CN102678879A - Profile number acquiring method of non-circular gears - Google Patents
Profile number acquiring method of non-circular gears Download PDFInfo
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- CN102678879A CN102678879A CN2012101529691A CN201210152969A CN102678879A CN 102678879 A CN102678879 A CN 102678879A CN 2012101529691 A CN2012101529691 A CN 2012101529691A CN 201210152969 A CN201210152969 A CN 201210152969A CN 102678879 A CN102678879 A CN 102678879A
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Abstract
The invention provides a profile number acquiring method of non-circular gears, which comprises the following step that the pitch curve of the non-circular gears is designed; the method is characterized in that the initial positions of all tooth spaces on the non-circular gears when the tooth spaces are started to be enveloped and the initial profile of a gear tooth on a circular gear cutter which corresponds to each initial position are worked out; from a first non-circular tooth space, the gear tooth on the circular gear cutter which corresponds to the tooth space is first enveloped clockwise on the pitch curve and then is enveloped counterclockwise, and a non-circular tooth space number is worked out with a numerical algorithm mentioned in a user manual in every two enveloping steps; and other non-circular tooth space numbers are acquired through the same method to acquire the tooth space numbers of all non-circular gears, and the profile numbers of all non-circular gears are acquired. According to the invention, the method not only has the advantages of simple process, small calculation amount and higher efficiency, but also is applicable to the non-circular gears on the concave and convex pitch curve.
Description
Technical field
The present invention relates to a kind of flank profil numerical value obtaining method of noncircular gear; This numerical method can directly obtain the flank profil data of real noncircular gear according to the pitch curve of noncircular gear; These flank profil data can be used for line cutting, three-dimensional modeling, technology and methods such as rapid shaping.
Background technique
In general each profile geometry of noncircular gear is different; And as long as flank profil residing position on pitch curve changes; Its profile of tooth also will change thereupon, thus come accurately to represent very grain granite of its profile of tooth with the mathematical analysis formula, and be difficult to especially describe with relationship definitely for its transition curve of the profile of tooth that a little undercut is arranged; Therefore; In order to represent the noncircular gear flank profil exactly, make things convenient for cutting of noncircular gear line or three-dimensional modeling etc., the method for solving that effectively obtains the wide enough numerical points of accurate and non-efficiently knuckle-tooth just seems extremely important.
The numerical method that two kinds of accurate noncircular gear flank profils are arranged now, a kind of is to utilize basic rack cutter generating method to find the solution the wide numerical point of non-knuckle-tooth, a kind of is to utilize standard round gear cutter generating method to find the solution the wide numerical point of non-knuckle-tooth.The former only is suitable for protruding pitch curve noncircular gear; And the latter is suitable for concavo-convex pitch curve noncircular gear; Just existing method has changed into normal direction equal space line and the wide intersection point process of Knucle-gear cutter tooth of asking non-circular gear pitch curve with the calculating of noncircular gear flank profil; Calculation of complex, amount are big, and efficient is lower.
Summary of the invention
It is simple and can be fit to the acquiring method of the whole flank profil profile of concavo-convex pitch curve noncircular gear numerical point to the purpose of this invention is to provide a kind of process.For this reason, establishing criteria cylindrical gears cutter of the present invention (hereinafter to be referred as the knuckle-tooth flywheel knife) envelope noncircular gear forms the wide principle of non-knuckle-tooth, provides these method concrete steps and is:
Step 1, design obtain the flank profil of the pitch curve and the corresponding knuckle-tooth flywheel knife of noncircular gear, it is characterized in that:
Step 2, obtain all non-knuckle-tooth grooves on the noncircular gear begin envelope initial position and with the corresponding knuckle-tooth flywheel knife of each initial position on the initial flank profil of certain gear teeth; Wherein, The initial position of i non-knuckle-tooth groove is the knuckle-tooth flywheel knife when pitch curve is rolled into this position, and the normal of the center bisector of the upper gear teeth in this position of knuckle-tooth flywheel knife and the pitch curve of this position coincides;
