CN107876902B - A kind of processing method for matching enveloping worm - Google Patents

A kind of processing method for matching enveloping worm Download PDF

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CN107876902B
CN107876902B CN201711190062.3A CN201711190062A CN107876902B CN 107876902 B CN107876902 B CN 107876902B CN 201711190062 A CN201711190062 A CN 201711190062A CN 107876902 B CN107876902 B CN 107876902B
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enveloping
twice
worm
enveloping worm
correction
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CN107876902A (en
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和法洋
李展山
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SHANGHAI HEZHONG HEAVY INDUSTRY MACHINERY CO LTD
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SHANGHAI HEZHONG HEAVY INDUSTRY MACHINERY CO LTD
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F13/00—Making worms by methods essentially requiring the use of machines of the gear-cutting type

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)
  • Power Steering Mechanism (AREA)

Abstract

The present invention relates to a kind of processing methods for matching enveloping worm: establishing tooth surface equation f (a1,i01,β,z,rb)；Its tooth surface error Δ e is measured by initial design parametersi；Tooth surface equation f (a ' after establishing correction of the flank shape1,i′01,β′,z′,r′b), it acquires when measuring the hobboing cutter flank of tooth after correction of the flank shape according to initial design parameters, obtains the tooth surface error Δ E of each corresponding pointsi；Construct objective functionSolve equation F (a '1,i′01,β′,z′,r′b) → min obtains profile modifying parameters a '1、i′01, β ', z ' and r 'bHomographic solution；The processing of first time envelope is carried out according to profile modifying parameters, obtains enveloping worm；Using tested twice-enveloping enveloping worm hob, according to worm gear sub-center away from a2, transmission ratio i12Second of envelope is carried out, twice-enveloping anchor ring worm gear is obtained；Twice-enveloping anchor ring worm gear and the enveloping worm pairing that rolling cut obtains, obtain I class or II class correction of the flank shape transmission, circular tooth contact are reasonably distributed；The present invention only passes through measurement and obtains hobboing cutter tooth surface error curve, corrects worm screw machined parameters, is consistent the error curve of the two, to obtain the well-distributed worm gear of contact (area) pattern.

