CN106808032A - A kind of method for reducing thread milling machining interference - Google Patents

A kind of method for reducing thread milling machining interference Download PDF

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Publication number
CN106808032A
CN106808032A CN201710117690.2A CN201710117690A CN106808032A CN 106808032 A CN106808032 A CN 106808032A CN 201710117690 A CN201710117690 A CN 201710117690A CN 106808032 A CN106808032 A CN 106808032A
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thread
tooth form
screw cutter
screw
cot
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胡自化
谭兆
秦长江
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Xiangtan University
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Xiangtan University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23G—THREAD CUTTING; WORKING OF SCREWS, BOLT HEADS, OR NUTS, IN CONJUNCTION THEREWITH
    • B23G1/00—Thread cutting; Automatic machines specially designed therefor
    • B23G1/32—Thread cutting; Automatic machines specially designed therefor by milling

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  • Mechanical Engineering (AREA)
  • Numerical Control (AREA)

Abstract

The invention provides a kind of method for reducing thread milling machining interference, category Computerized Numerical Control processing technology field.It is comprised the following steps：1）Theorized the Mathematical Modeling of form of thread and actual thread tooth form using screw thread and milling cutter basic parameter；2）It is compared by theoretical form of thread and actual thread tooth form, sets up the computation model of thread milling machining interference value；3）The iterative algorithm that screw cutter tooth form is dynamically adjusted is set up using maximum interference value, optimizes six characteristic points of screw cutter tooth form；4）Preferable screw cutter tooth form is generated using six characteristic points after optimization.The present invention not only can significantly reduce the interference produced in thread milling processing by optimizing screw cutter tooth form, improve the machining accuracy and processing efficiency of screw thread, and reduce production cost.

Description

A kind of method for reducing thread milling machining interference
Technical field
The present invention relates to a kind of method for reducing thread milling machining interference, especially for big pitch, large-diameter thread NC milling.
Background technology
Used as a kind of connected mode the most frequently used in plant equipment, the quality of its performance directly influences machinery for threaded connection The service life of equipment.Traditional thread turning and screw tap, screw die processing efficiency be low, cutting force is big, it is difficult to adapt to large-scale precision The manufacture demand of screw thread.And with the appearance of Craftwork of Numerical Control Milling for Screw Thread, the deficiency of conventional threads processing method is compensate for well, spiral shell Line Milling Process is compared with the mode of other processing screw threads, and high in machining efficiency, applicability is good, occurs easily to be moved during disconnected sword Remove, therefore be widely used.
Thread milling processing be cutter on one side with lathe main shaft gyration, an edge workpiece centre of gyration development cutting movement, It is axially moved simultaneously.In thread milling process, interference is produced because screw cutter tooth form does not meet target surface, So as to greatly influence screw thread process precision, if therefore can obtain it is a kind of reduce thread milling machining interference method, will Machining accuracy is greatly enhanced, expands thread milling range of application, reduce high-precision screw thread production cost.
The method for reducing thread milling machining interference is to improve an important research direction of accuracy of thread, existing main point It is two classes：One class is that the interference produced in processing is reduced by optimizing the method for thread milling technique, and the country is mainly studied This class, but in actual production, many enterprises wish to improve screw thread production precision in original technique, therefore such method exists Using very few in later stage thread milling optimization；Another kind of is that generation in thread milling processing is reduced by optimizing milling cutter tooth form Interference, is readily applicable to, in the case where original technique is constant, improve accuracy of thread, domestic in less, the foreign study of this kind of research There are certain research, such as document 1《Interference Modeling in thread milling process》(Fromentin G, Poulachon G. Modeling of interferences during thread milling operation[J]. Adv Manuf Tech 2010,49 (1) 41-51.）Propose by optimize milling cutter profile and reduce milling cutter diameter come reduce thread milling process in Interference, but its process is complicated, calculate big, is unfavorable for popularization and application.
The content of the invention
For the shortcomings of the prior art, the present invention provides a kind of side for reducing thread milling machining interference Method, the method ensure that the interference values produced in the actual milling process of screw thread in the interference margin of tolerance, and cause screw thread Actual tooth form is optimal.
To achieve the above object, the technical solution adopted by the present invention is as follows：A kind of side for reducing thread milling machining interference Method, comprises the following steps：
Step 1）Theorized the Mathematical Modeling of form of thread and actual thread tooth form using screw thread and milling cutter basic parameter；
Step 2）It is compared by theoretical form of thread and actual thread tooth form, sets up interference values in thread milling processing Computation model；
Step 3）The iterative algorithm that screw cutter tooth form is dynamically adjusted is worth to using maximum interference, optimization screw cutter tooth form Six characteristic points；
Step 4）Preferable screw cutter tooth form is generated using six characteristic points after optimization.
