CN102681488A - Modeling method for milling surface appearance of workpiece - Google Patents

Modeling method for milling surface appearance of workpiece Download PDF

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Publication number
CN102681488A
CN102681488A CN2012101623585A CN201210162358A CN102681488A CN 102681488 A CN102681488 A CN 102681488A CN 2012101623585 A CN2012101623585 A CN 2012101623585A CN 201210162358 A CN201210162358 A CN 201210162358A CN 102681488 A CN102681488 A CN 102681488A
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cutting
point
tool
cutter
angle
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CN102681488B (en
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张臣
郭松
周来水
张海艳
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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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

Modeling method for milling workpiece surface appearance
Technical Field
The invention belongs to the field of numerical control milling, and particularly relates to the field of modeling of workpiece surface appearance caused by tool abrasion in numerical control milling.
Background
With the development of the modern machine manufacturing industry, the requirement on the machining precision of parts is higher and higher. In the actual milling process, machining errors are inevitably generated due to the influence of various factors. The machining error is a very important factor influencing the machining quality of the workpiece, the machining precision of the workpiece is obviously reduced, the excessive machining error even causes the scrapping of parts, and the machining efficiency and the benefit are seriously influenced. The microstructure of the surface of the workpiece is closely related to the roughness of the surface of the workpiece, the wear resistance and the assembly precision of the workpiece are greatly influenced, the important index reflecting the processing quality of the surface of the workpiece is also provided, the coordinate value of any position point on the workpiece can be obtained by predicting the morphology of the surface of the workpiece, and the coordinate value is compared with the theoretical coordinate value of the point, so that the processing error value of the point can be obtained.
In order to improve the processing quality of the surface of a workpiece, reduce processing errors and reduce roughness, many scholars at home and abroad study the surface appearance of the workpiece from a microscopic angle, and some achievements are obtained. Successively, some modeling methods for establishing a workpiece surface appearance model are provided.
The existing modeling method for the surface topography of the workpiece is mainly used for researching the influence of factors such as cutting parameter selection, cutter positioning error, cutter deformation caused by cutting force and the like on the surface topography of the workpiece, and at present, the related research is rarely carried out on the influence of dynamic wear of a cutter in the milling process of a ball-end milling cutter on the surface topography of the workpiece.
Therefore, the modeling method overcomes the defects of the modeling method for the surface topography of the workpiece, establishes a cutting track equation according to the characteristics of the cutting edge of the ball end mill, further considers the influence of the tool wear on the cutting track, and researches the surface topography of the workpiece after the tool wear. The shape change of the edge line of the outer contour of the ball head cutting edge after the cutter is worn is analyzed, so that the cutting track of the worn cutting edge relative to the workpiece can be further analyzed, a cutting track equation considering the wear is established, and the surface appearance of the machined workpiece is further obtained.
Disclosure of Invention
The invention aims to provide a modeling method for the surface appearance of a milling workpiece, which can solve the problems of modeling and visual simulation of the surface appearance of the workpiece caused by tool abrasion in the milling process.
In order to achieve the above purpose, the solution of the invention is:
a modeling method for milling the surface topography of a workpiece is characterized by comprising the following steps:
(1) dispersing a ball head part cutting edge into a series of cutting micro-elements according to a cutting motion track of a milling cutter, wherein the linear velocity of different cutting micro-elements is different during cutting, and linear feed motion and rotation motion of the ball head part cutting edge around a cutter main shaft exist simultaneously in the processing process, so that motion tracks of other points on a ball head cutting edge except a ball head cutter point form a series of trochoids, in order to analyze the appearance formed on a workpiece by the cutting track of the cutter, a dispersed cutting micro-element P point is used as a research object, the motion of a point P in the cutter feeding process is analyzed to obtain the cutting track of the point P finally left on the workpiece after the processing is finished, and the track line cut off in the processing is removed to obtain the track finally forming the appearance of the workpiece; considering the linear motion track and the rotation track, when the tool is not worn, the theoretical cutting track equation of the point P is shown as the formula (1):
Figure 177055DEST_PATH_IMAGE002
(1)
wherein,
Figure 2012101623585100002DEST_PATH_IMAGE004
、
Figure 2012101623585100002DEST_PATH_IMAGE006
is the coordinate of the point P after the cutting time,
Figure 2012101623585100002DEST_PATH_IMAGE008
、
Figure DEST_PATH_IMAGE010
