CN110091008A - A kind of Gear Hobbing Parameters and path compensation method for highly-efficient processing face gear - Google Patents
A kind of Gear Hobbing Parameters and path compensation method for highly-efficient processing face gear Download PDFInfo
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- CN110091008A CN110091008A CN201910447679.1A CN201910447679A CN110091008A CN 110091008 A CN110091008 A CN 110091008A CN 201910447679 A CN201910447679 A CN 201910447679A CN 110091008 A CN110091008 A CN 110091008A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
- B23F19/002—Modifying the theoretical tooth flank form, e.g. crowning
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/20—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling
- B23F5/22—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling the tool being a hob for making spur gears
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Abstract
The invention discloses a kind of Gear Hobbing Parameters for highly-efficient processing face gear and path compensation methods, including step S1, S2, S3；The relative position of measurement, is subtracted the relative position of cutter and workpiece setting, obtains the installation error of lathe by S1, the installation error for obtaining cutter and workpiece relative position, the relative position after cutter and workpiece installation are obtained by measurement cutter and the location of workpiece；S2, error of the cutter under cutting force and centrifugal force effect and under torque effect is obtained by calculating；S3, machined parameters and machining path are compensated, the error obtained by step S1 compensates the machined parameters of setting, obtains compensated machined parameters；The machining path of setting is compensated by the error that step S1 and S2 are obtained, obtains compensated machining path.The present invention realizes the accurate processing of gear by compensating to mismachining tolerance, improves the precision of workpiece.
Description
Technical field
The present invention relates to machining fields, more particularly to a kind of Gear Hobbing Parameters for highly-efficient processing face gear and
Path compensation method.
Background technique
Currently, a kind of effective method of the gear hobbing (face hobbing) as processing gear, as shown in Fig. 2, in cutterhead
Serrated knife and outer serrated knife in upper installation, in the cutter of one tooth of processing and the relative movement of workpiece, interior serrated knife processing tooth
Inside tooth form, the outside tooth form of outer serrated knife processing tooth, forms the Continuous maching of tooth, has been widely used for all kinds of bevel gears and add
Work.Compared with conventional machining process, ultrasonic vibration secondary process has cutting force smaller in process, and tool wear is more
Low, workpiece surface quality is more preferable, the advantages such as higher excision efficiency.It, can foundation after assisting gear hobbing process using ultrasonic vibration
Change cutting parameter in the requirement of Roughing and fine machining, further increases processing efficiency, surface quality and profile accuracy.But it is existing to add
Work method as during gear hobbing process relative motion it is complex and its caused by mismachining tolerance be difficult to control, and existing mistake
Poor compensation method is difficult to the comprehensive process error of accurate compensation complex condition, is not able to satisfy precision machined requirement, is not suitable for
Gear hobbing process is assisted using ultrasonic vibration.
Summary of the invention
The present invention is directed to solve above-mentioned technical problem at least to a certain extent.For this purpose, the present invention proposes a kind of processing essence
Spend the high Gear Hobbing Parameters and path compensation method for highly-efficient processing face gear.
The technical solution adopted by the present invention to solve the technical problems is: a kind of gear hobbing for highly-efficient processing face gear adds
Work parameter and path compensation method, including step S1, S2, S3；
S1, the installation error for obtaining gear hobbing cutter and workpiece relative position, are obtained by measurement gear hobbing cutter and the location of workpiece
Relative position after gear hobbing cutter and workpiece installation, by the relative position of measurement subtract gear hobbing cutter set with workpiece it is opposite
Position obtains the installation error of lathe；
S2, error of the gear hobbing cutter under cutting force and centrifugal force effect and under torque effect is obtained by calculating；
S3, machined parameters and machining path are compensated, machined parameters of the error obtained by step S1 to setting
It compensates, obtains compensated machined parameters；The machining path of setting is mended by the error that step S1 and S2 are obtained
It repays, obtains compensated machining path.