In the step 1, the number of theorized using screw thread and milling cutter basic parameter form of thread and actual thread tooth form Learn model, including herein below：
1）Nominal form of thread Mathematical Models, mainly include the following steps that；
According to Major DiamDAnd thread pitchP, calculate diameter of threadD 1, the pitch diameter of threadD 2；
Calculate six coordinate points of form of threadP tj =(P tjr ,P tjz )：
P t1=(P t1r ,P t1z )=(D 1/ 2,0),
P t2=(P t2r ,P t2z )=(D 1/2,(P/2+△r 1 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))-△r 1),
P t3=(P t3r ,P t3z )=(D/2,(P/2+△r 2 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))+△r 2),
P t4=(P t4r ,P t4z )=(D/2,P/2+ P/2·sin(α 1)(cos(α 2)sec(α 1+α 2)-△r 2 tan(α 2),
P t5=(P t5r ,P t5z )=(D 1/2,(P/2+△r 1 tan(α 2))cot(α 1)+Pcot(α 2))/(cot(α 1)+cot(α 2))+△r 2),
P t6=(P t6r ,P t6z )=(D 1/2,P),
Wherein,P tj It is on form of threadjPoint,j=1,2,3,4,5,6；P tjr It is form of threadjThe radial coordinate of point,P tjz It is form of threadjThe axial coordinate of point, △r 1=(D 2-D 1)/2, △r 2=(D-D 2)/2,α 1、α 2It is screw thread flank angle；
Build nominal form of threadNTPMathematical Modeling：
NTP(z)=( r(z), z) （2）
Wherein,r(z) it is the radial coordinate of form of thread,zIt is the axial coordinate of form of thread,zSpan is 0<z<P,r(z) WithzFunctional relation be：
（3）
2）Actual thread tooth form Mathematical Models, mainly include the following steps that：
According to the big footpath of screw cutterD m With screwer pitchP, calculate screw cutter pathD m1, screw cutter central diameterD m2；
Calculate screw cutter six coordinate points of tooth formP mj =(P mjr ,P mjz )：
P m1=(P m1r ,P m1z )=( D m1, 0),
P m2=(P m2r ,P m2z )=( D m1/2,(P/2+△r m1 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))-△r m1),
P m3=(P m3r ,P m3z )=( D m /2,(P/2+△r 2 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))+△r m2),
P m4=(P m4r ,P m4z )=( D m /2,P/2+ P/2·sin(α 1)(cos(α 2)sec(α 1+α 2)-△r m2 tan(α 2),
P m5=(P m5r ,P m5z )=(D m1/2,(P/2+△r m1 tan(α 2))cot(α 1)+Pcot(α 2))/(cot(α 1)+cot(α 2))+△r m2),
P m6=(P m6r ,P m6z )=( D m1/2,P),
Wherein,P mj It is on screw cutter tooth formjPoint,j=1,2,3,4,5,6；P mjr It is screw cutter tooth formjThe radial direction of point Coordinate,P mjz It is screw cutter tooth formjThe axial coordinate of point, △r m1=(D m2-D m1)/2, △r m2=(D m -D m2)/2,α 1、α 2For Screw thread flank angle；
Construct screw cutter tooth formMPMathematical Modeling：
MP(z m )=(r m (z m ), z m ) （5）
Wherein,r m (z m ) it is the radial coordinate of screw cutter tooth form,z m It is the axial coordinate of screw cutter tooth form,z m Span It is 0<z m <P,r m (z m ) withz m Functional relation be：
（6）
3）Actual thread tooth form Mathematical Models, mainly include the following steps that：
Calculate screw cutter machining locus radiusR mc ：
R mc = (D 2-D m )/2 （7）
According to the speed of mainshaftS, feed speedV f , calculate milling cutter spin velocityω, milling cutter revolution angular speedψ：
ω= π·S/30 （8）
ψ=m m ·V f / S·ω/ (2π·(q 2+R 2 mc)1/2) （9）
Wherein,q=P/2π；
Using resulting parameter, screw cutter machining locus are set upMC：
MC(t)=( R mc ·cos(ψ·t), R mc ·sin(ψ·t), t d ·p·ψ·t) （10）
Again by screw cutter machining locusMCObtain screw cutter enveloping surfaceME
ME(t, θ, z m )=MC(t)+ (R mc ·cos(ψ·t)+r m (z m )·cos(θ),r m (z m )·sin(θ),z m ) （11）
Wherein, milling cutter rotation angleθ(t, z m )= -arcsin(R mc ·sin(ψ·t)/MP r (z m )),tIt is the revolution time,tTake Value scope is 0<t<L/V f ,LIt is screw thread process length,z m Span is 0<z m <P, thread rotary orientationt d （Dextrorotationt d =1, it is left-handedt d =-1）；
Then screw cutter enveloping surface is utilizedMECarrying out horizontal frontal plane projection can set up screw cutter envelope trackMETMathematical modulo Type：
MET( t, z m)=(R mc ·cos(ψ·t)+r m (z m ), t d ·q·ψ·t +z m ) （12）
Wherein,z m Span be 0<z m <P；
Finally by screw cutter envelope trackMETConstruct actual thread tooth formGTPMathematical Modeling：
GTP(z m )=(r g (z m ), z m ) （13）
