CN102681488B - Modeling method for milling surface appearance of workpiece - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 49
- 238000003801 milling Methods 0.000 title claims abstract description 43
- 238000005520 cutting process Methods 0.000 claims abstract description 152
- 241000220317 Rosa Species 0.000 claims description 26
- 210000001138 tear Anatomy 0.000 claims description 8
- 230000002459 sustained effect Effects 0.000 claims description 5
- 238000012876 topography Methods 0.000 claims description 5
- 238000004458 analytical method Methods 0.000 claims description 4
- 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 claims description 3
- 238000005299 abrasion Methods 0.000 claims description 3
- 230000001550 time effect Effects 0.000 claims description 3
- 230000000875 corresponding effect Effects 0.000 description 37
- 238000010586 diagram Methods 0.000 description 5
- 238000003754 machining Methods 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 230000002596 correlated effect Effects 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 230000003746 surface roughness Effects 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
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Abstract
The invention discloses a modeling method for milling the surface appearance of a workpiece, belonging to the field of digital milling. The modeling method comprises the steps of carrying out dispersing treatment on the cutting edge of a ball-end mill according to cutting movement locus of a milling cutter; establishing infinitesimal cutting locus equation of the cutting edge of the ball-end mill, wherein the surface appearance of the cutting locus equation is formed by the outermost side locus in the established locus equation; determining corresponding cutter turning angle range for milling the outermost side locus by judging the cutting infinitesimal position angle range corresponding to the outermost side locus; calculating corresponding milling time for milling the locus by combining with angular rotation speed obtained through a cutter spindle rotation speed; and obtaining the outermost side milling locus through a helical lag angle at the cutting infinitesimal position, thus obtaining the surface appearance of the milling workpiece. The modeling method can solve the generation problem on the surface appearance of the workpiece in milling process.
Description
Technical field
The invention belongs to numerical control milling manufacture field, the workpiece surface appearance modeling field that particularly in numerical control milling processing, tool wear causes.
Background technology
Along with the development of modern mechanical manufacturing industry, more and more higher to the requirement of part processing precision.And in actual Milling Processes, owing to being subject to the impact of various factors inevitably can produce mismachining tolerance.Mismachining tolerance is to affect the very important factor of workpiece crudy, can make Workpiece Machining Accuracy obviously reduce, and excessive mismachining tolerance even can cause part to scrap, and has a strong impact on working (machining) efficiency and benefit.The microscopic appearance of surface of the work and workpiece surface roughness have close contact, the wearing quality of workpiece and assembly precision are had to material impact, also be the important indicator of reflection surface of the work crudy simultaneously, by the pattern of prediction surface of the work, can obtain the coordinate figure of any location point on workpiece, the theoretical coordinate value of itself and this point is contrasted, can obtain the mismachining tolerance value at this some place.
In order to improve the crudy of surface of the work, reduce mismachining tolerance, reduce roughness, domestic and international many scholars are studied workpiece surface appearance from microcosmic angle, have obtained some achievements.Successively propose some and set up the modeling method of workpiece surface appearance model.
The research that the factors such as the cutter distortion mostly modeling method of existing workpiece surface appearance is to cause with regard to cutting parameter selection, cutter positioning error, cutting force are carried out the impact of workpiece surface appearance, also seldom has the research of the impact of workpiece surface appearance being correlated with for the cutter Dynamic wear in rose cutter milling process at present.
For this reason, the present invention has overcome the deficiency of the modeling method existence of above-mentioned workpiece surface appearance, according to the feature of rose cutter cutting edge, sets up Cutting trajectory equation, and further tool wear is taken into account the impact of Cutting trajectory, the workpiece surface appearance after Cutter wear is studied.Analyze the change of shape of bulb cutting edge outline sword line after tool wear, can further analyze accordingly the Cutting trajectory of the relative workpiece of cutting edge after wearing and tearing, set up the Cutting trajectory equation of considering wearing and tearing, and then the workpiece surface appearance after being processed.
Summary of the invention
Object of the present invention, is to provide a kind of modeling method of Milling Process workpiece surface appearance, and it can solve modeling and the visual simulating problem of the workpiece surface appearance that in Milling Processes, tool wear causes.