Further, cutter and the relative position after workpiece installation are obtained by sensor measurement in the step S1, work
Part center, interior serrated knife center and outer serrated knife center are respectively equipped with a sensor, and the location parameter measured is Δ xw-t, Δ yw-t,
Δzw-t, θxz, θxy, θyz, the relative position parameter of cutter and workpiece set is Δ x 'w-t, Δ y 'w-t, Δ z 'w-t, θ 'xz, θ
′xy, θ 'yz；Thus to obtain the installation error ξ of lathex、ξy、ξz、ζxz、ζxy、ζyz；
ξx=Δ x 'w-t-Δxw-t；
ξy=Δ y 'w-t-Δyw-t；
ξz=Δ z 'w-t-Δzw-t；
ζxz=θ 'xz-θxz；
ζxy=θ 'xy-θxy；
ζyz=θ 'yz-θyz；
Wherein Δ xw-t, Δ yw-t, Δ zw-t, θxz, θxy, θyzThe opposite position in the direction x respectively after cutter and workpiece installation
Set, the relative position in the direction y, the relative position in the direction z, the relative angle in xz plane, the relative angle on x/y plane, yz it is flat
Relative angle on face；Δx′w-t, Δ y 'w-t, Δ z 'w-t, θ 'xz, θ 'xy, θ 'yzThe direction x set for cutter and workpiece it is opposite
Position, the relative position in the direction y, the relative position in the direction z, the relative angle in xz plane, the relative angle on x/y plane,
Relative angle in yz plane；
ξx、ξy、ξz、ζxz、ζxy、ζyzThe respectively direction x displacement error, the direction y displacement error, the direction z displacement error, machine
Angular error, cutter spindle and the work spindle that bed cutter spindle and work spindle are moved in x-z-plane intrinsic deflection are in x-y plane
The angular error that angular error, cutter spindle and the work spindle of intrinsic deflection movement are moved in y-z plane intrinsic deflection.
Further, machined parameters are cutting depth and feed speed, compensated cutting depth a in step S3p cAnd feeding
Speed fz cIt is respectively as follows:
ap c=ap+ξx；
fz c=fz+ξy；
Wherein ap、fzFor the cutting depth and feed speed of setting.
Further, the difference calculation process runs under the action of cutting force and centrifugal force are as follows: acquisition cutterhead practical center first
Deflection angle θ,The offset distance Δ l of cutterhead practical center is obtained by calculating again,
Finally by formula Δ xt=Δ l sin θ, Δ yt=Δ l cos θ, θM=θ obtains cutterhead since cutting force and centrifugal force act on
Under displacement error and angular error；Wherein Δ xt、Δyt、θMCutter head center axis respectively under cutting force and centrifugal force effect
Angular error into displacement error, cutter head center radial displacement error, cutter head center axially and radially plane；Wherein M=
(Fy-Fr)l-FxR,Fx、Fy、 FrRespectively serrated knife axial cutting force, radial cutting force and centrifugal force, l, r, I, d
Respectively cutter spindle length, cutter radius, cutter spindle section are to the moment of inertia of central axis, the diameter of cutter spindle.
Further, the error calculation under torque effect is as follows: passing through the kinetic equation of angular responseCalculating acquires cutter spindle displacement and angular error is Δ zt1=r sin θt, Δ yt1
=Δ zt1tanθt；Wherein T=FzR, J0,ct,kt, θ, T are respectively the rotary inertia of main shaft, main shaft
Angular acceleration, main shaft torsion damped coefficient, main shaft torsion angular speed, the torsion stiffness of main shaft, main shaft windup-degree,
The torque that main shaft is subject to；Fz, G be respectively the cutting force in cutterhead linear velocity direction, modulus of shearing.
Further, cutter is with work pieces process path setting
s(xw, yw, zw, θw x-y, θw x-z, θw y-z, xt, yt, zt, θt x-y, θt x-z, θt y-z) ；
The machining path of compensated cutter and workpiece is
s′(x′w, y 'w, z 'w, θw′x-y, θw′x-z, θw′y-z, x 't, y 't, z 't, θt′x-y, θt′x-z, θt′y-z)；It is compensated
Cutter and work pieces process path parameter and the machining path parameters relationship of setting are as follows:
x′w=xw；
y′w=yw；
z′w=ξz+zw；
θw′x-y=θw x-y+ζxy；
θw′x-z=θw x-z+ζxz；
θw′y-z=θw y-z+ζyz；
x′t=Δ xt+xt；
y′t=Δ yt+yt+Δyt1；
zt′y-z=zt y-z+Δzt1；
θt′x-y=θt x-y+θM；
θt′x-z=θt x-z；
θt′y-z=θt y-z。
The beneficial effects of the present invention are: the installation error and gear hobbing cutter (cutterhead) to lathe are due to bending stress and torsion
Stress bring distortion inaccuracy accounts for calculating, obtain processing required for compensate error, and by error compensation to process
In parameter and machining path, to eliminate the influence of error bring machining accuracy, the accurate processing of gear is realized, workpiece is improved
Precision, and can be used for carrying out precise high-efficiency gear hobbing process under the conditions of ultrasonic vibration secondary process.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples.