Earlier along envelope clockwise, every envelope once just uses the noncircular gear numerical algorithm No. one time, until a tooth pitch on pitch curve for step 3,2 states set by step, the gear teeth on the knuckle-tooth flywheel knife; And then get back to step 2 state; The gear teeth on the knuckle-tooth flywheel knife are counterclockwise envelope on pitch curve; Make the tooth pitch of envelope that uses the same method just can obtain a complete non-knuckle-tooth groove numerical value, other non-knuckle-tooth groove repeats said process to all, can obtain all noncircular gear teeth groove and also just obtain all noncircular gear flank profil numerical value; Wherein, the concrete steps of the employed noncircular gear numerical algorithm of every front and back two step envelopes process are:
Step 3.1, by with the corresponding knuckle-tooth flywheel knife of initial position of i non-knuckle-tooth groove on the gear teeth with the initial position of this non-knuckle-tooth groove be basic point by etc. the arc step-length along one step of envelope clockwise; Obtain clockwise generated profile; Data point on the clockwise therewith generated profile of the initial flank profil of these gear teeth is carried out algorithm relatively obtain middle generated profile; Again with generated profile in the middle of this as initial flank profil, the gear teeth by waiting arc step-length along one step of envelope more clockwise, are obtained next step clockwise generated profile; Initial flank profil and current clockwise generated profile are carried out algorithm relatively; Recycle said method successively,, obtain the final flank profil of clockwise envelope until a tooth pitch;
Step 3.2, the employing method identical with step 3.1 obtain same non-knuckle-tooth groove along the final flank profil of anticlockwise counterclockwise envelope, final flank profil of clockwise envelope and the counterclockwise final flank profil of envelope are carried out algorithm obtain the wide data point of non-knuckle-tooth more at last.
Preferably, the step of the algorithm comparison in said step 3.1 and the said step 3.2 is:
Steps A, flank profil called after first flank profil that back is obtained, flank profil called after second flank profil that one step of back obtains is regarded first flank profil and second flank profil as oriented line segment, and with the definite successively sequence number of the data point on the flank profil;
Step B, the search radius that confirm to be fit to, first data point on second flank profil travels through all data points on second flank profil, with the data point of all storages flank profil data point as current non-knuckle-tooth groove, the steps include:
Step B.1, be the center of circle with the current data point on second flank profil, judging in the search radius has the data point that does not have on first flank profil;
Step B.2, if do not have, then store all data points except that maximum sequence number on all second flank profils in the search radius, and be the center of circle with the maximum sequence number data point on second flank profil, get back to step and B.1 continue search; If have, then get into next step;
Step B.3, judge these be positioned on first flank profil data point be positioned at data point on second flank profil and whether have and intersect; Do not intersect if having; Then store all data points except that maximum sequence number on all second flank profils in the search radius; And be the center of circle with the maximum sequence number data point on second flank profil, get back to step and B.1 continue to search; If intersection arranged, data point and the crossing number strong point on first flank profil before the store interleaving then.Simultaneously, with data point on first flank profil after intersecting and the exchange of the data point on second flank profil, be the center of circle with first data point on second flank profil after the exchange, get back to step and B.1 continue to search.
The present invention is from flank profil envelope forming process; Arc length envelope process principles such as utilization (it is higher that the flank profil data point distribution that this principle obtains evenly makes profile form precision); The pitch curve that only obtains according to design; When utilizing revolution to cross a tooth pitch, the tooth distribution of whole knuckle-tooth flywheel knife and phase place will reproduce identical original state and each teeth groove of noncircular gear (obtaining all flank profils that all non-knuckle-tooth grooves have also just obtained noncircular gear accordingly) can by centering gear teeth of knuckle-tooth flywheel knife clockwise, the rule that forms of tooth pitch of each envelope and obtain the whole flank profil data of noncircular gear counterclockwise.Method provided by the invention not only process is simple, and amount of calculation is little, and efficient is higher, and concavo-convex pitch curve noncircular gear all is suitable for.
Description of drawings
Fig. 1 is noncircular gear and knuckle-tooth flywheel knife envelope process principle figure;
Fig. 2 is the initial position figure of all non-knuckle-tooth grooves;
The choice numerical value point diagram that Fig. 3 compares the non-knuckle-tooth groove profile data of two steps of front and back in the envelope process for algorithm;
The noncircular gear whole flank profil line of Fig. 4 for finally obtaining.
Embodiment
For making the present invention more obviously understandable, now with a preferred embodiment, and conjunction with figs. elaborates as follows.
