology simulation prediction method and system | |
| CN112387995B (en) | Surface morphology prediction method after ultra-precise turning of free-form surface | |
| CN102591260A (en) | Method for judging transient contact region of cutter and workpiece in five-axis milling process | |
| CN112883505B (en) | Ultra-precise end face turning surface modeling method considering relative vibration of cutter workpiece | |
| CN110090967A (en) | Great surface quality ultra precision cutting manufacturing process based on multi-freedom-degree vibration | |
| CN108196511A (en) | A kind of error prediction method of helical tooth blade turning track | |
| CN111474899A (en) | Triangular-based complex cavity high-speed numerical control milling spiral path generation method | |
| Rabiey et al. | Simulation of workpiece surface roughness after flat grinding by electroplated wheel | |
| CN108000246B (en) | A kind of three-dimensional class cycloid polishing path generation method based on geodesic distance |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20191029 |