Wherein,r g (z m ) it is the radial coordinate of screw cutter tooth form,z m It is the axial coordinate of screw cutter tooth form,z m Span It is 0<z m <2,r g (z m ) withz m Functional relation be：
（14）
Wherein,。
In the step 2, it is compared by theoretical form of thread and actual thread tooth form, sets up thread milling processing The computation model of middle interference values, including herein below：
1）Calculate the interference values of form of thread：
E (z m )= z m (r g )- z(r g ) （15）
Wherein,r g Span isD 1 < r g < D 2 , and withP/ 20 are calculated for step-length, when the difference of adjacent interference values twice It is more thanE (z m ) 1/10th when, then reduction step-length is carried out using dichotomy；
2）By comparing formula（15）In the interference values size that calculates, obtain the maximum interference value of form of threadE x , and judge Maximum interference valueE x Whether the interference margin of tolerance is exceeded, when maximum interference valueE max During less than the interference margin of tolerance, into step 4, Preferable screw cutter tooth form is generated using six characteristic points after optimization, if being not above, into step 3, using maximum Interference values set up the iterative algorithm that screw cutter tooth form is dynamically adjusted, and optimize six characteristic points of screw cutter tooth form.
In the step 3, the iterative algorithm that screw cutter tooth form is dynamically adjusted is set up using maximum interference value, optimize screw thread Six characteristic points of milling cutter tooth form, mainly including herein below：
1）Calculate the difference △ between the adjacent value of maximum interference twiceE：
△E=E 1 max -E 2 max （16）
Wherein,E 1 max 、E 2 max For adjacent maximum interference value twice；
2）Judge △EDuring whether less than Measurement Allowance, if △EDuring less than Measurement Allowance, into step 4, utilize Six characteristic points after optimization generate preferable screw cutter tooth form, will otherwise continue as follows：
First to tooth form summitP m3WithP m4Coordinate transform is carried out, new coordinate points are obtainedP m3 n、P m4 n, described coordinate transformation equation For：
P m3g n =( P m3r, P m3z- E(P m3z ))；P m4g n = (P m4r, P m4z- E(P m4z )) （17）
Then by milling cutter tooth form bottomP m2WithP m5Screw thread point produced by 2 pointsP m2gWithP m5g, Coordinate Conversion is carried out, obtain new seat PunctuateP m2g nWithP m5g nCoordinate, described coordinate transformation equation is：
P m2g n = (rg(P t2z ), P t2z - E(P t2z ))；P m5g n =(rg(P t5z ), P t2z - E(P t5z )) （18）
Finally by milling cutter tooth form bottomP m1WithP m62 lines respectively with straight lineP m2g n P m3 nAnd straight lineP m5g n P m4 nIt is intersecting, obtain To two new milling cutter tooth form pointsP m2 nWithP m5 n；
Six coordinate points after generation optimization, repeat step 2 compares by theoretical form of thread and actual thread tooth form Compared with, set up thread milling processing in interference values computation model.
In the step 4, using the screw cutter tooth form after the six characteristic points generation optimization after optimization, it is main include with Lower content：
1）Six characteristic points after by optimization substitute into formula（5）In, it is calculated the screw cutter Mathematical Modeling after optimization；
2）By MATLAB softwares, the screw cutter Mathematical Modeling after optimization is programmed, is calculated, export screw cutter tooth Type.
The invention has the advantages that and advantage：The present invention has considered many factors, by optimizing screw thread Milling cutter profile and diameter, have an obvious effect to reducing the interference in thread milling processing, and method is simple, highly versatile.Profit With the method, the interference in screw thread high-rate wireless LAN can be efficiently reduced, improve the machining accuracy of screw thread, reduce high accuracy The percent defective and production cost of screw thread.
