CN103995979B - Grinding force computing method for aspheric surface parallel grinding machining - Google Patents
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Abstract
The invention relates to a grinding force computing method for aspheric surface parallel grinding machining. The method comprises the steps that 1, single-abrasive-particle cutting force computing is carried out, namely single-abrasive-particle stress analysis is carried out, and the cutting component force of a single abrasive particle in three axial directions is obtained; 2, effective abrasive particle searching is carried out, namely according to the moving relation of a grinding wheel and a workpiece, all effective abrasive particles participating in a machining process are determined; and 3, grinding wheel grinding zone grinding force computing is carried out, namely according to cutting force computing of the single abrasive particle, all the effective abrasive particles are subjected to accumulation, and the grinding component force in the three axial directions of the grinding wheel are computed. According to the grinding force computing method for aspheric surface parallel grinding machining, theoretical calculation on the grinding component force in the lathe X-Y-Z three axial directions can be achieved. According to the computing method, a needed theoretical foundation can be provided for related lathe design, aspheric surface grinding process intelligent control and other study and design works.
Description
Technical field
The present invention relates to aspherical parallel grinding and cutting processing method, the grinding of more particularly, to a kind of aspherical parallel grinding and cutting processing
Power computational methods.
Background technology
Aspheric-surface workpiece due to its complicated face shape profile, object always more difficult to process in grinding.Non- axle pair
Claim aspheric-surface workpiece special aspherical as one kind, its processing method is relatively more complicated, generally enters using three-shaft linkage lathe
Row processing.Parallel grinding and cutting is a kind of effective processing method for non-axisymmetric aspheric surface workpiece（See Patent No. ZL
200710009306.3 " parallel grinding and cutting method of non-axisymmetric aspheric surface optical element "）, the method is using circular arc diamond
Emery wheel（Abbreviation emery wheel）, make the cutting direction of emery wheel identical with the direction of motion of workpiece during processing, i.e. grinding speed and work
Part velocity attitude is parallel, and the grinding locus of points on emery wheel is circumferentially distributed.The maximum advantage of this method is on emery wheel during grinding
Grinding points are mobile, that is, the effective cutting edge participating in grinding increases, and emery wheel is effectively increased using width, and abrasion of grinding wheel substantially subtracts
Little, machining accuracy is protected.
Grinding force is an extremely important parameter in Grinding Process, and it not only affects system variant, grinding effect
Rate, machining accuracy, surface quality, emery wheel durability, grinding heat, grinding vibration, and be also superfine grinding Machine Tool design
When need one of parameter of paying close attention to.Due in aspherical parallel grinding and cutting processing method, the movement relation of emery wheel and workpiece
Complex, traditional grinding force computational methods accurately cannot be calculated to the grinding force under this processing mode, Patent No.
200710009306.3 " parallel grinding and cutting method of non-axisymmetric aspheric surface optical element " detailed this processing method of elaboration, but
It is the grinding force computational methods not being related to parallel grinding and cutting.Accordingly, it is difficult to accurately calculate the grinding force of this processing method, right
The work in every such as associated machine tool parameter designing and process environmental monitoring brings greater inconvenience.The present invention is directed to aspherical flat
The needs of the links such as row grinding equipment Design, processing monitoring, fault diagnosis, have invented a kind of aspherical parallel grinding and cutting processing
Grinding force computational methods.
Content of the invention
The present invention is to provide for a kind of grinding force computational methods of aspherical parallel grinding and cutting processing, should add for accurate calculating
The grinding force of work method, the convenience that the work in every such as associated machine tool parameter designing and process environmental monitoring is brought.
For achieving the above object, the technical scheme is that：
A kind of grinding force computational methods of aspherical parallel grinding and cutting processing are it is characterised in that comprise the following steps：
1）Single abrasive grain cutting power calculates
（1）Single abrasive grain cutting power size calculates.
