CN110377932B - Molded line representation method of steel ball speed reducer swing wire coil - Google Patents
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Abstract
The application discloses a molded line representation method of a cycloid disc of a steel ball speed reducer, which comprises the following steps of obtaining a cycloid disc data model; determining a node vector of a line-placing disc type line data point according to the data model; reversely obtaining a control vertex of the NURBS interpolation curve by using a node vector of the data point; obtaining an interpolation spline curve output result; and (5) verifying curve fitting accuracy errors. The application has the beneficial effects that: the cycloid disc molded line can be locally modified, and the local characteristic of the molded line is improved on the premise of not affecting the performance in other intervals, so that the molded line of the cycloid disc is optimized.
Description
Technical Field
The application relates to the technical field of cycloidal steel ball reducers, in particular to a molded line representation method of a cycloidal disc of a steel ball reducer.
Background
In recent years, cycloidal discs are taken as one of important components of cycloidal steel ball reducers, and the cycloidal disc molded lines of the cycloidal steel ball reducers directly influence the performance of the reducers. The design parameters of the molded lines of the cycloid disc are closely related to whether the cycloid grooves are undercut or not, and the design parameters have obvious influence on the efficiency and the bearing of the speed reducer.
The existing research is to analyze the influence of the value of the short-range coefficient on the transmission performance of the steel ball speed reducer and research the value range of the short-range coefficient, but the research generally ensures tooth profile bearing by reducing the efficiency by the value of K, and the common optimization of the efficiency and the bearing cannot be realized. Meanwhile, researchers have optimized designs based on genetic algorithm on the efficiency, volume and bearing of the steel ball speed reducer, and the researches optimize design parameters of the steel ball speed reducer to a certain extent, but the researches reach the relative optimization of objective functions by adjusting the values of all parameters within a certain range, and cannot enable all targets to obtain optimal values.
The theoretical tooth profile curve of the speed reducing mechanism is a pair of intermeshed short-amplitude inner and outer cycloids, the forming method of the short-amplitude inner and outer cycloids comprises a core-wrapping method and a non-core-wrapping method for deducing inner and outer cycloid equations, but modification of a certain design parameter of a profile can lead to integral profile change, efficiency and bearing capacity are reduced while radical cutting is avoided, and optimization of integral performance of the speed reducer cannot be achieved.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the application and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description of the application and in the title of the application, which may not be used to limit the scope of the application.
The present application has been made in view of the above-described problems occurring in the prior art.
Therefore, the technical problems solved by the application are as follows: aiming at the fact that the internal cycloid equation and the external cycloid equation can not finish local modification of the molded line, a NURBS curve design method is introduced to realize local adjustment of the molded line of the cycloid disc.
In order to solve the technical problems, the application provides the following technical scheme: the method for representing the molded line of the cycloid disc of the steel ball speed reducer comprises the following steps of obtaining a cycloid disc data model; determining a node vector of a line-placing disc type line data point according to the data model; reversely obtaining a control vertex of the NURBS interpolation curve by using a node vector of the data point; obtaining an interpolation spline curve output result; and (5) verifying curve fitting accuracy errors.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the cycloid disc data model acquisition comprises the following steps of knowing design parameters of a cycloid disc molded line in a speed reducer; inputting the design parameters into a parameter equation to obtain the inner cycloid disc molded line of the speed reducer; and discretizing and sampling the cycloid disc molded line to obtain a data model.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the parameter equation is a representation equation of the wobble plate, and is as follows:
the hypocycloid equation is:
the epicycloidal equation is:
wherein d is s The diameter of the steel ball distribution circle is calculated as follows: d, d s ＝r d /sin(180/n h ) And r is d The radius of the steel ball, the theta is the angle of the base circle rolled when the non-core rolling circle rolls on the base circle, c is half of the eccentric distance, n h Is the number of steel balls, n b The number of the steel balls is the number of the steel balls.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the integrated chord length parameter method is adopted to carry out unified parameterization on the data points of the molded lines of the data model, and the method also comprises the following steps,
let L be the total length of the curve,let u 0 ＝0u n =1; then->i＝1,...,n-1。
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: back-calculating a control vertex of the NURBS curve according to the node vector determined by the model value point on the curve, comprising the steps of back-calculating the control vertex by taking the model value point as the data point; firstly taking the weight factors of all the control vertexes as 1, and adjusting the curve according to the weight factors corresponding to the control vertexes after obtaining the corresponding control vertexes; the cubic non-uniform B-spline curve equation for interpolating n+1 data points is:
will Q i Substituting the corresponding node value into the above formula to obtain a linear equation set consisting of n+1 vector equations, wherein the equation is as follows
Two additional equations given by boundary conditions are additionally complemented:
C 0 '，C n ' is the tangent vector at the end point, resulting in the following system of equations:
wherein the method comprises the steps of
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the interpolation spline curve output result comprises the following sampling modes, wherein the first type is a result obtained by taking any section of waveform on a cycloid disc line as an example for uniform sampling; the second class takes half of waveforms at any two ends of a cycloid disc line as an example to uniformly sample the obtained result; and the third class takes half of waveforms at any two ends of the cycloid disc line as an example to uniformly sample and increase the number of control points.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the fitting accuracy error verification includes the steps of calculating a distance from a data point to a curve, including calculating an average distance and a maximum distance; and performing accuracy error analysis on the curve fitting result by using two fitting curve error analysis methods of the MATLAB tool, wherein the accuracy error analysis comprises calculation, variance and determination coefficients.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: wherein the sum variance is SSE:it calculates the sum of squares of the errors of the corresponding points of the fitted data and the original data, and when the SSE is closer to 0, the better the model selection and fitting, the more successful the data prediction.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the determination coefficient is R-square:it features that a fitting is performed by the variation of data, and the normal range of coefficient is 0,1]The closer it is to 1, the stronger the interpretation of the variables of the equation to y, and the better the model fits to the data.
As a preferable scheme of the line representation method of the steel ball speed reducer wire arranging disc, the application comprises the following steps: the sampling mode of the interpolation spline curve output result is respectively corresponding to three fitting precision errors for verification; the first type is a fitting precision error of a fitting curve obtained by taking any section of waveform on a cycloid disc line as an example to uniformly sample the first sampling method; the second type is a fitting precision error of a fitting curve obtained by taking half waveforms at any two ends of a cycloid disc line as an example for uniform sampling; the third class is to take half of waveforms at any two ends of the cycloid disc line as examples for uniform sampling and increase the accuracy error of the fitting curve obtained by the number of control points; wherein the third class of errors reaches 0.1 microns and the determined coefficient reaches 0.999.
The application has the beneficial effects that: firstly, a molded line NURBS expression method is provided, so that a molded line expression mode is increased; aiming at the problem that the degree of freedom of the traditional regular curve cannot meet the flexibility of the design of the molded line, a NURBS curve method is provided to obtain a cycloid disc molded line with higher degree of freedom and curve continuity; secondly, the cycloid disc molded line can be locally modified, and the local characteristic of the molded line is improved on the premise of not affecting the performance in other sections, so that the molded line of the cycloid disc is optimized.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
fig. 1 is a schematic diagram of the epicycloidal generation principle according to the first embodiment of the present application;
fig. 2 is a schematic diagram of the hypocycloid generation principle according to the first embodiment of the present application;
FIG. 3 is a flow chart of NURBS curve design according to a first embodiment of the present application;
FIG. 4 is a schematic diagram of a BR85us-10G-6 inner wobble plate profile according to a first embodiment of the application;
FIG. 5 is a profile diagram of a first class NURBS curve fit according to a first embodiment of the present application;
FIG. 6 is a profile diagram of a second class NURBS curve fit according to a first embodiment of the present application;
FIG. 7 is a hypocycloidal ensemble plot of a third class NURBS curve fit according to a first embodiment of the present application;
FIG. 8 is an enlarged partial schematic view of a hypocycloidal ensemble profile of a third class NURBS curve fitting in accordance with a first embodiment of the present application;
fig. 9 is an error plot of a NURBS curve fit line according to a first embodiment of the present application.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present application can be understood in detail, a more particular description of the application, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, but the present application may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present application is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the application. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
While the embodiments of the present application have been illustrated and described in detail in the drawings, the cross-sectional view of the device structure is not to scale in the general sense for ease of illustration, and the drawings are merely exemplary and should not be construed as limiting the scope of the application. In addition, the three-dimensional dimensions of length, width and depth should be included in actual fabrication.
