CN110399681A - A kind of parametric modeling method of radius end mill edge curve - Google Patents
A kind of parametric modeling method of radius end mill edge curve Download PDFInfo
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Abstract
The present invention discloses a kind of parametric modeling method of radius end mill edge curve, is segmented first to radius end mill edge curve and defines its geometric parameter；Then coordinate system needed for edge curve models is defined；Finally provide each section of edge curve upper knife edge point calculation expression.Invention defines each geometric parameters of radius end mill edge curve for meeting modeling demand, it is ensured that the integrality of geometric parameter；It is smooth continuously for condition with the single order between each section of curve, the expression formula of curve upper knife edge point coordinate is derived, ensure that the slickness connected between each section of curve；The calculating formula of blade point is given in the form of formula, avoids equation solution bring unstable result.
Description
Technical field
The present invention relates to solid end mill processing technique field, specially a kind of parameter of radius end mill edge curve
Change modeling method.
Background technique
Radius end mill is more common high speed cutting tool, has the characteristics that manufacturing cost is low, material-removal rate is big.
In workpieces processing circular arc, radius end mill is rigidly bigger than ball end mill, high in machining efficiency；In high hard material processing, height
It is higher than the anti-defect performance of right-angle head slotting cutter when fast roughing feed processing, deep carving Three-dimension process.However, radius end mill
Design and sharpening be always cutter manufacture field difficult point.
Monoblock type slotting cutter mathematical model is that the basis of parametric modeling is carried out to it, and method for building up and precision determine
The efficiency and precision of parametric modeling.In addition, " blade point Following CNC Grinding Method " is used in slotting cutter and added by the propositions such as Gong Zhihui
In work, the difficult point for sharpening monoblock type slotting cutter is concentrated on blade point calculating method.Therefore, a kind of general, satisfaction is established
The radius end mill edge curve modeling method of every geometric parameter is very necessary.
Geometric parameter existing for existing radius end mill edge curve modeling method is imperfect and solving result is unstable
The problems such as, be characterized in particular in: partial trace parametric equation does not consider cutter taper angle；Ball-end mill curvilinear equation does not consider that end tooth is straight
Line sword；Being asked using plane with arc rotary surface hands over normal equation sufficiently complex, and calculating process is cumbersome and unstable result, part are initial
Equation is without solution under parameter.
Summary of the invention
In view of the above-mentioned problems, the purpose of the present invention is to provide one kind to make up radius end mill edge curve modeling method
The parametric modeling method of existing insufficient radius end mill edge curve, it can be ensured that the integrality of geometric parameter is protected
The slickness connected between each section of curve is demonstrate,proved, equation solution bring unstable result is avoided.Technical solution is as follows:
A kind of parametric modeling method of radius end mill edge curve, comprising the following steps:
Step 1: defining edge curve segmentation and geometric parameter
Defining the length of edge curve in the axial direction is edge length l；Wherein, the length of all land lines in the axial direction
Degree is all tine length lw, the length of end tooth sword line in the axial direction is end tooth length lr；
The cutter begining revolving radius for defining edge curve starting point is Rw；
The angle for defining helix tangent vector and cutter revolving body bus is helixangleβ；
The angle for defining cutter revolving body outer profile and cutter gyration central axis is cutter taper angle κ；
The distance for defining end tooth straight line sword to end face center point is tooth partial center amount h；
It is that tooth crosses center amount l that end tooth straight line sword, which is defined, along the distance that straight line sword direction is more than end face center pointh；
Definition end tooth arc rotary surface radius is r；
Defining end tooth straight line sword and the angle of the plane perpendicular to cutter axis of rotation is end tooth straight line sword leaning angle η；
Step 2: defining coordinate system
Workpiece coordinate system Ow-XwYwZwIt is Z with cutter rotary middle spindlewAxis, with end face where all tooth helical edges line starting points
For XwOwYwPlane；
End tooth coordinate system Od-XdYdZdIt is Z with cutter rotating shaftdAxis is X with circular arc revolving body bottom surfacedOdYdPlane；
Step 3: edge curve modeling
Step A) week tooth helical edges curve modeling
Any blade point P (x, y, z) on all tooth helical edges curved sections, the expression formula of coordinate is as follows, independent variable ZwAxis
Coordinate value z；
In formula, ρ (z) indicates the radius of gyration on sword line at P point, expression formula are as follows:
ρ (z)=Rw-ztanκ (2)
Indicate the angle of revolution at blade point P.
