CN106064255A - A kind of method being homogenized planar double enveloping worm flank of tooth grinding allowance - Google Patents

A kind of method being homogenized planar double enveloping worm flank of tooth grinding allowance Download PDF

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Publication number
CN106064255A
CN106064255A CN201610591445.0A CN201610591445A CN106064255A CN 106064255 A CN106064255 A CN 106064255A CN 201610591445 A CN201610591445 A CN 201610591445A CN 106064255 A CN106064255 A CN 106064255A
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China
Prior art keywords
tooth
grinding allowance
worm
planar double
flank
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CN106064255B (en
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和法洋
李开卫
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
    • B23F13/02—Making worms of cylindrical shape
    • B23F13/04—Making worms of cylindrical shape by grinding

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

Abstract

The present invention relates to be homogenized grinding allowance technical field, specifically a kind of method being homogenized planar double enveloping worm flank of tooth grinding allowance, it is characterised in that described method is specific as follows: a. sets up the Mathematical Modeling of planar double enveloping worm flank of tooth grinding allowance；B. with tooth punching centre-to-centre spacingWith tooth punching base radiusFor parameter, building equation makes reference circle anchor ring helix upper inlet consistent with the grinding allowance in exit；Entrance tooth top helix is consistent with the grinding allowance at outlet tooth root helix；C. solving equation, adjusts lathe parameter and carries out tooth punching according to tooth punching centre-to-centre spacing and base radius；D. on the flank of tooth, the maximum point of grinding allowance and the difference of smallest point are minimum grinding allowance.The present invention compared with the existing technology, has an advantage in that: can reduce integral grinding surplus, homogenizing gateway grinding allowance, homogenizing tooth root tooth top grinding allowance.