Description

A kind of processing method for matching enveloping worm
[technical field]
The present invention relates to twice-enveloping enveloping worm drive field, specifically a kind of processing side for matching enveloping worm Method.
[background technique]
Twice-enveloping enveloping worm drive includes Double enveloping hourglass worm gearing, conical surface twice-enveloping enveloping worm The forms such as transmission and double-cone double-enveloping toroidal worm transmission.It is known as the first time by the process that generating surface envelope goes out enveloping worm Enveloping worm is fabricated to the hobboing cutter process that rolling cut goes out worm gear again and is known as second of envelope by envelope, enveloping worm and has its envelope The driving form of twice-enveloping worm gear composition out is just referred to as twice-enveloping enveloping worm drive.When generating surface is plane For Double enveloping hourglass worm gearing.The worm screw that first time envelope processes then is known as planar double enveloping worm.Second The worm gear that secondary envelope processes then is known as planar double-enveloping wormwheel.
Twice-enveloping enveloping worm drive has many advantages, such as that bearing capacity is strong, transmission efficiency is high, and practice have shown that correction of the flank shape energy Enough further increase its transmission performance.Correction of the flank shape is realized by modifying the partial parameters of first time envelope.These corrections of the flank shape ginseng Number can be center away from, transmission ratio, generating surface inclination angle, main base radius, relative axial position etc..The variable quantity of these parameters is Profiling quantity allows its value in a certain range there is no specific standard.According to the difference of value, correction of the flank shape transmission can be divided into The correction of the flank shape of I class and II class correction of the flank shape.
Usual twice-enveloping enveloping worm drive is antithesis processing, that is, is used to cut the twice-enveloping worm gear hob of worm gear Parameter and the parameter of enveloping worm are completely the same, and enveloping worm and twice-enveloping worm gear hob are that have same equipment processing Made of.Due to twice-enveloping worm gear hob molding after need rolling cut a worm gears up to a hundred, this just need up to a hundred enveloping worms and The design parameter of twice-enveloping worm gear hob is consistent.For large-scale, single-piece twice-enveloping enveloping worm drive, twice-enveloping snail The processing quantity of wheel is few, and the service life of twice-enveloping worm gear hob was up to for more than ten years.Therefore it can produce always and twice-enveloping The identical enveloping worm of worm gear hob is the key that guarantee meshing quality.
When the twice-enveloping worm gear hob flank of tooth is there are when foozle, pass through the available tooth surface error of measurement.In order to mention High meshing quality, it is common practice that using error correcting technology, reconditioning hobboing cutter is again to eliminate foozle, but reconditioning again The hobboing cutter will lead to transverse tooth thickness and be thinned, and need further manual relief grinding relief angle, there is a problem of manufacturing cycle length.And from correction of the flank shape Angle modification design and processing are carried out to enveloping worm, make enveloping worm and twice-enveloping worm gear hob mistake having the same Poor curve, the worm gear that pairing uses so still can obtain preferable meshing quality.
[summary of the invention]
For above-mentioned problem, the present invention proposes a kind of method, by measuring twice-enveloping worm gear hob tooth surface error, to matching Pair enveloping worm carry out correction of the flank shape, so that the error curve both made is consistent, ensure that the engagement matter of worm gear in this way Amount.
To achieve the above object, a kind of processing method for matching enveloping worm is proposed, which is characterized in that including following step It is rapid:
Step 1, the tooth surface equation f (a of twice-enveloping worm gear hob is established1,i01,β,z,rb), wherein initial design parameters Center is away from for a1, transmission ratio i01, generating surface inclination angle be β, relative axial position z, main base radius are rb；
Step 2, according to initial design parameters center away from for a1, transmission ratio i01, generating surface inclination angle be β, axially opposing position It is set to z, main base radius is rb, generative theory measures motion profile to measure the tooth surface error of twice-enveloping worm gear hob, obtains To the normal error Δ e of flank of tooth each pointi, the quantity of measured point is n；