In order to reach above-mentioned purpose, solution of the present invention is:
A modeling method for Milling Process workpiece surface appearance, is characterized in that comprising the steps:
(1) according to Milling Process Tool in Cutting movement locus, dividing cutting edge discrete ball head is a series of cutting infinitesimals, because difference cutting infinitesimal linear velocity when cutting is different, and in process, there is straight-line feed motion and self rotatablely moving around cutter spindle simultaneously, therefore, the movement locus that removes other point on bulb point of a knife ectosphere head cutting edge will form a series of trochoid, the pattern forming on workpiece in order to analyze Tool in Cutting track, the cutting infinitesimal P point of usining after discrete is as research object, motion by analysis site P in feed process, obtain putting the Cutting trajectory that P finally stays on workpiece after process finishing, remove the track that the cut trajectory of falling of work in-process obtains finally forming workpiece pattern, consider straight-line trajectory and rotational trajectory, when cutter weares and teares, the desired cut equation of locus that P is ordered as the formula (1):
Wherein, X ', Y ' for P point through cut the coordinate after the time, X
0, Y
0for P point origin coordinates, the tool feeding speed that v is the unit interval, t
1for cut time, t
2for the impact on this process time of the spiral drag angle of P point present position,
t=t
1-t
2,
for cutter spiral drag angle corresponding to P point,
for the residing position angle of P point
the cutter radial radius at place,
the rose cutter radius of R when not wearing and tearing, ω is cutter spindle angular velocity of rotation,
for the line of P point and bulb center O and the angle of cutter spindle Z, the angle that is description cutting infinitesimal position is called position angle;
When the impact of tool wear is taken into account, along with cutter constantly weares and teares, the corresponding radially radius of point on cutting edge on sustained height
and corresponding position angle
all will change, therefore, during tool abrasion in considering process, the Cutting trajectory that P is ordered can be represented by formula (2):
Wherein, X, Y for consider tool wear P point through cut the coordinate after the time, X
0, Y
0for P point origin coordinates, the tool feeding speed that v is the unit interval, t
1for cut time, t
2for the impact on this process time of the spiral drag angle of P point present position, and
for cutter spiral drag angle corresponding to P point, ω is cutter spindle angular velocity of rotation;
for the bulb of P point At The Height after tool wear radius radially, by formula (3), solved;
In formula, R is the radius of rose cutter while not wearing and tearing,
for the cutting plane height at cutting infinitesimal place, VB is
the tool flank wear of At The Height Tool in Cutting sword;
(2) the milling track obtaining according to milling equation of locus is not all to form workpiece surface appearance, part trajectory work in-process can be cut, only have outermost trajectory to form workpiece surface appearance, in order to determine outermost trajectory, need to solve the position of Tool in Cutting sword corresponding to outermost trajectory
angle span
obtain
in interval each
the Tool in Cutting trajectory that angle is corresponding, the set of these Cutting trajectory lines has just formed the workpiece surface appearance after processing;
Cutter is along the feeding of x axle, and the trajectory that y axle both sides are finally left to surface of the work is respectively P
1p
1' and P
2p
2', wanting to guarantee the existence of outermost track, the coordinate figure that cutting edge track must meet trajectory and feed shaft intersection point is greater than the straight-line feed amount f that cutter rotates a circle
p, obtain thus formula (5):
Above formula obtains
for the minimum value satisfying condition;
The maximal value of position angle is the position angle of the cutting point that the residual high highest point of workpiece surface appearance is corresponding, namely section angle of cut of twice feed in vertical feed direction axial cross section before and after cutter;
For direction of feed right side P
1p
1' this section of track,
size to discuss in two kinds of situation;
1) feed for the first time,
can be directly according to cutting depth a
pcalculate formula (6) with the geometric relationship of Z value maximum point in cutter under this cutting depth and workpiece contact point:
2) from feed for the second time,
with feed line-spacing f
psize have direct relation, can draw shown in the relational expression (7) between them:
P for direction of feed left side
2p
2' track,
size and P
1p
1' there is relative relation, for last feed,
size is shown in formula (8):
Feed is for the first time in the process of second from the bottom feed, and the outmost trajectory in left side is corresponding
value be all shown in formula (9):
(3) in order to obtain each position
the Cutting trajectory line that angle is corresponding, need to obtain respectively outermost trajectory P
1p
1' section and P
2p
2the tool motion time in ' section is interval, by obtaining the corner that P is ordered in this is interval, then try to achieve corresponding process time in conjunction with the speed of mainshaft of cutter, consider the spiral drag angle at place, cutting infinitesimal position, can obtain outermost pattern track, thereby obtain the surface topography of workpiece;
In order to set up P
1and P
2corresponding corner
with
formula, analyze P
1and P
2the corner of point in milling process;
For P
1point, from the negative y axle of starting point, x=0 place forwards P to
1time, P
1point horizontal ordinate meets formula (10) below:
That is:
Wherein, v is the amount of feeding of bulb cutter unit interval, and ω is cutter shaft rotational speed, and R is tool radius,
for P
1the position angle of point,
for position angle
locate corresponding cutter corner, and meet
For P
2point, from the negative y axle of starting point, x=0 place forwards P to
2time, P
2point horizontal ordinate meets formula (11) below:
That is:
Wherein, v is the amount of feeding of bulb cutter unit interval, and ω is cutter shaft rotational speed, and R is tool radius,
for P
2the position angle of point,
for position angle
locate corresponding cutter corner, and meet
Use Newton iteration method to solve nonlinear equation (10) and (11), obtain correspondence position
the cutter corner value at angle, in conjunction with the angular velocity of rotation of cutter, can be in the hope of the cutting time t in this segment of cutting
1=φ/ω, φ is the cutter anglec of rotation; ;
Because the spiral cutting sword of rose cutter will cause spiral hysteresis phenomenon, the time that will participate in cutting to place, diverse location angle cutting point exerts an influence, and then affects Cutting trajectory, each position angle
corresponding cutter spiral drag angle
can be expressed as formula (12):
Wherein, β
0for the maximum spiral drag angle of cutter,
for the position angle of cutting point on Tool in Cutting sword, the time effects that spiral lags behind and produces
By the position angle of trying to achieve
scope, cutter tried to achieve
interval in corner φ, time that cutter turns over this corner be updated in the Cutting trajectory equation (2) of considering tool wear, can obtain the workpiece surface appearance of rose cutter milling, be expressed as formula (13);
Adopt after such scheme, the present invention carries out discrete processes according to Milling Process Tool in Cutting movement locus by rose cutter cutting edge, set up rose cutter Tool in Cutting sword infinitesimal milling equation of locus, Cutting trajectory equation surface topography outermost track in the equation of locus of above-mentioned foundation forms, by judging the positional angle range of the corresponding cutting of these outermost tracks infinitesimal, determine the cutter angle range that these outermost tracks of milling are corresponding, in conjunction with process time corresponding to angular velocity of rotation calculating these tracks of milling being obtained by speed of cutter spindle, consider the spiral drag angle at place, cutting infinitesimal position, obtain these outermost milling tracks, thereby obtain milling workpiece surface appearance, solve the workpiece surface appearance problem being caused by tool wear in Milling Processes.
Accompanying drawing explanation
Fig. 1 is the discrete schematic diagram of bulb cutting edge in the present invention;
Fig. 2 is rose cutter cutting edge Cutting trajectory in the present invention;
Fig. 3 is the tracing point that forms surface topography in the present invention;
Fig. 4 cuts infinitesimal position view before and after tool wear in the present invention;
Fig. 5 is rose cutter monodentate Cutting trajectory schematic diagram in the present invention;
Fig. 6 is that in the present invention, adjacent twice feed cuts angle of cut schematic diagram;
Fig. 7 is the cutter corner schematic diagram in tool cutting process of the present invention;
Number in the figure title: 1-the first cutting edge; 2-the second cutting edge, 3-Cutting trajectory, the point that 4-remains, the point that 5-cuts away, 6-workpiece is surface finally, the point that 7-remains.
Embodiment
Below with reference to accompanying drawing, technical scheme of the present invention is elaborated.
