CN102049572A - Design method for hob of cylindrical gear - Google Patents
Design method for hob of cylindrical gear Download PDFInfo
- Publication number
- CN102049572A CN102049572A CN2009101028357A CN200910102835A CN102049572A CN 102049572 A CN102049572 A CN 102049572A CN 2009101028357 A CN2009101028357 A CN 2009101028357A CN 200910102835 A CN200910102835 A CN 200910102835A CN 102049572 A CN102049572 A CN 102049572A
- Authority
- CN
- China
- Prior art keywords
- point
- tooth
- hobcutter
- profile
- phi
- 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.)
- Granted
Links
Images
Landscapes
- Gear Processing (AREA)
Abstract
The invention relates to a design method for a hob of a cylindrical gear, in particular to a design method for a hob of a timing gear of an automobile engine. The coordinate point of a tooth form of the hob is obtained by machining the given coordinate point of a tooth form of the cylindrical gear. The hob designed by the method can machine all given coordinate points on the tooth form of the cylindrical gear, the machined tooth form is smooth, and singular points do not protrude, so that the quality of a cylindrical gear product is improved.
Description
Technical field
The present invention relates to a kind of method for designing of roller gear hobcutter, relate in particular to a kind of method for designing of timing gear ofr automobile engine hobcutter.
Background technology
Gear drive part of a great variety just can be divided into involute, cycloid, circular arc line and various modification curves etc. on profile of tooth; On the kind of drive, can be divided into roller gear, bevel gear, worm and gear etc.; Processing technology mainly contains gear hobbing, gear shaping, powder metallurgy forming, hot investment casting etc. also in continuous progress.For roller gear, generally adopt hobcutter to process profile of tooth (the operation name is called gear hobbing), adopt shaving or roll flute to come the refine profile of tooth at last, the height of gear hobbing precision directly influences the final mass of roller gear.
For timing gears,, can't carry out the profile of tooth refine thereafter and handle, so the height of gear hobbing quality has directly determined the quality of product because the particularity of its tooth profile parameter is processed the final operation that profile of tooth is it with hobcutter.The main factor that influences timing gears and the belt cooperation transmission life-span is that tooth Shape Design is unreasonable and machining accuracy is not high.Improve the machining accuracy of timing gears, just need design hobcutter accurately, but because the timing gears drawing provides generally is the point coordinates that disperses, design difficulty is bigger, dyscalculia.The approximate processing of general employing profile of tooth replaces design tooth profile on the technology at present, and approximate profile of tooth off-design profile of tooth is bigger, and precision is relatively poor.The method of extensive use adopts powder metallurgy forming or hot investment casting etc. in addition in addition, but its manufacturing cost height, the accuracy of gear also is difficult to meet design requirement.
Summary of the invention
The objective of the invention is to have invented a kind of method for designing of roller gear hobcutter in order to solve the problems of the technologies described above.
(1) technical problem that will solve
For the hobcutter design of gear, generally the formula according to mechanical design handbook calculates.If but the form of gear tooth that design of gears unit provides be modification curve or discrete after point coordinate data, then can't carry out the hobcutter design by mechanical design handbook; Also can't carry out the calculating of slope of a curve and curvature for single point coordinates, also can't be connected with consecutive points, to carry out the design of hobcutter also infeasible so use Principles of Gear Connection.
(2) technical scheme
In order to solve the problems of the technologies described above, the present invention realizes by following technical method:
This method adopts cubic spline interpolation exactly, the point that each is discrete couples together with the curve fitting method, its slope and curvature are continuous everywhere on given characteristic point, to the profile of tooth analysis with calculate highly beneficially, have fundamentally solved the theoretical question of hobcutter design fully.
Owing to take above-mentioned technical method, make the present invention have following advantage and effect:
The curve of cubic spline interpolation structure contains given point coordinates set fully, the most similar to the theoretical teeth outline of design, its slope and curvature are continuous everywhere on given point coordinates, to the profile of tooth analysis with calculate highly beneficial, and also very convenient for computer programming.Utilize the hobcutter of this method design can process whole coordinate points given on the roller gear profile of tooth accurately, the profile of tooth that processes is smooth-going smooth, does not have the singular point projection, has improved the machining accuracy of roller gear product; Because gear hobbing technology is simple, the manufacturing cost of roller gear product is also reduced greatly.
Description of drawings
The profile of tooth point coordinates figure that Fig. 1 provides for gear,
The profile of tooth point coordinates that the 1-gear is given.
