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 PDFInfo
- 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
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
[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)
- 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 establishedO0O1For 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>&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>&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>&Delta;</mi> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>)</mo> <mo>=</mo> <mi>&Delta;</mi> <mo>(</mo> <msub> <mi>&theta;</mi> <mi>o</mi> </msub> <mo>,</mo> <msub> <mi>r</mi> <mn>1</mn> </msub> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mi>&Delta;</mi> <mo>(</mo> <msub> <mi>&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>&Delta;</mi> <mo>(</mo> <msub> <mi>&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. 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.
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)
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)
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 |
-
2016
- 2016-07-26 CN CN201610591445.0A patent/CN106064255B/en active Active
Patent Citations (7)
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)
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 | |
EP3130822A1 (en) | Point contact gear based on conjugate curves, meshing pair and machining tool therefor | |
CN107273612B (en) | Spiral bevel gear female die tooth surface design method and spiral bevel gear machining method | |
JP2010228092A (en) | Method and device for generating control data for controlling tool in machine tool including at least five shafts | |
CN105531059B (en) | Generation and attached equipment | |
CN103777568B (en) | A kind of monoblock type slotting cutter chip pocket modeling method based on the honed journey of sword | |
CN101318303B (en) | Abrasive machining method for ball end mill and four-shaft linkage equipment for abrasive machining | |
CN104907897B (en) | Finishing pinion cutter method is diagonally transformed into using taper worm abrasion wheel | |
Shih et al. | A novel method for producing a conical skiving tool with error-free flank faces for internal gear manufacture | |
JP2017061028A (en) | Dressing method of tool | |
JP2017052084A (en) | Method for manufacturing toothed workpiece having modified surface shape | |
CN106292531A (en) | Algorithm for calculating profile boundary of ZN1 worm disc-shaped forming cutter | |
CN111967096A (en) | Design method of diamond roller and worm grinding wheel | |
CN113486475B (en) | Prediction method for cylindrical gear hobbing machining cutting force | |
EP2732894A1 (en) | Method for manufacturing screw-shaped tool | |
EP1027464A1 (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 | |
CN103286387B (en) | Quasi-dual-lead spiroid gear processing method | |
CN114918494B (en) | Design method of instantaneous equivalent model for gear generating and grinding |
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 |