CN103886154A - Method for optimizing cycloid gear tooth outline modification amount based on matlab - Google Patents
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Abstract
The invention discloses a method for optimizing the cycloid gear tooth outline modification amount based on a matlab. The method comprises the first step of calculating the inflection point position of the cycloidal gear tooth outline according to basic parameters of a cycloidal gear, the second step of calculating the optimal modification angle according to the oil film thickness and the inflection point position, the third step of calculating the optimal isometry and the shifting modification amount according to the optimizing function of the matlab, and the fourth step of acquiring testing parameters tested conveniently. Compared with the prior art, the method has the advantages that the analyzing method for improving and optimizing the cycloid gear tooth outline through a MATLAB optimization toolbox by analyzing a mathematical model of cycloidal gear modification is put forward, the optimal modification angle is obtained according to the oil film thickness, the range of the optimal modification amount is found out according to the inflection point position in a meshing area, and the optimal isometry and shifting modification tooth outline is obtained; the calculation period of the tooth outline modification amount is greatly shortened, the number of teeth meshed at the same time is guaranteed, the stability of transmission is guaranteed, and the transmission efficiency is improved.
Description
Technical Field
The invention relates to the technical field of design and manufacture of a cycloid wheel, in particular to a method for optimizing the tooth profile modification quantity of the cycloid wheel based on matlab.
Background
The planetary cycloidal speed reducer is a speed reducing mechanism which applies the planetary transmission principle and adopts the meshing of cycloidal needle teeth. Due to the unique advantages of advanced design and novel structure, the steel plate is increasingly widely applied to the aspects of military industry, aerospace, metallurgy, hoisting and transportation and the like.
The cycloidal pin gear meshing pair is a core element of the planetary cycloidal reducer. The cycloidal pair belongs to a tooth difference internal engaged gear set, theoretically conjugate tooth profile has no radial gap, the number of meshing points is always equal to the number of teeth of a pin gear, and a meshing line is a symmetrical closed curve. In practical application of the cycloid pin gear planetary transmission, in order to compensate manufacturing errors, facilitate assembly and disassembly and ensure lubrication, a meshing clearance is required between the cycloid gear teeth and the pin gear teeth. Therefore, the actual cycloid wheel must be modified, and reasonable and accurate modification is an important guarantee for realizing strong transmission capability and stable operation of the cycloid wheel teeth.
In the current production practice, the modification of the tooth profile of the cycloidal gear generally adopts a modification method of equal distance and displacement, and for the modification amount of the equal distance and the displacement, the repeated test and verification are needed depending on the experience of workers. In theory, when the equidistant pitch modification amount is determined, the obtained result is not very same due to different methods. The document [1] proposes that the equidistant modified quantity of the displacement is obtained by approaching the cycloidal tooth profile of the corner modification, and the method only leads the two tooth profiles to be similar, but the normal clearances really determining the meshing quality are not equal, thus the requirement of improving the meshing performance can not be achieved. The document [2] proposes the tooth thickness modification amount, and because an optimization theory is not adopted, the result precision is low, and the use requirement cannot be met. Document [3] document [4] presents a trimming method that applies a MATLAB optimization toolbox to find the optimum trimming amount of the equidistant shift, but does not consider the meshing position of the cycloid wheel, and therefore, the calculated trimming amount cannot be applied to an actual production process, nor can it be considered as optimum.
For the machined gear, the length of a common normal line is generally adopted for verification, a cad graph is generally required to be drawn in the production engineering, and the length of the common normal line is given in a gradual approximation mode. Document [5] proposes to use transcendental equation, but the phenomena of virtual solution and missing solution are easy to occur when the transcendental equation is solved, and the length of the common normal line is also an approximate numerical value.
The above documents [1] to [5] are specifically:
[1] the optimization of Wangchuncheng cycloidal gear tooth profile trimming (J), proceedings of Zhejiang academy of Industrial science, 1989,42(1):7-15.
[2] Zulanyi, Qin Wei, preliminary discussion of modification of the tooth profile of the cycloidal pin gear meshing pair [ J ]. proceedings of Jilin university of industry, 1982, (4):94-106.
[3] Optimization design of cycloidal gear tooth profile modification [ J ] mechanical transmission, 2009,33 (1): 41-43
[4] Design of modification of tooth profile of meshing pair of tie-bar-free cycloidal pin gear [ J ]. college university (natural science edition), 2010,38 (1): 108-112
[5] Xuanping, wear Tianwei, trojanxia, etc., cycloidal gear tooth profile modification detection and common normal line length calculation [ J ]. proceedings of Hebei university of industry, 1997,26 (4): 56-59
Disclosure of Invention
The invention aims to: in order to improve the meshing quality of the cycloid wheel, an analysis method for improving and optimizing the tooth profile of the cycloid wheel by applying an MATLAB optimization tool box is provided by analyzing a mathematical model for the modification of the cycloid wheel. Obtaining an optimal modification angle through the oil film thickness, and searching the range of the optimal modification amount according to the inflection point position in the meshing area so as to obtain an optimal equidistant shifting distance modification tooth profile; further provides a method for optimizing the trimming amount of the tooth profile of the cycloidal gear based on matlab, which has short calculation period and high transmission efficiency.
The technical scheme adopted by the invention for solving the technical problems in the prior art is as follows:
a method for optimizing the modification quantity of a cycloid wheel tooth profile based on matlab comprises the following steps:
step one, calculating the inflection point position of the tooth profile of the cycloidal gear according to the basic parameters of the cycloidal gear;
secondly, calculating an optimal shape correction angle according to the oil film thickness and the position of a combined inflection point;
step three, calculating the optimal equidistant and displacement modification quantity according to the optimization function of matlab;
and step four, obtaining inspection parameters convenient for inspection.
As a preferable scheme, the invention also adopts the following technical scheme:
the first step is specifically as follows:
firstly, selecting basic parameters of a cycloidal gear, wherein the basic parameters comprise: the tooth number zc of the cycloid gear, the tooth number zp of the pin gear, the eccentricity a, the radius rp of the central circle of the pin gear and the radius rrp of the excircle of the pin gear sleeve;
then calculating the position of the inflection point of the cycloid wheel; the inflection point is a concave and convex dividing point of the curve; the specific process of calculating the inflection point of the cycloid wheel comprises the following steps: if f (x) is continuous in (a, b), any two points x1, x2 in the curve pair (a, b) always have <math>
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</math> If the curve is a concave curve; if there is always <math>
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<mi>x</mi>
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</msub>
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<mrow>
<mi>f</mi>
<mrow>
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<msub>
<mi>x</mi>
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</math> The curve is a convex curve; for the cycloidal gear tooth profile curve, the curve equation is f (x), if a point x existsnSo that And is X is thennThe point is the inflection point of the profile curve of the cycloid wheel.
The second step is specifically as follows:
calculating an optimal reshaping angle: when the cycloid wheel is subjected to corner modification, the corners delta of all parts of the tooth profile are the same, and the variation L in the normal direction is in direct proportion to the force arm, namelyWherein,
for shorthand purposes of angle of rotation of arm relative to central radial of a particular tooth, i.e. phase angle of engagement, k1Is a short amplitude coefficient, k1=azp/rp；Therefore, the optimal modification angle delta is calculated according to the given oil film thickness L, namely the normal variation, so that the corner modification tooth profile curve is determined.
The third step is specifically as follows:
first, an objective function containing an equidistant modification amount Δ rrp and a distance modification amount Δ rp is determined: according to the followingPitch, offset modified back profile curve L1(x,iyi) The modified-angle tooth-profile curve L2(x,i，y,i) The most consistent principle is thati=y,i(i =1,2, 3.. m), xiAnd (c) a reaction product of x,i(i =1,2, 3.. m) and the deviation index of the curve L1 from the curve L2 can be measured as the average of the absolute values of the deviations of the m points, i.e. the deviation index is measured as the absolute value of the deviation of the m points
When the value of F (delta rrp, delta rp) is minimum, the two curves are most consistent, namely the objective function is to find the minimum value of F (delta rrp, delta rp);
then determining the constraint conditions: determining constraint conditions of the optimization variables according to the meanings and the relations of the parameters;
Δ rrp <0, Δ rp <0, Δ rrp- Δ rp ≧ Δ j, where Δ j is the minimum root distance that prevents tooth surface gluing.
The fourth step is specifically as follows:
obtaining an optimized variable value by adopting an optimization function Fmincon statement in a matlab optimization tool box;
the common normal line refers to the normal distance between tooth profiles when crossing n teeth; the solving process of the common normal line length is based on the characteristic that the cycloidal gear curve equation is based on x-axis symmetry and based on an actual measurement and inspection method, if the number n of cross teeth is an even number, twice of the maximum value of the Y coordinate on the nth/2 cycloidal gears which are symmetrical to the x axis in the-x axis direction is taken as the common normal line length; if the number of the cross teeth n is an odd number, taking twice the maximum value of Y coordinates on the (n-1)/2 th cycloid gears which are symmetrical to the x axis in the + x axis direction as the length of the common normal; when there is no common normal or the number of teeth across is too large, the system reports an error.
The invention has the advantages and positive effects that:
the invention provides an analysis method for improving and optimizing the tooth profile of a cycloidal gear by applying an MATLAB optimization tool box through analyzing a mathematical model for the modification of the cycloidal gear; obtaining an optimal modification angle through the oil film thickness, and searching the range of the optimal modification amount according to the inflection point position in the meshing area so as to obtain an optimal equidistant shifting distance modification tooth profile; therefore, the calculation period of the tooth profile modification amount is greatly shortened, and the number of simultaneously meshed teeth is ensured, so that the transmission stability is ensured, and the transmission efficiency is improved.
The invention optimizes the objective function by adopting the optimization statement in matlab, and overcomes the defect of repeated experimental verification depending on experience in the traditional design process of the cycloid wheel.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
In order to further understand the contents, features and effects of the present invention, the following embodiments are illustrated and described in detail with reference to the accompanying drawings:
referring to fig. 1, a method for optimizing the modification amount of the tooth profile of a cycloid wheel based on matlab includes the following steps:
step one, calculating the inflection point position of the tooth profile of the cycloidal gear according to the basic parameters of the cycloidal gear; the specific process is as follows:
firstly, selecting basic parameters of a cycloidal gear, wherein the basic parameters comprise: the tooth number zc of the cycloid gear, the tooth number zp of the pin gear, the eccentricity a, the radius rp of the central circle of the pin gear and the radius rrp of the excircle of the pin gear sleeve;
then calculating the position of the inflection point of the cycloid wheel; the inflection point is a concave and convex dividing point of the curve; the specific process of calculating the inflection point of the cycloid wheel comprises the following steps: if f (x) is continuous in (a, b), any two points x1, x2 in the curve pair (a, b) always have <math>
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<mi>f</mi>
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</math> If the curve is a concave curve; if there is always <math>
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</math> The curve is a convex curve; for the cycloidal gear tooth profile curve, the curve equation is f (x), if there is a point xn, such that And is And the xn point is the inflection point of the profile curve of the cycloidal gear.
Secondly, calculating an optimal shape correction angle according to the oil film thickness and the position of a combined inflection point; the specific process is as follows:
calculating an optimal reshaping angle: when the cycloid wheel is subjected to corner modification, the corners delta of all parts of the tooth profile are the same, and the variation L in the normal direction is in direct proportion to the force arm, namelyWherein,is the rotation of the rotating arm relative to the radial of the center of a certain needleAngle, i.e. shorthand for the phase angle of engagement, k1Is a short amplitude coefficient, k1=azp/rp；
Therefore, the optimal modification angle delta is calculated according to the given oil film thickness L, namely the normal variation, so that the corner modification tooth profile curve is determined.
Step three, calculating the optimal equidistant and displacement modification quantity according to the optimization function of matlab; the specific process is as follows:
first, an objective function containing an equidistant modification amount Δ rrp and a distance modification amount Δ rp is determined: according to the equidistant, shifted-pitch modified rear tooth profile curve L1(x,iyi) The modified-angle tooth-profile curve L2(x,i，y,i) The most consistent principle is thati=y,i(i =1,2, 3.. m), xiAnd (c) a reaction product of x,i(i =1,2, 3.. m) and the deviation index of the curve L1 from the curve L2 can be measured as the average of the absolute values of the deviations of the m points, i.e. the deviation index is measured as the absolute value of the deviation of the m pointsWhen the value of F (delta rrp, delta rp) is minimum, the two curves are most consistent, namely the objective function is to find the minimum value of F (delta rrp, delta rp);
then determining the constraint conditions: determining constraint conditions of the optimization variables according to the meanings and the relations of the parameters;
Δ rrp <0, Δ rp <0, Δ rrp- Δ rp ≧ Δ j, where Δ j is the minimum root distance that prevents tooth surface gluing.
And step four, obtaining inspection parameters convenient for inspection. The specific process is as follows:
obtaining an optimized variable value by adopting an optimization function Fmincon statement in a matlab optimization tool box;
the common normal line refers to the normal distance between tooth profiles when crossing n teeth; the solving process of the common normal line length is based on the characteristic that the cycloidal gear curve equation is based on x-axis symmetry and based on an actual measurement and inspection method, if the number n of cross teeth is an even number, twice of the maximum value of the Y coordinate on the nth/2 cycloidal gears which are symmetrical to the x axis in the-x axis direction is taken as the common normal line length; if the number of the cross teeth n is an odd number, taking twice the maximum value of Y coordinates on the (n-1)/2 th cycloid gears which are symmetrical to the x axis in the + x axis direction as the length of the common normal; when there is no common normal or the number of teeth across is too large, the system reports an error.
In the following, specific parameters are combined, for example, 320s series products of Tianjin Bailey celestial star drive Co., Ltd,
s1, inputting basic parameters: rp =114.5, rrp =5, Zp =40, a = 2.2;
s2, calculating the position of the inflection point of the curve of the tooth profile of the cycloidal gear, and using the position for calculating the objective function;
s3, the oil film thickness is given according to experience, namely the normal variation L =0.015mm of the cycloid wheel, the optimal modification angle delta is obtained,
for the calculation of the objective function;
s4, determining an objective function: within 10 degrees before and after the inflection point, the corner modification curve is closest to the equidistant and distance-shifting modification curve, namely the objective function is
The minimum value is taken, namely minF (delta rrp, delta rp) is taken as an objective function.
S5, determining constraint conditions, namely, delta rrp <0, delta rp <0, delta rrp-delta rp ≧ delta j, where delta j is the minimum tooth root distance for preventing tooth surface gluing, and in this calculation, delta j =0.025mm is determined empirically.
S6, utilizing an optimization function Fmincon statement in matlab to obtain a final optimization result, wherein delta rrp = -0.037 and delta rp = -0.062;
s7, testing parameters: when the number of the span teeth is 15 teeth, the common normal length is 202.975. Other cross-tooth numbers can also be input to calculate the length of the common normal line.
Analysis of the results of the above examples:
through cad analysis, when the tooth profile curve modification is carried out on the cycloidal gear by adopting the equal-distance modification amount and the displacement modification amount, the number of teeth participating in meshing is 10, and 1/4 of the number of teeth of the whole cycloidal gear is reached.
The traditional empirical values are Δ rrp = -0.02, Δ rp = -0.07; the number of teeth engaged at the same time is 6.
The calculation period is short, and the whole optimization process is completed in a very short time; the inspection parameters can be directly calculated.
The embodiments of the present invention have been described in detail, but the description is only for the preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention shall fall within the scope of the present invention.
Claims (5)
1. A method for optimizing the modification quantity of a cycloid wheel tooth profile based on matlab comprises the following steps:
step one, calculating the inflection point position of the tooth profile of the cycloidal gear according to the basic parameters of the cycloidal gear;
secondly, calculating an optimal shape correction angle according to the oil film thickness and the position of a combined inflection point;
step three, calculating the optimal equidistant and displacement modification quantity according to the optimization function of matlab;
and step four, obtaining inspection parameters convenient for inspection.
2. The matlab-based cycloidal gear tooth profile modification amount optimization method according to claim 1, wherein: the first step is specifically as follows:
firstly, selecting basic parameters of a cycloidal gear, wherein the basic parameters comprise: the tooth number zc of the cycloid gear, the tooth number zp of the pin gear, the eccentricity a, the radius rp of the central circle of the pin gear and the radius rrp of the excircle of the pin gear sleeve;
then calculating the position of the inflection point of the cycloid wheel; the inflection point is a concave and convex dividing point of the curve; the specific process of calculating the inflection point of the cycloid wheel comprises the following steps: if f (x) is continuous in (a, b), x is any two points in the curve pair (a, b)1，x2Constantly have <math>
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mfrac>
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<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
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<mi>x</mi>
<mn>2</mn>
</msub>
</mrow>
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<mo>)</mo>
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</msub>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</mfrac>
<mo>,</mo>
</mrow>
</math> The curve is a concave curve; if there is always <math>
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</math> The curve is a convex curve; for the cycloidal gear tooth profile curve, the curve equation is f (x), if a point x existsnSo that And is X is thennThe point is the inflection point of the profile curve of the cycloid wheel.
3. The matlab-based cycloidal gear tooth profile modification amount optimization method according to claim 2, wherein: the second step is specifically as follows:
calculating an optimal reshaping angle: when the cycloid wheel is subjected to corner modification, the corners delta of all parts of the tooth profile are the same, and the variation L in the normal direction is in direct proportion to the force arm, namely
Wherein,
for shorthand purposes of angle of rotation of arm relative to central radial of a particular tooth, i.e. phase angle of engagement, k1Is a short amplitude coefficient, k1=azp/rp；
Therefore, the optimal modification angle delta is calculated according to the given oil film thickness L, namely the normal variation, so that the corner modification tooth profile curve is determined.
4. The matlab-based cycloidal gear tooth profile modification amount optimization method according to claim 3, wherein: the third step is specifically as follows:
first, an objective function containing an equidistant modification amount Δ rrp and a distance modification amount Δ rp is determined: according to the equidistant, shifted-pitch modified rear tooth profile curve L1(x,iyi) The modified-angle tooth-profile curve L2(x,i，y,i) The most consistent principle is thati=y,i(i =1,2, 3.. m), xiAnd (c) a reaction product of x,ithe difference between (i =1,2, 3.. m) can be measured by m, and the deviation of the curve L1 from the curve L2 can be measured by mMeasured as the mean of the absolute values of the point deviations, i.e.When the value of F (delta rrp, delta rp) is minimum, the two curves are most consistent, namely the objective function is to find the minimum value of F (delta rrp, delta rp);
then determining the constraint conditions: determining constraint conditions of the optimization variables according to the meanings and the relations of the parameters;
Δ rrp <0, Δ rp <0, Δ rrp- Δ rp ≧ Δ j, where Δ j is the minimum root distance that prevents tooth surface gluing.
5. The matlab-based cycloidal gear tooth profile modification amount optimization method according to claim 4, wherein: the fourth step is specifically as follows:
obtaining an optimized variable value by adopting an optimization function Fmincon statement in a matlab optimization tool box;
the common normal line refers to the normal distance between tooth profiles when crossing n teeth; the solving process of the common normal line length is based on the characteristic that the cycloidal gear curve equation is based on x-axis symmetry and based on an actual measurement and inspection method, if the number n of cross teeth is an even number, twice of the maximum value of the Y coordinate on the nth/2 cycloidal gears which are symmetrical to the x axis in the-x axis direction is taken as the common normal line length; if the number of the cross teeth n is an odd number, taking twice the maximum value of Y coordinates on the (n-1)/2 th cycloid gears which are symmetrical to the x axis in the + x axis direction as the length of the common normal; when there is no common normal or the number of teeth across is too large, the system reports an error.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410120389.3A CN103886154B (en) | 2014-03-27 | 2014-03-27 | Method for optimizing cycloid gear tooth outline modification amount based on matlab |
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| CN105404737A (en) * | 2015-11-17 | 2016-03-16 | 天津百利机械装备研究院有限公司 | MATLAB based cycloid gear parameter optimization method |
| CN106152945A (en) * | 2015-03-25 | 2016-11-23 | 比亚迪股份有限公司 | A kind of cycloid planetary speed reducer cycloid disc eccentric throw deviation detecting method |
| CN106227918A (en) * | 2016-07-10 | 2016-12-14 | 北京工业大学 | Cycloidal-pin wheel flank profil based on particle cluster algorithm repaiies type amount optimization method |
| CN107229836A (en) * | 2017-07-04 | 2017-10-03 | 河南科技大学 | Cycloid tooth profile correction method and Cycloidal Wheel, RV decelerators |
| CN107256282A (en) * | 2017-05-08 | 2017-10-17 | 华南理工大学 | A kind of RV Key Part of Cycloid Cam Planetary Speed Reducer profile modification methods compensated based on deformation quantity |
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| CN108460186A (en) * | 2018-02-05 | 2018-08-28 | 哈工大机器人（合肥）国际创新研究院 | A kind of Cycloid tooth profile profiling quantity optimization method based on ant group algorithm |
| CN108620691A (en) * | 2018-03-21 | 2018-10-09 | 湖北工业大学 | A kind of Cycloid tooth profile correction method and Cycloidal Wheel, RV retarders |
| CN108920816A (en) * | 2018-06-29 | 2018-11-30 | 江苏国茂减速机股份有限公司 | A kind of method for solving of the two teeth difference cycloidal tooth profile equivalent substitution tooth form based on Matlab |
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| CN106152945A (en) * | 2015-03-25 | 2016-11-23 | 比亚迪股份有限公司 | A kind of cycloid planetary speed reducer cycloid disc eccentric throw deviation detecting method |
| CN106152945B (en) * | 2015-03-25 | 2019-04-19 | 比亚迪股份有限公司 | A kind of cycloid planetary speed reducer cycloid disc eccentricity deviation detecting method |
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| CN107229836A (en) * | 2017-07-04 | 2017-10-03 | 河南科技大学 | Cycloid tooth profile correction method and Cycloidal Wheel, RV decelerators |
| CN107387722A (en) * | 2017-08-17 | 2017-11-24 | 燕山大学 | A kind of design method of fan-shaped non-circular gear |
| CN107992679A (en) * | 2017-11-30 | 2018-05-04 | 江苏国茂减速机股份有限公司 | A kind of two teeth difference the form of cycloidal gear tooth optimization method based on Matlab |
| CN108052763A (en) * | 2017-12-26 | 2018-05-18 | 哈工大机器人（合肥）国际创新研究院 | A kind of Cycloid tooth profile profiling quantity optimization method based on genetic algorithm |
| CN108331899A (en) * | 2017-12-29 | 2018-07-27 | 河南科技大学 | A kind of RV retarders cycloid gear profile modification design method and system |
| WO2019136857A1 (en) * | 2018-01-12 | 2019-07-18 | 大连民族大学 | Cycloid tooth profile general equation design method based on tooth profile normal method |
| CN108460186A (en) * | 2018-02-05 | 2018-08-28 | 哈工大机器人（合肥）国际创新研究院 | A kind of Cycloid tooth profile profiling quantity optimization method based on ant group algorithm |
| CN108620691A (en) * | 2018-03-21 | 2018-10-09 | 湖北工业大学 | A kind of Cycloid tooth profile correction method and Cycloidal Wheel, RV retarders |
| CN108920816A (en) * | 2018-06-29 | 2018-11-30 | 江苏国茂减速机股份有限公司 | A kind of method for solving of the two teeth difference cycloidal tooth profile equivalent substitution tooth form based on Matlab |
| CN109396567A (en) * | 2018-11-06 | 2019-03-01 | 重庆大学 | The digital envelope method of worm abrasion wheel profile is determined in correction of the flank shape cycloid gear generating grinding |
| CN109396567B (en) * | 2018-11-06 | 2020-04-28 | 重庆大学 | Digital envelope method for determining profile of worm grinding wheel in generating grinding of shape-modified cycloid gear |
| CN109783882A (en) * | 2018-12-21 | 2019-05-21 | 哈尔滨工程大学 | A kind of gas turbine fuel system modeling and simulating method for combining matlab and flowmaster |
| CN109783882B (en) * | 2018-12-21 | 2022-09-09 | 哈尔滨工程大学 | Modeling simulation method for gas turbine fuel system combining matlab and flowmaster |
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