Also in the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper, lower, inner and outer", etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the apparatus or elements referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present application. Furthermore, the terms "first, second, or third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected, and coupled" should be construed broadly in this disclosure unless otherwise specifically indicated and defined, such as: can be fixed connection, detachable connection or integral connection; it may also be a mechanical connection, an electrical connection, or a direct connection, or may be indirectly connected through an intermediate medium, or may be a communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
Example 1
For the research of the steel ball speed reducer, the existing research is to analyze the influence of the value of the short-range coefficient on the transmission performance of the steel ball speed reducer and research the value range of the short-range coefficient, but the research generally ensures tooth profile bearing with reduced efficiency by the value of K, and cannot realize the common optimization of the efficiency and the bearing. According to the prior research analysis, the efficiency is improved along with the increase of the short-amplitude coefficient K, and the load is firstly reduced and then increased along with the increase of K, so that the efficiency and the load can not be simultaneously obtained by adjusting the value of K.
In the embodiment, the nurbs curve is used for redesigning the cycloid disc molded line, so that the cycloid disc molded line is ensured not to be integrally changed on the premise of not changing the short-range coefficient of the molded line, and the cycloid disc molded line is locally modified, so that the stress concentration is reduced, and the bearing is improved.
Specifically, referring to fig. 3, a schematic diagram of a NURBS curve design flow in the method for representing a molded line of a wire coil of a steel ball speed reducer according to this embodiment is shown, where the method includes calculating control points by using a known curve, obtaining an interpolation spline curve, determining whether the obtained spline curve has a required precision, continuously modifying parameters, and finally obtaining the interpolation spline curve meeting the required precision. More specifically, the method comprises the steps of obtaining a cycloid disc data model, determining node vectors of cycloid disc molded line data points according to the data model, reversely obtaining control vertexes of NURBS interpolation curves by using the node vectors of the data points, obtaining interpolation spline curve output results and verifying curve fitting accuracy errors. Wherein,
acquiring the cycloidal disk data model includes:
the design method of the inner cycloid disc molded line and the outer cycloid disc molded line of the speed reducer is the same, so that the inner cycloid disc molded line is taken as an example for design in the embodiment, and the design of the outer cycloid disc molded line can be completed by referring to the design flow of the inner cycloid disc molded line. In this embodiment, referring to the schematic diagram of fig. 4, the design parameters of the cycloidal disc type line in the BR85us-10G-6 speed reducer are known, the cycloidal disc type line in the speed reducer can be obtained according to a parameter equation, and the cycloidal disc type line is discretized and sampled to obtain a data model.
It should be noted that, the current design method of cycloid disc molded lines is widely used to draw inner and outer cycloid disc molded lines according to cycloid equations and given condition parameters. The theoretical tooth profile curve of the speed reducing mechanism is a pair of intermeshed short-amplitude inner cycloid and outer cycloid, and the forming method of the short-amplitude inner cycloid and outer cycloid comprises a core-wrapping method and a non-core-wrapping method, and in the embodiment, the inner cycloid equation and the outer cycloid equation are deduced by taking the non-core-wrapping method as an example. The following are provided:
FIG. 1 is a schematic diagram of epicycloidal generation, O in the diagram 0 Around O 1 The pure rolling is performed, M is a point in a round occurrence circle, and the eccentricity e=O 0 M, generating the number of the external cycloid teeth to be Z 1 ＝R 1 /R 0 The motion trail of the M point is epicycloidal;
FIG. 2 is a schematic diagram of hypocycloid generation in which O 0 Around O 2 Pure rolling, M' is the point within the circle where the occurrence occurs, the eccentricity a=o 0 M' to generate hypocycloid tooth number Z 1 ＝R 2 /R 0 The motion trail of the M' point is hypocycloid. The equation for the representation of the wobble plate in the conventional design method is shown below.