A modeling method for Milling Process workpiece surface appearance, comprises the steps:
(1) rose cutter cutting edge is discrete, sets up rose cutter Tool in Cutting sword infinitesimal milling equation of locus.
According to Milling Process Tool in Cutting movement locus, dividing cutting edge discrete ball head is a series of cutting infinitesimals, be illustrated in figure 1 the discrete schematic diagram of bulb cutting edge in the present invention, in figure, dotted line is depicted as a spiral cutting sword in bulb part, P is a cutting infinitesimal on it, O is ball head branch center
for the line of P point and bulb center O and the angle of cutter spindle Z, the angle that is description cutting infinitesimal position is called position angle.Because difference cutting infinitesimal linear velocity when cutting is different, and in process, there is straight-line feed motion and self rotatablely moving around cutter spindle simultaneously, therefore, except the movement locus of other point on bulb point of a knife ectosphere head cutting edge is actual, it is a series of trochoid, the Cutting trajectory that trochoid forms as shown in Figure 2, solid line represents certain some Cutting trajectory on rose cutter the first cutting edge, dotted line represents the Cutting trajectory of sustained height point on rose cutter the second cutting edge, the outermost tracing point in track above and below has formed workpiece pattern, by the tracing point in this region amplify show after as shown in Figure 3.In Fig. 3, the point that hollow dots representative is cut in cutting process, solid dot is the point remaining, and namely forms the point of workpiece surface appearance.
The pattern forming on workpiece in order to analyze Tool in Cutting track, the cutting infinitesimal P point of usining after discrete is as research object, motion by analysis site P in feed process, obtain putting the Cutting trajectory that P finally stays on workpiece after process finishing, remove the track that the cut trajectory of falling of work in-process obtains finally forming workpiece pattern.On cutter, P space of points movement locus consists of rectilinear motion and rotatablely moving, therefore when cutter weares and teares, the desired cut equation of locus that P is ordered as the formula (1):
Wherein, X ', Y ' for P point through cut the coordinate after the time, X
0, Y
0for P point origin coordinates, the tool feeding speed that v is the unit interval, t
1for cut time, t
2for the impact on this process time of the spiral drag angle of P point present position,
t=t
1-t
2,
for cutter spiral drag angle corresponding to P point,
for the residing position angle of P point
the cutter radial radius at place,
the rose cutter radius of R when not wearing and tearing, ω is cutter spindle angular velocity of rotation.
When the impact of tool wear is taken into account, along with cutter constantly weares and teares, the corresponding radially radius of point on cutting edge on sustained height
and corresponding position angle
all will change, therefore, during tool abrasion in considering process, the Cutting trajectory that P is ordered can be represented by formula (2):
Wherein, X, Y for consider tool wear P point through cut the coordinate after the time, X
0, Y
0for P point origin coordinates, the tool feeding speed that v is the unit interval, t
1for cut time, t
2for the impact on this process time of the spiral drag angle of P point present position, and
for cutter spiral drag angle corresponding to P point,
for the bulb of P point At The Height after tool wear radius radially, ω is cutter spindle angular velocity of rotation.
Fig. 4 has shown position angle
the variation of the cutting infinitesimal P that chooses of place present position before and after cutting edge wearing and tearing, while there is not tool wear, P point is positioned on the profile of bulb outermost, and at cutter, after processing after a while, ball head divides and weares and teares, identical with P point place height
section, the physical location after the wearing and tearing of P point becomes P ', the part of PP ' for being worn in process.Therefore, work as position angle
while getting different numerical value, just can solve the position coordinates of the cutting infinitesimal after a series of cutting edge wearing and tearing, thereby set up the geometric relationship model of the rear cutter outline sword line of wearing and tearing.
In Fig. 4, while not there are not wearing and tearing, P point place level
locate radially radius of corresponding rose cutter
can be expressed as:
In formula, R
0radius while not wearing and tearing for rose cutter,
position angle corresponding to P point while not wearing and tearing for cutter.
