CN106064255B - A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance - Google Patents

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

Info

Publication number
CN106064255B
CN106064255B CN201610591445.0A CN201610591445A CN106064255B CN 106064255 B CN106064255 B CN 106064255B CN 201610591445 A CN201610591445 A CN 201610591445A CN 106064255 B CN106064255 B CN 106064255B
Authority
CN
China
Prior art keywords
tooth
msub
mrow
grinding allowance
worm
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201610591445.0A
Other languages
Chinese (zh)
Other versions
CN106064255A (en
Inventor
和法洋
李开卫
李展山
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
SHANGHAI HEZHONG HEAVY INDUSTRY MACHINERY CO LTD
Original Assignee
SHANGHAI HEZHONG HEAVY INDUSTRY MACHINERY CO LTD
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by SHANGHAI HEZHONG HEAVY INDUSTRY MACHINERY CO LTD filed Critical SHANGHAI HEZHONG HEAVY INDUSTRY MACHINERY CO LTD
Priority to CN201610591445.0A priority Critical patent/CN106064255B/en
Publication of CN106064255A publication Critical patent/CN106064255A/en
Application granted granted Critical
Publication of CN106064255B publication Critical patent/CN106064255B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • 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

Landscapes

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

Abstract

The present invention relates to homogenizing grinding allowance technical field, specifically it is a kind of be homogenized planar double enveloping worm flank of tooth grinding allowance method, it is characterised in that the method is specific as follows：A. the mathematical model of planar double enveloping worm flank of tooth grinding allowance is established；B. with tooth punching centre-to-centre spacingWith tooth punching base radiusFor parameter, structure equation makes indexing 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. equation is solved, adjustment lathe parameter carries out tooth punching according to tooth punching centre-to-centre spacing and base radius；D. the difference of the maximum point of grinding allowance and smallest point is minimum grinding allowance on the flank of tooth.The present invention compared with the existing technology, the advantage is that：Integral grinding surplus, homogenizing entrance grinding allowance, homogenizing tooth root tooth top grinding allowance can be reduced.

