CN103995979A - Grinding force computing method for aspheric surface parallel grinding machining - Google Patents
Grinding force computing method for aspheric surface parallel grinding machining Download PDFInfo
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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 aspheric surface parallel grinding and cutting job operation, relate in particular to a kind of grinding force computing method of aspheric surface parallel grinding and cutting processing.
Background technology
Aspheric surface workpiece, due to its complicated face shape profile, is more unmanageable object in grinding always.Non-axisymmetric aspheric surface workpiece is as a kind of special aspheric surface, and its job operation is relatively more complicated, conventionally adopts three-shaft linkage lathe to process.Parallel grinding and cutting is a kind of effective job operation for non-axisymmetric aspheric surface workpiece (seeing that the patent No. is " parallel grinding and cutting method of non-axisymmetric aspheric surface optical element " of ZL 200710009306.3), the method adopts Arc Diamond Wheel (abbreviation emery wheel), add and make man-hour the cutting direction of emery wheel identical with the direction of motion of workpiece, be that grinding speed is parallel with work speed direction, the grinding points track on emery wheel is circle distribution.When the advantage of this method maximum is grinding, on emery wheel, grinding points is mobile, and the effective cutting edge that participates in grinding increases, and emery wheel effectively uses width to increase, and abrasion of grinding wheel obviously reduces, and machining precision is protected.
Grinding force is an extremely important parameter in Grinding Process, one of it not only affects system variant, grinding efficiency, machining precision, surface quality, emery wheel durability, grinding heat, grinding vibration, and the parameter that need to pay close attention to while being superfine grinding Machine Tool design.Due in aspheric surface parallel grinding and cutting job operation, the kinematic relation of emery wheel and workpiece is comparatively complicated, tradition grinding force computing method cannot accurately be calculated the grinding force under this processing mode, the patent No. is " parallel grinding and cutting method of non-axisymmetric aspheric surface optical element " detailed this job operation of elaboration of 200710009306.3, but does not relate to the grinding force computing method of parallel grinding and cutting.Therefore, be difficult to accurately calculate the grinding force of this job operation, the work in everies such as associated machine tool parameter designing and process environmental monitoring are brought greater inconvenience.The present invention is directed to the needs of the links such as the design of aspheric surface parallel grinding and cutting process unit, processing monitoring, fault diagnosis, invented a kind of grinding force computing method of aspheric surface parallel grinding and cutting processing.
Summary of the invention
The present invention is the grinding force computing method that a kind of aspheric surface parallel grinding and cutting processing will be provided, for accurately calculating the grinding force of this job operation, the convenience that the work in everies such as associated machine tool parameter designing and process environmental monitoring are brought.
For achieving the above object, technical scheme of the present invention is:
Grinding force computing method for aspheric surface parallel grinding and cutting processing, is characterized in that, comprise the following steps:
1) single abrasive grain cutting power is calculated
(1) single abrasive grain cutting power size is calculated.
(1)
In formula
f p---unit grinding force (main cutting force when unit grinding force is grinding work piece on the unit's of acting on grinding area);
θ p---half cone apex angle of abrasive particle;
θ d---the angle of cutting force direction and 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 the different processing stands of surface of the work, calculate the spatial attitude of single abrasive particle of emery wheel and workpiece contact area, obtain the vector that represents single abrasive grain cutting direction
n f , step is as follows:
1. aspheric surface equation is
y=
y(
x,
z) (2)
The current processing stand of surface of the work position unit normal vector
n(
nxi,
nzi,
nyi) be:
(3)
n mfor representing the unit vector of abrasive particle direction of motion, by emery wheel speed of feed
n swith geostrophic single the abrasive particle linear velocity of emery wheel
v pafter superposition calculation, obtain, then calculate
nwith
n mvector product
n a:
(4)
According to equivalent axis rotation matrix method, by left hand criterion by unit vertical vector
n abe made as equivalent axis direction;
2. according to rotation matrix shift theory, represent the vector of single abrasive grain cutting direction
n ffor:
(5)
In formula:
trot---standard rotation matrix
By vector
n f calculate this single abrasive grain cutting direction with
x,
y,
zshaft space angle
θ x ,
θ y with
θ z:
(6)
(3) single abrasive particle
x,
y,
zthree axially cutting component calculating
According to single abrasive grain cutting direction, by single abrasive grain cutting power
f gbe decomposed into
xaxially cut component
f x ,
yaxially cut component
f y with
zaxially cut component
f z, by geometric relationship, known:
(7)
2) active grain search
(1) search contact area abrasive particle
1. set up single abrasive particle position relationship model
It is 2 that the shape of abrasive particle is set as to cone apex angle
θ ptaper shape, abrasive particle is uniformly distributed on wheel face, abrasive particle spacing is
λ g.According to geometric relationship, wheel face equation is:
，
(8)
In formula:
r---abrasive wheel grinding wheel arc radius;
θ---abrasive wheel grinding wheel arc rotation angle;
r---emery wheel base radius;
β---emery wheel basis rotation angle;
θ a---emery wheel greatest circle hook corner;
x o---emery wheel center
xaxial coordinate;
y o---emery wheel center
yaxial coordinate;
z o---emery wheel center
zaxial coordinate.