For the cylindrical type cutter of cutter taper angle κ=0
For the pyramid type cutter of cutter taper angle κ ≠ 0
In formula,Indicate initial angle of revolution.In the model, the maximum value of independent variable z is all tine length lw, expression formula
Are as follows:
lw=l- (1-sin κ) r (5)
Step B) modeling of end tooth Circular Nose Cutting Edge curve:
It is described respectively using segmented version, tooth Circular Nose Cutting Edge curve highest point is denoted as P1, curve P0P1Section is returned by circular arc
Turn face and asks intersection to obtain with nonopiate helicoid, curve P1P2Section is crossing P1And it is established on tangent plane M with eccentricity cylinder；
It is specific as follows:
B1) arc rotary surface curved portion P0P1
Curve P0P1The expression formula of any blade point P (x, y, z) in section are as follows:
In formula, θ indicates angle of latitude, is independent variable；The expression formula of ρ (θ) are as follows:
ρ (θ)=R+rcos θ (7)
Wherein R indicates center of arc away from expression formula are as follows:
R=Rw-rcosκ-lw tanκ (8)
Indicate angle of revolution at end tooth Circular Nose Cutting Edge blade point P, expression formula consists of three parts, it may be assumed that
Wherein,Indicate the initial angle of revolution of Circular Nose Cutting Edge；Indicate lead screw line angle of revolution, expression formula are as follows:
In formula, βεIndicate lead screw line helical angle；Indicate eccentricity compensation angle of revolution, expression formula are as follows:
Connect to meet all tooth helical edges with the single order continuous and derivable of end tooth Circular Nose Cutting Edge, need to satisfy two conditions:: end tooth
Circular Nose Cutting Edge starting point angle of latitudeAll tooth helical edges helical angles are equal with end tooth Circular Nose Cutting Edge starting point helical angle.To
Have:
Formula (10) (11) (12) (13) are substituted into (9) to obtainComplete expression are as follows:
B2) plane curve part P1P2
Obtain space curve end point P1(x1,y1,z1) coordinate value, θ=pi/2, which is substituted into formula (6), to be obtained:
To the expression formula of plane curve part are as follows:
Wherein,Indicate plane M and XdThe angle of axis, expression formula are as follows:
In formula,For an intermediate variable；
B3 it) transforms under workpiece coordinate system
Under workpiece coordinate system, the expression formula of end tooth Circular Nose Cutting Edge blade point P' are as follows:
P '=Md-wP+Td-w (18)
In formula, P, P' are the coordinate vector of point P, P'；Md-wIndicate the spin moment from bulb coordinate system to workpiece coordinate system
Battle array, Td-wIndicate the translation matrix from bulb coordinate system to workpiece coordinate system, expression is as follows:
In formula,Indicate the angle of revolution of all teeth end point.
Step C: end tooth straight line sword curve modeling
C1 end tooth straight line sword length) is calculated
End tooth straight line sword P is established on plane M2P3, straight line P2P3Segment length is end tooth straight line sword length lh0, will be in grinding wheel
Under heart point coordinate transform to workpiece coordinate system, the grinding wheel center point coordinate O under workpiece coordinate system is obtainedg(xg,yg,zg):
C2 end tooth Circular Nose Cutting Edge end point coordinate and tangent vector) are calculated
End tooth Circular Nose Cutting Edge end point P2(x2,y2,z2) coordinate value are as follows:
End tooth Circular Nose Cutting Edge end point P2The tangent vector F at placep(fpx,fpy,fpz) are as follows:
C3) end tooth straight line sword curve models
Directly establish end tooth straight line angle of throat sword curvilinear equation under end tooth coordinate system, introduce parameter t, then blade point P (x,
Y, z) expression formula are as follows:
Then coordinate value substitution formula (18) is obtained into the end tooth straight line angle of throat sword point under workpiece coordinate system.
The beneficial effects of the present invention are: the present invention first defines the radius end mill edge curve for meeting modeling demand
Each geometric parameter, it is ensured that the integrality of geometric parameter；It is smooth continuously for condition with the single order between each section of curve, it derives bent
The expression formula of line upper knife edge point coordinate, ensure that the slickness connected between each section of curve；Blade is given in the form of formula
The calculating formula of point, avoids equation solution bring unstable result.
Detailed description of the invention
Fig. 1 is edge curve segmentation and geometric parameter schematic diagram.
Fig. 2 is all tooth helical edges modeling schematic diagrames.
Fig. 3 is end tooth Circular Nose Cutting Edge modeling schematic diagram.