In conjunction with Fig. 1, knuckle-tooth flywheel knife processing noncircular gear process can be regarded as knuckle-tooth flywheel knife pitch curve 3 process according to movement locus line 2 pure rolling on oval knot curve 1.If the left focus O with oval knot curve 1 is that initial point is set up fixed coordinate system XOY as shown in Figure 1, locating exterior normal with point of contact E (F) is Y
oAxle, its vertical shaft that rotates counterclockwise 90 ° is X
oAxle is with knuckle-tooth flywheel knife center of circle O
oFor initial point is set up corresponding moving axes X
oO
oY
o, then when knuckle-tooth flywheel knife pitch curve 3 rolled across arc length E ' F, the then corresponding F point that forwarded to of E point of correspondence on the oval knot curve 1 remembered that the corresponding angle of arc length EF is φ, the angle that arc length E ' F is corresponding is θ, Y
oAxle is ψ with the angle of X axle, and then according to the engagement correlation theory, this moment, arc length E ' F should equate to have with arc length EF:
If the coordinate of knuckle-tooth flywheel knife centre of pitch circle in fixed coordinate system XOY is x
0And y
0, then have:
x
0＝x-r
1cosψ，y
0＝y-r
1sinψ。
If the wide curve point of Knucle-gear cutter tooth is at moving axes X
oO
oY
oMiddle corresponding coordinate is respectively x
1And y
1Respective coordinates is respectively X and Y in fixed coordinate system XOY; Then that this coordinate is corresponding coordinate points is converted into the coordinate points under fixed coordinate system, can be unified in and express the Knucle-gear cutter position among the fixed coordinate system XOY, and so just progressively envelope goes out the noncircular gear flank profil.Its mathematical relationship is:
X＝-x
1×cosψ+y
1×sinψ+x
0，Y＝-x
1×sinψ-y
1×cosψ+y
0。
According to above-mentioned principle, the flank profil numerical value obtaining method of a kind of noncircular gear provided by the invention, step is:
Step 1, design obtain the flank profil of the pitch curve and the corresponding knuckle-tooth flywheel knife of noncircular gear:
Step 2, obtain all non-knuckle-tooth grooves on the noncircular gear begin envelope initial position and with the corresponding knuckle-tooth flywheel knife of each initial position on the initial flank profil of certain gear teeth; Wherein, The initial position of i non-knuckle-tooth groove is the knuckle-tooth flywheel knife when pitch curve is rolled into this position; The normal of the center bisector of the upper gear teeth in this position of knuckle-tooth flywheel knife and the pitch curve of this position coincides, like the sequence number 4 sensing positions of Fig. 2;
Earlier along envelope clockwise, every envelope once just uses the noncircular gear numerical algorithm No. one time, until a tooth pitch on pitch curve for step 3,2 states set by step, the gear teeth on the knuckle-tooth flywheel knife; And then get back to step 2 state; The gear teeth on the knuckle-tooth flywheel knife are counterclockwise envelope on pitch curve; Make the tooth pitch of envelope that uses the same method just can obtain a complete non-knuckle-tooth groove numerical value, other non-knuckle-tooth groove repeats said process to all, can obtain all noncircular gear teeth groove and also just obtain all noncircular gear flank profil numerical value; Wherein, the concrete steps of the employed noncircular gear numerical algorithm of every front and back two step envelopes process are:
Step 3.1, by with the corresponding knuckle-tooth flywheel knife of initial position of i non-knuckle-tooth groove on the gear teeth with the initial position of this non-knuckle-tooth groove be basic point by etc. the arc step-length along one step of envelope clockwise; Obtain clockwise generated profile; Data point on the clockwise therewith generated profile of the initial flank profil of these gear teeth is carried out algorithm relatively obtain middle generated profile; Again with generated profile in the middle of this as initial flank profil, the gear teeth by waiting arc step-length along one step of envelope more clockwise, are obtained next step clockwise generated profile; Initial flank profil and current clockwise generated profile are carried out algorithm relatively; Recycle said method successively,, obtain the final flank profil of clockwise envelope until a tooth pitch;
Step 3.2, the employing method identical with step 3.1 obtain same non-knuckle-tooth groove along the final flank profil of anticlockwise counterclockwise envelope, final flank profil of clockwise envelope and the counterclockwise final flank profil of envelope are carried out algorithm obtain the wide data point of non-knuckle-tooth more at last.