(1)
In formula
F p(specific cutting force is the main cutting acting on during grinding work piece on unit grinding area to specific cutting force
Power)；
θ pHalf cone-apex angle of abrasive particle；
θ dCutting force direction and the angle of emery wheel direction of feed；
ρ——For abrasive particle element of cone effective length；
（2）Single abrasive grain cutting direction calculating
According to the locus of surface of the work difference processing stand, calculate the sky of emery wheel and single abrasive particle of workpiece contact zone
Between attitude, obtain represent single abrasive grain cutting direction vectorN F , step is as follows：
1. aspheric surface equation is
y=y(x,z) (2)
Surface of the work current processing stand position unit normal vectorN(nxi,nzi,nyi) be：
(3)
N mFor representing the unit vector in grain motion direction, by emery wheel feed speedN SGeostrophic with emery wheel single
Abrasive particle linear velocityV pObtain after superposition calculation, then calculateNWithN mVector productN a：
(4)
According to equivalent axis rotation matrix method, by left hand criterion by specific vertical vectorN aIt is set to equivalent direction of principal axis；
2. according to spin matrix shift theory, represent the vector in single abrasive grain cutting directionN FFor：
(5)
In formula：
TrotStandard spin matrix
By vectorN F Calculate this single abrasive grain cutting direction withX、Y、ZShaft space angleθ x 、θ y Withθ z：
(6)
（3）Single abrasive particleX、Y、ZThree axially cutting component calculating
According to single abrasive grain cutting direction, by single abrasive grain cutting powerF gIt is decomposed intoXAxially cutting componentF x 、YAxially
Cutting componentF y WithZAxially cutting componentF z, known by geometrical relationship：
(7)
2）Active grain is searched for
（1）Search contact area abrasive particle
1. set up single abrasive grain locations relational model
The shape of abrasive particle is set as that cone-apex angle is 2θ pCone, abrasive particle is uniformly distributed on wheel face, between abrasive particle
Away from forλ g.According to geometrical relationship, wheel face equation is：
,(8)
In formula：
rAbrasive wheel grinding wheel arc radius；
θThe abrasive wheel grinding wheel arc anglec of rotation；
REmery wheel base radius；
βThe emery wheel basis anglec of rotation；
θ AEmery wheel greatest circle hook corner；
X oEmery wheel centerXAxial coordinate；
Y oEmery wheel centerYAxial coordinate；
Z oEmery wheel centerZAxial coordinate.
By formula（8）Determine the locus of any abrasive particle.
2. at processing stand, abrasive particle locus calculates
Current processing stand P i Locating abrasive particle space position parameter is（θ i ,β i ）, calculate the abrasive wheel grinding wheel arc anglec of rotationθ i
(9)
Calculate the emery wheel basis anglec of rotationβ i
(10)
3. contact area abrasive particle judges
By the step 2. abrasive wheel grinding wheel arc anglec of rotationθ i , emery wheel basis the anglec of rotationβ i It is updated to formula（8）In, try to achieve at processing stand
The locus coordinate on abrasive particle summitP g（x pi ,z pi ,y pi ）, according tox pi 、z pi It is brought into formula（2）Calculate the workpiece of this position
Space surface coordinateW(x pi ,z pi ,y wi ).Calculatel yi =y wi -y pi , according to given threshold valueK l （K l =ρ/2）, whenl yi <K l , that is, abrasive particle apex coordinate in workpiece to be processed interior surface it is believed that this abrasive particle belongs to the contact area of emery wheel and workpiece
Abrasive particle, is otherwise not belonging to contact area abrasive particle；
4. searching loop contact area abrasive particle
Centered on single abrasive particle at processing stand, respectively along this abrasive particle locus（θ i 、β i ）'sθWithβJust
（Negative）Direction, travels through the continuous abrasive particle of surrounding, judges whether current abrasive particle belongs to contact area abrasive particle according to step method 3.,
So that it is determined that the scope of contact area, obtain all contact area abrasive particles；
（2）The judgement of active grain
According to emery wheel opposite piece direction of feed, determine effective mill of actual participation cutting in wheel face contact area
Grain.By current processing stand position P i Point to next processing stand position P i+1Calculate current emery wheel direction of feedN S.Calculate contact
Region abrasive particle normal directionN p（N p=-N）With emery wheel direction of feedN SAngleθ LS ：
(11)
Whenθ LS Less than or equal to pi/2 is then active grain, and the abrasive particle that angle is more than pi/2 is then considered as non-effective abrasive particle.