Step 3, the tooth surface equation f (a of the twice-enveloping worm gear hob after establishing correction of the flank shape1′,i0′1,β′,z′,rb'), wherein Profile modifying parameters a1' it is correction of the flank shape center away from, i0′1For correction of the flank shape transmission ratio, β ' be correction of the flank shape generating surface inclination angle, z ' is the axially opposing position of correction of the flank shape It sets, rb' it is the main base radius of correction of the flank shape；After according to theory measurement motion profile measurement correction of the flank shape when the flank of tooth, each corresponding points are obtained Normal error Δ Ei；
Step 4, objective function is constructedSolve equation F (a1′,i0′1,β′,z′, rb') → min, obtain profile modifying parameters a1′、i0′1, β ', z ' and rb' homographic solution；
Step 5, the processing of first time envelope is carried out according to profile modifying parameters, obtains enveloping worm；
Step 6, using tested twice-enveloping worm gear hob, according to worm gear sub-center away from a2, transmission ratio i12It carries out second Envelope obtains twice-enveloping anchor ring worm gear；
Step 7, twice-enveloping worm gear and the enveloping worm pairing that rolling cut obtains obtain I class or II class correction of the flank shape transmission, the flank of tooth Contact zone is reasonably distributed.
If twice-enveloping worm gear hob flank of tooth each point normal error Δ eiIt is zero, then profile modifying parameters and initial design parameters one It causes.
ConstructorSolve equation F (a1′,i0′1,β′,z′,rb') → min, it asks Solution uses optimization algorithm.
The processing method is equally applicable to straight trough twice-enveloping worm gear hob and helicla flute twice-enveloping worm gear hob.
It can be from center away from, transmission ratio, generating surface inclination angle, relative axial position and main base radius, in this five parameters Selected part is remained unchanged as profile modifying parameters, other parameters.
The processing method is also applied for hobboing cutter having been carried out the twice-enveloping enveloping worm drive of modification design.
The processing method be suitable for Double enveloping hourglass worm gearing, conical surface twice-enveloping enveloping worm drive, Double-cone double-enveloping toroidal worm transmission and other types of twice-enveloping enveloping worm drive.
Method designed by the present invention, by measuring twice-enveloping worm gear hob tooth surface error, to the enveloping worm of pairing Correction of the flank shape is carried out, so that the error curve of the two be made to be consistent.
[Detailed description of the invention]
The instantaneous contact line of the non-correction of the flank shape planar double-enveloping wormwheel flank of tooth of Fig. 1
Fig. 2 is planar double-enveloping wormwheel hobboing cutter tooth surface error curve 1
Fig. 3 is I class correction of the flank shape planar double-enveloping wormwheel flank of tooth instantaneous contact line
Fig. 4 is planar double-enveloping wormwheel hobboing cutter tooth surface error curve 2
Fig. 5 is II class correction of the flank shape planar double-enveloping wormwheel flank of tooth instantaneous contact line
Fig. 6 is the method for the present invention flow chart
[specific embodiment]
Technical solution of the present invention is further elaborated now in conjunction with accompanying drawings and embodiments, it is believed that those skilled in the art For be clear.
A kind of processing method of pairing enveloping worm of the invention, comprising the following steps:
Step 1, the tooth surface equation f (a of twice-enveloping worm gear hob is established1,i01,β,z,rb), wherein initial design parameters Center is away from for a1, transmission ratio i01, generating surface inclination angle be β, relative axial position z, main base radius are rb；
Step 2, according to initial design parameters center away from for a1, transmission ratio i01, generating surface inclination angle be β, axially opposing position It is set to z, main base radius is rb, generative theory measures motion profile to measure the tooth surface error of twice-enveloping worm gear hob, obtains To the normal error Δ e of flank of tooth each pointi, the quantity of measured point is n；
Step 3, the tooth surface equation f (a of the twice-enveloping worm gear hob after establishing correction of the flank shape1′,i0′1,β′,z′,rb'), wherein Profile modifying parameters a1' it is correction of the flank shape center away from, i0′1For correction of the flank shape transmission ratio, β ' be correction of the flank shape generating surface inclination angle, z ' is the axially opposing position of correction of the flank shape It sets, rb' it is the main base radius of correction of the flank shape；After according to theory measurement motion profile measurement correction of the flank shape when the flank of tooth, each corresponding points are obtained Normal error Δ Ei；
Step 4, objective function is constructedSolve equation F (a1′,i0′1,β′,z′, rb') → min, obtain profile modifying parameters a1′、i0′1, β ', z ' and rb' homographic solution；