By formula (8), determined the locus of any abrasive particle.
2. calculate abrasive particle locus, processing stand place
Current processing stand P
i place's abrasive particle space position parameter be (
θ i ,
β i ), calculate abrasive wheel grinding wheel arc rotation angle
θ i
(9)
Calculate emery wheel basis rotation angle
β i
(10)
3. contact area abrasive particle is judged
By 2. abrasive wheel grinding wheel arc rotation angle of step
θ i , emery wheel basis rotation angle
β i be updated in formula (8), try to achieve the locus coordinate on abrasive particle summit, processing stand place
p g(
x pi ,
z pi ,
y pi ), according to
x pi ,
z pi be brought into formula (2) and calculate the surface of the work volume coordinate of this position
w(
x pi ,
z pi ,
y wi ).Calculate
l yi =
y wi -
y pi , according to given threshold value
k l (
k l =
ρ/ 2), when
l yi <
k l , abrasive particle apex coordinate, in workpiece to be processed interior surface, is thought that this abrasive particle belongs to the contact area abrasive particle of emery wheel and workpiece, otherwise is not belonged to contact area abrasive particle;
4. searching loop contact area abrasive particle
Centered by single the abrasive particle at processing stand place, respectively along this abrasive particle locus (
θ i ,
β i )
θwith
βjust (bear) direction, the continuous abrasive particle of traversal surrounding, judges according to step method 3. whether current abrasive particle belongs to contact area abrasive particle, thereby determines the scope of contact area, obtains all contact area abrasive particles;
(2) judgement of active grain
According to the relative workpiece direction of feed of emery wheel, 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+ 1
calculate current emery wheel direction of feed
n s.Calculate contact area abrasive particle normal direction
n p(
n p=-
n) and emery wheel direction of feed
n sangle
θ lS :
(11)
When
θ lS what be less than or equal to pi/2 is active grain, and the abrasive particle that angle is greater than pi/2 is considered as non-effective abrasive particle.
3) wheel grinding region grinding force calculates
According to single abrasive particle
xaxially cut component
f gx
,
yaxially cut component
f gy with
zaxially cut component
f gz
, by all active grains above-mentioned three axially cutting component add up, obtain finally adding the three axial grinding component of emery wheel in man-hour at current processing stand place and be:
(12)
Above-mentioned searching loop contact area abrasive particle concrete grammar is as follows:
(1) for respectively to abrasive wheel grinding wheel arc rotation angle
θ i , emery wheel basis rotation angle
β i just (bear) direction circulation deflection, search
θ,
βadjacent abrasive particle in direction, according to abrasive wheel grinding wheel arc radius
r, emery wheel base radius
rwith abrasive particle spacing
λ g, by geometric relationship, calculated
θ,
βoffset Δ
θ, Δ
β:
(13)
(2) edge
βjust (bear) and in direction, be offset a Δ
β, then according to step, 3. judge whether to belong in contact area;
(3) in the time of within belonging to contact area, edge
θjust (bear) and in direction, start to be offset a Δ
θ, and 3. judge according to step whether current abrasive particle belongs to contact area abrasive particle, if result of determination is upwards to continue a Δ of skew the party
θcontinue step judgement 3., until the party makes progress, abrasive particle result of determination is no (not belonging to contact area abrasive particle), then returns to step b;
(4) until in step (2),
βthe abrasive particle of just (bearing) in direction after skew by step, 3. judge and all do not belong to contact area abrasive particle, finish whole search.
The invention has the beneficial effects as follows:
Aspheric surface parallel grinding and cutting processing grinding force computing method of the present invention can realize lathe
x,
y,
zthe theory of three axial grinding component is calculated.Research, the design efforts such as these computing method can design for associated machine tool, Aspheric grinding Intelligent Process Control provide required theoretical foundation.