3）Wheel grinding region grinding force calculates
According to single abrasive particleXAxially cutting componentF gx、YAxially cutting componentF gy WithZAxially cutting componentF gz, will
Axially cutting component are added up above-mentioned the three of all active grains, when finally being processed emery wheel at current processing stand three
Axial grinding component is：
(12)
Above-mentioned searching loop contact area abrasive particle concrete grammar is as follows：
（1）In order to respectively to the abrasive wheel grinding wheel arc anglec of rotationθ i , emery wheel basis the anglec of rotationβ i Just（Negative）Direction circulation deflection,
Searchθ、βAdjacent abrasive grains on direction, according to abrasive wheel grinding wheel arc radiusr, emery wheel base radiusRWith abrasive particle spacingλ g, by several
What relation calculatesθ、βOffset Δθ、Δβ：
(13)
（2）EdgeβJust (bear) side offset up a Δβ, then 3. judge whether to belong to contact area according to step
Interior；
（3）When belonging in contact area, edgeθJust（Negative）Start on direction to offset a Δθ, and according to step 3.
Judge whether current abrasive particle belongs to contact area abrasive particle if it is decided that as a result, then continuing one Δ of skew in this directionθ
Continue step judgement 3., until abrasive particle result of determination is no in this direction（It is not belonging to contact area abrasive particle）, it is then back to
Step b；
（4）Until step（2）In,βJust（Negative）3. abrasive particle after side offsets up judges to be not admitted to by step
Contact area abrasive particle, then terminate all to search for.
The invention has the beneficial effects as follows：
The aspherical parallel grinding and cutting processing grinding force computational methods of the present invention can achieve to latheX、Y、ZThree axially grind
Cut the theoretical calculation of component.This computational methods can design for associated machine tool, the research such as Aspheric grinding Intelligent Process Control, set
Meter work provides required theoretical foundation.
Brief description
Fig. 1 is the basic step schematic flow sheet of the present invention；
Fig. 2 is the active grain search routine schematic diagram of the present invention.
Specific embodiment
In conjunction with accompanying drawing, technical scheme is further elaborated.
As shown in figure 1, the grinding force computational methods of the aspherical parallel grinding and cutting processing of the present invention, step includes：1st, single
Abrasive grain cutting power calculates：Carry out single abrasive particle force analysis, obtain the cutting component in three axial directions for the single abrasive particle；2nd, active grain
Search：According to the movement relation of emery wheel and workpiece, determine all active grains participating in cutting in process；3rd, wheel grinding
Region grinding force calculates：Cutting force according to single abrasive particle calculates, and whole active grains are added up, and calculates three axles of emery wheel
To grinding component.
Calculate single abrasive grain cutting power first, according to single abrasive particle geometry, emery wheel direction of feed, specific cutting force meter
Calculate single abrasive grain cutting power sizeF g, calculate locus on emery wheel for the single abrasive particle using wheel face equation, by non-
Unit normal vector at spherical surface shape equation solution work pieces process pointN, calculateNThe unit vector consistent with grain motion directionN m
Vector productN a, determine equivalent direction of principal axis, according to spin matrix shift theory, byN aWith standard spin matrixTrotTake advantage of
The long-pending vector calculating single abrasive grain cutting direction of expressionN F, by single abrasive grain cutting power sizeF gAnd cutting directionN FCalculate
Single abrasive particle existsX、Y、ZThree axially cut component；Then carry out active grain search, single abrasive particle at calculating processing point
Locus, is less than the depth of surface of the work, judges whether this abrasive particle is in the contact zone of emery wheel and workpiece according to abrasive particle top
Domain, is distributed in wheel face according to abrasive particle, is circulated traversal to the abrasive particle of surrounding at processing stand, determines all of contact area
Abrasive particle, according to the direction of feed of emery wheel opposite piece, determines the active grain of actual participation cutting in contact area abrasive particle；Finally
Carry out wheel grinding region grinding force to calculate, the three of active grain are axially cut component and added up, obtain emery wheel current
The axial grinding component of the three of processing stand；The all processing stands of surface of the work are traveled through by said method, realizes whole process
Grinding force calculates.