the starting coordinates of the point P are shown,
Figure DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,
Figure 2012101623585100002DEST_PATH_IMAGE014
in order to shorten the machining time, the machining time is shortened,the influence of the spiral lag angle of the position of the point P on the processing time of the point,，
Figure 2012101623585100002DEST_PATH_IMAGE020
, is the spiral lag angle of the cutter corresponding to the P point,
Figure 2012101623585100002DEST_PATH_IMAGE024
is the position angle of the point PThe radial radius of the tool at (a),
Figure DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE030
is the radius of the ball end mill when not worn,
Figure DEST_PATH_IMAGE032
is the angular velocity of rotation of the tool spindle,the included angle between the connecting line of the point P and the center O of the ball head and the main axis Z of the cutter is called a position angle, namely the angle describing the position of the cutting infinitesimal;
when the influence of tool wear is taken into account, as the tool wears, the radial radius corresponding to a point at the same height on the cutting edge
Figure 201960DEST_PATH_IMAGE024
And the corresponding position angle
Figure 155134DEST_PATH_IMAGE026
Will vary, and therefore, when considering the amount of tool wear during machining, the cutting trajectory of point P can be represented by equation (2):
(2)
wherein,
Figure DEST_PATH_IMAGE036
、
Figure DEST_PATH_IMAGE038
in order to take into account the coordinates of the tool wear point P over the machining time,
Figure 439485DEST_PATH_IMAGE008
、the starting coordinates of the point P are shown,
Figure 739065DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,
Figure 920648DEST_PATH_IMAGE014
in order to shorten the machining time, the machining time is shortened,
Figure 375900DEST_PATH_IMAGE016
the influence of the helical lag angle of the position of the point P on the machining time of the point P, and
Figure 901822DEST_PATH_IMAGE018
，is the spiral lag angle of the cutter corresponding to the P point,
Figure 504021DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle;
Figure DEST_PATH_IMAGE040
solving the radial radius of the ball head at the height of the P point after the cutter is worn by the formula (3);
Figure DEST_PATH_IMAGE042
(4)
in the formula,
Figure DEST_PATH_IMAGE044
is half of ball end mill when not wornThe diameter of the steel wire is measured,
Figure DEST_PATH_IMAGE046
to cut the height of the cross-sectional plane where the infinitesimal element is located,
Figure DEST_PATH_IMAGE048
is composed of
Figure 254809DEST_PATH_IMAGE046
The flank wear of the cutting edge of the tool at the height;
(2) the milling track obtained according to the milling track equation does not completely form the surface appearance of the workpiece, part of the track line can be cut off in the processing, only the outermost track line forms the surface appearance of the workpiece, and in order to determine the outermost track line, the position of the cutting edge of the tool corresponding to the outermost track line needs to be solved
Figure 2447DEST_PATH_IMAGE026
Angle value range [ 2 ]
Figure DEST_PATH_IMAGE050
，
Figure DEST_PATH_IMAGE052
]Determining the value of
Figure 372248DEST_PATH_IMAGE050
,
Figure 528423DEST_PATH_IMAGE052
]Each within the intervalThe cutting trajectory lines of the cutter corresponding to the angles form the surface appearance of the machined workpiece by the collection of the cutting trajectory lines;
knife edgexThe shaft is fed in the feeding direction,ythe final paths left on the workpiece surface on both sides of the shaft are respectively
Figure DEST_PATH_IMAGE054
And
Figure DEST_PATH_IMAGE056
to ensure the existence of the outermost path, the path of the cutting edge must satisfy the condition that the coordinate value of the intersection point of the path line and the feed axis is larger than the linear feed amount of the tool rotating for one circle
Figure DEST_PATH_IMAGE058
Thereby obtaining formula (5):
Figure DEST_PATH_IMAGE060
(5)
obtained by the above formulaIs the minimum value that satisfies the condition;
the maximum value of the position angle is the position angle of the cutting point corresponding to the highest residual height of the surface appearance of the workpiece, namely the intersection angle of the front and back feeding of the cutter in the axial section in the vertical feeding direction;
to the right in the feed direction
Figure 569522DEST_PATH_IMAGE054
In the case of this segment of the trajectory,
Figure 580203DEST_PATH_IMAGE052
the size of (c) is discussed in two cases;
1) the first time of the feeding is carried out,
Figure 548159DEST_PATH_IMAGE052
can be directly dependent on the cutting depth
Figure DEST_PATH_IMAGE062
And calculating the geometrical relation of the point with the maximum Z value in the contact points of the tool and the workpiece at the cutting depth to obtain an expression (6):
Figure DEST_PATH_IMAGE064
（6）
2) starting from the second feed of the machine,
Figure 768925DEST_PATH_IMAGE052
distance from feed
Figure 480529DEST_PATH_IMAGE058
The magnitude of (2) has a direct relationship, and the relationship (7) between them can be obtained:
Figure DEST_PATH_IMAGE066
（7）
to the left of the feed direction
Figure 237395DEST_PATH_IMAGE056
In the case of a track, the position of the track,size and of
Figure 694101DEST_PATH_IMAGE054
There is a relative relationship, for the last feed,
Figure 209396DEST_PATH_IMAGE052
the size is represented by formula (8):
Figure 319303DEST_PATH_IMAGE064
（8）
in the process from the first feed to the penultimate feed,the outermost track line on the left side corresponds to
Figure 629062DEST_PATH_IMAGE052
The values of (A) are all represented by formula (9):
Figure 434207DEST_PATH_IMAGE066
（9）