Fig. 2 is the design flow diagram of timing gears hobcutter
2-gets whole point coordinates given on the profile of tooth
The 3-coordinate transform
4-determines the point on the I section
5-determines the point on the V section
6-determines the point on the IV section
7-determines the point on the II section
8-determines the point on the III section
The match of 9-cubic spline interpolation
10-expands fitting result
11-defines reference frame
12-finds the solution the tangent slope of putting in the matched curve
The 13-iterative computation
The 14-linear transformation
All the other calculation of parameter of 15-
The design of 16-hobcutter is published picture
The specific embodiment
As shown in Figure 1, we at first carry out rough segmentation to the given profile of tooth point coordinates (1) of the gear in the drawing, generally can be divided into five sections curve: I, II, III, IV, V.
As shown in Figure 2, progressively determine the coordinate points that each section on the given profile of tooth point coordinates (1) of Fig. 1 middle gear should comprise, promptly determine the decomposition point of each section by the step of design flow diagram; Design simultaneously the point coordinates on the blade profile of tooth of hobcutter of each section of processing profile of tooth set by step.
I section described in Fig. 1 is the some set on the Gear Root circle, and the II section is the some set on the fillet curve, and the III section is the operating point set, and the IV section is the set of tooth top transition arc point, and the V section is the some set on the outside circle.
Because the not segmentation of point coordinates that provides in the gear drawing, the profile of tooth point coordinates (1) given at Fig. 1 middle gear also only carried out rough segmentation to profile of tooth, so need further to determine the decomposition point of each section.
The flow chart step that specific design provides by Fig. 2:
Step 2, coordinate transform (3) just transforms to all point coordinates in the plane right-angle coordinate first quartile shown in Figure 1, and initial point O is a gear centre.
Step 3 is determined the point (4) on the I section, and the point (4) among Fig. 1 on the I section is on the root circle of gear, and the radius vector value of available point is compared with the Gear Root radius of circle to determine, according to given pitch circle radius, can be calculated the hobcutter outside pitch line length then.
Step 4 is determined the point (5) on the V section, and the point (5) among Fig. 1 on the V section is on the outside circle of gear, and the radius vector value of available point is compared with the gear teeth tips radius of circle to determine, according to given pitch circle diameter, can be calculated the hobcutter inside pitch line length then.
Step 5 is determined the point (6) on the IV section, and the point (6) among Fig. 1 on the IV section is on the tooth top transition arc, because curve is short, available involute replaces, and precision meets design requirement fully, can calculate angle and the height dimension of hobcutter profile of tooth at the tooth root position then.
Step 6 is determined the point (7) on the II section, and the point (7) among Fig. 1 on the II section is on fillet curve, owing to do not participate in work, this section curve can be given by the recommendation of Tool Design handbook.The Fitting Calculation is carried out in the back for convenience, can suppose that the hobcutter tooth top is the circular arc of certain diameter, and the epicycloid that calculating cutter tip circle arc forms on gear gets final product.
Step 7 is determined the point (8) on the III section, and through the calculating of front, final remaining point is exactly the point on the III section, supposes that quantity is m, and the curve that these points are formed is the operate as normal curve of gear.
Step 8 is carried out cubic spline interpolation match (9) to the point on the III section.Utilize the cubic spline interpolation method, can simulate n=m-1 section cubic spline curve, all corresponding monobasic cubic function independently of each section curve, each independent function all has the coefficient of four the unknowns, amounts to 4n unknown number.For any two neighboring sections curve, must satisfy following condition: the starting point of curve and terminal point equate with given point coordinates value; The terminal point coordinate value of leading portion curve equates (representative function is continuous at the node place) with the starting point coordinate value of back segment curve; The ending slope of leading portion curve equates (the representative function slope is continuous) with the starting slope of back segment curve; The terminal point curvature of front end curve equates (representative function curvature is continuous) with the starting point curvature of back segment curve; For two limit points of curve, adjacent with the two-end-point of a section III respectively point on our desirable section II of border and the section IV just.Utilize above relation promptly can obtain whole curvilinear equations of family of curves.
Step 9 can be expanded the calculating of fitting result (10).Just from these curves, arbitrarily obtain the parameter of point how arbitrarily, conveniently carry out more accurate research.
Step 11 is found the solution the tangent slope of putting in the matched curve (12).By finding the solution the first derivative of matched curve equation, can obtain the tangent slope of each point in the matched curve.
According to Principles of Gear Connection, cross the common normal at public point of contact on the form of gear tooth and the hobcutter profile of tooth and must pass through instantaneous point.Suppose that any point in the form of gear tooth is rotated counterclockwise certain angle, the normal of this point is just in time by public instantaneous, and then postrotational point coordinates also is simultaneously the point on the hobcutter profile of tooth.Find the solution gear and the cutter velocity vector relation at public point of contact, can obtain the tangent slope at public point of contact, it and any point tangent slope before rotation differs an anglec of rotation.Obtain following equation by this relation:
In the formula: K
2---the tangent slope of each point in the matched curve;
α
2---before rotating to an angle, the angle of the line of each point and gear centre and vertical coordinate axle in the matched curve;
φ
2---the anglec of rotation.