Fig. 4 is end tooth Circular Nose Cutting Edge P0P1Duan Jianmo schematic diagram.
Fig. 5 is end tooth Circular Nose Cutting Edge P1P2Duan Jianmo schematic diagram.
Fig. 6 is end tooth straight line sword modeling schematic diagram.
Fig. 7 is two tooth radius end mill edge curves modeling schematic diagram.
In figure: 1- weeks tooth helical edges；2- end tooth Circular Nose Cutting Edge；3- end tooth vertial knife edge；4- eccentricity cylinder；5- straight edge line；6-
Arc rotary surface；7- lead screw line；The nonopiate spiral surface of revolution of 8-.
Specific embodiment
The present invention is described in further details in the following with reference to the drawings and specific embodiments.The present invention proposes a kind of arc head
Slotting cutter edge curve parameterized model, which defines the complete parameter of radius end mill edge curve, with formula
Form gives the calculating formula of edge curve upper knife edge point, avoids equation solution bring unstable result.
Implementation method of the invention is the following steps are included: being segmented and being defined to radius end mill edge curve first
Its geometric parameter；Then coordinate system needed for edge curve models is defined；Each section of edge curve upper knife edge point is finally provided to calculate
Expression formula.It is specific as follows
Step 1: edge curve segmentation and geometric parameter definition
As shown in Figure 1, radius end mill edge curve includes all tooth helical edges, end tooth Circular Nose Cutting Edge and end tooth straight line sword 3
A part.The definition of edge curve geometric parameter:
(1) edge length l.The length of edge curve in the axial direction is defined as edge length l.Wherein, all land lines
Length in the axial direction is all tine length lw, the length of end tooth sword line in the axial direction is end tooth length lr。
(2) cutter begining revolving radius Rw.The cutter radius of gyration of edge curve starting point is defined as cutter begining revolving
Radius Rw。
(3) helixangleβ.There are two types of the definition of helical angle, the first is the angle of helix tangent vector and cutter rotating shaft；
Second of angle for helix tangent vector and cutter revolving body bus.In view of second of definition method uses extensive, this hair
It is bright to be modeled using second of definition method.
(4) taper angle κ.The angle of cutter revolving body outer profile and cutter gyration central axis is defined as cutter taper angle
κ。
(5) tooth partial center amount h.Tooth partial center amount h (or eccentricity) is distance of the end tooth straight line sword to end face center point.
(6) tooth crosses center amount lh.It is more than end face center point along straight line sword direction that tooth, which crosses center amount as end tooth straight line sword,
Distance.
(7) end tooth arc radius r.The definition of end tooth arc radius r is end tooth arc rotary surface radius.
(8) end tooth straight line sword leaning angle η.End tooth straight line sword and the angle of the plane perpendicular to cutter axis of rotation are defined
For end tooth straight line sword leaning angle η.
Step 2: coordinate system definition
(1) workpiece coordinate system Ow-XwYwZw: workpiece coordinate system is complete used in the modeling of radius end mill edge curve
Office's coordinate system.The curve model established under other coordinate systems will be by under the formal argument to workpiece coordinate system of coordinate transform
Unify legislation.Workpiece coordinate system Ow-XwYwZwIt is Z with cutter rotary middle spindlewAxis is with end face where all tooth helical edges line starting points
XwOwYwPlane.
(2) end tooth coordinate system Od-XdYdZd: the coordinate system is Z with cutter rotating shaftdAxis is with circular arc revolving body bottom surface
XdOdYdPlane.
Step 3: edge curve modeling
A: all tooth helical edges curve modelings
As shown in Fig. 2, the expression formula of any blade point P (x, y, z) coordinate is as follows on this section of curve, independent variable ZwAxis is sat
Scale value z.
In formula, ρ (z) indicates the radius of gyration on sword line at P point, expression formula are as follows:
ρ (z)=Rw-ztanκ (26)
Indicate the angle of revolution at blade point P,
For cylindrical type cutter (κ=0)
For pyramid type cutter (κ ≠ 0)
In formula,Indicate initial angle of revolution.
In the model, the maximum value of independent variable z is all tine length lw, expression formula are as follows:
lw=l- (1-sin κ) r (29)
B: end tooth Circular Nose Cutting Edge curve modeling
As shown in figure 3, setting on lead screw line a bit, it is parallel to XdOdYdPlane and with tangent straight of eccentricity cylinder
Line is end tooth straight edge line, and end tooth straight edge line can form the nonopiate spiral surface of revolution along lead screw line sweeping, by using
The nonopiate spiral surface of revolution and spherical surface ask the mode of intersection to obtain bulb edge curve.It is independent variable by introducing angle of latitude θ, builds
Found itself and angle of revolutionRelational expression, to obtain the expression formula of bulb sword line.