After processing a period of time, cutter bulb partly will wear and tear, rose cutter sustained height
having there is variation in the actual Working position of the cutting point on place's cutting edge, is changed to P ' point, as shown in Figure 4 by P point.Now, rose cutter cross section diameter corresponding to this plane highly of living in to radius by theoretical value
be changed to
therefore, after wearing and tearing
the radially radius of the cutter that At The Height is corresponding can be expressed as:
In formula, R is the radius of rose cutter while not wearing and tearing,
for the cutting plane height at cutting infinitesimal place, VB is
the tool flank wear of At The Height Tool in Cutting sword.
(2) solve the position of Tool in Cutting sword corresponding to outermost trajectory
angle span
The milling track obtaining according to milling equation of locus is not all to form workpiece surface appearance, part trajectory work in-process can be cut, only have outermost trajectory to form workpiece surface appearance, in order to determine outermost trajectory, need to solve the position of Tool in Cutting sword corresponding to outermost trajectory
angle span
obtain
in interval each
the Tool in Cutting trajectory that angle is corresponding, the set of these Cutting trajectory lines has just formed the workpiece surface appearance after processing;
Analysis chart 5, cutter is along the feeding of x axle, and the trajectory that y axle both sides are finally left to surface of the work is respectively P
1p
1' and P
2p
2' these outermost tracks.In order to try to achieve this part final track that forms workpiece surface appearance, remove the cut track of all the other work in-processes, need to obtain respectively Tool in Milling P
1p
1' and P
2p
2the cutting-edge angle that ' time is corresponding
scope, illustrate below and how to try to achieve P
1p
1' and P
2p
2' corresponding
angle value.
Want to guarantee P
2p
2' exist, the track of cutting edge is this situation of prolate cycloid, must meet Fig. 5 mid point P
3x coordinate figure be greater than the straight-line feed amount f that cutter rotates a circle
p.Shown in Fig. 5, solid line represents that position angle is
the Cutting trajectory of certain point, the Cutting trajectory of this point finally can form workpiece surface appearance; Dotted line represents that position comparatively
the Cutting trajectory of certain point, the Cutting trajectory of this point finally can not form workpiece surface appearance.While meeting following the relation, Cutting trajectory finally can form workpiece surface appearance, and namely corner is that 90 ° of corresponding x coordinates are greater than the x coordinate that corner is (360+270) °, that is:
Formula (5) obtains
for the minimum value satisfying condition.
The maximal value of position angle is the position angle of the cutting point that the residual high highest point of workpiece surface appearance is corresponding, namely section angle of cut of twice feed in vertical feed direction axial cross section before and after cutter.Direction of feed in Fig. 6 (X-direction) is pointed in paper by O point.
Can find out as shown in Figure 6: for direction of feed right side P
1p
1' this section of track,
size to discuss in two kinds of situation.
1) feed for the first time,
can be directly according to cutting depth a
pcalculate formula (6) with the geometric relationship of Z value maximum point in cutter under this cutting depth and workpiece contact point:
2) from feed for the second time,
with feed line-spacing f
psize have direct relation, can draw shown in the relational expression (7) between them:
P for direction of feed left side
2p
2' track,
size and P
1p
1' there is relative relation, for last feed,
size is shown in formula (8):
Feed is for the first time in the process of second from the bottom feed, and the outmost trajectory in left side is corresponding
value be all shown in formula (9):
(3) outermost trajectory P
1p
1' section and P
2p
2the calculating of tool motion time in ' section is interval
In order to obtain each position
the Cutting trajectory line that angle is corresponding, need to obtain respectively outermost trajectory P
1p
1' section and P
2p
2the tool motion time in ' section is interval, by obtaining the corner that P is ordered in this is interval, then try to achieve corresponding process time in conjunction with the speed of mainshaft of cutter, consider the spiral drag angle at place, cutting infinitesimal position, can obtain outermost pattern track, thereby obtain the surface topography of workpiece.
In order to set up P in Fig. 7
1and P
2corresponding corner
with
formula, analyze P
1and P
2the corner of point in milling process.