Description

A kind of method being homogenized planar double enveloping worm flank of tooth grinding allowance
[technical field]
The present invention relates to be homogenized grinding allowance technical field, specifically a kind of homogenizing planar double enveloping worm flank of tooth The method of grinding allowance.
[background technology]
The conventional processing technology of the planar double enveloping worm flank of tooth is divided into rough turn tooth punching and fine grinding flank of tooth two procedures, rough turn Obtain after processing according to design parameter during tooth punching is hindley worm, along transverse tooth thickness such as toroidal direction.Fine grinding the flank of tooth when in order to Ensureing female planar inclination, emery wheel needs certain angle, and this will cause along toroidal direction flank of tooth entrance stock removal big, outlet Stock removal is little, and the grinding allowance of tooth top is more than the grinding allowance of tooth root, the topping of worm screw after whole flank of tooth grinding.This Exist for that grinding allowance is big, uneven, the problem of long processing time.
[content of the invention]
The purpose of the present invention is aiming at the deficiency of above-mentioned prior art condition, provide one reduce integral grinding surplus, Homogenizing gateway grinding allowance, the method for homogenizing tooth root tooth top grinding allowance, solve the problem that existing method exists.
To achieve these goals, designing a kind of method being homogenized planar double enveloping worm grinding allowance, its feature exists Specific as follows in described method:
A. the Mathematical Modeling of planar double enveloping worm flank of tooth grinding allowance is set up
O0O1For line of centres, σ0(O0；x0,y0,z0) it is the dynamic frame connecting firmly with female plane phase, around z0With angular velocity omega0Turn Dynamic.s3(O3；u,n,z3) it is the auxiliary coordinates in female plane.σ1(O1；x1,y1,z1) it is the dynamic frame connecting firmly with worm screw phase, around z1With angular velocity omega1Rotate.w1=w0i01, i01For gearratio.β is female planar inclination, rbFor base radius, a1Centered on away from.u, N is female plane parameter.According to Principles of Gear Connection and homogeneous coordinate transformation matrix, the tooth surface equation of planar double enveloping worm For:
WhereinFor female Plane Rotation angle, j1=j0i01For worm screw rotational angle.Point p on worm screw anchor ring helix (x1,y1,z1) should meet:
Wherein R is the radius of anchor ring, and θ is PO in mid-plane0With O0O1Angle.
If tooth punching centre-to-centre spacingTooth punching base radius,The hindley worm obtaining as b=0, v=0 Tooth surface equation be:
Planar double enveloping worm reference circle anchor ring helix is p with the intersection point of line of centres0, rotate hindley worm tooth Face makes its reference circle and line of centres intersection pointWith p0Overlap, remember that this normal distance is zero.Cross the planar double enveloping worm flank of tooth On some p (x1,y1,z1) do its normal, hand over Tooth Surface for Enveloping Worm with Straight Line Generatrix in pointThe then distance of 2:
Definition Tooth Surface for Enveloping Worm with Straight Line Generatrix is negative less than normal distance during the planar double enveloping flank of tooth, thenTo p (x1,y1,z1) normal distance put is grinding allowance:
B. with tooth punching centre-to-centre spacingWith tooth punching base radiusFor parameter, building equation makes on reference circle anchor ring helix Grinding allowance at entrance and exit is consistent；Entrance tooth top helix is consistent with the grinding allowance at outlet tooth root helix.
Equation is as follows:
Wherein qi=-(a-jw) corresponding porch, qo=zk*t-(a-jw) it is exit.α is pressure angle of graduated circle, and zk is Enveloping teeth,It is angular pitch for work half-angle, τ.r1For worm indexing circular arc radius, Rf1For tip circle of worm arc radius, Ra1 For root circle of worm arc radius.
C. solving equation, adjusts lathe parameter and carries out tooth punching according to tooth punching centre-to-centre spacing and base radius.
D. on the flank of tooth, the maximum point of grinding allowance and the difference of smallest point are minimum grinding allowance.
Dmin=maxD (q, R)-minD (q, R)
Wherein q？[(a-jw),zk*t-(a-jw)],
Described method is applied to numerically controlled lathe tooth punching or general car tooth punching.
The present invention compared with the existing technology, has an advantage in that: can reduce more than integral grinding surplus, homogenizing gateway grinding Amount, homogenizing tooth root tooth top grinding allowance.
[brief description]
Fig. 1 is process principle schematic diagram；
Fig. 2 is normal error schematic diagram；
Fig. 3 is grinding allowance schematic diagram before homogenizing；
Fig. 4 is grinding allowance schematic diagram after homogenizing；
In figure: 1. planar double enveloping worm 2. hindley worm.
[detailed description of the invention]
Below in conjunction with the accompanying drawings, and by embodiment the invention will be further described, and the principle of this method is to this specialty People for be very clearly.
With centre-to-centre spacing a1=125.2, gearratio i01=33, female planar inclination b=10 °, worm indexing radius of circle r1= 27.5th, base radius rb=37.5, enveloping teeth the 3.5th, pressure angle of graduated circle a=22.33 °, work half-angle jw=16.64 °, tooth Elongation t=10.91 °, tip circle of worm arc radius Ra1=94.51, root circle of worm arc radius Rf1The right-hand face of=104.08 As a example by double enveloping worm.According to Principles of Gear Connection and homogeneous coordinate transformation matrix, for example following equation of the tooth surface equation of worm screw Shown in group:
Wherein
In mid-plane, it is R that the flank of tooth meets arc radius, and line and line of centres angle with female plane rotation center are Point p (the x of q1,y1,z1), should meet following equation group:
Wherein q？[0.37,0.29],Choose different R and q, obtain different points.
If tooth punching centre-to-centre spacingTooth punching base radius,The hindley worm obtaining as b=0, v=0 Tooth surface equation be:
With p0P (x is crossed after coincidence1,y1,z1) do its normal, hand over Tooth Surface for Enveloping Worm with Straight Line Generatrix in pointPass through This equation group obtainsValue, thus can be obtained distance and the grinding allowance of PP ' point-to-point transmission by following formula:
And make it meet following equation, try to achieve suitable tooth punching centre-to-centre spacing with thisWith tooth punching base radius
Such as following formula, on the flank of tooth, the maximum point of grinding allowance and the difference of smallest point are minimum grinding allowance:
Dmin=maxD (q, R)-minD (q, R)
When carrying out tooth punching according to the parameter of planar double enveloping worm, minimum grinding allowance is 0.97.According to the present invention Method try to achieve tooth punching centre-to-centre spacingTooth punching base radius,After carrying out tooth punching, minimum grinding allowance is 0.46.Grinding allowance is only original 47.4%, and grinding allowance is little and gateway surplus uniform, tooth root tooth top surplus is uniform.