Accompanying drawing explanation
Fig. 1 is basic step schematic flow sheet of the present invention;
Fig. 2 is active grain search routine schematic diagram of the present invention.
Embodiment
Now by reference to the accompanying drawings technical scheme of the present invention is further elaborated.
As shown in Figure 1, the grinding force computing method of aspheric surface parallel grinding and cutting processing of the present invention, step comprises: 1, single abrasive grain cutting power is calculated: carry out single abrasive particle force analysis, obtain single abrasive particle at three axial cutting component; 2, active grain search: according to the kinematic relation of emery wheel and workpiece, determine the active grain of all participation cuttings in process; 3, wheel grinding region grinding force calculates: according to the cutting force of single abrasive particle, calculate, whole active grains are added up, calculate three axial grinding component of emery wheel.
First calculate single abrasive grain cutting power, according to single abrasive particle geometric configuration, emery wheel direction of feed, unit grinding force, calculate single abrasive grain cutting power size
f g, utilize wheel face equation to calculate the locus of single abrasive particle on emery wheel, by aspheric surface equation solution workpiece processing stand place unit normal vector
n, calculate
nthe unit vector consistent with abrasive particle direction of motion
n mvector product
n a, determine equivalent axis direction, according to rotation matrix shift theory, by
n awith standard rotation matrix
trotproduct calculate to represent the vector of single abrasive grain cutting direction
n f, by single abrasive grain cutting power size
f gand cutting direction
n fcalculating single abrasive particle exists
x,
y,
zthree axially cut component; Then carry out active grain search, the locus of single the abrasive particle in calculating processing point place, the degree of depth according to abrasive particle top lower than surface of the work, judge the whether contact area in emery wheel and workpiece of this abrasive particle, according to abrasive particle, at wheel face, distribute, the abrasive particle of processing stand place surrounding is carried out to searching loop, determine all contact area abrasive particles, according to the direction of feed of the relative workpiece of emery wheel, determine the active grain of actual participation cutting in contact area abrasive particle; Finally carry out wheel grinding region grinding force and calculate, by three of active grain, axially cut component and add up, obtain emery wheel at three axial grinding component of current processing stand; By said method, travel through all processing stands of surface of the work, the grinding force of realizing whole process calculates.
Circular of the present invention:
1) single abrasive grain cutting power is calculated
(1) single abrasive grain cutting power size
f gcalculate
Abrasive particle is with grinding depth
a gfeeding incision surface of the work, when abrasive particle starts to contact workpiece, is subject to the effect of elastic resistance of workpiece, single abrasive grain cutting power
f gvertically act on the abrasive particle conical surface, be expressed as
(1)
In formula:
f p---unit grinding force (main cutting force when unit grinding force is grinding work piece on the unit's of acting on grinding area);
a---the contact surface area of abrasive particle and workpiece;
θ p---half cone apex angle of abrasive particle;
θ d---the angle of abrasive grain cutting force direction and emery wheel direction of feed.
The contact surface area of abrasive particle and workpiece
afor
(2)
In formula
ρ---for abrasive particle element of cone effective length.Simultaneous formula (1) and (2), single abrasive grain cutting power
f gfor
(3)
(2) single abrasive grain cutting direction
n f calculate
The cutting direction of wheel face abrasive particle changes with machining locus, according to the locus of the different processing stands of surface of the work, calculates single abrasive particle spatial attitude of emery wheel and workpiece contact area, obtains the vector that represents single abrasive grain cutting direction
n f , step is as follows:
1. establishing aspheric surface equation is
y=
y(
x,
z) (4)
The current processing stand position coordinates of surface of the work is P
i (
x i ,
z i ,
y i ), this P
i point place unit normal vector
n(
nxi,
nzi,
nyi) be
(5)
n mfor representing the unit vector of abrasive particle direction of motion, by emery wheel speed of feed
n swith geostrophic single the abrasive particle linear velocity of emery wheel
v pafter superposition calculation, obtain,
nwith
n mtwo vectors unit vertical vector under right hand rule
n a(
q 1,
q 2,
q 3) be
(6)
According to equivalent axis rotation matrix method, by left hand criterion by unit vertical vector
n abe made as equivalent axis direction.