The circular of the present invention：
1）Single abrasive grain cutting power calculates
（1）Single abrasive grain cutting power sizeF gCalculate
Abrasive particle is with grinding deptha gFeeding incision surface of the work, when abrasive particle comes into contact with workpiece, by the drag of workpiece
Effect, single abrasive grain cutting powerF gAct perpendicularly to, on the abrasive particle conical surface, be expressed as
(1)
In formula：
F p(specific cutting force is the main cutting acting on during grinding work piece on unit grinding area to specific cutting force
Power)；
AAbrasive particle and the contact surface area of workpiece；
θ pHalf cone-apex angle of abrasive particle；
θ dAbrasive grain cutting force direction and the angle of emery wheel direction of feed.
Abrasive particle and the contact surface area of workpieceAFor
(2)
In formulaρ ——For abrasive particle element of cone effective length.Simultaneous formula（1）With（2）, then single abrasive grain cutting powerF gFor
(3)
（2）Single abrasive grain cutting directionN F Calculate
The cutting direction of wheel face abrasive particle changes with machining locus and changes, according to the sky of surface of the work difference processing stand
Between position, calculate single abrasive particle spatial attitude of emery wheel and workpiece contact zone, obtain the arrow representing single abrasive grain cutting direction
AmountN F , step is as follows：
1. set aspheric surface equation as
y=y(x,z) (4)
Surface of the work current processing stand position coordinates is P i （x i ,z i ,y i ）, then this P i Unit normal vector at pointN
(nxi,nzi,nyi) be
(5)
N mFor representing the unit vector in grain motion direction, by emery wheel feed speedN SGeostrophic with emery wheel single
Abrasive particle linear velocityV pObtain after superposition calculation, thenNWithN mTwo vectors specific vertical vector under right hand ruleN a（q 1,q 2,q 3）For
(6)
According to equivalent axis rotation matrix method, by left hand criterion by specific vertical vectorN aIt is set to equivalent direction of principal axis.
2. according to spin matrix shift theory, represent the vector in single abrasive grain cutting directionN FFor
(7)
In formula：TrotStandard spin matrix.N FFor 4D homogeneous coordinates（q x ,q y,q z, 1）, byN F Respectively
Calculate single abrasive particle cutting direction withX、Y、ZShaft space angleθ x 、θ y 、θ z：
(8)
（3）Single abrasive particleX、Y、ZThree axially cutting component calculating
According to single abrasive grain cutting direction, calculate single abrasive grain cutting power and existX、YAndZThe cutting component of axial directionF x 、F y WithF zFor：
(9)
2）Active grain is searched for（Fig. 2）
The active grain cutting is participated in search process.Face shape first according to workpiece and emery wheel, in conjunction between abrasive particle
Away fromλ gWith grinding and feeding amounta g, determine all abrasive particles with absorption surface in process；Further according to emery wheel direction of feed with connect
The position relationship of abrasive particle in tactile region, determines the active grain of all actual participation cuttings.