For P
1point, from the negative y axle of starting point, x=0 place forwards P to
1time, P
1point horizontal ordinate meets formula (10) below:
That is:
Wherein, v is the amount of feeding of bulb cutter unit interval, and ω is cutter shaft rotational speed, and R is tool radius,
for P
1the position angle of point,
for position angle
locate corresponding cutter corner, and meet
For P
2point, from the negative y axle of starting point, x=0 place forwards P to
2time, P
2point horizontal ordinate meets formula (11) below:
That is:
Wherein, v is the amount of feeding of bulb cutter unit interval, and ω is cutter shaft rotational speed, and R is tool radius,
for P
2the position angle of point,
for position angle
locate corresponding cutter corner, and meet
Use Newton iteration method to solve nonlinear equation (10) and (11), obtain correspondence position
the cutter corner value at angle, in conjunction with the angular velocity of rotation of cutter, can be in the hope of the cutting time t in this segment of cutting
1=φ/ω, φ is the cutter anglec of rotation; .
Because the spiral cutting sword of rose cutter will cause spiral hysteresis phenomenon, the time that will participate in cutting to place, diverse location angle cutting point exerts an influence, and then affects Cutting trajectory, each position angle
corresponding cutter spiral drag angle
can be expressed as formula (12):
Wherein, β
0for the maximum spiral drag angle of cutter,
for the position angle of cutting point on Tool in Cutting sword, the time effects that spiral lags behind and produces
By the position angle of trying to achieve
scope, cutter tried to achieve
interval in corner φ, time that cutter turns over this corner be updated in the Cutting trajectory equation (2) of considering tool wear, can obtain the workpiece surface appearance of rose cutter milling, be expressed as formula (13);
Above example only, for explanation technological thought of the present invention, can not limit protection scope of the present invention with this, every technological thought proposing according to the present invention, and any change of doing on technical scheme basis, within all falling into protection domain of the present invention.
Claims (1)
1. a modeling method for Milling Process workpiece surface appearance, is characterized in that comprising the steps:
(1) according to Milling Process Tool in Cutting movement locus, dividing cutting edge discrete ball head is a series of cutting infinitesimals, because difference cutting infinitesimal linear velocity when cutting is different, and in process, there is straight-line feed motion and self rotatablely moving around cutter spindle simultaneously, therefore, the movement locus that removes other point on bulb point of a knife ectosphere head cutting edge will form a series of trochoid, the pattern forming on workpiece in order to analyze Tool in Cutting track, the cutting infinitesimal P point of usining after discrete is as research object, motion by analysis site P in feed process, obtain putting the Cutting trajectory that P finally stays on workpiece after process finishing, remove the track that the cut trajectory of falling of work in-process obtains finally forming workpiece pattern, consider straight-line trajectory and rotational trajectory, when cutter weares and teares, the desired cut equation of locus that P is ordered as the formula (1):
Wherein, X ', Y ' for P point through cut the coordinate after the time, X
0, Y
0for P point origin coordinates, the tool feeding speed that v is the unit interval, t
1for cut time, t
2for the impact on this process time of the spiral drag angle of P point present position,
t=t
1-t
2,
for cutter spiral drag angle corresponding to P point,
for the residing position angle of P point
the cutter radial radius at place,
the rose cutter radius of R when not wearing and tearing, ω is cutter spindle angular velocity of rotation,
for the line of P point and bulb center O and the angle of cutter spindle Z, the angle that is description cutting infinitesimal position is called position angle;
When the impact of tool wear is taken into account, along with cutter constantly weares and teares, the corresponding radially radius of point on cutting edge on sustained height
and corresponding position angle
all will change, therefore, during tool abrasion in considering process, the Cutting trajectory that P is ordered can be represented by formula (2):
Wherein, X, Y for consider tool wear P point through cut the coordinate after the time, X
0, Y
0for P point origin coordinates, the tool feeding speed that v is the unit interval, t
1for cut time, t
2for the impact on this process time of the spiral drag angle of P point present position, and
for cutter spiral drag angle corresponding to P point, ω is cutter spindle angular velocity of rotation;
In formula, R is the radius of rose cutter while not wearing and tearing,
for the cutting plane height at cutting infinitesimal place, VB is
the tool flank wear of At The Height Tool in Cutting sword;