2. according to rotation matrix shift theory, represent the vector of single abrasive grain cutting direction
n ffor
(7)
In formula:
trot---standard rotation matrix.
n ffor 4D homogeneous coordinates (
q x ,
q y,
q z, 1), by
n f the cutting direction of calculating respectively single abrasive particle with
x,
y,
zshaft space angle
θ x ,
θ y ,
θ z:
(8)
(3) single abrasive particle
x,
y,
zthree axially cutting component calculating
According to single abrasive grain cutting direction, calculate single abrasive grain cutting power and exist
x,
yand
zaxial cutting component
f x ,
f y with
f zfor:
(9)
2) active grain search (Fig. 2)
In search process, participate in the active grain of cutting.First according to the face shape of workpiece and emery wheel, in conjunction with abrasive particle spacing
λ gwith grinding and feeding amount
a g, determine all abrasive particles that contact with workpiece in process; According to the position relationship of abrasive particle in emery wheel direction of feed and contact area, determine the active grain of all actual participation cuttings again.
(1) search contact area abrasive particle
1. set up single abrasive particle position relationship model
Wheel face equation is:
，
(10)
In formula
r---abrasive wheel grinding wheel arc radius;
θ---abrasive wheel grinding wheel arc rotation angle;
r---emery wheel base radius;
β---emery wheel basis rotation angle;
θ a---emery wheel greatest circle hook corner;
x o---emery wheel center
xaxial coordinate;
y o---emery wheel center
yaxial coordinate;
z o---emery wheel center
zaxial coordinate.
According to formula (10), can determine the locus of any abrasive particle.The shape of abrasive particle is set as having to the circular cone of certain drift angle, cone apex angle is 2
θ p, and abrasive particle is uniformly distributed on wheel face, and abrasive particle spacing is
λ g.
2. calculate abrasive particle locus, processing stand place
According to formula (10), establish current processing stand P
i place abrasive particle locus be (
θ i ,
β i ), according to parallel grinding and cutting principle, processing stand place unit normal vector
nwith abrasive wheel grinding wheel arc rotation angle
θ i with emery wheel basis rotation angle
β i possess following relation:
θ i for processing stand place unit normal vector
nby
zOYin plane
yaxle rotates to
nin the angle of this plane projection, during rotation, guarantee that the angle of rotation is acute angle,
n yi during >0, by
yaxle forward is rotated,
n yi during <0, by
yaxle negative sense is rotated; When
n zi during >0,
θ i get positive number,
n zi during <0,
θ i get negative.
(11)
β i for processing stand unit normal vector
nby
xOYin plane
xaxle forward is rotated counterclockwise
nin the angle of this plane projection,
(12)
Try to achieve abrasive particle locus, processing stand place (
θ i ,
β i ).
3. contact area abrasive particle is judged
By abrasive wheel grinding wheel arc rotation angle
θ i , emery wheel basis rotation angle
β i be updated in formula (10), try to achieve the locus coordinate on abrasive particle summit, processing stand place
p g(
x pi ,
z pi ,
y pi ), will
x pi ,
z pi be brought into formula (4) and calculate the surface of the work volume coordinate of this position
w(
x pi ,
z pi ,
y wi ).Calculate
l yi =
y wi -
y pi , according to given threshold value
k l (
k l =
ρ/ 2), when
l yi <
k l , abrasive particle apex coordinate, in workpiece to be processed interior surface, judges that this abrasive particle belongs to the contact area abrasive particle of emery wheel and workpiece.
4. searching loop contact area abrasive particle
Centered by single, processing stand place abrasive particle, respectively along the abrasive particle locus of emery wheel (
θ i ,
β i )
θwith
βjust (bearing) direction, the continuous abrasive particle of traversal surrounding, determines whether and belongs to contact area abrasive particle according to step method 3., thereby determines the scope of contact area.Searching loop method is as follows:
A. for respectively to abrasive wheel grinding wheel arc rotation angle
θ i , emery wheel basis rotation angle
β i just (bear) direction deflection, search
θ,
βadjacent abrasive particle in direction, according to abrasive wheel grinding wheel arc radius
r, emery wheel base radius
rwith abrasive particle spacing
λ g, by geometric relationship, calculate adjacent abrasive particle and exist
θ,
βon offset Δ
θ, Δ
β:
(13)
B. edge
βjust (bear) and in direction, be offset a Δ
β, then according to step, 3. judge whether to belong in contact area;
C. in the time of within belonging to contact area, edge
θjust (bear) and in direction, be offset a Δ
θ, and 3. judge according to step whether current abrasive particle belongs to contact area abrasive particle, if result of determination is upwards to continue a Δ of skew the party
θ, and continue step judgement 3., until the party makes progress, abrasive particle result of determination is no (not belonging to contact area abrasive particle), then returns to step b;
D. until in step b,
βthe abrasive particle of just (bearing) in direction after skew by step, 3. judge and all do not belong to contact area abrasive particle, finish whole search.