Step 5, the processing of first time envelope is carried out according to profile modifying parameters, obtains enveloping worm；
Step 6, using tested twice-enveloping worm gear hob, according to worm gear sub-center away from a2, transmission ratio i12It carries out second Envelope obtains twice-enveloping anchor ring worm gear；
Step 7, twice-enveloping worm gear and the enveloping worm pairing that rolling cut obtains obtain I class or II class correction of the flank shape transmission, the flank of tooth Contact zone is reasonably distributed.
If twice-enveloping worm gear hob flank of tooth each point normal error Δ eiIt is zero, then profile modifying parameters and initial design parameters one It causes.
ConstructorSolve equation F (a1′,i0′1,β′,z′,rb') → min, it asks Solution uses optimization algorithm.
The processing method is equally applicable to straight trough twice-enveloping worm gear hob and helicla flute twice-enveloping worm gear hob.
It can be from center away from, transmission ratio, generating surface inclination angle, relative axial position and main base radius, in this five parameters Selected part is remained unchanged as profile modifying parameters, other parameters.
The processing method is also applied for hobboing cutter having been carried out the twice-enveloping enveloping worm drive of modification design.
The processing method be suitable for Double enveloping hourglass worm gearing, conical surface twice-enveloping enveloping worm drive, Double-cone double-enveloping toroidal worm transmission and other types of twice-enveloping enveloping worm drive.
Embodiment:
With the worm gear sub-center do not practiced Buddhism or Taoism away from a2For 160mm, transmission ratio i12It is passed for 50 planar double-enveloping worm For dynamic.As planar double enveloping worm with the initial design parameters of plane-generated double enveloping worm gear hob is with tooth surface equation 's.Initial design parameters center is away from a1For 160mm, transmission ratio i01For 50, generating surface angle of inclination beta be 10 degree, relative axial position z is 300mm, main base radius rbFor 55mm.According to the theory of engagement, the tooth surface equation f (a of planar double-enveloping wormwheel hobboing cutter1,i01, β,z,rb) are as follows:
Wherein u, v be generating surface parameter,For generating surface rotational angle, (X0,Y0,Z0) it is in generating surface coordinate system The coordinate of point, (X1,Y1,Z1) be hobboing cutter coordinate system midpoint coordinate.The instant contact of the non-correction of the flank shape planar double-enveloping wormwheel flank of tooth Line is as shown in Figure 1.
Tooth surface equation f (a of planar double-enveloping wormwheel hobboing cutter after correction of the flank shape1′,i0′1,β′,z′,rb') are as follows:
Wherein u, v be generating surface parameter,WithRespectively generating surface and hobboing cutter rotational angle, (X0′,Y0′,Z0') be Coordinate at generating surface coordinate system midpoint, (X1′,Y1′,Z1') be hobboing cutter coordinate system midpoint coordinate.
The tooth surface error of twice-enveloping worm gear hob is detected according to initial design parameters.Its tooth top spiral is measured respectively Line, the normal error for indexing helix and tooth root helix.When twice-enveloping worm gear hob is straight trough hobboing cutter, cutting edge number is 24 When, institute measuring point number n is 72.If its tooth surface error curve as shown in Fig. 2, if construct objective functionSolve equation F (a1′,i0′1,β′,z′,rb') → min, obtain the correspondence of profile modifying parameters Solution, a1' it is 160.1mm, i0′1For 20.1, β ' be 10.1 degree, z ' is 300.1mm, rb' it is 55.1mm.Using above-mentioned data as repairing Shape parameter carries out the processing of first time envelope, i.e. the grinding enveloping worm flank of tooth.Then use the hobboing cutter according to center away from a2For 160mm, transmission ratio i12Second of envelope, i.e. rolling cut worm gear are carried out for 50.The twice-enveloping worm gear and enveloping worm that rolling cut obtains Match and ensures that the meshing quality of worm gear.Worm gear engage when worm gear surface instantaneous contact line distribution as shown in figure 3, It is driven at this time for I type.
If its tooth surface error curve is solved as shown in figure 4, equally constructing objective function, profile modifying parameters are finally obtained a1' it is 159.9mm, i0′1For 19.9, β ' be 9.9 degree, z ' is 299.9mm, rb' it is 54.9mm.According to profile modifying parameters to anchor ring snail Bar carries out correction of the flank shape processing.Still use the hobboing cutter according to center away from a2For 160mm, transmission ratio i12Second of envelope is carried out for 50, i.e., Rolling cut worm gear.The distribution of worm gear surface instantaneous contact line for II type as shown in figure 5, be driven at this time when worm gear engages.