Brief description of the drawings
Fig. 1 is flow chart of steps of the invention；
Fig. 2 is form of thread figure used in the present invention；
Fig. 3 is screw cutter tooth form figure used in the present invention；
Fig. 4 is form of thread adjustment algorithm figure of the invention；
Fig. 5 is screw cutter optimization tooth form figure of the present invention.
Specific embodiment
The present invention is described in more detail with reference to the accompanying drawings and detailed description.The present embodiment is with the present invention Implemented under premised on content, given detailed implementation steps, but protection scope of the present invention is not limited to following implementations Example.
Objective for implementation of the present invention is common right-handed thread hole, its depthL=10mm, Major DiamD=16mm, thread pitchP= 2mm, flank angleα 1=α 2=30o, the big footpath of screw cutterD m =12Mm,The speed of mainshaftS s =3000 r/min, feed speedV f =1500Mm/min,According to Fig. 1 flow chart of steps, a kind of method for reducing thread milling machining interference of the present invention is comprised the following steps:
Step 1）Theorized the Mathematical Modeling of form of thread and actual thread tooth form using screw thread and milling cutter basic parameter；
Step 2）It is compared by theoretical form of thread and actual thread tooth form, sets up interference values in thread milling processing Computation model；
Step 3）The iterative algorithm that screw cutter tooth form is dynamically adjusted is set up using maximum interference value, optimization screw cutter tooth form Six characteristic points；
Step 4）Preferable screw cutter tooth form is generated using six characteristic points after optimization.
In the step 1, the number of theorized using screw thread and milling cutter basic parameter form of thread and actual thread tooth form Learn model, including herein below：
1）Nominal form of thread Mathematical Models, mainly include the following steps that；
According to Major DiamDAnd thread pitchP, calculate diameter of threadD 1, the pitch diameter of threadD 2；
D 1=D-5 P/8=13.8mm；D 2=D-3 P/8=14.8mm（1）
Six points on form of thread are as shown in Fig. 2 calculate six coordinate points of form of threadP tj =(P tjr ,P tjz )：
P t1=(P t1r ,P t1z )=(6.9,0),
P t2=(P t2r ,P t2z )=(D 1/2,(P/2+△r 1 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))-△r 1)=(6.9,0.25),
P t3=(P t3r ,P t3z )=(D/2,(P/2+△r 2 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))+△r 2)=(8,0.75),
P t4=(P t4r ,P t4z )=(D/2,P/2+ P/2·sin(α 1)(cos(α 2)sec(α 1+α 2)-△r 2 tan(α 2)=(8,1.125),
P t5=(P t5r ,P t5z )=(D 1/2,(P/2+△r 1 tan(α 2))cot(α 1)+Pcot(α 2))/(cot(α 1)+cot(α 2))+△r 2)
=(6.9,1.75),
P t6=(P t6r ,P t6z )=(6.9,2),
Wherein,P tj It is on form of threadjPoint,j=1,2,3,4,5,6；P tjr It is form of threadjThe radial coordinate of point,P tjz It is form of threadjThe axial coordinate of point, △r 1=(D 2-D 1)/2=0.5, △r 2=(D-D 2)/2=0.6,α 1、α 2It is ridge side Angle；
Build nominal form of threadNTPMathematical Modeling：
NTP(z)=( r(z), z) （2）
Wherein,r(z) it is the radial coordinate of form of thread,zIt is the axial coordinate of form of thread,zSpan is 0<z<P,r(z) WithzFunctional relation be：
（3）
Wherein,r(z) it is the radial coordinate in form of thread,zIt is the axial coordinate in form of thread,zSpan is 0<z<2；
2）Actual thread tooth form Mathematical Models, mainly include the following steps that：
According to the big footpath of screw cutterD m , screwer pitchP, calculate screw cutter pathD m1, screw cutter central diameterD m2；
D m1=D-3 P/8=10.8mm；D m2=D- P/8=11.6mm（4）