Description

A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance
[technical field]
It is specifically a kind of to be homogenized the planar double enveloping worm flank of tooth the present invention relates to homogenizing grinding allowance technical field The method of grinding allowance.
[background technology]
The common 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 What is obtained after being processed during tooth punching according to design parameter is hindley worm, along transverse tooth thickness such as toroidal directions.Refine the flank of tooth when in order to Ensure female planar inclination, emery wheel needs to tilt certain angle, this will cause, outlet big along toroidal direction flank of tooth entrance stock removal Stock removal is small, and the grinding allowance of tooth top is more than the grinding allowance of tooth root, the topping of worm screw after entire flank of tooth grinding.This The problem of there is big grinding allowance, uneven, long processing time.
[content of the invention]
The purpose of the present invention aiming at the deficiency of above-mentioned prior art condition, provide a kind of reduction integral grinding surplus, Entrance grinding allowance, the method for being homogenized tooth root tooth top grinding allowance are homogenized, solves the problems, such as that existing method exists.
To achieve these goals, a kind of method for being homogenized planar double enveloping worm grinding allowance is designed, feature exists It is specific as follows in the method：
A. the mathematical model of planar double enveloping worm flank of tooth grinding allowance is established
O0O1For line of centres, σ0(O0；x0,y0,z0) it is the dynamic frame mutually connected firmly with female plane, around z0With angular velocity omega0Turn It is dynamic.s3(O3；u,n,z3) for the auxiliary coordinates in female plane.σ1(O1；x1,y1,z1) it is the dynamic frame mutually connected firmly with worm screw, around z1With angular velocity omega1It rotates.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 obtained as b=0, v=0 Tooth surface equation be：
It is p that planar double enveloping worm, which indexes anchor ring helix and the intersection point of line of centres,0, rotate hindley worm tooth Face makes its reference circle and line of centres intersection pointWith p0It overlaps, it is zero to remember the normal distance.Cross the planar double enveloping worm flank of tooth On point p (x1,y1,z1) its normal is done, Tooth Surface for Enveloping Worm with Straight Line Generatrix is handed in pointThen 2 points of distance：
Normal distance is negative when defining Tooth Surface for Enveloping Worm with Straight Line Generatrix less than the planar double enveloping flank of tooth, thenTo p (x1,y1,z1) point normal distance be grinding allowance：
B. with tooth punching centre-to-centre spacingWith tooth punching base radiusFor parameter, structure equation makes on indexing 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) correspond to inlet, 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 arc radius, Rf1For tip circle of worm arc radius, Ra1 For root circle of worm arc radius.
C. equation is solved, adjustment lathe parameter carries out tooth punching according to tooth punching centre-to-centre spacing and base radius.
D. the difference of the maximum point of grinding allowance and smallest point is minimum grinding allowance on the flank of tooth.
Dmin=maxD (q, R)-minD (q, R)
Wherein q[(a-jw),zk*t-(a-jw)],
The method is applied to numerically controlled lathe tooth punching or general vehicle tooth punching.
The present invention compared with the existing technology, the advantage is that：Integral grinding surplus can be reduced, be homogenized more than entrance grinding Amount, homogenizing tooth root tooth top grinding allowance.
[description of the drawings]
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. 2. hindley worm of planar double enveloping worm.
[specific embodiment]
Below in conjunction with the accompanying drawings, and pass through embodiment the invention will be further described, 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 b=10 ° of planar inclination, worm indexing radius of circle r1= 27.5th, base radius rb=37.5, enveloping teeth 3.5, a=22.33 ° of pressure angle of graduated circle, work half-angle jw=16.64 °, tooth T=10.91 ° of elongation, tip circle of worm arc radius Ra1=94.51, root circle of worm arc radius Rf1=104.08 right-hand face Exemplified by double enveloping worm.According to Principles of Gear Connection and homogeneous coordinate transformation matrix, for example following equations of tooth surface equation of worm screw Shown in group：
Wherein
Meet arc radius in mid-plane, on the flank of tooth for R, line and line of centres angle with female plane rotation center are Point p (the x of q1,y1,z1), following equation groups should be met：
Wherein q[0.37,0.29],Different R and q are chosen, obtains different points.
If tooth punching centre-to-centre spacingTooth punching base radius,The hindley worm obtained as b=0, v=0 Tooth surface equation be：
With p0P (x are crossed after coincidence1,y1,z1) its normal is done, Tooth Surface for Enveloping Worm with Straight Line Generatrix is handed in pointPass through This equation group obtainsValue, it is possible thereby to obtain the distance and grinding allowance of PP ' point-to-point transmissions by following formula：
And it is made to meet following equations, suitable tooth punching centre-to-centre spacing is acquired with thisWith tooth punching base radius
Such as following formula, the difference of the maximum point of grinding allowance and smallest point is minimum grinding allowance on the flank of tooth：
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 acquire 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%, grinding allowance is small and entrance surplus uniformly, tooth root tooth top surplus it is uniform.

Claims (2)