Use the above method herein, by the nonopiate spiral surface of revolution and arc rotary surface ask intersection in the way of the end that obtains
Tooth Circular Nose Cutting Edge line.However, due to the presence of end tooth straight line sword leaning angle, smoothly transits, hold with end tooth straight line sword in order to realize
Tooth Circular Nose Cutting Edge is by highest point P1(i.e. independent variable θ be greater than 90 °) is to X afterwardsdOdYdPlane extends up to P2Point.If curve P1P2Section
Still it is obtained using the above method, then the tooth partial center amount h' actually obtained will be less than theoretical value h.
In order to guarantee that the accuracy of tooth partial center amount h, the present invention improve end tooth Circular Nose Cutting Edge curve modeling method, adopt
It is described respectively with segmented version, and guarantees that it is smoothly connected.Wherein, curve P0P1Section is by arc rotary surface and nonopiate spiral shell
Radial facing asks intersection to obtain；Curve P1P2Crossing P1And it is established on tangent plane M with eccentricity cylinder.
1) arc rotary surface curved portion
As shown in figure 4, on this section of curve any blade point P (x, y, z) expression formula are as follows:
In formula, the expression formula of ρ (θ) are as follows:
ρ (θ)=R+rcos θ (31)
Wherein R indicates center of arc away from expression formula are as follows:
R=Rw-rcosκ-lw tanκ (32)
Indicate angle of revolution at end tooth Circular Nose Cutting Edge blade point P, expression formula consists of three parts, it may be assumed that
Wherein,Indicate the initial angle of revolution of Circular Nose Cutting Edge；Indicate lead screw line angle of revolution, expression formula are as follows:
β in formulaεIndicate lead screw line helical angle；Indicate eccentricity compensation angle of revolution, expression formula are as follows:
Realize that all tooth helical edges are connect with the single order continuous and derivable of end tooth Circular Nose Cutting Edge, need to satisfy two conditions:: end tooth
Circular Nose Cutting Edge starting point angle of latitudeAll tooth helical edges helical angles are equal with end tooth Circular Nose Cutting Edge starting point helical angle.To
Have:
Formula (10) (11) (12) (13) substitution (9) can be obtainedComplete expression are as follows:
2) plane curve part
Curve P is established on plane M1P2Section.This section of curve is one section of circular arc, center of circle P1Point is in XdOdYdThe throwing of plane
Shadow point.Due to P1Point is arc rotary surface highest point, and the point is located on straight edge line, therefore curve P0P1Section is in P1Arrow is cut at point
Measure FtIt must be located on end tooth straight edge line.Since end tooth straight edge line also is located on plane M, therefore circular arc P1P2Section is in P1Arrow is cut at point
Amount is also Ft.Therefore, from curve P0P1Section arrives curve P1P2The connection of section is that single order is continuous.
As shown in figure 5, obtaining space curve end point P first1(x1,y1,z1) coordinate value, θ=pi/2 is substituted into formula (6) can
:
To the expression formula of this section of curve are as follows:
Wherein,Indicate plane M and XdThe angle of axis, expression formula are as follows:
In formula,For an intermediate variable.
3) it transforms under workpiece coordinate system
Since edge curve needs to be described under unified coordinate system, it is therefore desirable to be obtained being calculated under end tooth coordinate system
The edge curve expression formula obtained transforms under workpiece coordinate system.
Under workpiece coordinate system, the expression formula of end tooth Circular Nose Cutting Edge blade point P' are as follows:
P '=Md-wP+Td-w (42)
In formula, P, P' are the coordinate vector of point P, P'；Md-wIndicate the spin moment from bulb coordinate system to workpiece coordinate system
Battle array, Td-wIndicate the translation matrix from bulb coordinate system to workpiece coordinate system, expression is as follows:
C: end tooth straight line sword curve modeling
As shown in fig. 6, establishing end tooth straight line sword P on plane M2P3.Since end tooth straight line sword is along end tooth Circular Nose Cutting Edge end point P2
The tangent vector direction at place, therefore the connection of itself and end tooth Circular Nose Cutting Edge is also that single order is continuous.
1) end tooth straight line sword length is calculated
Straight line P2P3Segment length is end tooth straight line sword length lh0, by calculating P2P3' segment length can count in plane M
Calculation obtains P2P3Segment length.