6 points on screw cutter tooth form as shown in figure 3, calculate screw cutter six coordinate points of tooth formP mj =(P mjr ,P mjz )：
P m1=(P m1r ,P m1z )=( D m1, 0)=(5.4,0),
P m2=(P m2r ,P m2z )=( D m1/2,(P/2+△r m1 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))-△r m1)
=(5.4,0.125),
P m3=(P m3r ,P m3z )=( D m /2,(P/2+△r 2 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))+△r m2)=(6.0.75),
P m4=(P m4r ,P m4z )=( D m /2,P/2+ P/2·sin(α 1)(cos(α 2)sec(α 1+α 2)-△r m2 tan(α 2)=(6,1.125),
P m5=(P m5r ,P m5z )=(D m1/2,(P/2+△r m1 tan(α 2))cot(α 1)+Pcot(α 2))/(cot(α 1)+cot(α 2))+△r m2)
=(5.4,1.875),
P m6=(P m6r ,P m6z )=( D m1/2,P)=(5.4,2),
Wherein,P mj It is on screw cutter tooth formjPoint,j=1,2,3,4,5,6,P mjr It is screw cutter tooth formjThe radial direction of point Coordinate,P mjz It is screw cutter tooth formjThe axial coordinate of point, △r m1=(D m2-D m1)/2=0.4, △r m2=(D m -D m2)/2=0.2,α 1、α 2It is screw thread flank angle；
Construct screw cutter tooth formMPMathematical Modeling：
MP(z m )=(r m (z m ), z m ) （5）
Wherein,r m (z m ) it is the radial coordinate of screw cutter tooth form,z m It is the axial coordinate of screw cutter tooth form,z m Span It is 0<z m <2,r m (z m ) withz m Functional relation be：
（6）
3）Actual thread tooth form Mathematical Models, mainly include the following steps that：
Calculate screw cutter machining locus radiusR mc ：
R mc = (D 2- D m2)=2mm（7）
Calculate milling cutter spin velocityω, milling cutter revolution angular speedψ：
ω= π·S s /30=314 rad/s；（8）
ψ=m m ·V f / S s ·ω/ (2π·)=88 rad/s（9）
Wherein,q=1/π；
Using resulting parameter, screw cutter machining locus are set upMC, screw cutter enveloping surfaceME：
MC(t)=(R mc ·cos(ψ·t), R mc ·sin(ψ·t), t d ·p·ψ·t) （10）
=(2cos(88t),2sin(88t),88π/t)
ME(t, θ, z m )=MC(t)+ (R mc ·cos(ψ·t)+r m (z m )·cos(θ),r m (z m )·sin(θ),z m ) （11）
=(4cos(88t)+r m (z m )·cos(θ),2sin(88t)+r m (z m )·sin(θ),88π/t+z m )
Wherein, milling cutter rotation angleθ(t, z m )=-arcsin(R mc ·sin(88·t)/MP r (z m )),t- revolution the time,tTake Value scope is 0<t<4,z m Span is 0<z m <2, thread rotary orientationt d =1（Dextrorotationt d =1, it is left-handedt d =-1）；
Then set up screw cutter envelope trackMET：
MET( t, z m)=(R mc ·cos(ψ·t)+r m (z m ), t d ·p·ψ·t +z m )=(2cos(88t)+r m (z m ), 88π/t+ z m ) （12）
Wherein,z m Span is 0<z m <P；
Finally set up actual thread profileGTP：
GTP(z m )=(r g (z m ), z m ) （13）
Wherein,r g (z m ) it is the radial coordinate of screw cutter tooth form,z m It is the axial coordinate of screw cutter tooth form,z m Span It is 0<z m <2,r g (z m ) withz m Functional relation be：
（14）
Wherein,。
In the step 2, it is compared by theoretical form of thread and actual thread tooth form, sets up thread milling processing The computation model of middle interference values, including herein below：
1）Calculate the interference values of form of thread：
E (z m )= z m (r g )- z(r g ) （15）
Wherein,r g Span isD 1 < r g < D 2 , and with 0.1mmFor step-length is calculated；
2）By comparing formula（15）In the interference values size that calculates, obtain the maximum interference value of form of threadE x , and judge Maximum interference valueE x Whether the interference margin of tolerance is exceeded, when maximum interference valueE max During less than the interference margin of tolerance, into step 4, Preferable screw cutter tooth form is generated using six characteristic points after optimization, if being not above, into step 3, using maximum Interference values set up the iterative algorithm that screw cutter tooth form is dynamically adjusted, and optimize six characteristic points of screw cutter tooth form.