（1）Search contact area abrasive particle
1. set up single abrasive grain locations relational model
Wheel face equation is：
,(10)
In formula
rAbrasive wheel grinding wheel arc radius；
θThe abrasive wheel grinding wheel arc anglec of rotation；
REmery wheel base radius；
βThe emery wheel basis anglec of rotation；
θ AEmery wheel greatest circle hook corner；
X oEmery wheel centerXAxial coordinate；
Y oEmery wheel centerYAxial coordinate；
Z oEmery wheel centerZAxial coordinate.
According to formula（10）Can determine that the locus of any abrasive particle.The shape of abrasive particle is set as the circle with certain drift angle
Cone, cone-apex angle is 2θ p, and abrasive particle is uniformly distributed on wheel face, abrasive particle spacing isλ g.
2. at processing stand, abrasive particle locus calculates
According to formula（10）If current processing stand P i Place abrasive particle locus is（θ i ,β i ）, according to parallel grinding and cutting principle,
Unit normal vector at processing standNWith the abrasive wheel grinding wheel arc anglec of rotationθ i With the emery wheel basis anglec of rotationβ i Possesses following relation：θ i For adding
Unit normal vector at work pointNByZOYIn planeYAxle rotates toNIn the angle of this plane projection, during rotation, ensure rotation
Angle be acute angle, that is,n yi >When 0, byYAxle forward direction is rotated,n yi <When 0, byYAxle negative sense is rotated；Whenn zi >0
When,θ i Take positive number,n zi <When 0,θ i Take negative.I.e.
(11)
β i For processing stand unit normal vectorNByXOYIn planeXAxle forward direction rotates counterclockwise toNThrow in this plane
The angle of shadow, that is,
(12)
Then try to achieve abrasive particle locus at processing stand（θ i ,β i ）.
3. contact area abrasive particle judges
By the abrasive wheel grinding wheel arc anglec of rotationθ i , emery wheel basis the anglec of rotationβ i It is updated to formula（10）In, try to achieve abrasive particle top at processing stand
The locus coordinate of pointP g（x pi ,z pi ,y pi ）, willx pi 、z pi It is brought into formula（4）Calculate the surface of the work space of this position
CoordinateW(x pi ,z pi ,y wi ).Calculatel yi =y wi -y pi , according to given threshold valueK l （K l =ρ/2）, whenl yi <K l , that is, abrasive particle apex coordinate in workpiece to be processed interior surface, then judge that this abrasive particle belongs to the contact area mill of emery wheel and workpiece
Grain.
4. searching loop contact area abrasive particle
Centered on single abrasive particle at processing stand, respectively along the abrasive particle locus of emery wheel（θ i 、β i ）'sθWithβJust
（Negative）Direction, travels through the continuous abrasive particle of surrounding, determines whether to belong to contact area abrasive particle according to step method 3., so that it is determined that
The scope of contact area.Searching loop method is as follows：
A. in order to respectively to the abrasive wheel grinding wheel arc anglec of rotationθ i , emery wheel basis the anglec of rotationβ i Just（Negative）Direction deflects, searchθ
、βAdjacent abrasive grains on direction, according to abrasive wheel grinding wheel arc radiusr, emery wheel base radiusRWith abrasive particle spacingλ g, by geometrical relationship
Calculate adjacent abrasive grains to existθ、βOn offset Δθ、Δβ：
(13)
B. edgeβJust (bear) side offset up a Δβ, then 3. judge whether to belong to contact area according to step
Interior；
C. when belonging in contact area, edgeθJust（Negative）Side offsets up a Δθ, and 3. judged according to step
Whether current abrasive particle belongs to contact area abrasive particle if it is decided that as a result, then continuing one Δ of skew in this directionθ, and continue
The judgement 3. of continuous step, until abrasive particle result of determination is no in this direction（It is not belonging to contact area abrasive particle）, it is then back to walk
Rapid b；
D. in step b,βJust（Negative）3. abrasive particle after side offsets up judges to be not admitted to connect by step
Tactile region abrasive particle, then terminate all to search for.
So far obtain and all be in the contact area abrasive particle that emery wheel is overlapped with workpiece.