Preferably, the algorithm in said step 3.1 and the said step 3.2 relatively the steps include:
Steps A, flank profil called after first flank profil that back is obtained, flank profil called after second flank profil that one step of back obtains is regarded first flank profil and second flank profil as oriented line segment, and with the definite successively sequence number of the data point on the flank profil;
Step B, the search radius that confirm to be fit to, first data point on second flank profil travels through all data points on second flank profil, with the data point of all storages flank profil data point as current non-knuckle-tooth groove, the steps include:
Step B.1, be the center of circle with the current data point on second flank profil, judging in the search radius has the data point that does not have on first flank profil;
Step B.2, if do not have, then store all data points except that maximum sequence number on all second flank profils in the search radius, and be the center of circle with the maximum sequence number data point on second flank profil, get back to step and B.1 continue search; If have, then get into next step;
Step B.3, judge these be positioned on first flank profil data point be positioned at data point on second flank profil and whether have and intersect; Do not intersect if having; Then store all data points except that maximum sequence number on all second flank profils in the search radius; And be the center of circle with the maximum sequence number data point on second flank profil, get back to step and B.1 continue to search; If intersection arranged, data point and the crossing number strong point on first flank profil before the store interleaving then.Simultaneously, with data point on first flank profil after intersecting and the exchange of the data point on second flank profil, be the center of circle with first data point on second flank profil after the exchange, get back to step and B.1 continue to search.
Steps A to the data point value among the step B can be with reference to figure 3; In the figure; Sequence number 5 is first flank profil, and sequence number 6 is second flank profil, and "+" is the flank profil data point of knuckle-tooth flywheel knife; " * " is the flank profil data point of the knuckle-tooth flywheel knife behind the envelope, the comparatively real noncircular gear flank profil data point that obtains after this numerical method of " o " representative utilization.
The whole flank profil line of noncircular gear through method provided by the invention obtains is as shown in Figure 4.
Claims (2)
1. the flank profil numerical value obtaining method of a noncircular gear, step is:
Step 1, design obtain the flank profil of the pitch curve and the respective standard cylindrical gears cutter of noncircular gear, it is characterized in that:
Step 2, obtain all non-knuckle-tooth grooves on the noncircular gear begin envelope initial position and with the corresponding standard cylinder gear cutter of each initial position on the initial flank profil of certain gear teeth; Wherein, The initial position of i non-knuckle-tooth groove is the standard cylinder gear cutter when pitch curve is rolled into this position, and the normal of pitch curve of center bisector and this position that is positioned at the gear teeth of this position on the standard cylinder gear cutter coincides;
Earlier along envelope clockwise, every envelope once just uses the noncircular gear numerical algorithm No. one time, until a tooth pitch on pitch curve for step 3,2 states set by step, the gear teeth on the standard cylinder gear cutter; And then get back to step 2 state; The gear teeth on the standard cylinder gear cutter are counterclockwise envelope on pitch curve; Make the tooth pitch of envelope that uses the same method just can obtain a complete non-knuckle-tooth groove numerical value, other non-knuckle-tooth groove repeats said process to all, can obtain all noncircular gear teeth groove and also just obtain all noncircular gear flank profil numerical value; Wherein, the concrete steps of the employed noncircular gear numerical algorithm of every front and back two step envelopes process are:
Step 3.1, by with the corresponding standard cylinder gear cutter of initial position of i non-knuckle-tooth groove on the gear teeth with the initial position of this non-knuckle-tooth groove be basic point by etc. the arc step-length along one step of envelope clockwise; Obtain clockwise generated profile; Data point on the clockwise therewith generated profile of the initial flank profil of these gear teeth is carried out algorithm relatively obtain middle generated profile; Again with generated profile in the middle of this as initial flank profil, the gear teeth by waiting arc step-length along one step of envelope more clockwise, are obtained next step clockwise generated profile; Initial flank profil and current clockwise generated profile are carried out algorithm relatively; Recycle said method successively,, obtain the final flank profil of clockwise envelope until a tooth pitch;
Step 3.2, the employing method identical with step 3.1 obtain same non-knuckle-tooth groove along the final flank profil of anticlockwise counterclockwise envelope, final flank profil of clockwise envelope and the counterclockwise final flank profil of envelope are carried out algorithm obtain the wide data point of non-knuckle-tooth more at last.