In the step 3, the iterative algorithm that screw cutter tooth form is dynamically adjusted is set up using maximum interference value, optimize screw thread Six characteristic points of milling cutter tooth form, mainly including herein below：
As shown in figure 4, setting up the iterative algorithm that screw cutter tooth form is dynamically adjusted using maximum interference value, optimize screw cutter tooth Six characteristic points of type are mainly included the following steps that：
1）Calculate the difference △ between the adjacent value of maximum interference twiceE：
△E=E 1 max -E 2 max （16）
Wherein,E 1 max 、E 2 max For adjacent maximum interference value twice；
2）Judge △EDuring whether less than Measurement Allowance, if △EDuring less than Measurement Allowance, into step 4, utilize Six characteristic points after optimization generate preferable screw cutter tooth form, will otherwise continue as follows：
First to tooth form summitP m3WithP m4Coordinate transform is carried out, as shown in figure 4, obtaining new coordinate pointsP m3 n、P m4 n, described seat Marking transformation equation is：
P m3g n =( P m3r, P m3z- E(P m3z ))；P m4g n = (P m4r, P m4z- E(P m4z )) （17）
Then by milling cutter tooth form bottomP m2WithP m5Screw thread point produced by 2 pointsP m2gWithP m5g, as shown in figure 4, carry out coordinate turning Change, obtain new coordinate pointsP m2g nWithP m5g nCoordinate, described coordinate transformation equation is：
P m2g n = (rg(P t2z ), P t2z - E(P t2z ))；P m5g n =(rg(P t5z ), P t2z - E(P t5z )) （18）
Finally by milling cutter tooth form bottomP m1WithP m62 lines respectively with straight lineP m2g n P m3 nAnd straight lineP m5g n P m4 nIt is intersecting, obtain To two new milling cutter tooth form pointsP m2 nWithP m5 n, as shown in Figure 4；
Six coordinate points after generation optimization, repeat step 2 compares by theoretical form of thread and actual thread tooth form Compared with, set up thread milling processing in interference values computation model.
Obtain wherein maximum interference valueE x0 = 58 μm, it is 15 example originally to be applied in addition and allows interference valuesμm,Allow to interfere difference It is 1.5μm, judge to obtain for the first timeE max0 >15μm, calculating carries out screw cutter tooth form adjustment.Repeat step 2, by reason It is compared by form of thread and actual thread tooth form, sets up the computation model of interference values in thread milling processing, obtains first The maximum interference value obtained after secondary iterationE max1 =9.2μm<15μm, and the difference △ between maximum interference valueE 2 =48.8μm> 1.5μm, continue repeat step 2, it is compared by theoretical form of thread and actual thread tooth form, set up thread milling processing The computation model of middle interference values, obtains the difference between second maximum interference valueE max2 = 8.6 μm <15μm, △E 1 =0.6μ m<1.5μm, into step 4, preferable screw cutter tooth form is generated using six characteristic points after optimization,
In the step 4, using the screw cutter tooth form after the six characteristic points generation optimization after optimization, mainly including following interior Hold：
1）Six characteristic points after by optimization substitute into formula（5）In, it is calculated the screw cutter Mathematical Modeling after optimization；
2）By MATLAB softwares, the screw cutter Mathematical Modeling after optimization is programmed, is calculated, export screw cutter tooth Type, as shown in Figure 5.
Further to embody the method for the present invention compared with prior art with part is significantly improved, below by the present invention Method and document《Interference Modeling in thread milling process》(Fromentin G, Poulachon G. Modeling of interferences during thread milling operation[J]. Adv Manuf Tech 2010,49 (1) 41-51.) in result of interference data be compared, as shown in table 1：
Knowable to the data ratio of table 1, using the method for the present invention, all interference values that obtain slightly have reduction.Although reduce amplitude compared with It is small, but the method for the present invention is simple, efficient, applied widely, and also the present invention has only carried out axial error adjustment, therefore will not So that the big footpath of actual thread exceedes theoretical value.
In sum, the present embodiment illustrates a kind of reduction thread milling machine of the invention by taking regular screw threads Milling Process as an example The method for cutting machining interference, the present invention reduces the interference in thread milling processing by optimizing milling cutter tooth form, lifts thread milling machine Cut machining accuracy, and easy, efficiency high.Additionally, the method for the present invention is also applied to trapezoidal thread, taper thread, sawtooth Shape screw thread.

Claims (5)

1. it is a kind of reduce thread milling machining interference method, it is characterised in that comprise the following steps：
Step 1）Theorized the Mathematical Modeling of form of thread and actual thread tooth form using screw thread and milling cutter basic parameter；
Step 2）It is compared by theoretical form of thread and actual thread tooth form, sets up interference values in thread milling processing Computation model；
Step 3）The iterative algorithm that screw cutter tooth form is dynamically adjusted is set up using maximum interference value, optimization screw cutter tooth form Six characteristic points；
Step 4）Preferable screw cutter tooth form is generated using six characteristic points after optimization.