(3) in order to obtain various positions
Figure 487613DEST_PATH_IMAGE026
The cutting path line corresponding to the corner needs to obtain the outermost path lines respectively
Figure 953492DEST_PATH_IMAGE054
Segment and
Figure 434152DEST_PATH_IMAGE056
the time of tool movement in the interval is determined by determining the time of tool movement in the intervalPThe turning angle of the point is combined with the rotating speed of a main shaft of a cutter to obtain corresponding processing time, and the spiral lag angle at the position of the cutting infinitesimal is considered, so that the appearance track at the outermost side can be obtained, and a surface appearance model of the workpiece is obtained;
to build up
Figure DEST_PATH_IMAGE068
Andcorresponding cornerAnd
Figure DEST_PATH_IMAGE074
formula (ii), analysis
Figure 116806DEST_PATH_IMAGE068
And
Figure 708324DEST_PATH_IMAGE070
turning a point in the milling process;
for the
Figure 668190DEST_PATH_IMAGE068
Point, from the starting point negative y-axis, at x =0 to
Figure 945850DEST_PATH_IMAGE068
When the following formula (10) is satisfied:
Figure DEST_PATH_IMAGE076
（10）
namely:
Figure DEST_PATH_IMAGE078
wherein,
Figure 725587DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,
Figure DEST_PATH_IMAGE080
is composed of
Figure 59802DEST_PATH_IMAGE068
The angle of the position of the point or points,is a position angle
Figure 149298DEST_PATH_IMAGE080
Is corresponding toAnd the corner of the tool is satisfied
Figure DEST_PATH_IMAGE082
；
For the
Figure 974297DEST_PATH_IMAGE070
Point, from the starting point negative y-axis, at x =0 to
Figure 643176DEST_PATH_IMAGE070
When the following formula (11) is satisfied:
Figure DEST_PATH_IMAGE084
（11）
namely:
Figure DEST_PATH_IMAGE086
wherein,
Figure 761173DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,
Figure 515503DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,
Figure DEST_PATH_IMAGE088
is composed ofThe angle of the position of the point or points,is a position angle
Figure 667578DEST_PATH_IMAGE088
At the corresponding corner of the tool and meet
Figure DEST_PATH_IMAGE092
；
Solving the non-linear equations (10) and (11) by using a Newton iteration method to obtain corresponding positions
Figure 831843DEST_PATH_IMAGE026
The tool angle value of the angle, combined with the rotational angular velocity of the tool, can be used to determine the cutting time in the cutting section
Figure DEST_PATH_IMAGE094
；
As the spiral cutting edge of the ball end mill causes spiral hysteresis, the spiral hysteresis influences the cutting time of the cutting points at different position angles, and further influences the cutting track, and each position angle
Figure 198102DEST_PATH_IMAGE026
Corresponding helical relief angle of tool
Figure 738805DEST_PATH_IMAGE022
Can be represented by formula (12):
Figure DEST_PATH_IMAGE096
(12)
wherein,
Figure DEST_PATH_IMAGE098
is the maximum helical lag angle of the cutter,
Figure 116697DEST_PATH_IMAGE026
time effects of helical lag for the position angle of the cutting point on the cutting edge of the tool；
The obtained position angle
Figure 343541DEST_PATH_IMAGE026
Range of (1), tool in
Figure 806883DEST_PATH_IMAGE026
Substituting the corner in the interval and the time for the cutter to rotate the corner into a cutting track equation (2) considering the cutter abrasion, so as to obtain the surface appearance of the workpiece milled by the ball-end milling cutter, which is expressed as an equation (13);
Figure DEST_PATH_IMAGE102
（13）
after the scheme is adopted, discrete processing is carried out on the cutting edges of the ball end milling cutter according to the cutting motion trail of the milling cutter, a micro element milling trail equation of the cutting edges of the ball end milling cutter is established, the surface appearance of the cutting trail equation is formed by the outermost side trail in the established trail equation, the cutter corner range corresponding to the outermost side trail is determined by judging the position angle range of the outermost side trail corresponding to the cutting micro element, the processing time corresponding to the milling trail is calculated by combining the rotation angular speed obtained by the rotation speed of the cutter main shaft, the spiral lag angle at the position of the cutting micro element is considered, the milling trail of the outermost side is obtained, the surface appearance of a milled workpiece is obtained, and the problem of the surface appearance of the workpiece caused by cutter abrasion in the milling process is solved.
Drawings
FIG. 1 is a discrete view of a ball nose cutting edge according to the present invention;
FIG. 2 is a cutting path of a cutting edge of the ball end mill of the present invention;
FIG. 3 is a plot of traces that form the surface topography of the present invention;
FIG. 4 is a schematic view of the positions of cutting elements before and after wear of the tool of the present invention;
FIG. 5 is a schematic view of a single-tooth cutting path of the ball end mill of the present invention;
FIG. 6 is a schematic diagram of a cross-sectional angle of two adjacent passes in the present invention;
FIG. 7 is a schematic view of the tool corner during cutting by the tool of the present invention;
number designation in the figures: 1-a first cutting edge; 2-second cutting edge, 3-cutting trajectory, 4-remaining point, 5-removed point, 6-final surface of workpiece, 7-remaining point.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
A modeling method for milling the surface topography of a workpiece comprises the following steps:
(1) and (4) dispersing the cutting edges of the ball end mill, and establishing a infinitesimal milling trajectory equation of the cutting edges of the ball end mill.