（2）The judgement of active grain
According to emery wheel opposite piece direction of feed, determine effective mill of actual participation cutting in wheel face contact area
Grain.By current processing stand P i Next processing stand position P is pointed in position i+1Calculate current emery wheel direction of feedN S.Calculate contact
Region abrasive particle normal directionN p（N p=-N）With emery wheel direction of feedN SAngleθ LS For：
(14)
Whenθ LS Less than or equal to pi/2 is then active grain, and the abrasive particle that angle is more than pi/2 is then considered as non-effective abrasive particle.
3）Wheel grinding region grinding force calculates
According to single abrasive particleX、Y、ZAxially cutting componentF gx、F gy WithF gz, the three of all active grains are axially cut
Cut component to be added up, when finally being processed, three axial grinding component at current processing stand for the emery wheel are：
(15)
The all processing stands of surface of the work are traveled through by said method, the grinding force realizing whole process calculates.
Claims (2)
1. a kind of grinding force computational methods of aspherical parallel grinding and cutting processing are it is characterised in that comprise the following steps：
1）Single abrasive grain cutting power calculates
（1）Single abrasive grain cutting power size calculates
(1)
In formula：
F pSpecific cutting force, specific cutting force is the main cutting force acting on during grinding work piece on unit grinding area；
θ pHalf cone-apex angle of abrasive particle；
θ dCutting force direction and the angle of emery wheel direction of feed；
ρ——For abrasive particle element of cone effective length；
（2）Single abrasive grain cutting direction calculating
According to the locus of surface of the work difference processing stand, calculate the space appearance of emery wheel and single abrasive particle of workpiece contact zone
State, obtains the vector representing single abrasive grain cutting directionN F , step is as follows：
1. aspheric surface equation is：
y=y(x,z) (2)
Surface of the work current processing stand position unit normal vectorN(n xi ,n zi ,n yi ) be：
(3)
N mFor representing the unit vector in grain motion direction, by emery wheel feed speedN SSingle abrasive particle line geostrophic with emery wheel
SpeedV pObtain after superposition calculation, then calculateNWithN mVector productN a：
(4)
According to equivalent axis rotation matrix method, by left hand criterion by specific vertical vectorN aIt is set to equivalent direction of principal axis；
2. according to spin matrix shift theory, represent the vector in single abrasive grain cutting directionN FFor：
(5)
In formula：
TrotStandard spin matrix；
By vectorN F Calculate this single abrasive grain cutting direction withX、Y、ZShaft space angleθ x 、θ y Withθ z：
(6)
（3）Single abrasive particleX、Y、ZThree axially cutting component calculating
According to single abrasive grain cutting direction, by single abrasive grain cutting powerF gIt is decomposed intoXAxially cutting componentF x 、YAxially cut
ComponentF y WithZAxially cutting componentF z, known by geometrical relationship：
(7)
2）Active grain is searched for
（1）Search contact area abrasive particle
1. set up single abrasive grain locations relational model
The shape of abrasive particle is set as that cone-apex angle is 2θ pCone, abrasive particle is uniformly distributed on wheel face, and abrasive particle spacing isλ g, according to geometrical relationship, wheel face equation is：
,(8)
In formula：
rAbrasive wheel grinding wheel arc radius；
θThe abrasive wheel grinding wheel arc anglec of rotation；
REmery wheel base radius；
βThe emery wheel basis anglec of rotation；
θ AEmery wheel greatest circle hook corner；
X oEmery wheel centerXAxial coordinate；
Y oEmery wheel centerYAxial coordinate；
Z oEmery wheel centerZAxial coordinate；
By formula（8）Determine the locus of any abrasive particle；
2. at processing stand, abrasive particle locus calculates
Current processing stand P i Locating abrasive particle space position parameter is（θ i ,β i ）, calculate the abrasive wheel grinding wheel arc anglec of rotationθ i
(9)
Calculate the emery wheel basis anglec of rotationβ i
(10)
3. contact area abrasive particle judges