Claims (2)

1. the method being homogenized planar double enveloping worm grinding allowance, it is characterised in that described method is specific as follows:
A. the Mathematical Modeling of planar double enveloping worm flank of tooth grinding allowance is set up
O0O1For line of centres, σ0(O0；x0,y0,z0) it is the dynamic frame connecting firmly with female plane phase, around z0With angular velocity omega0Rotate.σ3 (O3；μ,ν,z3) it is the auxiliary coordinates in female plane.
σ1(O1；x1,y1,z1) it is the dynamic frame connecting firmly with worm screw phase, around z1With angular velocity omega1Rotate.
w1=w0i01, i01For gearratio.β is female planar inclination, rbFor base radius, a1Centered on away from.μ, ν are female plane ginseng Number.According to Principles of Gear Connection and homogeneous coordinate transformation matrix, the tooth surface equation of planar double enveloping worm is:
WhereinFor female Plane Rotation angle, j1=j0i01For worm screw rotational angle.Point p (x on worm screw anchor ring helix1,y1, z1) should meet:
Wherein R is anchor ring radius, and θ is PO in mid-plane0With line of centres O0O1Angle.
If tooth punching centre-to-centre spacingTooth punching base radius,The tooth of the hindley worm obtaining as b=0, v=0 Face equation is:
Planar double enveloping worm reference circle anchor ring helix is p with the intersection point of line of centres0, rotating Tooth Surface for Enveloping Worm with Straight Line Generatrix makes Its reference circle and line of centres intersection pointWith p0Overlap, remember that this normal distance is zero.Cross on the planar double enveloping worm flank of tooth Point p (x1,y1,z1) do its normal, hand over Tooth Surface for Enveloping Worm with Straight Line Generatrix in pointThe then distance of 2:
Definition Tooth Surface for Enveloping Worm with Straight Line Generatrix is negative less than normal distance during the planar double enveloping flank of tooth, thenTo p (x1, y1,z1) normal distance put is grinding allowance:
D (q, R)=sign (z1ⅱ-z1)*pp
B. with tooth punching centre-to-centre spacingWith tooth punching base radiusFor parameter, build equation make reference circle anchor ring helix upper inlet and The grinding allowance in exit is consistent；Entrance tooth top helix is consistent with the grinding allowance at outlet tooth root helix.
Equation is as follows:
Wherein q？[(a-jw),zk*t-(a-jw)],Corresponding porch, qo=zk*t-(a-jw) For exit.α is pressure angle of graduated circle, zk be enveloping teeth,It is angular pitch for work half-angle, τ.r1For worm indexing circular arc Radius, Rf1For tip circle of worm arc radius, Ra1For root circle of worm arc radius.
C. solving equation, adjusts lathe parameter and carries out tooth punching according to tooth punching centre-to-centre spacing and base radius.
D. on the flank of tooth, the maximum point of grinding allowance and the difference of smallest point are minimum grinding allowance.
Dmin=maxD (q, R)-minD (q, R).
2. a kind of method being homogenized planar double enveloping worm grinding allowance as claimed in claim 1, it is characterised in that described Method be applied to numerically controlled lathe tooth punching or general car tooth punching.
CN201610591445.0A 2016-07-26 2016-07-26 A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance Active CN106064255B (en)

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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN107931743A (en) * 2017-11-24 2018-04-20 上海合纵重工机械有限公司 A kind of method of accurate control plane double enveloping worm transverse tooth thickness
CN113028029A (en) * 2021-02-03 2021-06-25 重庆大学 Cylindrical ring surface combined worm, transmission pair and design and forming method thereof
CN113941741A (en) * 2021-11-16 2022-01-18 天津理工大学 Processing method of homogenization allowance curved surface of multi-head double-conical enveloping worm

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Publication number Priority date Publication date Assignee Title
CN107931743A (en) * 2017-11-24 2018-04-20 上海合纵重工机械有限公司 A kind of method of accurate control plane double enveloping worm transverse tooth thickness
CN107931743B (en) * 2017-11-24 2019-05-28 上海合纵重工机械有限公司 A kind of method of accurate control planar double enveloping worm transverse tooth thickness
CN113028029A (en) * 2021-02-03 2021-06-25 重庆大学 Cylindrical ring surface combined worm, transmission pair and design and forming method thereof
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
CN113941741A (en) * 2021-11-16 2022-01-18 天津理工大学 Processing method of homogenization allowance curved surface of multi-head double-conical enveloping worm
CN113941741B (en) * 2021-11-16 2022-08-05 天津理工大学 Processing method of homogenization allowance curved surface of multi-head double-conical enveloping worm

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