(2) the milling track obtaining according to milling equation of locus is not all to form workpiece surface appearance, part trajectory work in-process can be cut, only have outermost trajectory to form workpiece surface appearance, in order to determine outermost trajectory, need to solve the position of Tool in Cutting sword corresponding to outermost trajectory
angle span
obtain
in interval each
the Tool in Cutting trajectory that angle is corresponding, the set of these Cutting trajectory lines has just formed the workpiece surface appearance after processing;
Cutter is along the feeding of x axle, and the trajectory that y axle both sides are finally left to surface of the work is respectively P
1p
1' and P
2p
2', wanting to guarantee the existence of outermost track, the coordinate figure that cutting edge track must meet trajectory and feed shaft intersection point is greater than the straight-line feed amount f that cutter rotates a circle
p, obtain thus formula (5):
Above formula obtains
for the minimum value satisfying condition;
The maximal value of position angle is the position angle of the cutting point that the residual high highest point of workpiece surface appearance is corresponding, namely section angle of cut of twice feed in vertical feed direction axial cross section before and after cutter;
For direction of feed right side P
1p
1' this section of track,
size to discuss in two kinds of situation;
1) feed for the first time,
can be directly according to cutting depth a
pcalculate formula (6) with the geometric relationship of Z value maximum point in cutter under this cutting depth and workpiece contact point:
2) from feed for the second time,
with feed line-spacing f
psize have direct relation, can draw shown in the relational expression (7) between them:
P for direction of feed left side
2p
2' track,
size and P
1p
1' there is relative relation, for last feed,
size is shown in formula (8):
Feed is for the first time in the process of second from the bottom feed, and the outmost trajectory in left side is corresponding
value be all shown in formula (9):
(3) in order to obtain each position
the Cutting trajectory line that angle is corresponding, need to obtain respectively outermost trajectory P
1p
1' section and P
2p
2the tool motion time in ' section is interval, by obtaining the corner that P is ordered in this is interval, then try to achieve corresponding process time in conjunction with the speed of mainshaft of cutter, consider the spiral drag angle at place, cutting infinitesimal position, can obtain outermost pattern track, thereby obtain the surface topography of workpiece;
In order to set up P
1and P
2corresponding corner
with
formula, analyze P
1and P
2the corner of point in milling process;
For P
1point, from the negative y axle of starting point, x=0 place forwards P to
1time, P
1point horizontal ordinate meets formula (10) below:
That is:
Wherein, v is the amount of feeding of bulb cutter unit interval, and ω is cutter shaft rotational speed, and R is tool radius,
for P
1the position angle of point,
for position angle
locate corresponding cutter corner, and meet
For P
2point, from the negative y axle of starting point, x=0 place forwards P to
2time, P
2point horizontal ordinate meets formula (11) below:
That is:
Wherein, v is the amount of feeding of bulb cutter unit interval, and ω is cutter shaft rotational speed, and R is tool radius,
for P
2the position angle of point,
for position angle
locate corresponding cutter corner, and meet
Use Newton iteration method to solve nonlinear equation (10) and (11), obtain correspondence position
the cutter corner value at angle, in conjunction with the angular velocity of rotation of cutter, can be in the hope of the cutting time in this segment of cutting
φ is the cutter anglec of rotation;
Because the spiral cutting sword of rose cutter will cause spiral hysteresis phenomenon, the time that will participate in cutting to place, diverse location angle cutting point exerts an influence, and then affects Cutting trajectory, each position angle
corresponding cutter spiral drag angle
can be expressed as formula (12):
Wherein, β
0for the maximum spiral drag angle of cutter,
for the position angle of cutting point on Tool in Cutting sword, the time effects that spiral lags behind and produces
By the position angle of trying to achieve
scope, cutter tried to achieve
interval in corner φ, time that cutter turns over this corner be updated in the Cutting trajectory equation (2) of considering tool wear, can obtain the workpiece surface appearance of rose cutter milling, be expressed as formula (13);
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210162358.5A CN102681488B (en) | 2012-05-24 | 2012-05-24 | Modeling method for milling surface appearance of workpiece |
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| CN102004818B (en) * | 2010-11-04 | 2012-08-29 | 西北工业大学 | Instantaneous milling force modeling method in free curve shape part peripheral milling process |
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