By the step 2. abrasive wheel grinding wheel arc anglec of rotationθ i , emery wheel basis the anglec of rotationβ i It is updated to formula（8）In, try to achieve abrasive particle top at processing stand
The locus coordinate of pointP g（x pi ,z pi ,y pi ）, according tox pi 、z pi It is brought into formula（2）The surface of the work calculating this position is empty
Between coordinateW(x pi ,z pi ,y wi )；Calculatel yi =y wi -y pi , according to given threshold valueK l , whereinK l =ρ/ 2, whenl yi <K l , that is, abrasive particle apex coordinate in workpiece to be processed interior surface it is believed that this abrasive particle belongs to the contact area of emery wheel and workpiece
Abrasive particle, is otherwise not belonging to contact area abrasive particle；
4. searching loop contact area abrasive particle
Centered on single abrasive particle at processing stand, respectively along this abrasive particle locus（θ i 、β i ）'sθWithβPositive negative direction,
According to step method 3., the traversal continuous abrasive particle of surrounding, judges whether current abrasive particle belongs to contact area abrasive particle, so that it is determined that
The scope of contact area, obtains all contact area abrasive particles；
（2）The judgement of active grain
According to emery wheel opposite piece direction of feed, determine the active grain of actual participation cutting in wheel face contact area；By
Current processing stand position P i Point to next processing stand position P i+1Calculate current emery wheel direction of feedN S；Calculate contact area mill
Grain normal directionN p, whereinN p=-N, with emery wheel direction of feedN SAngleθ LS ：
(11)
Whenθ LS Less than or equal to pi/2 is then active grain, and the abrasive particle that angle is more than pi/2 is then considered as non-effective abrasive particle；
3）Wheel grinding region grinding force calculates
According to single abrasive particleXAxially cutting componentF gx、YAxially cutting componentF gy WithZAxially cutting componentF gz, will own
Axially cutting component is added up above-mentioned the three of active grain, three axial directions at current processing stand for emery wheel when finally being processed
Grinding component is：
(12) .
2. aspherical parallel grinding and cutting processing according to claim 1 grinding force computational methods it is characterised in that：Described follow
Ring traversal contact area abrasive particle concrete grammar is as follows：
（1）In order to respectively to the abrasive wheel grinding wheel arc anglec of rotationθ i , emery wheel basis the anglec of rotationβ i The circulation deflection of positive negative direction, searchθ、βAdjacent abrasive grains on direction, according to abrasive wheel grinding wheel arc radiusr, emery wheel base radiusRWith abrasive particle spacingλ g, by geometrical relationship meter
Calculateθ、βOffset Δθ、Δβ：
(13)
（2）EdgeβJust (bear) side offset up a Δβ, then 3. judge whether to belong in contact area according to step；
（3）When belonging in contact area, edgeθPositive negative direction on start to offset a Δθ, and 3. judge to work as according to step
Whether front abrasive particle belongs to contact area abrasive particle if it is decided that as a result, then continuing one Δ of skew in this directionθContinue step
Rapid judgement 3., until abrasive particle result of determination is no in this direction, that is, is not belonging to contact area abrasive particle, is then back to step b；
（4）Until step（2）In,βPositive negative direction on offset after abrasive particle 3. judge to be not admitted to contact zone by step
Domain abrasive particle, then terminate all to search for.
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| CN106446403A (en) * | 2016-09-22 | 2017-02-22 | 北京航空航天大学 | Virtual grinding wheel simulation method based on randomly distributed multiple abrasive particles |
| CN106971078B (en) * | 2017-04-11 | 2020-01-14 | 重庆大学 | Grinding force accurate prediction method considering motion parameters in screw grinding process |
| CN108287955B (en) * | 2018-01-10 | 2021-08-03 | 南京理工大学 | Method for predicting surface morphology of zirconia ceramic by ultrasonic vibration assisted grinding |
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