Fig. 1 is serrated knife and workpiece relative displacement and angular error model schematic in world coordinate system；
Fig. 2 is gear hobbing process schematic diagram；
Fig. 3 is that main shaft is displaced and error schematic diagram by caused by torque in process；
Fig. 4 is the rotary inertia and windup-degree schematic diagram of main shaft；
Fig. 5 is displacement and angular error schematic diagram after main shaft cutting force and centrifugal forces affect.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
A kind of Gear Hobbing Parameters and path compensation method for highly-efficient processing face gear of the invention, including step
S1、S2、S3。
S1: obtaining the installation error of gear hobbing cutter and workpiece relative position, is obtained by measurement gear hobbing cutter and the location of workpiece
The relative position of measurement, is subtracted the relative position of cutter and workpiece setting, obtained by the relative position after obtaining cutter and workpiece installation
Obtain the installation error of lathe；Specifically, after installation hobcutter, the practical relative position P of cutter and workpiecet-PwWith ideal opposite position
Set Pt′-Pw' as shown in Figure 1.The desired relative positions of cutter and workpiece can be obtained by decrypting the program code of gear hobbing lathe,
The practical relative position of cutter and workpiece can be obtained by the relative position of cutter and workpiece after measurement installation, can be by non-contact
A pair of sensors of formula detects, and a sensor arrangement is in workpiece centre, and another 2 sensor arrangements are at interior serrated knife center and outside
The position data of serrated knife center, interior serrated knife center and the measurement of outer serrated knife center takes central value to represent the position of cutter, cutter with this
Position data and the available station-keeping data of location of workpiece data.
Being defined to the installation error of gear hobbing lathe first, if the direction x displacement error is ξx, the direction y displacement error
For ξy, the direction z displacement error is ξz, machine tool spindle and work spindle are in the angular error that x-z-plane intrinsic deflection moves
ζxz, cutter spindle and work spindle are ζ in the angular error that x-y plane intrinsic deflection movesxy, cutter spindle and work spindle exist
The angular error of y-z plane intrinsic deflection movement is ζyz.X, y, z direction is orthogonal.
In the identification of machine tool error, ideal cutter and workpiece relative position Pt′-Pw' x, y, the direction z position and angle
For Δ x 'w-t, Δ y 'w-t, Δ z 'w-t, θ 'xz, θ 'xy, θ 'yz.Practical cutter and workpiece relative position Pt-PwX, y, the direction z position
And angle is Δ xw-t, Δ yw-t, Δ zw-t, θxz, θxy, θyz.Relative position and the angular error of front and back cutter and workpiece are then installed
It is respectively as follows:
ξx=Δ x 'w-t-Δxw-t；
ξy=Δ y 'w-t-Δyw-t；
ξz=Δ z 'w-t-Δzw-t；
ζxz=θ 'xz-θxz；
ζxy=θ 'xy-θxy；
ζyz=θ 'yz-θyz。
S2, error of the cutter under cutting force and centrifugal force effect and under torque effect is obtained by calculating.Specifically,
Wherein xt-yt-ztIt is the coordinate system established centered on cutter, wherein xtFor the axial direction of workpiece (axle), ytTo be in workpiece lead to
Cross the radial direction of rotary head, ztFor with xtAnd ytTo vertical direction, i.e. the linear velocity direction of cutterhead rotation.
Cutterhead (gear hobbing cutter) and main shaft are influenced with angular velocity omega rotation by cutting torque and centrifugal moment, in cutterhead
The deflection angle θ of the heart, the centrifugal mass m of cutterhead, cutterhead be subject in xt-ytBending moment M in face, the bending stiffness of main shaft
K, compared with main shaft, the diameter of cutterhead is much larger than major axis diameter, and rigidity is very big, cutting force away from and centrifugal moment it is made
At bending angle it is very small, can be ignored.And interior cutter tooth due to gear hobbing and outer serrated knife are on different arc surfaces, therefore
It is also contemplated that centrifugal force.