Unknown number in the following formula is anglec of rotation φ
2, all corresponding unique anglec of rotation φ of each point in the matched curve
2
Step 12 utilizes computer programming and iterative computation (13) can obtain φ accurately
2
Step 13 is carried out linear transformation (14).The new coordinate that obtains after any point in the matched curve rotated to an angle transforms in the translate coordinate system again, just can obtain the profile of tooth point coordinates of hobcutter, and its accounting equation is:
In the formula: X
1, Y
1---the profile of tooth point abscissa of hobcutter, ordinate;
X
2, Y
2---abscissa, the ordinate put on the form of gear tooth;
So far, the point coordinates that is used to process on the hobcutter profile of tooth of the form of gear tooth is all obtained.
Step 14 is carried out all the other calculation of parameter (15).According in the mechanical design handbook about the design part of hobcutter, all the other structural parameters of roller gear hobcutter can be decided.
Step 15 is carried out hobcutter design publish picture (16) at last.
Claims (2)
1. the method for designing of a roller gear hobcutter, mainly handle given roller gear profile of tooth coordinate points data by segmentation, it is characterized in that: the coordinate points The data cubic spline interpolation to the profile of tooth working portion carries out curve fitting, and utilizes the theory of engagement and linear transformation to draw the profile of tooth coordinate points of hobcutter again; After the curve match finishes, can get more coordinate points on the curve of match and calculate, the hobcutter profile of tooth coordinate points quantity that draws so also will increase, for the hobcutter manufacturing provides more gross data.
2. the method for designing of a kind of roller gear hobcutter according to claim 1 is characterized in that using following formula one to solve the accurate anglec of rotation of each coordinate points, and utilizes the anglec of rotation finally to calculate whole coordinate points of tool-tooth profile.
In the formula: K
2---the tangent slope of each point in the matched curve;
α
2---before rotating to an angle, the angle of the line of each point and gear centre and vertical coordinate axle in the matched curve;
φ
2---the anglec of rotation.
Unknown number in the following formula is anglec of rotation φ
2, all corresponding unique anglec of rotation φ of each point in the matched curve
2
Utilize computer programming and iterative computation can obtain φ accurately
2
Carry out linear transformation, the new coordinate that obtains after any point in the matched curve is rotated to an angle transforms in the translate coordinate system again, just can obtain the profile of tooth point coordinates of hobcutter, and its accounting equation is:
In the formula: X
1, Y
1---the profile of tooth point abscissa of hobcutter, ordinate;
X
2, Y
2---abscissa, the ordinate put on the form of gear tooth.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN2009101028357A CN102049572B (en) | 2009-11-06 | 2009-11-06 | Design method for hob of cylindrical gear |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN2009101028357A CN102049572B (en) | 2009-11-06 | 2009-11-06 | Design method for hob of cylindrical gear |
Publications (2)
Publication Number | Publication Date |
---|---|
CN102049572A true CN102049572A (en) | 2011-05-11 |
CN102049572B CN102049572B (en) | 2012-08-08 |
Family
ID=43954555
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN2009101028357A Active CN102049572B (en) | 2009-11-06 | 2009-11-06 | Design method for hob of cylindrical gear |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN102049572B (en) |
Cited By (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN102689054A (en) * | 2012-05-25 | 2012-09-26 | 上海第二工业大学 | Processing method of tooth thickness-variable gear with intersecting axles and hob of tooth thickness-variable gear |
CN102699449A (en) * | 2012-06-21 | 2012-10-03 | 浙江工商职业技术学院 | Design method of hobbing cutter with special circular tooth shape |
CN102744469A (en) * | 2012-07-30 | 2012-10-24 | 浙江工商职业技术学院 | Hob design method |
CN103331494A (en) * | 2013-07-10 | 2013-10-02 | 上海第二工业大学 | Intersecting shaft tooth-thickness-changing gear tooth-shape error analysis method |
CN104408266A (en) * | 2014-12-16 | 2015-03-11 | 厦门大学 | Design method of planar meshed profile based on computer graphics |
CN113124811A (en) * | 2021-04-21 | 2021-07-16 | 泸州高新中航传动转向***有限公司 | Method for accurately controlling gear shaving cutter grinding parameters |
Family Cites Families (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7520698B2 (en) * | 2004-12-20 | 2009-04-21 | Gleason Cutting Tools Corporation | Cutting tool for gears and other toothed articles |