2. the flank profil numerical value obtaining method of a kind of noncircular gear as claimed in claim 1, it is characterized in that: the step of the algorithm comparison in said step 3.1 and the said step 3.2 is:
Steps A, flank profil called after first flank profil that back is obtained, flank profil called after second flank profil that one step of back obtains is regarded first flank profil and second flank profil as oriented line segment, and with the definite successively sequence number of the data point on the flank profil;
Step B, the search radius that confirm to be fit to, first data point on second flank profil travels through all data points on second flank profil, with the data point of all storages flank profil data point as current non-knuckle-tooth groove, the steps include:
Step B.1, be the center of circle with the current data point on second flank profil, judging in the search radius has the data point that does not have on first flank profil;
Step B.2, if do not have, then store all data points except that maximum sequence number on all second flank profils in the search radius, and be the center of circle with the maximum sequence number data point on second flank profil, get back to step and B.1 continue search; If have, then get into next step;
Step B.3, judge these be positioned on first flank profil data point be positioned at data point on second flank profil and whether have and intersect; Do not intersect if having; Then store all data points except that maximum sequence number on all second flank profils in the search radius; And be the center of circle with the maximum sequence number data point on second flank profil, get back to step and B.1 continue to search; If intersection arranged, data point and the crossing number strong point on first flank profil before the store interleaving then.Simultaneously, with data point on first flank profil after intersecting and the exchange of the data point on second flank profil, be the center of circle with first data point on second flank profil after the exchange, get back to step and B.1 continue to search.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210152969.1A CN102678879B (en) | 2012-05-15 | 2012-05-15 | Profile number acquiring method of non-circular gears |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210152969.1A CN102678879B (en) | 2012-05-15 | 2012-05-15 | Profile number acquiring method of non-circular gears |
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| CN102678879A true CN102678879A (en) | 2012-09-19 |
| CN102678879B CN102678879B (en) | 2014-10-15 |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105972185A (en) * | 2016-07-10 | 2016-09-28 | 北京工业大学 | Calculation method for working tooth profile of cycloidal gear based on fruit fly optimization algorithm |
| CN106151452A (en) * | 2016-08-27 | 2016-11-23 | 武汉理工大学 | A kind of method for designing of non-cylindrical gear-profile |
| CN113761683A (en) * | 2021-09-06 | 2021-12-07 | 温州理工学院 | Improved design method of heart-shaped non-circular gear pitch curve |
| CN114800032A (en) * | 2022-04-26 | 2022-07-29 | 兰州理工大学 | Non-circular gear design method |
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| US2585971A (en) * | 1946-10-11 | 1952-02-19 | Goodman Mfg Co | Gearing |
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| JPH04181049A (en) * | 1990-11-14 | 1992-06-29 | Toyota Motor Corp | Elliptic gear having constant speed part |
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| DE19932876A1 (en) * | 1999-07-16 | 2001-01-18 | Ims Morat & Soehne Gmbh | Non-circular gears |
| WO2008031123A2 (en) * | 2006-09-12 | 2008-03-20 | Miba Sinter Austria Gmbh | Method for producing non-circular toothed belt pulleys or sprockets |
| CN101251181A (en) * | 2008-03-25 | 2008-08-27 | 东华大学 | Helical teeth elliptic gear as well as method for three-dimensional model-building accurately and entity shaping producing thereof |
| CN102094938A (en) * | 2011-03-04 | 2011-06-15 | 北京航空航天大学 | Elliptic bevel gear pair |
-
2012
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Patent Citations (8)
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|---|---|---|---|---|
| US2585971A (en) * | 1946-10-11 | 1952-02-19 | Goodman Mfg Co | Gearing |
| DE947584C (en) * | 1949-07-07 | 1956-08-16 | Goodman Mfg Co | Speed change transmission |
| JPH04181049A (en) * | 1990-11-14 | 1992-06-29 | Toyota Motor Corp | Elliptic gear having constant speed part |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105972185A (en) * | 2016-07-10 | 2016-09-28 | 北京工业大学 | Calculation method for working tooth profile of cycloidal gear based on fruit fly optimization algorithm |
| CN106151452A (en) * | 2016-08-27 | 2016-11-23 | 武汉理工大学 | A kind of method for designing of non-cylindrical gear-profile |
| CN113761683A (en) * | 2021-09-06 | 2021-12-07 | 温州理工学院 | Improved design method of heart-shaped non-circular gear pitch curve |
| CN113761683B (en) * | 2021-09-06 | 2023-12-15 | 温州理工学院 | Improved design method of heart-shaped non-circular gear pitch curve |
| CN114800032A (en) * | 2022-04-26 | 2022-07-29 | 兰州理工大学 | Non-circular gear design method |
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| Publication number | Publication date |
|---|---|
| CN102678879B (en) | 2014-10-15 |
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