The cutting edges of the ball head part are dispersed into a series of cutting microelements according to the cutting motion trail of the milling cutter, as shown in figure 1, the discrete schematic diagram of the ball head cutting edge in the invention is shown, in the figure, a broken line shows a spiral cutting edge on the ball head part, P is a cutting microelement on the spiral cutting edge, O is the center of the ball head part,
Figure 275911DEST_PATH_IMAGE026
the included angle between the connecting line of the point P and the center O of the ball head and the main axis Z of the cutter is called as a position angle, namely the angle describing the position of the cutting infinitesimal. The linear velocity of different cutting elements is different during cutting, and linear feeding motion and self rotation motion around the main shaft of the cutter exist simultaneously in the machining process, so that the motion tracks of other points on the ball head cutting edge except the ball head cutter point are actualThe cutting tracks formed by the trochoids are a series of trochoids, as shown in figure 2, the solid line represents the cutting track of a certain point on a first cutting edge of the ball end mill, the dotted line represents the cutting track of a certain point on a second cutting edge of the ball end mill at the same height, the outermost track points above and below the track form the appearance of the workpiece, and the track points in the area are enlarged and displayed as shown in figure 3. In fig. 3, the open dots represent the dots cut off during the cutting process, and the solid dots are the remaining dots, i.e., the dots constituting the surface topography of the workpiece.
In order to analyze the appearance formed on the workpiece by the cutting track of the cutter, the discrete cutting micro-element P point is taken as a research object, the movement of the point P in the feeding process is analyzed to obtain the cutting track which is finally left on the workpiece by the point P after the machining is finished, and the track line which is cut off in the machining process is removed to obtain the track which finally forms the appearance of the workpiece. The space motion track of the point P on the cutter consists of linear motion and rotary motion, so when the cutter is not worn, the theoretical cutting track equation of the point P is shown as the formula (1):
Figure 508309DEST_PATH_IMAGE002
(1)
wherein,
Figure 279956DEST_PATH_IMAGE004
、
Figure 230594DEST_PATH_IMAGE006
is the coordinate of the point P after the cutting time,、
Figure 91682DEST_PATH_IMAGE010
the starting coordinates of the point P are shown,
Figure 34230DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,
Figure 472165DEST_PATH_IMAGE014
in order to shorten the machining time, the machining time is shortened,
Figure 158361DEST_PATH_IMAGE016
the influence of the spiral lag angle of the position of the point P on the processing time of the point,
Figure 489985DEST_PATH_IMAGE018
，
Figure 603435DEST_PATH_IMAGE020
，
Figure 528666DEST_PATH_IMAGE022
is the spiral lag angle of the cutter corresponding to the P point,is the position angle of the point P
Figure 706148DEST_PATH_IMAGE026
The radial radius of the tool at (a),
Figure 724920DEST_PATH_IMAGE028
，
Figure 137447DEST_PATH_IMAGE044
is the radius of the ball end mill when not worn,
Figure 165446DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle.
When the influence of tool wear is taken into account, as the tool wears, the radial radius corresponding to a point at the same height on the cutting edge
Figure 347028DEST_PATH_IMAGE024
And the corresponding position angleWill vary, and therefore, when considering the amount of tool wear during machining, the cutting trajectory of point P can be represented by equation (2):
(2)
wherein,
Figure 127268DEST_PATH_IMAGE036
、
Figure 428937DEST_PATH_IMAGE038
in order to take into account the coordinates of the tool wear point P over the machining time,
Figure 681189DEST_PATH_IMAGE008
、
Figure 802728DEST_PATH_IMAGE010
the starting coordinates of the point P are shown,
Figure 172530DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,
Figure 328705DEST_PATH_IMAGE014
in order to shorten the machining time, the machining time is shortened,
Figure 250393DEST_PATH_IMAGE016
the influence of the helical lag angle of the position of the point P on the machining time of the point P, and
Figure 859229DEST_PATH_IMAGE018
，
Figure 767142DEST_PATH_IMAGE022
is the spiral lag angle of the cutter corresponding to the P point,the radial radius of the ball head at the point P height after the cutter is worn,
Figure 745780DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle.
FIG. 4 shows the position angle
Figure 468010DEST_PATH_IMAGE026
Cutting micro-element selected fromPWhen the position of the cutting edge changes before and after the cutting edge is worn and the cutter is not worn,Pthe point is located on the outermost profile of the ball head, and after the tool has been machined for a period of time, the ball head is worn and is engaged with the toolPThe points being at the same height
Figure 179614DEST_PATH_IMAGE046
At the position of the cross section, the cross section of the steel pipe is,Pthe actual position of the point after abrasion becomes
Figure DEST_PATH_IMAGE104
，Is the part that is worn away during machining. Therefore, when the angle is at
Figure 169436DEST_PATH_IMAGE026
When different values are taken, the position coordinates of a series of cutting microelements of the worn cutting edge can be solved, so that a geometric relation model of the edge line of the outer contour of the worn cutter is established.
In fig. 4, when no wear has occurred,Pheight of the plane of the point
Figure 308293DEST_PATH_IMAGE046
Radial radius of ball end millCan be expressed as:
Figure 407016DEST_PATH_IMAGE028
(3)
in the formula,
Figure 126711DEST_PATH_IMAGE030
is the radius of the ball-end mill when not worn,
Figure 62568DEST_PATH_IMAGE026
when the tool is not wornPThe corresponding location angle.