Claims (9)

1. a kind of processing method for matching enveloping worm, which comprises the following steps:
Step 1, the tooth surface equation f (a of twice-enveloping worm gear hob is established1,i01,β,z,rb), wherein initial design parameters center away from For a1, transmission ratio i01, generating surface inclination angle be β, relative axial position z, main base radius are rb；
Step 2, according to initial design parameters center away from for a1, transmission ratio i01, generating surface inclination angle be β, relative axial position is Z, main base radius is rb, generative theory measures motion profile to measure the tooth surface error of twice-enveloping worm gear hob, obtains tooth The normal error Δ e of face each pointi, the quantity of measured point is n；
Step 3, the tooth surface equation f (a ' of the twice-enveloping worm gear hob after establishing correction of the flank shape1,i′01,β′,z′,rb'), wherein correction of the flank shape Parameter a '1It is correction of the flank shape center away from, i '01Be correction of the flank shape generating surface inclination angle for correction of the flank shape transmission ratio, β ', z ' be correction of the flank shape relative axial position, rb' it is the main base radius of correction of the flank shape；After according to theory measurement motion profile measurement correction of the flank shape when the flank of tooth, the normal direction of each corresponding points is obtained Error delta Ei；
Step 4, objective function is constructedSolve equation F (a '1,i′01,β′,z′,rb′)→ Min obtains profile modifying parameters a '1、i′01, β ', z ' and rb' homographic solution；
Step 5, the processing of first time envelope is carried out according to profile modifying parameters, obtains enveloping worm；
Step 6, using tested twice-enveloping worm gear hob, according to worm gear sub-center away from a2, transmission ratio i12Second of envelope is carried out, Obtain twice-enveloping anchor ring worm gear；
Step 7, twice-enveloping worm gear and the enveloping worm pairing that rolling cut obtains obtain I class or II class correction of the flank shape transmission, face Area is reasonably distributed.
2. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that with plane-generated double enveloping ring For surface-worm transmission, the tooth surface equation f (a of planar double-enveloping wormwheel hobboing cutter1,i01,β,z,rb) are as follows:
Wherein u, v be generating surface parameter,For generating surface rotational angle, (X0,Y0,Z0) it is at generating surface coordinate system midpoint Coordinate, (X1,Y1,Z1) be hobboing cutter coordinate system midpoint coordinate.
3. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that with plane-generated double enveloping ring For surface-worm transmission, the tooth surface equation f (a ' of the planar double-enveloping wormwheel hobboing cutter after correction of the flank shape1,i′01,β′,z′,rb') are as follows:
Wherein u, v be generating surface parameter,WithRespectively generating surface and hobboing cutter rotational angle, (X0′,Y0′,Z0') it is to produce The coordinate at shape areal coordinate system midpoint, (X '1,Y1′,Z1') be hobboing cutter coordinate system midpoint coordinate.
4. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that if twice-enveloping worm gear rolls Cutter tooth face each point normal error Δ eiIt is zero, then profile modifying parameters are consistent with initial design parameters.
5. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that constructorSolve equation F (a '1,i′01,β′,z′,rb') → min, it solves and uses optimization algorithm.
6. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that the processing method is same Suitable for straight trough twice-enveloping worm gear hob and helicla flute twice-enveloping worm gear hob.
7. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that can from center away from, pass It is dynamic than, generating surface inclination angle, relative axial position and main base radius, in this five parameters selected part as profile modifying parameters, Its parameter remains unchanged.
8. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that the processing method is also fitted For hobboing cutter having been carried out the twice-enveloping enveloping worm drive of modification design.
9. a kind of processing method for matching enveloping worm as described in claim 1, which is characterized in that the processing method is applicable in It is passed in Double enveloping hourglass worm gearing, conical surface twice-enveloping enveloping worm drive, double-cone double-enveloping toroidal worm Dynamic and other types of twice-enveloping enveloping worm drive.
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CN113028029B (en) * 2021-02-03 2022-11-18 重庆大学 Cylindrical ring surface combined worm, transmission pair and design and forming method thereof

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JPS6478720A (en) * 1987-09-22 1989-03-24 Nippon Gia Kogyo Kk Corrective tooth cutting method for saddle type worm gear
JP2006247801A (en) * 2005-03-11 2006-09-21 Nsk Ltd Working method of worm gear
CN102389996B (en) * 2011-08-18 2013-04-17 武汉科技大学 Modified double-toroid secondary enveloping toroid worm gear pair and manufacturing method thereof
CN103093054B (en) * 2013-01-29 2016-02-24 福州大学 Double enveloping hourglass worm gearing worm gear hob flank profil modeling method
CN103791869B (en) * 2014-02-18 2016-05-25 北京工业大学 A kind of measuring method of plane-generated double enveloping anchor ring hobboing cutter
CN107269801B (en) * 2017-08-23 2019-08-02 淮阴工学院 A kind of point contact correction method of Niemann worm gear

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