2. it is according to claim 1 it is a kind of reduce thread milling machining interference method, it is characterised in that the step 1 In, the Mathematical Modeling of theorized using screw thread and milling cutter basic parameter form of thread and actual thread tooth form, including it is following interior Hold：
1）Nominal form of thread Mathematical Models, mainly include the following steps that；
According to Major DiamDAnd thread pitchP, calculate diameter of threadD 1, the pitch diameter of threadD 2；
Calculate six feature point coordinates of form of threadP tj =(P tjr ,P tjz )：
P t1=(P t1r ,P t1z )=(D 1/ 2,0),
P t2=(P t2r ,P t2z )=(D 1/2,(P/2+△r 1 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))-△r 1),
P t3=(P t3r ,P t3z )=(D/2,(P/2+△r 2 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))+△r 2),
P t4=(P t4r ,P t4z )=(D/2,P/2+ P/2·sin(α 1)(cos(α 2)sec(α 1+α 2)-△r 2 tan(α 2),
P t5=(P t5r ,P t5z )=(D 1/2,(P/2+△r 1 tan(α 2))cot(α 1)+Pcot(α 2))/(cot(α 1)+cot(α 2))+△r 2),
P t6=(P t6r ,P t6z )=(D 1/2,P),
Wherein,P tj It is on form of threadjPoint,j=1,2,3,4,5,6,P tjr It is form of threadjThe radial coordinate of point,P tjz For Form of threadjThe axial coordinate of point, △r 1=(D 2-D 1)/2, △r 2=(D-D 2)/2,α 1、α 2It is screw thread flank angle；
Build nominal form of threadNTPMathematical Modeling：
NTP(z)=( r(z), z) （2）
Wherein,r(z) it is the radial coordinate of form of thread,zIt is the axial coordinate of form of thread,zSpan is 0<z<P,r(z) WithzFunctional relation be：
（3）
2）Screw cutter tooth form Mathematical Models, mainly include the following steps that：
According to the big footpath of screw cutterD m And thread pitchP, calculate screw cutter pathD m1, screw cutter central diameterD m2；
Calculate screw cutter six feature point coordinates of tooth formP mj =(P mjr ,P mjz )：
P m1=(P m1r ,P m1z )=( D m1, 0),
P m2=(P m2r ,P m2z )=( D m1/2,(P/2+△r m1 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))-△r m1),
P m3=(P m3r ,P m3z )=( D m /2,(P/2+△r 2 tan(α 1))cot(α 2)/(cot(α 1)+cot(α 2))+△r m2),
P m4=(P m4r ,P m4z )=( D m /2,P/2+ P/2·sin(α 1)(cos(α 2)sec(α 1+α 2)-△r m2 tan(α 2),
P m5=(P m5r ,P m5z )=(D m1/2,(P/2+△r m1 tan(α 2))cot(α 1)+Pcot(α 2))/(cot(α 1)+cot(α 2))+△r m2),
P m6=(P m6r ,P m6z )=( D m1/2,P),
Wherein,P mj It is on screw cutter tooth formjPoint,j=1,2,3,4,5,6；P mjr It is screw cutter tooth formjThe radial direction of point is sat Mark,P mjz It is screw cutter tooth formjThe axial coordinate of point, △r m1=(D m2-D m1)/2, △r m2=(D m -D m2)/2,α 1、α 2It is spiral shell Line flank angle；
Construct screw cutter tooth formMPMathematical Modeling：
MP(z m )=(r m (z m ), z m ) （5）
Wherein,r m (z m ) it is the radial coordinate of screw cutter tooth form,z m It is the axial coordinate of screw cutter tooth form,z m Span is 0<z m <P,r m (z m ) withz m Functional relation be：
（6）
3）Actual thread tooth form Mathematical Models, mainly include the following steps that：
Calculate screw cutter machining locus radiusR mc ：
R mc = (D 2-D m )/2 （7）
According to the speed of mainshaftS, feed speedV f , calculate milling cutter spin velocityω, milling cutter revolution angular speedψ：
ω= π·S/30 （8）
ψ=m m ·V f / S·ω/ (2π·) （9）
Wherein,q=P/2π；
Using resulting parameter, screw cutter machining locus are set upMC：
MC(t)=( R mc ·cos(ψ·t), R mc ·sin(ψ·t), t d ·p·ψ·t) （10）
Again by screw cutter machining locusMCObtain screw cutter enveloping surfaceME
ME(t, θ, z m )=MC(t)+ (R mc ·cos(ψ·t)+r m (z m )·cos(θ),r m (z m )·sin(θ),z m ) （11）
Wherein, milling cutter rotation angleθ(t, z m )= -arcsin(R mc ·sin(ψ·t)/MP r (z m )),tIt is the revolution time,tTake Value scope is 0<t<L/V f ,LIt is screw thread process length,z m Span is 0<z m <P, thread rotary orientationt d （Dextrorotationt d =1, it is left-handedt d =-1）；
Then screw cutter enveloping surface is utilizedMECarrying out horizontal frontal plane projection can set up screw cutter envelope trackMETMathematical modulo Type：
MET( t, z m)=(R mc ·cos(ψ·t)+r m (z m ), t d ·q·ψ·t +z m ) （12）
Wherein,z m Span be 0<z m <P；
Finally by screw cutter envelope trackMETConstruct actual thread tooth formGTPMathematical Modeling：