After a period of machining, the cutter ball head part is worn and the ball head milling cutter has the same heightThe actual machining position of the cutting point on the cutting edge is changed byPPoint change is as followsP ’ Dots, as shown in fig. 4. At the moment, the radial radius of the section circle of the ball end mill corresponding to the plane with the height is from the theoretical valueIs changed into
Figure 26479DEST_PATH_IMAGE040
Thus, after wearing
Figure 631772DEST_PATH_IMAGE046
The corresponding radial radius of the tool at height can be expressed as:
Figure 189793DEST_PATH_IMAGE042
(4)
in the formula,
Figure 781311DEST_PATH_IMAGE044
as ball end milling cutterThe radius of the pipe when it is not worn,
Figure 475598DEST_PATH_IMAGE046
to cut the height of the cross-sectional plane where the infinitesimal element is located,is composed of
Figure 798574DEST_PATH_IMAGE046
Flank wear of the cutting edge of the tool at the height.
(2) Solving the position of the cutting edge of the tool corresponding to the outermost trajectoryAngle value range [ 2 ]
Figure 8155DEST_PATH_IMAGE050
，
Figure 830618DEST_PATH_IMAGE052
]
The milling track obtained according to the milling track equation does not completely form the surface appearance of the workpiece, part of the track line can be cut off in the processing, only the outermost track line forms the surface appearance of the workpiece, and in order to determine the outermost track line, the position of the cutting edge of the tool corresponding to the outermost track line needs to be solvedAngle value range [ 2 ]
Figure 421185DEST_PATH_IMAGE050
，
Figure 90064DEST_PATH_IMAGE052
]Determining the value of
Figure 83428DEST_PATH_IMAGE050
,
Figure 463856DEST_PATH_IMAGE052
]Each within the interval
Figure 200867DEST_PATH_IMAGE026
The cutting trajectory lines of the cutter corresponding to the angles form the surface appearance of the machined workpiece by the collection of the cutting trajectory lines;
analysis of FIG. 5, tool edgexThe shaft is fed in the feeding direction,ythe final paths left on the workpiece surface on both sides of the shaft are respectively
Figure 724253DEST_PATH_IMAGE054
And
Figure 154097DEST_PATH_IMAGE056
these outermost tracks. In order to determine the path of this part which ultimately forms the surface topography of the workpiece, and to remove the remaining paths which are removed during the machining, it is necessary to determine the tool milling separately
Figure 395722DEST_PATH_IMAGE054
And
Figure 795480DEST_PATH_IMAGE056
angle of position of cutting edge
Figure 438951DEST_PATH_IMAGE026
How to obtain the range of (1) is explained in detail below
Figure 774117DEST_PATH_IMAGE054
Andcorresponding to
Figure 207952DEST_PATH_IMAGE026
The angular value.
Want to guarantee
Figure 705929DEST_PATH_IMAGE056
There is a case where the trajectory of the cutting edge is a prolate cycloid, and it is necessary to be fullPoint in foot diagram 5Is/are as followsxThe coordinate value is larger than the linear feeding amount of one rotation of the cutter. As shown in connection with FIG. 5, the solid line represents a position angle of
Figure 428215DEST_PATH_IMAGE026
2The cutting track of a certain point can finally form the surface appearance of the workpiece; the dotted line represents the position
Figure 435354DEST_PATH_IMAGE026
1The cutting track of a certain point can not form the surface appearance of the workpiece finally. Namely, the cutting track finally forms the surface topography of the workpiece when the following relation is satisfied, namely, the x coordinate corresponding to the rotation angle of 90 degrees is larger than the x coordinate corresponding to the rotation angle of (360 + 270) degrees, namely:
Figure 787838DEST_PATH_IMAGE060
（5）
obtained by the formula (5)
Figure 730386DEST_PATH_IMAGE050
Is the minimum value that satisfies the condition.
The maximum value of the position angle is the position angle of the cutting point corresponding to the highest residual height of the surface appearance of the workpiece, namely the intersection angle of the front and back feeding of the cutter in the axial section in the vertical feeding direction. The feed direction (X-axis direction) in fig. 6 is directed from point O into the paper.
As can be seen from fig. 6: to the right in the feed direction
Figure 168320DEST_PATH_IMAGE054
In the case of this segment of the trajectory,
Figure 215036DEST_PATH_IMAGE052
the size of (c) is discussed in two cases.