M=(Fy-Fr)l-Fxr
Wherein l, r are respectively main axis length and cutter radius, centrifugal force Fr=m ω2r。
FyAnd FxRespectively ytDirection and xtThe cutting force in direction；It is calculated and is obtained by cutting force formula according to cutting parameter,
Cutting force formula is as follows:
Fy=Ky·a·f；
Fx=Kx·a·f；
Fz=Kz·a·f；
Kx、Ky、Kz、a、f、FzRespectively xtCutting Force Coefficient, the y in directiontCutting Force Coefficient, the z in directiontThe cutting in direction
Force coefficient, cutting depth and feed engagement (feed speed), ztThe cutting force in direction.A, f is the numerical value of setting, can be by cutting
It cuts power experiment and obtains cutting force numerical value, and K is obtained with thisx、Ky、Kz。
K=EI
E is the elasticity modulus of spindle material, and I is the inertia of main axis cross section centering mandrel away from since main shaft is round shape, d
For the diameter of main shaft, therefore
Then according under the action of bending moment, section corner calculation formula at the hinged support of main shaft, can winner's shaft section in knife
The deflection angle θ of disk practical center:L be hinged support at a distance from cutter head center (i.e. cutter spindle
Length).
Under cutting force effect, the distance for deviateing ideal position is sin θ l, due to θ very little, sin θ ≈ θ, in cutting force
Under square effect, the distance for deviateing ideal position is θ l.Under the action of bending moment, according to the corner formula under hinged support,
Deflection angle of the main shaft under hinged support is caused to beAlso due toNumerical value very little,Therefore it is being bent
Deviateing ideal position distance under moment loading is
So main shaft is under the action of cutting force, centrifugal force and its torque, cutterhead practical center and cutterhead desired center
Distance, delta l are as follows:
Deflection angle and eccentric distance cause position and angular error in process, and with the movement road of cutter
Diameter requires supplementation with position and angular error caused by it.
As shown in figure 5, main-shaft core is in x under cutting force and centrifugal force effectt-ytDeviate ideal position in plane to exist
xt、ytThe distance in direction and in xt-ytThe deflection angle of plane are as follows: Δ xt=Δ l sin θ；
Δyt=Δ l cos θ；
θM=θ.
Kinetic equation of the main shaft by the angular response after distorting stress are as follows:
Wherein J0、ct、kt, θ, T be respectively the rotary inertia of axis, the angular acceleration of axis, axis torsion damping system
It counts, the torque that torsion angular speed, the torsion stiffness of axis, the windup-degree of axis and the axis of axis are subject to.
T=Fzr
As shown in figure 4, J0For rotary inertia, can directly be found out by integral come miFor the quality of unit, riFor list
The distance of first off-axis heart.
ct=α J0+βkt
In the rotary motion of axis, the damping due to rotation coefficient of axis is set as ratio torsion damping, and ratio reverses damped coefficient
α, β are as follows:
α=100
β=10-7
Theoretical, the torque according to torsion of bar are as follows:
Wherein Mt, G, I0, l is respectively torque, modulus of shearing, pole inertia away from, main axis length.
The pole inertia in main shaft section away from are as follows:
The torsion stiffness of main shaft are as follows:
With main shaft in primary condition: t=0, θ=0,It is solved, obtaining its response is θ (t).
θ0Angle for the rotation of cutter ideal for the parameter of setting is it is known that θ0Equal to angular speed multiplied by the time, after derivation
For angular speedIt is again angular acceleration after derivation.
As shown in figure 3, in y caused by main shaft torsion retrotorsion angular responset-ztY in planet、 ztDisplacement error difference
Are as follows: Δ yt, Δ zt, it is respectively as follows:
Δzt1=r sin θt；
Δyt1=Δ zt1 tanθt；
R is the distance between serrated knife and axle center on cutterhead, i.e. cutter radius, θ (t)=θt
Cutter is 0 by angular error caused by distorting stress, this is because yt-ztPlane torsion and the angle that generates is missed
Difference, after bit shift compensation, angular error has been eliminated, therefore can be regarded torsion as and not caused angular error, and curved
What the axis that angular error caused by bent torque is not about cutter spindle was formed, it cannot be compensated by displacement error.