The hypocycloid equation is:
the epicycloidal equation is:
d s the diameter of the steel ball distribution circle is calculated as follows: d, d s ＝r d /sin(180/n h ) Wherein r is d The radius of the steel ball is; theta is that the base circle is rolled when the non-core rolling circle makes pure rolling on the base circleIs a function of the angle of (2); c is half of the eccentricity; n is n h The number of the steel balls is the number; n is n b The number of the steel balls is the number of the steel balls.
In the embodiment, the inner cycloid disc molded lines and the outer cycloid disc molded lines are drawn according to the cycloid equation and given condition parameters, but the modification of a certain design parameter of the molded lines can lead to the change of the integral molded lines, so that the efficiency and the bearing capacity are reduced while radical cutting is avoided, and the optimization of the integral performance of the speed reducer cannot be realized.
Determining a node vector of cycloid disk profile data points includes:
parameterization of the data points is an important step in the construction of the curve, with an important impact on the curve's smoothness. In order to obtain better smoothness, the embodiment adopts the cumulative chord length parameter method to carry out unified parameterization on profile data points, comprising the following steps,
let L be the total length of the curve,let u 0 ＝0u n =1; then->i=1..n-1. The adoption of the parameterization faithfully reflects the distribution condition of the data points according to the chord length, and the obtained interpolation curve has better smoothness.
The inverse NURBS interpolation curve control vertex includes:
in this embodiment, if a series of data points on the cycloid disk profile is to be expressed by using a NURBS curve three times, the control points of the NURBS curve must be calculated back first according to the node vectors determined by the profile points on the curve. The model value points are used as data points to determine node vectors, and the data points are obtained by obtaining a data model through discretizing sampling of cycloid disc molded lines.
The control vertex is obtained as follows:
the same processing method of inverse calculation of the non-uniform B spline curve is adopted, namely, model value points are used as data points to obtain control points in an inverse calculation mode, the weight factors of all control vertexes are firstly taken as 1 in calculation, then the obtained primary control vertexes are corresponding, and the curve is adjusted according to the weight factors corresponding to the needs to obtain the final control vertexes corresponding to the needs.
The present embodiment defines a cubic non-uniform B-spline curve equation for interpolating n+1 data points as:
will Q i Substituting the corresponding node value into the above formula to obtain a linear equation set consisting of n+1 vector equations, wherein the equation is as follows
Two additional equations given by boundary conditions are additionally complemented:
C 0 '，C n ' is the tangent vector at the end point, resulting in the following system of equations:
wherein the method comprises the steps of
Outputting a result of interpolation spline curve:
two different sampling methods are adopted in fig. 5 and fig. 6, and fig. 5 illustrates the first result obtained by taking any section of waveform on the cycloid disc line as an example for uniform sampling; FIG. 6 illustrates the second type of uniform sampling using half of the waveforms taken from either end of the cycloid disc line as an example; the third example of fig. 7 is to take half of the waveform at each of the two ends of the cycloid disc line for uniform sampling and increase the number of control points. The curvature change speed of the left end point and the right end point of the fitted curve obtained by the first sampling method is high, so that the deviation degree of the molded line obtained by fitting and the original molded line is high.
In order to avoid the influence of rapid curvature change of the curve at the fitting end points, the sampling method shown in fig. 6 is adopted, so that the curves at the two end points are gentle, the sampling frequency of the middle section is increased, and the influence of rapid curvature change on the trend of the fitting curve is reduced.