1) The first time of the feeding is carried out,can be directly dependent on the cutting depth
Figure 801055DEST_PATH_IMAGE062
And calculating the geometrical relation of the point with the maximum Z value in the contact points of the tool and the workpiece at the cutting depth to obtain an expression (6):
Figure 726286DEST_PATH_IMAGE064
（6）
2) starting from the second feed of the machine,
Figure 950594DEST_PATH_IMAGE052
distance from feed
Figure 136725DEST_PATH_IMAGE058
The magnitude of (2) has a direct relationship, and the relationship (7) between them can be obtained:
Figure 421075DEST_PATH_IMAGE066
（7）
to the left of the feed direction
Figure 833602DEST_PATH_IMAGE056
In the case of a track, the position of the track,
Figure 861601DEST_PATH_IMAGE052
size and of
Figure 692720DEST_PATH_IMAGE054
There is a relative relationship, for the last feed,
Figure 882393DEST_PATH_IMAGE052
the size is represented by formula (8):
Figure 782216DEST_PATH_IMAGE064
（8）
during the process from the first feed to the penultimate feed, the outermost track line on the left side corresponds to
Figure 348326DEST_PATH_IMAGE052
The values of (A) are all represented by formula (9):
Figure 774628DEST_PATH_IMAGE066
（9）
(3) outermost trajectory line
Figure 135203DEST_PATH_IMAGE054
Segment and
Figure 522322DEST_PATH_IMAGE056
calculation of tool movement time within segment interval
In order to obtain various positions
Figure 892123DEST_PATH_IMAGE026
The cutting path line corresponding to the corner needs to obtain the outermost path lines respectively
Figure 782719DEST_PATH_IMAGE054
Segment and
Figure 205872DEST_PATH_IMAGE056
the time of tool movement in the interval is determined by determining the time of tool movement in the intervalPAnd (4) calculating the corresponding processing time by combining the rotating angle of the point and the rotating speed of the main shaft of the cutter, and considering the spiral lag angle at the position of the cutting infinitesimal to obtain the appearance track at the outermost side so as to obtain the surface appearance model of the workpiece.
To build up the structure of FIG. 7
Figure 814708DEST_PATH_IMAGE068
And
Figure 988200DEST_PATH_IMAGE070
corresponding corner
Figure 998882DEST_PATH_IMAGE072
And
Figure 91471DEST_PATH_IMAGE074
formula (ii), analysis
Figure 187603DEST_PATH_IMAGE068
And
Figure 899207DEST_PATH_IMAGE070
the corner of the point during milling.
For the
Figure 764395DEST_PATH_IMAGE068
Point, from the starting point negative y-axis, at x =0 to
Figure 903252DEST_PATH_IMAGE068
When the following formula (10) is satisfied:
Figure 112779DEST_PATH_IMAGE076
（10）
namely:
Figure 362495DEST_PATH_IMAGE078
wherein,
Figure 347768DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,
Figure 657527DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,
Figure 728251DEST_PATH_IMAGE080
is composed of
Figure 906292DEST_PATH_IMAGE068
The angle of the position of the point or points,
Figure 746072DEST_PATH_IMAGE072
is a position angle
Figure 226732DEST_PATH_IMAGE080
At the corresponding corner of the tool and meet
Figure 519173DEST_PATH_IMAGE082
。
For the
Figure 2369DEST_PATH_IMAGE070
Point, from the starting point negative y-axis, at x =0 to
Figure 696655DEST_PATH_IMAGE070
When the following formula (11) is satisfied:
Figure 348217DEST_PATH_IMAGE084
（11）
namely:
wherein,the feed amount of the ball head cutter in unit time,
Figure 462169DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,
Figure 550211DEST_PATH_IMAGE088
is composed of
Figure 817244DEST_PATH_IMAGE070
The angle of the position of the point or points,
Figure 16144DEST_PATH_IMAGE090
is a position angle
Figure 45542DEST_PATH_IMAGE088
At the corresponding corner of the tool and meet
Figure 304485DEST_PATH_IMAGE092
；
Solving the non-linear equations (10) and (11) by using a Newton iteration method to obtain corresponding positions
Figure 58815DEST_PATH_IMAGE026
The tool angle value of the angle, combined with the rotational angular velocity of the tool, can be used to determine the cutting time in the cutting section
Figure 795827DEST_PATH_IMAGE094
。
As the spiral cutting edge of the ball end mill causes spiral hysteresis, the spiral hysteresis influences the cutting time of the cutting points at different position angles, and further influences the cutting track, and each position angle
Figure 443846DEST_PATH_IMAGE026
Corresponding helical relief angle of tool
Figure 873690DEST_PATH_IMAGE022
Can be represented by formula (12):
Figure 849736DEST_PATH_IMAGE096
(12)
wherein,
Figure 390439DEST_PATH_IMAGE098
is the maximum helical lag angle of the cutter,time effects of helical lag for the position angle of the cutting point on the cutting edge of the tool
Figure 995175DEST_PATH_IMAGE100
。
The obtained position angle
Figure 724097DEST_PATH_IMAGE026
Range of (1), tool in
Figure 802911DEST_PATH_IMAGE026
Substituting the corner in the interval and the time for the cutter to rotate the corner into a cutting track equation (2) considering the cutter abrasion, so as to obtain the surface appearance of the workpiece milled by the ball-end milling cutter, which is expressed as an equation (13);
Figure 300888DEST_PATH_IMAGE102
（13）
the above examples are only for illustrating the technical idea of the present invention, and the scope of the present invention should not be limited thereby, and all modifications made on the basis of the technical solution according to the technical idea of the present invention are within the scope of the present invention.