CN101108432B (en) * | 2006-07-19 | 2010-06-02 | 陆联精密股份有限公司 | Gear cutter and molding method of the same |
CN101028660B (en) * | 2007-04-06 | 2010-12-08 | 吉林大学 | Gear precisive hob configuration and its configured precisive hob |
CN201172134Y (en) * | 2008-05-13 | 2008-12-31 | 南京金鑫传动设备有限公司 | Round-head grinding hob and round-head grinding self-chamfering hob |
CN101439461B (en) * | 2008-12-31 | 2010-06-02 | 山西大同齿轮集团有限责任公司 | Technique for producing and processing chamfering tool for cylindrical gear double-side tooth profile |
-
2009
- 2009-11-06 CN CN2009101028357A patent/CN102049572B/en active Active
Cited By (9)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN102689054A (en) * | 2012-05-25 | 2012-09-26 | 上海第二工业大学 | Processing method of tooth thickness-variable gear with intersecting axles and hob of tooth thickness-variable gear |
CN102699449A (en) * | 2012-06-21 | 2012-10-03 | 浙江工商职业技术学院 | Design method of hobbing cutter with special circular tooth shape |
CN102744469A (en) * | 2012-07-30 | 2012-10-24 | 浙江工商职业技术学院 | Hob design method |
CN102744469B (en) * | 2012-07-30 | 2014-02-26 | 浙江工商职业技术学院 | Hob design method |
CN103331494A (en) * | 2013-07-10 | 2013-10-02 | 上海第二工业大学 | Intersecting shaft tooth-thickness-changing gear tooth-shape error analysis method |
CN103331494B (en) * | 2013-07-10 | 2015-10-28 | 上海第二工业大学 | A kind of concurrent aces variable tooth thickness gear profile error analytical method |
CN104408266A (en) * | 2014-12-16 | 2015-03-11 | 厦门大学 | Design method of planar meshed profile based on computer graphics |
CN113124811A (en) * | 2021-04-21 | 2021-07-16 | 泸州高新中航传动转向***有限公司 | Method for accurately controlling gear shaving cutter grinding parameters |
CN113124811B (en) * | 2021-04-21 | 2023-03-31 | 泸州高新中航传动转向***有限公司 | Method for accurately controlling gear shaving cutter grinding parameters |
Also Published As
Publication number | Publication date |
---|---|
CN102049572B (en) | 2012-08-08 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN102049572B (en) | Design method for hob of cylindrical gear | |
CN103678818B (en) | Precise modeling method for biarc correction cycloidal gear | |
CN101251181B (en) | Helical teeth elliptic gear as well as method for three-dimensional model-building accurately and entity shaping | |
CN102567596A (en) | Parametric modeling method of face gear teeth | |
CN106874596A (en) | A kind of Precise modeling of Niemann worm gear | |
CN107323520A (en) | A kind of New Cycle ball steering gear with variable ratio rocker arm shaft tooth fans rack pair | |
CN110968917A (en) | Envelope slotting high-order multi-section deformation elliptic gear pair parametric design method | |
CN109027186A (en) | The discretization envelope design method of diverter gear ratio rack | |
CN107273612A (en) | Spiral bevel gear cavity plate tooth surface design method and Machining Spiral Bevel Gear method | |
CN107657134A (en) | A kind of arc surfaced indexing cam modeling method based on Creo | |
CN112705794A (en) | Tooth cutting tool for machining cycloid gear and design method thereof | |
CN113486466B (en) | Linear contact spiral bevel gear shaping method | |
JP4763611B2 (en) | Evaluation method of edge profile of re-sharpened pinion cutter | |
CN114101807B (en) | Edge shape design method of gear workpiece end face continuous equidistant chamfering cutting tool | |
CN114769737A (en) | Forming and grinding processing method for gear with small number of teeth | |
CN109887079A (en) | Spiral bevel gear three-dimensional modeling method | |
CN111553037B (en) | Spiral rotor modeling method based on virtual generating machining | |
CN107584177B (en) | The processing method of pinion and-rack no-load voltage ratio diverter gear pair rack tooth profile | |
CN115186493A (en) | Accurate modeling method for small-modulus involute cylindrical gear | |
CN114918494A (en) | Gear generating grinding instantaneous equivalent model and design method thereof | |
CN109812544B (en) | Arc tooth surface gear transmission pair and design method | |
CN113434969A (en) | Method for calculating axial modification of tooth profile of spherical involute straight bevel gear | |
CN114818183B (en) | Non-circular helical gear design method | |
CN113145943B (en) | Design method of equal-front-angle tooth cutting knife for machining cycloid wheel | |
CN110766801B (en) | Three-dimensional modeling method for involute line contact conical worm transmission pair |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
C14 | Grant of patent or utility model | ||
GR01 | Patent grant | ||
CP03 | Change of name, title or address |
Address after: 550000 No. 1111 Liyang Road, Baiyun District, Guiyang City, Guizhou Province Patentee after: Chinese Hangfa Guizhou Liyang aero Power Co. Ltd. Address before: Mailbox No. 207, Pingba County, Guizhou Province Patentee before: Guizhou Liyang Aerospace Power Co., Ltd. |
|
CP03 | Change of name, title or address |