The grinding wheel center point coordinate O that under the coordinate transform to workpiece coordinate system, will be obtained under workpiece coordinate systemg(xg,yg,
zg):
2) end tooth Circular Nose Cutting Edge end point coordinate and tangent vector are calculated
End tooth Circular Nose Cutting Edge end point P2(x2,y2,z2) coordinate value are as follows:
End tooth Circular Nose Cutting Edge end point P2The tangent vector F at placep(fpx,fpy,fpz) are as follows:
3) end tooth straight line sword curve models
Directly establish end tooth straight line angle of throat sword curvilinear equation under end tooth coordinate system, introduce parameter t, then blade point P (x,
Y, z) expression formula are as follows:
Then the end tooth straight line angle of throat sword point under workpiece coordinate system is can be obtained into coordinate value substitution formula (18).
Based on above-mentioned modeling algorithm, in a set of algoritic module of VC++ environment exploitation, input relevant parameter shown in table 1 with
Afterwards, blade point can be obtained, partial arithmetic result is as shown in table 2.Verifying, which is carried out, using CAD obtains result as shown in Figure 7.
1 cutter hub batch technique relevant parameter of table
2 part Path operation result of table
The characteristics of the present embodiment parameterized model, is: first by analyzing geometric parameter lacking in existing modeling method
First define each geometric parameter of radius end mill edge curve for meeting modeling demand, it is ensured that geometric parameter it is complete
Property；It is smooth continuously for condition with the single order between each section of curve, the expression formula of curve upper knife edge point coordinate is derived, ensure that each section
The slickness connected between curve；The calculating formula of blade point is given in the form of formula, avoids equation solution bring knot
Fruit is unstable.
Claims (1)
1. a kind of parametric modeling method of radius end mill edge curve, which comprises the following steps:
Step 1: define edge curve segmentation and geometric parameter:
(1) length of edge curve in the axial direction is defined as edge length l；Wherein, the length of all land lines in the axial direction
Degree is all tine length lw, the length of end tooth sword line in the axial direction is end tooth length lr；
(2) the cutter radius of gyration of edge curve starting point is defined as cutter begining revolving radius Rw；
(3) angle of helix tangent vector and cutter revolving body bus is defined as helixangleβ；
(4) angle of cutter revolving body outer profile and cutter gyration central axis is defined as cutter taper angle κ；
It (5) is tooth partial center amount h by the distance definition of end tooth straight line sword to end face center point；
It (6) is that tooth crosses center amount l along the distance definition that straight line sword direction is more than end face center point by end tooth straight line swordh；
(7) end tooth arc rotary surface radius is defined as end tooth arc radius r；
(8) end tooth straight line sword and the angle of the plane perpendicular to cutter axis of rotation are defined as end tooth straight line sword leaning angle η；
Step 2: defining coordinate system
Workpiece coordinate system Ow-XwYwZwIt is Z with cutter rotary middle spindlewAxis is X with end face where all tooth helical edges line starting pointswOwYw
Plane；
End tooth coordinate system Od-XdYdZdIt is Z with cutter rotating shaftdAxis is X with circular arc revolving body bottom surfacedOdYdPlane；
Step 3: edge curve modeling
Step A) week tooth helical edges curve modeling:
Any blade point P (x, y, z) on all tooth helical edges curved sections, the expression formula of coordinate is as follows, independent variable ZwAxial coordinate value
z；
In formula, ρ (z) indicates the radius of gyration on sword line at P point, expression formula are as follows:
ρ (z)=Rw-ztanκ (2)
Indicate the angle of revolution at blade point P；
For the cylindrical type cutter of cutter taper angle κ=0
For the pyramid type cutter of cutter taper angle κ ≠ 0
In formula,Indicate initial angle of revolution；
In the model, the maximum value of independent variable z is all tine length lw, expression formula are as follows:
lw=l- (1-sin κ) r (5)
Step B) modeling of end tooth Circular Nose Cutting Edge curve:
It is described respectively using segmented version, tooth Circular Nose Cutting Edge curve highest point is denoted as P1, curve P0P1Section is by arc rotary surface
Intersection is asked to obtain with nonopiate helicoid, curve P1P2Section is crossing P1And it is established on tangent plane M with eccentricity cylinder；Specifically
It is as follows:
B1) arc rotary surface curved portion P0P1
Curve P0P1The expression formula of any blade point P (x, y, z) in section are as follows:
In formula, θ indicates angle of latitude, is independent variable；The expression formula of ρ (θ) are as follows:
ρ (θ)=R+rcos θ (7)
Wherein R indicates center of arc away from expression formula are as follows:
R=Rw-rcosκ-lwtanκ (8)
Indicate angle of revolution at end tooth Circular Nose Cutting Edge blade point P, expression formula consists of three parts, it may be assumed that
Wherein,Indicate the initial angle of revolution of Circular Nose Cutting Edge；Indicate lead screw line angle of revolution, expression formula are as follows:
In formula, βεIndicate lead screw line helical angle；Indicate eccentricity compensation angle of revolution, expression formula are as follows:
Connect to meet all tooth helical edges with the single order continuous and derivable of end tooth Circular Nose Cutting Edge, need to satisfy two conditions:: end tooth circular arc
Sword starting point angle of latitudeAll tooth helical edges helical angles are equal with end tooth Circular Nose Cutting Edge starting point helical angle；To have:
Formula (10) (11) (12) (13) are substituted into (9) to obtainComplete expression are as follows:
B2) plane curve part P1P2
Obtain space curve end point P1(x1,y1,z1) coordinate value, θ=pi/2, which is substituted into formula (6), to be obtained:
To the expression formula of plane curve part are as follows:
Wherein,Indicate plane M and XdThe angle of axis, expression formula are as follows:
In formula,For an intermediate variable；
B3 it) transforms under workpiece coordinate system
Under workpiece coordinate system, the expression formula of end tooth Circular Nose Cutting Edge blade point P' are as follows:
P '=Md-wP+Td-w (18)
In formula, P, P' are the coordinate vector of point P, P'；Md-wIndicate the spin matrix from bulb coordinate system to workpiece coordinate system, Td-w
Indicate the translation matrix from bulb coordinate system to workpiece coordinate system, expression is as follows:
In formula,Indicate the angle of revolution of all teeth end point；
Step C: end tooth straight line sword curve modeling
C1 end tooth straight line sword length) is calculated
End tooth straight line sword P is established on plane M2P3, straight line P2P3Segment length is end tooth straight line sword length lh0, by grinding wheel central point
Under coordinate transform to workpiece coordinate system, the grinding wheel center point coordinate O under workpiece coordinate system is obtainedg(xg,yg,zg):
C2 end tooth Circular Nose Cutting Edge end point coordinate and tangent vector) are calculated
End tooth Circular Nose Cutting Edge end point P2(x2,y2,z2) coordinate value are as follows:
End tooth Circular Nose Cutting Edge end point P2The tangent vector F at placep(fpx,fpy,fpz) are as follows:
C3) end tooth straight line sword curve models
End tooth straight line angle of throat sword curvilinear equation is directly established under end tooth coordinate system, introduces parameter t, then blade point P (x, y, z)
Expression formula are as follows:
Then coordinate value substitution formula (18) is obtained into the end tooth straight line angle of throat sword point under workpiece coordinate system.
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| CN111230194B (en) * | 2020-02-19 | 2021-04-09 | 西南交通大学 | Edge line design method for end tooth linear edge of cylindrical flat-end milling cutter with chamfer |
| CN113100013A (en) * | 2021-04-01 | 2021-07-13 | 北京理工大学 | Two-section-edge inserted tooth type special high-speed tapping cutter and design method |
| CN113505482A (en) * | 2021-07-08 | 2021-10-15 | 张家港荣盛特钢有限公司 | Method and device for solving taper curve of copper pipe of square billet crystallizer and storage medium |
| CN113505482B (en) * | 2021-07-08 | 2024-03-08 | 张家港荣盛特钢有限公司 | Method and device for obtaining taper curve of copper pipe of square billet crystallizer and storage medium |
| CN114065405A (en) * | 2022-01-17 | 2022-02-18 | 成都飞机工业（集团）有限责任公司 | Prediction method for cutting width of corner finish milling of aircraft structural part |
| CN114912228A (en) * | 2022-07-12 | 2022-08-16 | 广东鼎泰高科技术股份有限公司 | Method and device for designing outline of grooved grinding wheel and computer readable storage medium |
| CN115017567A (en) * | 2022-07-12 | 2022-09-06 | 广东鼎泰高科技术股份有限公司 | Method and device for designing outline of grooved grinding wheel and computer readable storage medium |
| CN114912228B (en) * | 2022-07-12 | 2023-03-24 | 广东鼎泰高科技术股份有限公司 | Method and device for designing outline of grooved grinding wheel and computer readable storage medium |
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