S3, machined parameters and machining path are compensated, machined parameters of the error obtained by step S1 to setting
It compensates, obtains compensated machined parameters；Machined parameters after compensation integration error: cutting depth, feed speed difference
Are as follows:
ap c=ap+ξx；
fz c=fz+ζy。
The machining path of setting is compensated by the error that step S1 and S2 are obtained, obtains compensated processing road
Diameter.In the machining path planning of lathe, former cutter and work pieces process
Path setting is
S(xw, yw, zw, θw x-y, θw x-z, θw y-z, xt, yt, zt, θt x-y, θt x-z, θt y-z) ；
The then machining path of compensated cutter and workpiece are as follows:
s′(x′w, y 'w, z 'w, θw′x-y, θw′x-z, θw′y-z, x 't, y 't, z 't, θt′x-y, θt′x-z, θt′y-z)；
Wherein:
x′w=xw
y′w=yw
z′w=ξz+zw
θw′x-y=θw x-y+ζxy
θw′x-z=θw x-z+ζxz
θw′y-z=θw y-z+ζyz
x′t=Δ xt+xt
y′t=Δ yt+yt+Δyt1
zt′y-z=zt y-z+Δzt1
θt′x-y=θt x-y+θM
θt′x-z=θt x-z
θt′y-z=θt y-z。
Originally needed to compensate cutterhead respectively in x-y plane, x-z-plane, the rotation angular error of y-z plane.But due to
Work in-process does not cause x-z-plane, the rotation angular error in y-z plane, therefore x-z-plane, y-z plane internal rotation angle degree
It needs not compensate for.
Workpiece displacement and angle machining path parameter are as follows:
(x′w, y 'w, z 'w, θw′x-y, θw′x-z, θw′y-z)。
Tool displacement and angle machining path parameter are as follows:
(x′t, y 't, z 't, θt′x-y, θt′x-z, θt′y-z)。
Position data after according to this compensation is processed, and the machining accuracy of workpiece is improved.
The above embodiments are merely illustrative of the technical solutions of the present invention and is not intended to limit it, all without departing from the present invention
Any modification of spirit and scope or equivalent replacement, shall fall within the scope of the technical solution of the present invention.
Claims (6)
1. a kind of Gear Hobbing Parameters and path compensation method for highly-efficient processing face gear, which is characterized in that including as follows
Step:
S1, the installation error for obtaining gear hobbing cutter and workpiece relative position: it is rolled by measurement gear hobbing cutter and the location of workpiece
The relative position of measurement, is subtracted the opposite position of gear hobbing cutter and workpiece setting by serrated knife tool and the relative position after workpiece installation
It sets, obtains the installation error of lathe；
S2, error of the gear hobbing cutter under cutting force and centrifugal force effect and under torque effect is obtained by calculating；
S3, compensate to machined parameters and machining path: the error obtained by step S1 carries out the machined parameters of setting
Compensation, obtains compensated machined parameters；The machining path of setting is compensated by the error that step S1 and S2 are obtained, is obtained
Obtain compensated machining path.
2. the Gear Hobbing Parameters and path compensation method according to claim 1 for highly-efficient processing face gear, special
Sign is: the relative position in the step S1 after cutter and workpiece installation is obtained by sensor measurement, workpiece centre, interior
Serrated knife center and outer serrated knife center are respectively equipped with a sensor, and the location parameter measured is Δ xw-t, Δ yw-t, Δ zw-t, θxz,
θxy, θyz, the relative position parameter of cutter and workpiece set is Δ x 'w-t, Δ y 'w-t, Δ z 'w-t, θ 'xz, θ 'xy, θ 'yz；Thus
Obtain the installation error ξ of lathex、ξy、ξz、ζxz、ζxy、ζyz；
ξx=Δ x 'w-t-Δxw-t；
ξy=Δ y 'w-t-Δyw-t；
ξz=Δ z 'w-t-Δzw-t；
ζxz=θ 'xz-θxz；
ζxy=θ 'xy-θxy；
ζyz=θ 'yz-θyz；
Wherein Δ xw-t, Δ yw-t, Δ zw-t, θxz, θxy, θyzThe relative position in the direction x respectively after cutter and workpiece installation, y
The relative position in direction, the relative position in the direction z, the relative angle in xz plane, the relative angle on x/y plane, in yz plane
Relative angle；
Δx′w-t, Δ y 'w-t, Δ z 'w-t, θ 'xz, θ 'xy, θ 'yzFor relative position, the direction y of cutter and the direction x of workpiece setting
Relative position, the relative position in the direction z, the relative angle in xz plane, the relative angle on x/y plane, the phase in yz plane
To angle；
ξx、ξy、ξz、ζxz、ζxy、ζyzThe respectively direction x displacement error, the direction y displacement error, the direction z displacement error, machine tool
Angular error, cutter spindle and the work spindle that main shaft and work spindle are moved in x-z-plane intrinsic deflection are in x-y plane intrinsic deflection
The angular error that angular error, cutter spindle and the work spindle of movement are moved in y-z plane intrinsic deflection.