  1. A kind of 1. method for being homogenized planar double enveloping worm grinding allowance, it is characterised in that the method is specific as follows：
    A. the mathematical model of planar double enveloping worm flank of tooth grinding allowance is established
    O0O1For line of centres, σ0(O0；x0,y0,z0) it is the dynamic frame mutually connected firmly with female plane, around z0With angular velocity omega0It rotates, σ3 (O3；μ,ν,z3) for the auxiliary coordinates in female plane, σ1(O1；x1,y1,z1) it is the dynamic frame mutually connected firmly with worm screw, around z1With angle Speed omega1It rotates, w1=w0i01, i01For gearratio, β is female planar inclination, rbFor base radius, a1Centered on away from μ, ν are Female plane parameter, 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,For worm screw rotational angle, the point p (x on worm screw anchor ring helix1,y1,z1) should expire Foot：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mi>x</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>y</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>*</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>R</mi> <mo>*</mo> <mi>sin</mi> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced>
    Wherein R is annulus radius surface, and θ is PO in mid-plane0With line of centres O0O1Angle；
    If tooth punching centre-to-centre spacing a1=a '1, tooth punching base radius, rb=r 'b, the hindley worm that is obtained as β=0, v=0 Tooth surface equation is：
    It is p that planar double enveloping worm, which indexes anchor ring helix and the intersection point of line of centres,0, rotating Tooth Surface for Enveloping Worm with Straight Line Generatrix makes Its reference circle and line of centres intersection point p '0With p0It overlaps, it is zero to remember the normal distance, is crossed on the planar double enveloping worm flank of tooth Point p (x1,y1,z1) its normal is done, Tooth Surface for Enveloping Worm with Straight Line Generatrix is handed in point p ' (x '1,y′1,z′1), then 2 points of distance：
    <mrow> <msup> <mi>pp</mi> <mi>t</mi> </msup> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msubsup> <mi>x</mi> <mn>1</mn> <mi>t</mi> </msubsup> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>y</mi> <mn>1</mn> <mi>t</mi> </msubsup> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mn>1</mn> <mi>t</mi> </msubsup> <mo>-</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
    Normal distance is negative when defining Tooth Surface for Enveloping Worm with Straight Line Generatrix less than the planar double enveloping flank of tooth, then p ' (x '1,y′1,z′1) arrive p(x1,y1,z1) point normal distance be grinding allowance：
    Δ (θ, R)=sign (z '1-z1)*pp′
    B. with tooth punching centre-to-centre spacing a '1With tooth punching base radius r 'bFor parameter, structure equation makes indexing anchor ring helix upper inlet It is consistent with the grinding allowance in exit；Entrance tooth top helix is consistent with the grinding allowance at outlet tooth root helix, and equation is such as Under：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>&amp;Delta;</mi> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>)</mo> <mo>=</mo> <mi>&amp;Delta;</mi> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>&amp;Delta;</mi> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>o</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>=</mo> <mi>&amp;Delta;</mi> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mi>f</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>
    WhereinCorresponding inlet,For exit, α is pressure angle of graduated circle, and zk is encirclement tooth Number,It is angular pitch for work half-angle, τ, r1For worm indexing arc radius, Rf1For tip circle of worm arc radius, Ra1For worm screw Fillet radius；
    C. equation is solved, adjustment lathe parameter carries out tooth punching according to tooth punching centre-to-centre spacing and base radius；
    D. the difference of the maximum point of grinding allowance and smallest point is minimum grinding allowance on the flank of tooth；
    Δmax=max Δ (θ, R)-min Δs (θ, R)
    WhereinR∈[Rf1,Ra1]。
  2. 2. a kind of method for being homogenized planar double enveloping worm grinding allowance as described in claim 1, it is characterised in that described Method be applied to numerically controlled lathe tooth punching or general vehicle 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)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201610591445.0A CN106064255B (en) 2016-07-26 2016-07-26 A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201610591445.0A CN106064255B (en) 2016-07-26 2016-07-26 A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance

Publications (2)

Publication Number Publication Date
CN106064255A CN106064255A (en) 2016-11-02
CN106064255B true CN106064255B (en) 2018-05-18

Family

ID=57207329

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201610591445.0A Active CN106064255B (en) 2016-07-26 2016-07-26 A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance

Country Status (1)

Country Link
CN (1) CN106064255B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
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
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

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1078931A (en) * 1992-05-16 1993-12-01 天津华盛昌齿轮有限公司 Ring Surface Worm Shaping method
CN1248504A (en) * 1999-07-26 2000-03-29 张光辉 Approximate grinding method for planer enveloping worm
JP2002103139A (en) * 2000-09-29 2002-04-09 Komatsu Ltd Gear grinding method, turret head for gear grinding, and gear grinding tool
CN101700576A (en) * 2009-10-21 2010-05-05 中国农业大学 Rough machining method of helical surface of hourglass worm
CN102275016A (en) * 2011-07-22 2011-12-14 重庆大学 Double-side accurate grinding method and equipment for toothed surface of toroid enveloping worm
CN102335753A (en) * 2011-10-18 2012-02-01 上海合纵重工机械有限公司 Turning method for enveloping worm helical surface based on common numerically controlled lathe
CN102430817A (en) * 2011-10-27 2012-05-02 上海交通大学 Five-axis side milling method for planar double-enveloping worm