So far obtain all contact area abrasive particles that overlap with workpiece in emery wheel.
(2) judgement of active grain
According to the relative workpiece direction of feed of emery wheel, determine the active grain of actual participation cutting in wheel face contact area.By current processing stand P
i next processing stand position P is pointed in position
i+ 1
calculate current emery wheel direction of feed
n s.Calculate contact area abrasive particle normal direction
n p(
n p=-
n) and emery wheel direction of feed
n sangle
θ lS for:
(14)
When
θ lS what be less than or equal to pi/2 is active grain, and the abrasive particle that angle is greater than pi/2 is considered as non-effective abrasive particle.
3) wheel grinding region grinding force calculates
According to single abrasive particle
x,
y,
zaxially cut component
f gx
,
f gy with
f gz
, by all active grains three axially cutting component add up, obtain finally adding the three axial grinding component of emery wheel in man-hour at current processing stand place and be:
(15)
By said method, travel through all processing stands of surface of the work, the grinding force of realizing whole process calculates.
Claims (2)
1. grinding force computing method for aspheric surface parallel grinding and cutting processing, is characterized in that, comprise the following steps:
1) single abrasive grain cutting power is calculated
(1) single abrasive grain cutting power size is calculated
(1)
In formula:
f p---unit grinding force (main cutting force when unit grinding force is grinding work piece on the unit's of acting on grinding area);
θ p---half cone apex angle of abrasive particle;
θ d---the angle of cutting force direction and 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 the different processing stands of surface of the work, calculate the spatial attitude of single abrasive particle of emery wheel and workpiece contact area, obtain the vector that represents single abrasive grain cutting direction
n f , step is as follows:
1. aspheric surface equation is:
y=
y(
x,
z) (2)
The current processing stand of surface of the work position unit normal vector
n(
nxi,
nzi,
nyi) be:
(3)
n mfor representing the unit vector of abrasive particle direction of motion, by emery wheel speed of feed
n swith geostrophic single the abrasive particle linear velocity of emery wheel
v pafter superposition calculation, obtain, then calculate
nwith
n mvector product
n a:
(4)
According to equivalent axis rotation matrix method, by left hand criterion by unit vertical vector
n abe made as equivalent axis direction;
2. according to rotation matrix shift theory, represent the vector of single abrasive grain cutting direction
n ffor:
(5)
In formula:
trot---standard rotation matrix
By vector
n f calculate this single abrasive grain cutting direction with
x,
y,
zshaft space angle
θ x ,
θ y with
θ z:
(6)
(3) single abrasive particle
x,
y,
zthree axially cutting component calculating
According to single abrasive grain cutting direction, by single abrasive grain cutting power
f gbe decomposed into
xaxially cut component
f x ,
yaxially cut component
f y with
zaxially cut component
f z, by geometric relationship, known:
(7)
2) active grain search
(1) search contact area abrasive particle
1. set up single abrasive particle position relationship model
It is 2 that the shape of abrasive particle is set as to cone apex angle
θ ptaper shape, abrasive particle is uniformly distributed on wheel face, abrasive particle spacing is
λ g;
According to geometric relationship, wheel face equation is:
，
(8)
In formula:
r---abrasive wheel grinding wheel arc radius;
θ---abrasive wheel grinding wheel arc rotation angle;
r---emery wheel base radius;
β---emery wheel basis rotation angle;
θ a---emery wheel greatest circle hook corner;
x o---emery wheel center
xaxial coordinate;
y o---emery wheel center
yaxial coordinate;
z o---emery wheel center
zaxial coordinate;
By formula (8), determined the locus of any abrasive particle;
2. calculate abrasive particle locus, processing stand place
Current processing stand P
i place's abrasive particle space position parameter be (
θ i ,
β i ), calculate abrasive wheel grinding wheel arc rotation angle
θ i
(9)
Calculate emery wheel basis rotation angle
β i
(10)
3. contact area abrasive particle is judged
By 2. abrasive wheel grinding wheel arc rotation angle of step
θ i , emery wheel basis rotation angle
β i be updated in formula (8), try to achieve the locus coordinate on abrasive particle summit, processing stand place
p g(
x pi ,
z pi ,
y pi ), according to
x pi ,
z pi be brought into formula (2) and calculate the surface of the work volume coordinate of this position
w(
x pi ,
z pi ,
y wi );
Calculate
l yi =
y wi -