3. the Gear Hobbing Parameters and path compensation method according to claim 2 for highly-efficient processing face gear, special
Sign is that machined parameters are cutting depth and feed speed, compensated cutting depth a in step S3p cWith feed speed fz cPoint
Not are as follows:
ap c=ap+ξx；
fz c=fz+ξy；
Wherein ap、fzFor the cutting depth and feed speed of setting.
4. the Gear Hobbing Parameters and path compensation method according to claim 2 for highly-efficient processing face gear, special
Sign is that the difference calculation process runs under cutting force and centrifugal force effect are as follows:
The deflection angle θ of cutterhead practical center is obtained first,
The offset distance Δ l of cutterhead practical center is obtained by calculating again,
Finally by formula Δ xt=Δ l sin θ, Δ yt=Δ l cos θ, θM=θ obtains cutterhead due to cutting force and centrifugal force
Displacement error and angular error under effect；
Wherein Δ xt、Δyt、θMRespectively cutting force and cutter head center axial displacement error, cutter head center under centrifugal force effect
Radial displacement error, the cutter head center axially and radially angular error in plane；
Wherein M=(Fy-Fr)l-FxR,
Fx、Fy、FrRespectively serrated knife axial cutting force, radial cutting force and centrifugal force, l, r, I, d be respectively cutter spindle length,
Cutter radius, cutter spindle section are to the moment of inertia of central axis, the diameter of cutter spindle.
5. the Gear Hobbing Parameters and path compensation method according to claim 4 for highly-efficient processing face gear, special
Sign is that the error calculation under torque effect is as follows:
Pass through the kinetic equation of angular responseCalculating acquires cutter spindle displacement and angle
Error is Δ zt1=r sin θt, Δ yt1=Δ zt1tanθt；
Wherein T=FzR,
J0,ct,kt, θ, T are respectively the rotary inertia of main shaft, the angular acceleration of main shaft, the torsion damped coefficient of main shaft, master
The torque that torsion angular speed, the torsion stiffness of main shaft, the windup-degree of main shaft, the main shaft of axis are subject to；
Fz, G be respectively the cutting force in cutterhead linear velocity direction, modulus of shearing.
6. the Gear Hobbing Parameters and path compensation method according to claim 5 for highly-efficient processing face gear, special
Sign is that cutter is with work pieces process path setting
s(xw, yw, zw, θw x-y, θw x-z, θw y-z, xt, yt, zt, θt x-y, θt x-z, θt y-z)；
The machining path of compensated cutter and workpiece is
s′(x′w, y 'w, z 'w, θw′ x-y, θw′ x-z, θw′ y-z, x 't, y 't, z 't, θt′ x-y, θt′ x-z, θt′ y-z)；
Compensated cutter and work pieces process path parameter and the machining path parameters relationship of setting are as follows:
x′w=xw；
y′w=yw；
z′w=ξz+zw；
θw′ x-y=θw x-y+ζxy；
θw′ x-z=θw x-z+ζxz；
θw′ y-z=θw y-z+ζyz；
x′t=Δ xt+xt；
y′t=Δ yt+yt+Δyt1；
zt′ y-z=zt y-z+Δzt1；
θt′ x-y=θt x-y+θM；
θt′ x-z=θt x-z；
θt′ y-z=θt y-z。
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