Claims (1)

1. A modeling method for milling the surface topography of a workpiece is characterized by comprising the following steps:
(1) dispersing a ball head part cutting edge into a series of cutting micro-elements according to a cutting motion track of a milling cutter, wherein the linear velocity of different cutting micro-elements is different during cutting, and linear feed motion and rotation motion of the ball head part cutting edge around a cutter main shaft exist simultaneously in the processing process, so that motion tracks of other points on a ball head cutting edge except a ball head cutter point form a series of trochoids, in order to analyze the appearance formed on a workpiece by the cutting track of the cutter, a dispersed cutting micro-element P point is used as a research object, the motion of a point P in the cutter feeding process is analyzed to obtain the cutting track of the point P finally left on the workpiece after the processing is finished, and the track line cut off in the processing is removed to obtain the track finally forming the appearance of the workpiece; considering the linear motion track and the rotation track, when the tool is not worn, the theoretical cutting track equation of the point P is shown as the formula (1):
Figure 257180DEST_PATH_IMAGE002
(1)
wherein,
Figure 840608DEST_PATH_IMAGE004
、
Figure 90324DEST_PATH_IMAGE006
is the coordinate of the point P after the cutting time,
Figure 200231DEST_PATH_IMAGE008
、
Figure 509990DEST_PATH_IMAGE010
the starting coordinates of the point P are shown,
Figure 580714DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,in order to shorten the machining time, the machining time is shortened,
Figure 473901DEST_PATH_IMAGE016
the influence of the spiral lag angle of the position of the point P on the processing time of the point,，
Figure 873100DEST_PATH_IMAGE020
, is the spiral lag angle of the cutter corresponding to the P point,
Figure 549118DEST_PATH_IMAGE024
is the position angle of the point P
Figure 826778DEST_PATH_IMAGE026
The radial radius of the tool at (a),
Figure 872094DEST_PATH_IMAGE028
，
Figure 267304DEST_PATH_IMAGE030
is the radius of the ball end mill when not worn,
Figure 816097DEST_PATH_IMAGE032
is the angular velocity of rotation of the tool spindle,
Figure 904138DEST_PATH_IMAGE026
the included angle between the connecting line of the point P and the center O of the ball head and the main axis Z of the cutter is called a position angle, namely the angle describing the position of the cutting infinitesimal;
when the influence of tool wear is taken into account, as the tool wears, the radial radius corresponding to a point at the same height on the cutting edge
Figure 295806DEST_PATH_IMAGE024
And the corresponding position angle
Figure 494706DEST_PATH_IMAGE026
Will vary, and therefore, when considering the amount of tool wear during machining, the cutting trajectory of point P can be represented by equation (2):
Figure 898005DEST_PATH_IMAGE034
(2)
wherein,
Figure 156948DEST_PATH_IMAGE036
、
Figure 537376DEST_PATH_IMAGE038
in order to take into account the coordinates of the tool wear point P over the machining time,
Figure 274388DEST_PATH_IMAGE008
、the starting coordinates of the point P are shown,
Figure 227618DEST_PATH_IMAGE012
is the feed speed of the tool per unit time,in order to shorten the machining time, the machining time is shortened,
Figure 869000DEST_PATH_IMAGE016
the influence of the helical lag angle of the position of the point P on the machining time of the point P, and
Figure 512471DEST_PATH_IMAGE018
，
Figure 847638DEST_PATH_IMAGE022
is the spiral lag angle of the cutter corresponding to the P point,
Figure 576559DEST_PATH_IMAGE032
is the rotational angular velocity of the tool spindle;
Figure 281472DEST_PATH_IMAGE040
solving the radial radius of the ball head at the height of the P point after the cutter is worn by the formula (3);
Figure 779450DEST_PATH_IMAGE042
(4)
in the formula,
Figure 285518DEST_PATH_IMAGE044
is the radius of the ball-end mill when not worn,
Figure 501735DEST_PATH_IMAGE046
to cut the height of the cross-sectional plane where the infinitesimal element is located,
Figure 508874DEST_PATH_IMAGE048
is composed ofThe flank wear of the cutting edge of the tool at the height;
(2) the milling track obtained according to the milling track equation does not completely form the surface appearance of the workpiece, part of the track line can be cut off in the processing, only the outermost track line forms the surface appearance of the workpiece, and in order to determine the outermost track line, the position of the cutting edge of the tool corresponding to the outermost track line needs to be solvedAngle value range [ 2 ]
Figure 867940DEST_PATH_IMAGE050
，]Determining the value of,
Figure 608997DEST_PATH_IMAGE052
]Each within the interval
Figure 658861DEST_PATH_IMAGE026
The cutting trajectory lines of the cutter corresponding to the angles form the surface appearance of the machined workpiece by the collection of the cutting trajectory lines;
knife edgexThe shaft is fed in the feeding direction,ythe final paths left on the workpiece surface on both sides of the shaft are respectively
Figure 883169DEST_PATH_IMAGE054
Andto ensure the existence of the outermost path, the path of the cutting edge must satisfy the condition that the coordinate value of the intersection point of the path line and the feed axis is larger than the linear feed amount of the tool rotating for one circle
Figure 494596DEST_PATH_IMAGE058
Thereby obtaining formula (5):
Figure 533222DEST_PATH_IMAGE060
(5)