GTP(z m )=(r g (z m ), z m ) （13）
Wherein,r g (z m ) it is the radial coordinate of screw cutter tooth form,z m It is the axial coordinate of screw cutter tooth form,z m Span is 0<z m <2,r g (z m ) withz m Functional relation be：
（14）
Wherein, t = arcsin ( P &sdot; t d &sdot; r m &bull; ) &sol; &psi; 。
3. it is according to claim 1 it is a kind of reduce thread milling machining interference method, it is characterised in that the step 2 In, it is compared by theoretical form of thread and actual thread tooth form, set up the calculating mould of interference values in thread milling processing Type, including herein below：
1）Calculate the interference values of form of thread：
E (z m )= z m (r g )- z(r g ) （15）
Wherein,r g Span isD 1 < r g < D 2 , and withP/ 20 are calculated for step-length, when the difference of adjacent interference values twice It is more thanE (z m ) 1/10th when, then reduction step-length is carried out using dichotomy；
2）By comparing formula（15）In the interference values size that calculates, obtain the maximum interference value of form of threadE x , and judge most Big interference valuesE x Whether the interference margin of tolerance is exceeded, when maximum interference valueE max During less than the interference margin of tolerance, into step 4, profit Preferable screw cutter tooth form is generated with six characteristic points after optimization, if being not above, into step 3, using maximum dry Relate to value and set up the iterative algorithm that screw cutter tooth form is dynamically adjusted, optimize six characteristic points of screw cutter tooth form.
4. it is according to claim 1 it is a kind of reduce thread milling machining interference method, it is characterised in that the step 3 In, the iterative algorithm that screw cutter tooth form is dynamically adjusted is set up using maximum interference value, optimize six spies of screw cutter tooth form Levy a little, mainly including herein below：
1）Calculate the difference △ between the adjacent value of maximum interference twiceE：
△E=E 1 max -E 2 max （16）
Wherein,E 1 max 、E 2 max For adjacent maximum interference value twice；
2）Judge △EDuring whether less than Measurement Allowance, if △EDuring less than Measurement Allowance, into step 4, utilize Six characteristic points after optimization generate preferable screw cutter tooth form, will otherwise continue as follows：
First to tooth form summitP m3WithP m4Coordinate transform is carried out, new coordinate points are obtainedP m3 n、P m4 n, described coordinate transformation equation For：
P m3g n =( P m3r, P m3z- E(P m3z ))；P m4g n = (P m4r, P m4z- E(P m4z )) （17）
Then by milling cutter tooth form bottomP m2WithP m5Screw thread point produced by 2 pointsP m2gWithP m5g, Coordinate Conversion is carried out, obtain new seat PunctuateP m2g nWithP m5g nCoordinate, described coordinate transformation equation is：
P m2g n = (rg(P t2z ), P t2z - E(P t2z ))；P m5g n =(rg(P t5z ), P t2z - E(P t5z )) （18）
Finally by milling cutter tooth form bottomP m1WithP m62 lines respectively with straight lineP m2g n P m3 nAnd straight lineP m5g n P m4 nIt is intersecting, obtain To two new milling cutter tooth form pointsP m2 nWithP m5 n；
Optimize six characteristic points of screw cutter tooth form, repeat step 2 is entered by theoretical form of thread and actual thread tooth form Row compares, and sets up the computation model of interference values in thread milling processing.
5. it is according to claim 1 it is a kind of reduce thread milling machining interference method, it is characterised in that the step 4 In, using the screw cutter tooth form after the six characteristic points generation optimization after optimization, mainly including herein below：
1）Six characteristic points after by optimization substitute into formula（5）In, it is calculated the screw cutter Mathematical Modeling after optimization；
2）By MATLAB softwares, the screw cutter Mathematical Modeling after optimization is programmed, is calculated, export screw cutter tooth Type.
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