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN1078931A (en) * 1992-05-16 1993-12-01 天津华盛昌齿轮有限公司 Ring Surface Worm Shaping method
CN1248504A (en) * 1999-07-26 2000-03-29 张光辉 Approximate grinding method for planer enveloping worm
JP2002103139A (en) * 2000-09-29 2002-04-09 Komatsu Ltd Gear grinding method, turret head for gear grinding, and gear grinding tool
CN101700576A (en) * 2009-10-21 2010-05-05 中国农业大学 Rough machining method of helical surface of hourglass worm
CN102275016A (en) * 2011-07-22 2011-12-14 重庆大学 Double-side accurate grinding method and equipment for toothed surface of toroid enveloping worm
CN102335753A (en) * 2011-10-18 2012-02-01 上海合纵重工机械有限公司 Turning method for enveloping worm helical surface based on common numerically controlled lathe
CN102430817A (en) * 2011-10-27 2012-05-02 上海交通大学 Five-axis side milling method for planar double-enveloping worm

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
基于磨削余量均化的平面包络环面蜗杆优化设计;谭昕;《湖北工业大学学报》;20090430;第24卷(第2期);第7-9页 *
平面二次包络环面蜗杆磨削余量均化的计算机优化方法;周汝忠;《机械》;19950131;第22卷(第1期);第21-25页 *
平面包络凸环面蜗杆齿形研究;陈永洪等;《中国机械工程》;20120831;第23卷(第16期);第1891-1895页 *

Also Published As

Publication number Publication date
CN106064255A (en) 2016-11-02

Similar Documents

Publication Publication Date Title
CN106064255B (en) A kind of method for being homogenized planar double enveloping worm flank of tooth grinding allowance
JP6667475B2 (en) Gear manufacturing process, gear manufacturing equipment, computer and software
CN106141326B (en) A kind of dressing method of face gear grinding worm abrasion wheel
CN107273612B (en) Spiral bevel gear female die tooth surface design method and spiral bevel gear machining method
CN103777568B (en) A kind of monoblock type slotting cutter chip pocket modeling method based on the honed journey of sword
CN104907897B (en) Finishing pinion cutter method is diagonally transformed into using taper worm abrasion wheel
CN106294986A (en) Screw rod grinding grinding force Forecasting Methodology
JP2017061028A (en) Dressing method of tool
CN101318303B (en) Abrasive machining method for ball end mill and four-shaft linkage equipment for abrasive machining
Shih et al. A novel method for producing a conical skiving tool with error-free flank faces for internal gear manufacture
JP2017052084A (en) Method for manufacturing toothed workpiece having modified surface shape
CN113486475B (en) Prediction method for cylindrical gear hobbing machining cutting force
WO1999007904A1 (en) Face-gear forging method
Dudás et al. Development of spiroid worm gear drive having arched profile in axial section and a new technology of spiroid worm manufacturing with lathe center displacement
CN106909729A (en) The method of adjustment of Double-conical-surface double enveloping worm emery wheel
CN106735612A (en) A kind of method for improving gear honing processing
CN110802280B (en) Involute spiral bevel gear tooth surface design method
CN110508879B (en) Numerical control turning flash and chamfering method for involute surface enveloping ring surface worm
CN114918494B (en) Design method of instantaneous equivalent model for gear generating and grinding
CN111967096A (en) Design method of diamond roller and worm grinding wheel
CN101362230A (en) External-gearing honing cylindrical gear machine-tool and method
CN107931743A (en) A kind of method of accurate control plane double enveloping worm transverse tooth thickness
US1934754A (en) Method and means for forming gears
Guo et al. A cylindrical skiving tool design method based on a conjugate surface for internal gear manufacture
CN106041224A (en) Spiral bevel gear machining method

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant