CN110377932A - A kind of molded line representation method of steel ball reducer cycloid disc - Google Patents
A kind of molded line representation method of steel ball reducer cycloid disc Download PDFInfo
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Abstract
The invention discloses a kind of molded line representation methods of steel ball reducer cycloid disc, include the following steps, obtain cycloid disc data model；The knot vector of cycloid disc molded line data point is determined according to the data model；The control vertex of NURBS interpolation curve is obtained using the knot vector reverse of data point；Obtain interpolant spline curve output result；The verifying of curve matching trueness error.Beneficial effects of the present invention: can carry out partial modification to cycloid disc molded line improves the local characteristics of molded line under the premise of not influencing performance in other sections, to optimize the molded line of cycloid disc.
Description
Technical field
The present invention relates to the technical field of Method of Cycloid Steel Ball Reducer more particularly to a kind of molded line of steel ball reducer cycloid disc
Representation method.
Background technique
Important component one of of the cycloid disc as Method of Cycloid Steel Ball Reducer in recent years, cycloid disc molded line, which directly influences, to be subtracted
The performance of fast device.The Profile Design parameter of cycloid disc and cycloid groove whether occur root cut it is closely related, efficiency to retarder and
Carrying influences significant.
Existing research is influence of the value of analysis curtate ratio to steel ball reducer transmission performance, to short width system
Several value ranges are studied, but the research under normal conditions K value with reduce efficiency guarantee flank profil carry, cannot
Realize the common optimization of efficiency and carrying.Also there is researcher to carry out base to the efficiency, volume and carrying of steel ball reducer simultaneously
In the optimization design of genetic algorithm, which is to a certain extent optimized the design parameter of steel ball reducer, still
The research is to reach the opposite optimization of objective function by adjusting each parameter value in a certain range, can not make each mesh
Mark obtains optimal value.
Theoretic profile curve when deceleration mechanism works is a pair of intermeshing short width internal and external cycloids, short width internal and external cycloids
Forming method include packet method and derive internal and external cycloids equation without two kinds of packet method, but to a certain design parameter of molded line into
Row modification will lead to whole molded line and change, and efficiency and bearing capacity are reduced while avoiding root from cutting, it is whole to can not achieve retarder
The optimization of body performance.
Summary of the invention
The purpose of this section is to summarize some aspects of the embodiment of the present invention and briefly introduce some preferable implementations
Example.It may do a little simplified or be omitted to avoid our department is made in this section and the description of the application and the title of the invention
Point, the purpose of abstract of description and denomination of invention it is fuzzy, and this simplification or omit and cannot be used for limiting the scope of the invention.
In view of above-mentioned existing problem, the present invention is proposed.
Therefore, technical problem solved by the present invention is the partial modification of molded line cannot be completed for internal and external cycloids equation, draw
Enter the realization of nurbs curve design method to the local directed complete set of cycloid disc molded line.
In order to solve the above technical problems, the invention provides the following technical scheme: a kind of molded line of steel ball reducer cycloid disc
Representation method includes the following steps, obtains cycloid disc data model；Cycloid disc molded line data point is determined according to the data model
Knot vector；The control vertex of NURBS interpolation curve is obtained using the knot vector reverse of data point；Obtain interpolating spline song
Line exports result；The verifying of curve matching trueness error.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: institute
The acquisition for stating cycloid disc data model includes the following steps, it is known that retarder hypocycloid dish-type line design parameter；By the design
Parameter input parametric equation obtains retarder hypocycloid dish-type line；Cycloid disc molded line discretization is sampled and obtains data model.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: institute
The expression equation that parametric equation is cycloid disc is stated, as follows:
Hypocycloid equation are as follows:
Epicycloid equation are as follows:
Wherein dsFor steel ball pitch circle diameter, its calculation formula is: ds=rd/sin(180/nh), and rdFor steel ball radius, θ
The angle that is scrolled through for the round as a ball basic circle when making pure rolling on basic circle of no packet, c are the half of eccentricity, nhFor steel ball number, nb
For steel ball number.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: adopt
The data point described in molded line of the accumulation chord length parameter method to the data model carries out unified parameters, further includes,
Enabling L is the overall length of curve,Enable u0=0un=1；ThenI=1 ...,
n-1。
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: root
The control vertex for carrying out inverse nurbs curve according to the knot vector determined by data point on curve, includes the following steps, by type
Value point carrys out inverse as the data point and obtains control vertex；The weight factor of all control vertexs is first taken as 1, is obtained corresponding
The control vertex after, corresponding weight factor is adjusted curve again as needed；Wherein it is used for n+1 data point of interpolation
Cubic nonratio- nal B-spline curve equation are as follows:
By QiAbove formula, which is substituted into, with corresponding nodal value obtains the system of linear equations of n+1 vector equation composition, such as following formula
In addition two additional equations given by boundary condition are supplemented:
C0', Cn' it is to cut arrow at endpoint, obtain following equation group:
Wherein
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: institute
Stating interpolant spline curve output result includes sampling mode below, and the first kind is with any one section of waveform on cycloid disc molded line
Example carries out uniform sampling acquired results；Second class carries out uniformly so that any two ends on cycloid disc molded line respectively take half waveform as an example
Sample acquired results；Third class carries out uniform sampling and is increased so that any two ends on cycloid disc molded line respectively take half waveform as an example
The number at control point.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: institute
It states fitting precision error validity to include the following steps, the distance of calculating data point to curve, including calculates average distance and maximum
Distance；Two kinds of matched curve error analysis methods by quoting MATLAB tool carry out trueness error point to curve-fitting results
Analysis, including calculate and variance and determining coefficient.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: its
Described in and variance be SSE:What it was calculated is the flat of the error of fitting data and initial data corresponding points
Fang He, and when SSE is closer to 0 indicates model selection and fitting is more preferable, data prediction is also more successful.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: institute
Stating determining coefficient is R-square:Its quality that a fitting is characterized by the variation of data determines system
Several normal range (NR)s is [0,1], when it is closer to 1, shows that the variable of equation is stronger to the interpretability of y, and model is quasi- to data
That closes is also preferable.
A kind of preferred embodiment of molded line representation method as steel ball reducer cycloid disc of the present invention, in which: also
Sampling mode including interpolant spline curve output result respectively corresponds three classes fitting precision error and is verified；The first kind
To carry out the quasi- of matched curve obtained by the first method of sampling of uniform sampling by taking any one section of waveform on cycloid disc molded line as an example
Close trueness error；Second class is to carry out intending obtained by uniform sampling so that any two ends on cycloid disc molded line respectively take half waveform as an example
Close the fitting precision error of curve；Third class is to carry out uniformly so that any two ends on cycloid disc molded line respectively take half waveform as an example
Sample and increase the trueness error of matched curve obtained by the number at control point；Wherein the error of third-kind-type reaches 0.1 micron, really
Determine coefficient and reaches 0.999.
Beneficial effects of the present invention: first is that by proposing molded line NURBS representation method, the representation of molded line is increased；
Aiming at the problem that construction freedom degree of traditional rule curve is not able to satisfy Profile Design flexibility, propose to utilize nurbs curve side
Method, to obtain more high-freedom degree and the successional cycloid disc molded line of curve；Second is that partial modification can be carried out to cycloid disc molded line,
Under the premise of not influencing performance in other sections, improve the local characteristics of molded line, to optimize the molded line of cycloid disc.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, required use in being described below to embodiment
Attached drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for this
For the those of ordinary skill of field, without any creative labor, it can also be obtained according to these attached drawings other
Attached drawing.Wherein:
Fig. 1 is epicycloid generating principle schematic diagram described in the first embodiment of the invention；
Fig. 2 is hypocycloid generating principle schematic diagram described in the first embodiment of the invention；
Fig. 3 is nurbs curve design cycle schematic diagram described in the first embodiment of the invention；
Fig. 4 is the schematic diagram of BR85us-10G-6 hypocycloid dish-type line described in the first embodiment of the invention；
Fig. 5 is the molded lines of first kind nurbs curve fitting described in the first embodiment of the invention；
Fig. 6 is the molded lines of the second class nurbs curve fitting described in the first embodiment of the invention；
Fig. 7 is the hypocycloid entirety molded lines of third class nurbs curve fitting described in the first embodiment of the invention；
Fig. 8 is the office of the hypocycloid entirety molded lines of third class nurbs curve fitting described in the first embodiment of the invention
Portion's enlarged diagram；
Fig. 9 is the Error Graph that nurbs curve described in the first embodiment of the invention is fitted molded line.
Specific embodiment
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, right with reference to the accompanying drawings of the specification
A specific embodiment of the invention is described in detail, it is clear that and described embodiment is a part of the embodiments of the present invention, and
It is not all of embodiment.Based on the embodiments of the present invention, ordinary people in the field is without making creative work
Every other embodiment obtained, all should belong to the range of protection of the invention.
In the following description, numerous specific details are set forth in order to facilitate a full understanding of the present invention, but the present invention can be with
Implemented using other than the one described here other way, those skilled in the art can be without prejudice to intension of the present invention
In the case of do similar popularization, therefore the present invention is not limited by the specific embodiments disclosed below.
Secondly, " one embodiment " or " embodiment " referred to herein, which refers to, may be included at least one realization side of the invention
A particular feature, structure, or characteristic in formula." in one embodiment " that different places occur in the present specification not refers both to
The same embodiment, nor the individual or selective embodiment mutually exclusive with other embodiments.
Combination schematic diagram of the present invention is described in detail, when describing the embodiments of the present invention, for purposes of illustration only, indicating device
The sectional view of structure can disobey general proportion and make partial enlargement, and the schematic diagram is example, should not limit this herein
Invent the range of protection.In addition, the three-dimensional space of length, width and depth should be included in actual fabrication.
Simultaneously in the description of the present invention, it should be noted that the orientation of the instructions such as " upper and lower, inner and outer " in term
Or positional relationship is to be based on the orientation or positional relationship shown in the drawings, and is merely for convenience of description of the present invention and simplification of the description, and
It is not that the device of indication or suggestion meaning or element must have a particular orientation, be constructed and operated in a specific orientation, therefore
It is not considered as limiting the invention.In addition, term " first, second or third " is used for description purposes only, and cannot understand
For indication or suggestion relative importance.
In the present invention unless otherwise clearly defined and limited, term " installation is connected, connection " shall be understood in a broad sense, example
Such as: may be a fixed connection, be detachably connected or integral type connection；It equally can be mechanical connection, be electrically connected or be directly connected to,
Can also indirectly connected through an intermediary, the connection being also possible to inside two elements.For the ordinary skill people of this field
For member, the concrete meaning of above-mentioned term in the present invention can be understood with concrete condition.
Embodiment 1
Research for steel ball reducer, existing research are to analyze the value of curtate ratio to steel ball reducer biography
The influence of dynamic performance, studies the value range of curtate ratio, but the value of research K under normal conditions is to reduce effect
Rate come guarantee flank profil carry, can not achieve the common optimization of efficiency and carrying.According to existing research analysis it is found that efficiency is with short width
COEFFICIENT K increases and improves, and carrying then increases as the increase of k first reduces afterwards, so the value by adjusting K can not achieve efficiency
With carrying and meanwhile obtain optimal value.
And the present embodiment redesigns cycloid disc molded line by using nurbs curve, is not changing the short width of molded line
Under the premise of coefficient, i.e. whole change does not occur for guarantee cycloid disc molded line, carries out partial modification to cycloid disc molded line, reduces stress
It concentrates, to improve carrying.
Specifically, illustrating referring to shown in Fig. 3 as the molded line representation method of steel ball reducer cycloid disc described in the present embodiment
Middle nurbs curve design cycle schematic diagram, signal this method goes out control point including the use of known curve anti-calculate in figure, obtains
Interpolant spline curve, and to obtain spline curve is made whether the judgement of required precision, constantly modify parameter, finally obtain
Meet the interpolant spline curve of required precision.More specifically, this method includes obtaining cycloid disc data model, according to
Data model determines the knot vector of cycloid disc molded line data point, obtains NURBS interpolation using the knot vector reverse of data point
The control vertex of curve obtains interpolant spline curve output result, the verifying of curve matching trueness error.Wherein,
Obtaining cycloid disc data model includes:
Retarder internal and external cycloids dish-type line design method is identical, thus in the present embodiment within carry out for cycloid disc molded line
Design, so that external cycloid disc Profile Design can be completed referring to hypocycloid dish-type line design cycle.The present embodiment is referring to Fig. 4's
Signal, it is known that BR85us-10G-6 retarder hypocycloid dish-type line design parameter, according in the available retarder of parametric equation
Cycloid disc molded line discretization is sampled and obtains data model by cycloid disc molded line.
It should also be noted that, the Profile Design method of cycloid disc molded line is using being more widely according to cycloid side at present
Journey and given conditional parameter draw internal and external cycloids dish-type line.Theoretic profile curve when deceleration mechanism works is that a pair is mutually nibbled
The short width internal and external cycloids closed, the forming method of short width internal and external cycloids includes packet method and without two kinds of packet method, in the present embodiment
By derivation internal and external cycloids equation for no packet method.It is as follows:
Fig. 1 show epicycloid generating principle figure, O in figure0Around O1Make pure rolling, M is to occur in round a bit, eccentric distance e
=O0M, the generation epicycloid number of teeth are Z1=R1/R0, the motion profile of M point is epicycloid；
Fig. 2 show hypocycloid generating principle figure, O in figure0Around O2Pure rolling, M' are to occur in round a bit, eccentricity A
=O0M', the generation hypocycloid number of teeth are Z1=R2/R0, the motion profile of M' point is hypocycloid.Cycloid disc in traditional design method
Expression equation it is as follows.
Hypocycloid equation are as follows:
Epicycloid equation are as follows:
dsFor steel ball pitch circle diameter, calculation formula is as follows: ds=rd/sin(180/nh), wherein rdFor steel ball half
Diameter；θ is round as a ball when making pure rolling on basic circle for no packet, the angle that basic circle is scrolled through；C is the half of eccentricity；nhFor steel ball
Number；nbFor steel ball number.
The present embodiment draws internal and external cycloids dish-type line according to cycloid equation and given conditional parameter, but sets to molded line is a certain
Meter parameter, which is modified, will lead to whole molded line change, and efficiency and bearing capacity are reduced while avoiding root from cutting, can not achieve
The optimization of retarder overall performance.
The knot vector for determining cycloid disc molded line data point includes:
The parametrization of data point is the important step of curve construction, and important influence is played to curve smoothing.In order to obtain
Preferable fairness is obtained, the present embodiment carries out unified parameters to molded line data point using accumulation chord length parameter method, including as follows
Step,
Enabling L is the overall length of curve,Enable u0=0un=1；ThenI=1 ...,
n-1.Data point is reflected strictly according to the facts using above-mentioned parameterization by the distribution situation of chord length, and gained interpolation curve has preferable light
It is pliable.
The control vertex of reverse NURBS interpolation curve includes:
To express the volume of data on measured cycloid disc molded line using cubic NURBS curve in this implementation
Point, then must first the knot vector according to determined by data point on curve come the control point of inverse nurbs curve.It needs to illustrate
It is that data point determines knot vector as data point, and the acquisition of data point by the sampling of cycloid disc molded line discretization by being obtained
Data model is obtained to obtain.
It is as follows that control vertex acquires process:
With processing method identical with non-uniform B-spline curve inverse, i.e., data point being carried out inverse as data point must control
Processed, the weight factor of all control vertexs is first taken as 1 by when calculating, obtains being root after corresponding preliminary control vertex later
According to needing again corresponding weight factor to be adjusted curve, final control vertex corresponding with demand is obtained.
The present embodiment defines the cubic nonratio- nal B-spline curve equation for n+1 data point of interpolation are as follows:
By QiAbove formula, which is substituted into, with corresponding nodal value obtains the system of linear equations of n+1 vector equation composition, such as following formula
In addition two additional equations given by boundary condition are supplemented:
C0', Cn' it is to cut arrow at endpoint, obtain following equation group:
Wherein
Interpolant spline curve exports result:
Fig. 5 and Fig. 6 takes two different sampling methods respectively, and Fig. 5 illustrates the first with appointing on cycloid disc molded line
It anticipates and carries out uniform sampling acquired results for one section of waveform；Fig. 6 illustrates respectively to take with any two ends on cycloid disc molded line for second
Uniform sampling acquired results are carried out for half waveform；Fig. 7 the third with any two ends on cycloid disc molded line respectively take a half-wave
Uniform sampling is carried out for shape and increases the number at control point.Wherein matched curve obtained by the first method of sampling is due to left and right end
Curvature varying fast speed at point, so that fitting gained molded line and basis lines departure degree are larger.
In order to avoid curvature of curve changes rapid bring influence at fitting endpoint, sampling method shown in fig. 6 is taken, is made
It is gentle to obtain curve at two-end-point, and increases the sample frequency of interlude, changes to walk matched curve rapidly to reduce curvature
The influence of gesture.
Fig. 7 is the hypocycloid entirety molded lines that gained is fitted using nurbs curve after rotation transformation, i.e. the present embodiment
The schematic diagram of middle third class sampling mode, and for clearer signal, Fig. 8 is third class nurbs curve of the present invention fitting
The partial enlargement diagram of hypocycloid entirety molded lines, the i.e. partial enlargement diagram of Fig. 7.
The verifying of curve matching trueness error:
The basic skills that error of fitting of the matched curve between data point calculates is calculated at a distance from data point to curve, is put down
Equal distance and maximum distance are main evaluation indexes, in order to existing for preferably more various approximating methods in the present embodiment
The size of error, by quote MATLAB tool two kinds of matched curve error analysis methods to curve-fitting results of upper stage into
Row precision and error analysis, two methods are and variance and determining coefficient.
It neutralizes variance and is expressed as SSE:What the statistical parameter calculated is fitting data and original number
According to the quadratic sum of the error of corresponding points, and when SSE is closer to 0, illustrate that model selection and fitting are more preferable, data prediction also more at
Function.
Determine that coefficient is expressed as R-square:The present embodiment determine coefficient by the variation of data come
The quality of a fitting is characterized, and determines that the normal range (NR) of coefficient is [0,1], when it is closer to 1, shows the variable of equation to y
Interpretability it is stronger, this model to data be fitted also preferably.
Embodiment 2
Referring to shown in Fig. 9, the sampling mode of interpolant spline curve output result respectively corresponds three classes (three in the present embodiment
Kind) fitting precision error verified.Wherein in Fig. 9 error 1 be the first method of sampling obtained by matched curve fitting precision
Error, error 2 are the fitting precision error of matched curve obtained by second of method of sampling, and error 3 is second of method of sampling
On the basis of increase the trueness error of matched curve obtained by the number at control point, in the case of three kinds, trueness error is substantially same
The order of magnitude, this also reflects the correctness of the design method, but more evenly, error reaches for trueness error branch office in the case of the third
It 0.1 micron, determines that coefficients R-square reaches 0.999, more can really reappear cycloid disc molded line.
It should be noted that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting, although referring to preferable
Embodiment describes the invention in detail, those skilled in the art should understand that, it can be to technology of the invention
Scheme is modified or replaced equivalently, and without departing from the spirit and scope of the technical solution of the present invention, should all be covered in this hair
In bright scope of the claims.
Claims (10)
1. a kind of molded line representation method of steel ball reducer cycloid disc, it is characterised in that: include the following steps,
Obtain cycloid disc data model；
The knot vector of cycloid disc molded line data point is determined according to the data model；
The control vertex of NURBS interpolation curve is obtained using the knot vector reverse of data point；
Obtain interpolant spline curve output result；
The verifying of curve matching trueness error.
2. the molded line representation method of steel ball reducer cycloid disc as described in claim 1, it is characterised in that: the cycloid disc number
Include the following steps according to the acquisition of model,
Known retarder hypocycloid dish-type line design parameter；
Design parameter input parametric equation is obtained into retarder hypocycloid dish-type line；
Cycloid disc molded line discretization is sampled and obtains data model.
3. the molded line representation method of steel ball reducer cycloid disc as claimed in claim 2, it is characterised in that: the parametric equation
It is as follows for the expression equation of cycloid disc:
Hypocycloid equation are as follows:
Epicycloid equation are as follows:
Wherein dsFor steel ball pitch circle diameter, its calculation formula is: ds=rd/sin(180/nh), and rdIt is nothing for steel ball radius, θ
Angle that the round as a ball basic circle when making pure rolling on basic circle of packet is scrolled through, c are the half of eccentricity, nhFor steel ball number, nbFor steel
Ball number.
4. the molded line representation method of the steel ball reducer cycloid disc as described in claims 1 to 3 is any, it is characterised in that: use
It accumulates data point described in molded line of the chord length parameter method to the data model and carries out unified parameters, further include,
Enabling L is the overall length of curve,Enable u0=0un=1；Then
5. the molded line representation method of steel ball reducer cycloid disc as claimed in claim 4, it is characterised in that: according to curve mo(u)ld top half
The knot vector determined by value point carrys out the control vertex of inverse nurbs curve, includes the following steps,
Data point is carried out into inverse as the data point and obtains control vertex；
The weight factor of all control vertexs is first taken as 1, after obtaining the corresponding control vertex, is corresponded to again as needed
Weight factor curve is adjusted；
Wherein it is used for the cubic nonratio- nal B-spline curve equation of n+1 data point of interpolation are as follows:
By QiAbove formula, which is substituted into, with corresponding nodal value obtains the system of linear equations of n+1 vector equation composition, such as following formula
In addition two additional equations given by boundary condition are supplemented:
C0', Cn' it is to cut arrow at endpoint, obtain following equation group:
Wherein
6. claims 1 to 3 or 5 it is any as described in steel ball reducer cycloid disc molded line representation method, it is characterised in that: institute
Stating interpolant spline curve output result includes sampling mode below,
The first kind carries out uniform sampling acquired results by taking any one section of waveform on cycloid disc molded line as an example；Second class is with cycloid disc
Any two ends on molded line carry out uniform sampling acquired results for respectively taking half waveform；Third class is with appointing on cycloid disc molded line
Meaning both ends respectively take the number for carrying out uniform sampling for half waveform and increasing control point.
7. the molded line representation method of steel ball reducer cycloid disc as claimed in claim 6, it is characterised in that: the fitting precision
Error validity includes the following steps,
Calculate the distance that data point arrives curve, including calculating average distance and maximum distance；
Two kinds of matched curve error analysis methods by quoting MATLAB tool carry out trueness error point to curve-fitting results
Analysis, including calculate and variance and determining coefficient.
8. the molded line representation method of steel ball reducer cycloid disc as claimed in claim 7, it is characterised in that: wherein described and side
Difference is SSE:What it was calculated is the quadratic sum of the error of fitting data and initial data corresponding points, and works as
SSE indicates model selection and fitting is more preferable, data prediction is also more successful closer to 0.
9. the molded line representation method of steel ball reducer cycloid disc as claimed in claim 7 or 8, it is characterised in that: the determination
Coefficient is R-square:Its quality that a fitting is characterized by the variation of data, determines coefficient just
Normal range is [0,1], when it is closer to 1, shows that the variable of equation is stronger to the interpretability of y, model is fitted data
Preferably.
10. the molded line representation method of steel ball reducer cycloid disc as claimed in claim 5, it is characterised in that: further include described
The sampling mode of interpolant spline curve output result respectively corresponds three classes fitting precision error and is verified；
The first kind is to carry out intending obtained by the first method of sampling of uniform sampling by taking any one section of waveform on cycloid disc molded line as an example
Close the fitting precision error of curve；Second class is to carry out uniformly so that any two ends on cycloid disc molded line respectively take half waveform as an example
The fitting precision error of sampling gained matched curve；Third class is respectively to take the half waveform to be with any two ends on cycloid disc molded line
Example carries out uniform sampling and increases the trueness error of matched curve obtained by the number at control point；Wherein the error of third-kind-type reaches
0.1 micron, determine that coefficient reaches 0.999.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910469105.4A CN110377932B (en) | 2019-05-31 | 2019-05-31 | Molded line representation method of steel ball speed reducer swing wire coil |
Applications Claiming Priority (1)
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| CN111156306A (en) * | 2020-01-06 | 2020-05-15 | 河南烛龙高科技术有限公司 | Undercut oscillating tooth transmission meshing pair and generation method thereof |
| CN111173895A (en) * | 2020-01-06 | 2020-05-19 | 河南烛龙高科技术有限公司 | Two-stage closed type undercut cycloid oscillating tooth transmission unit |
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| CN106959666A (en) * | 2017-03-31 | 2017-07-18 | 华南理工大学 | A kind of space free curve approximating method based on NURBS |
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| CN111156306A (en) * | 2020-01-06 | 2020-05-15 | 河南烛龙高科技术有限公司 | Undercut oscillating tooth transmission meshing pair and generation method thereof |
| CN111173895A (en) * | 2020-01-06 | 2020-05-19 | 河南烛龙高科技术有限公司 | Two-stage closed type undercut cycloid oscillating tooth transmission unit |
| CN111173895B (en) * | 2020-01-06 | 2021-05-04 | 河南烛龙高科技术有限公司 | Two-stage closed type undercut cycloid oscillating tooth transmission unit |
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