obtained by the above formula
Figure 295641DEST_PATH_IMAGE050
Is the minimum value that satisfies the condition;
the maximum value of the position angle is the position angle of the cutting point corresponding to the highest residual height of the surface appearance of the workpiece, namely the intersection angle of the front and back feeding of the cutter in the axial section in the vertical feeding direction;
to the right in the feed direction
Figure 477224DEST_PATH_IMAGE054
In the case of this segment of the trajectory,
Figure 932476DEST_PATH_IMAGE052
the size of (c) is discussed in two cases;
1) the first time of the feeding is carried out,can be directly dependent on the cutting depth
Figure 523043DEST_PATH_IMAGE062
And calculating the geometrical relation of the point with the maximum Z value in the contact points of the tool and the workpiece at the cutting depth to obtain an expression (6):
（6）
2) starting from the second feed of the machine,
Figure 185286DEST_PATH_IMAGE052
distance from feed
Figure 572405DEST_PATH_IMAGE058
The magnitude of (2) has a direct relationship, and the relationship (7) between them can be obtained:
Figure 904242DEST_PATH_IMAGE066
（7）
to the left of the feed direction
Figure 60417DEST_PATH_IMAGE056
In the case of a track, the position of the track,
Figure 857472DEST_PATH_IMAGE052
size and of
Figure 466308DEST_PATH_IMAGE054
There is a relative relationship, for the last feed,
Figure 390532DEST_PATH_IMAGE052
the size is represented by formula (8):
Figure 401214DEST_PATH_IMAGE064
（8）
during the process from the first feed to the penultimate feed, the outermost track line on the left side corresponds to
Figure 369170DEST_PATH_IMAGE052
The values of (A) are all represented by formula (9):
（9）
(3) in order to obtain various positions
Figure 911327DEST_PATH_IMAGE026
The cutting path line corresponding to the corner needs to obtain the outermost path lines respectively
Figure 166727DEST_PATH_IMAGE054
Segment and
Figure 305585DEST_PATH_IMAGE056
the time of tool movement in the interval is determined by determining the time of tool movement in the intervalPThe turning angle of the point is combined with the rotating speed of the main shaft of the cutter to obtain the corresponding processing time, and the spiral lag angle at the position of the cutting infinitesimal is considered, so that the appearance track at the outermost side can be obtained, and the appearance track is obtainedObtaining a surface appearance model of the workpiece;
to build up
Figure 889013DEST_PATH_IMAGE068
And
Figure 138729DEST_PATH_IMAGE070
corresponding corner
Figure 750101DEST_PATH_IMAGE072
Andformula (ii), analysis
Figure 130584DEST_PATH_IMAGE068
And
Figure 183990DEST_PATH_IMAGE070
turning a point in the milling process;
for the
Figure 23770DEST_PATH_IMAGE068
Point, from the starting point negative y-axis, at x =0 to
Figure 629064DEST_PATH_IMAGE068
When the following formula (10) is satisfied:
Figure 921505DEST_PATH_IMAGE076
（10）
namely:
Figure 778603DEST_PATH_IMAGE078
wherein,
Figure 472889DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,
Figure 750549DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,is composed of
Figure 191075DEST_PATH_IMAGE068
The angle of the position of the point or points,
Figure 739868DEST_PATH_IMAGE072
is a position angle
Figure 827909DEST_PATH_IMAGE080
At the corresponding corner of the tool and meet
Figure 219576DEST_PATH_IMAGE082
；
For the
Figure 152897DEST_PATH_IMAGE070
Point, from the starting point negative y-axis, at x =0 toWhen the following formula (11) is satisfied:
Figure 80719DEST_PATH_IMAGE084
（11）
namely:
Figure 195568DEST_PATH_IMAGE086
wherein,
Figure 198159DEST_PATH_IMAGE012
the feed amount of the ball head cutter in unit time,
Figure 721544DEST_PATH_IMAGE032
for the rotational speed of the tool shaft,Rwhich is the radius of the cutter,is composed of
Figure 252069DEST_PATH_IMAGE070
The angle of the position of the point or points,
Figure 792771DEST_PATH_IMAGE090
is a position angle
Figure 170663DEST_PATH_IMAGE088
At the corresponding corner of the tool and meet
Figure 771409DEST_PATH_IMAGE092
；
Solving the non-linear equations (10) and (11) by using a Newton iteration method to obtain corresponding positions
Figure 234751DEST_PATH_IMAGE026
The tool angle value of the angle, combined with the rotational angular velocity of the tool, can be used to determine the cutting time in the cutting section
Figure 205243DEST_PATH_IMAGE094
；
As the spiral cutting edge of the ball end mill causes spiral hysteresis, the spiral hysteresis influences the cutting time of the cutting points at different position angles, and further influences the cutting track, and each position angle
Figure 703221DEST_PATH_IMAGE026
Corresponding helical relief angle of tool
Figure 209288DEST_PATH_IMAGE022
Can be represented by formula (12):
Figure 425506DEST_PATH_IMAGE096
(12)
wherein,
Figure 432645DEST_PATH_IMAGE098
is the maximum helical lag angle of the cutter,time effects of helical lag for the position angle of the cutting point on the cutting edge of the tool
Figure 462098DEST_PATH_IMAGE100
；
The obtained position angle
Figure 900033DEST_PATH_IMAGE026
Range of (1), tool in
Figure 212328DEST_PATH_IMAGE026
Substituting the corner in the interval and the time for the cutter to rotate the corner into a cutting track equation (2) considering the cutter abrasion, so as to obtain the surface appearance of the workpiece milled by the ball-end milling cutter, which is expressed as an equation (13);
Figure 419318DEST_PATH_IMAGE102
（13）
。
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