y pi , according to given threshold value
k l (
k l =
ρ/ 2), when
l yi <
k l , abrasive particle apex coordinate, in workpiece to be processed interior surface, is thought that this abrasive particle belongs to the contact area abrasive particle of emery wheel and workpiece, otherwise is not belonged to contact area abrasive particle;
4. searching loop contact area abrasive particle
Centered by single the abrasive particle at processing stand place, respectively along this abrasive particle locus (
θ i ,
β i )
θwith
βjust (bear) direction, the continuous abrasive particle of traversal surrounding, judges according to step method 3. whether current abrasive particle belongs to contact area abrasive particle, thereby determines the scope of contact area, obtains all contact area abrasive particles;
(2) judgement of active grain
According to the relative workpiece direction of feed of emery wheel, 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+ 1
calculate current emery wheel direction of feed
n s;
Calculate contact area abrasive particle normal direction
n p(
n p=-
n) and emery wheel direction of feed
n sangle
θ lS :
(11)
When
θ lS what be less than or equal to pi/2 is active grain, and the abrasive particle that angle is greater than pi/2 is considered as non-effective abrasive particle;
3) wheel grinding region grinding force calculates
According to single abrasive particle
xaxially cut component
f gx
,
yaxially cut component
f gy with
zaxially cut component
f gz
, by all active grains above-mentioned three axially cutting component add up, obtain finally adding the three axial grinding component of emery wheel in man-hour at current processing stand place and be:
(12)。
2. the grinding force computing method that aspheric surface parallel grinding and cutting according to claim 1 is processed, is characterized in that: described searching loop contact area abrasive particle concrete grammar is as follows:
(1) for respectively to abrasive wheel grinding wheel arc rotation angle
θ i , emery wheel basis rotation angle
β i just (bear) direction circulation deflection, search
θ,
βadjacent abrasive particle in direction, according to abrasive wheel grinding wheel arc radius
r, emery wheel base radius
rwith abrasive particle spacing
λ g, by geometric relationship, calculated
θ,
βoffset Δ
θ, Δ
β:
(13)
(2) edge
βjust (bear) and in direction, be offset a Δ
β, then according to step, 3. judge whether to belong in contact area;
(3) in the time of within belonging to contact area, edge
θjust (bear) and in direction, start to be offset a Δ
θ, and 3. judge according to step whether current abrasive particle belongs to contact area abrasive particle, if result of determination is upwards to continue a Δ of skew the party
θcontinue step judgement 3., until the party makes progress, abrasive particle result of determination is no (not belonging to contact area abrasive particle), then returns to step b;
(4) until in step (2),
βthe abrasive particle of just (bearing) in direction after skew by step, 3. judge and all do not belong to contact area abrasive particle, finish whole search.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105574249A (en) * | 2015-12-14 | 2016-05-11 | 北京工业大学 | Grinding force model for worm-shaped grinding wheel gear grinding |
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| CN106971078A (en) * | 2017-04-11 | 2017-07-21 | 重庆大学 | The accurate Forecasting Methodology of grinding force of kinematic parameter is considered in screw rod grinding process |
| CN108287955A (en) * | 2018-01-10 | 2018-07-17 | 南京理工大学 | A kind of prediction technique of supersonic vibration assistant grinding zirconia ceramics surface topography |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105574249A (en) * | 2015-12-14 | 2016-05-11 | 北京工业大学 | Grinding force model for worm-shaped grinding wheel gear grinding |
| CN105574249B (en) * | 2015-12-14 | 2018-08-28 | 北京工业大学 | The grinding force model of worm grinding wheel roll flute |
| 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 |
| CN106971078A (en) * | 2017-04-11 | 2017-07-21 | 重庆大学 | The accurate Forecasting Methodology of grinding force of kinematic parameter is considered in screw rod grinding process |
| CN106971078B (en) * | 2017-04-11 | 2020-01-14 | 重庆大学 | Grinding force accurate prediction method considering motion parameters in screw grinding process |
| CN108287955A (en) * | 2018-01-10 | 2018-07-17 | 南京理工大学 | A kind of prediction technique of supersonic vibration assistant grinding zirconia ceramics surface topography |
| 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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|---|---|
| CN103995979B (en) | 2017-02-15 |
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