Fig. 7 is a hypocycloid integral pattern diagram using NURBS curve fitting obtained after rotation transformation, i.e., a schematic diagram of a third sampling mode in this embodiment, and fig. 8 is a partially enlarged schematic diagram of the hypocycloid integral pattern diagram using NURBS curve fitting of the third type of the present application, i.e., a partially enlarged schematic diagram of fig. 7, for more clarity.
And (3) verifying curve fitting accuracy errors:
the basic method of fitting error calculation between the fitting curve and the data points is to calculate the distance from the data points to the curve, the average distance and the maximum distance are main evaluation indexes, and in order to better compare the sizes of errors existing in various fitting methods, in this embodiment, two fitting curve error analysis methods referring to MATLAB tools are used for carrying out precision error analysis on the curve fitting result in the upper stage, and the two methods are sum variance and determination coefficients.
Wherein the sum of variances is denoted SSE:the statistical parameters calculate the sum of squares of errors of corresponding points of the fitting data and the original data, and when SSE is closer to 0, the model selection and fitting are better, and the data prediction is successful.
The determination coefficients are expressed as R-square:the present embodiment determines the change of the coefficient passing dataTo characterize the fit and determine the normal range of coefficients to be 0,1]The closer it is to 1, the stronger the interpretation of the variables of the equation to y, and the better this model fits the data.
Example 2
Referring to fig. 9, in this embodiment, the sampling manner of the output result of the interpolation spline curve is verified corresponding to three types (three types) of fitting accuracy errors, respectively. In fig. 9, the error 1 is the fitting precision error of the fitting curve obtained by the first sampling method, the error 2 is the fitting precision error of the fitting curve obtained by the second sampling method, the error 3 is the precision error of the fitting curve obtained by increasing the number of control points on the basis of the second sampling method, and in the three cases, the precision errors are basically in the same order of magnitude, which also reflects the correctness of the design method, but in the third case, the precision error is more uniform, the error reaches 0.1 micrometer, the determination coefficient R-square reaches 0.999, and the cycloid disc line can be more truly reproduced.
It should be noted that the above embodiments are only for illustrating the technical solution of the present application and not for limiting the same, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present application may be modified or substituted without departing from the spirit and scope of the technical solution of the present application, which is intended to be covered in the scope of the claims of the present application.
Claims (1)
1. A molded line representation method of a steel ball speed reducer wire arranging disc is characterized by comprising the following steps of: comprises the steps of,
obtaining a cycloid disc data model;
determining a node vector of a line-placing disc type line data point according to the data model;
reversely obtaining a control vertex of the NURBS interpolation curve by using a node vector of the data point;
obtaining an interpolation spline curve output result;
verifying curve fitting accuracy errors;
the cycloid disc data model acquisition comprises the following steps of knowing design parameters of a cycloid disc molded line in a speed reducer;
inputting the design parameters into a parameter equation to obtain the inner cycloid disc molded line of the speed reducer;
discretizing and sampling cycloid disc molded lines to obtain a data model;
the parameter equation is a representation equation of the wobble plate, and is as follows:
the hypocycloid equation is:
the epicycloidal equation is:
wherein ds is the diameter of a steel ball distribution circle, and the calculation formula is as follows: d, d s ＝r d /sin (180/nh), and r d The radius of the steel ball, the theta is the angle of the base circle rolled when the non-core rolling circle rolls on the base circle, c is half of the eccentric distance, n b The number of the steel balls is the number;
the integrated chord length parameter method is adopted to carry out unified parameterization on the data points of the molded lines of the data model, and the method also comprises the following steps,
let L be the total length of the curve,let u 0 ＝0，u n =1; then->
Back-computing the control vertex of the NURBS curve from said node vector determined by the model value point on the curve, comprising the steps of,
reversely calculating a control vertex by taking the model value point as the data point;
firstly taking the weight factors of all the control vertexes as 1, and adjusting the curve according to the weight factors corresponding to the control vertexes after obtaining the corresponding control vertexes;
the cubic non-uniform B-spline curve equation for interpolating n+1 data points is:
will Q i Substituting the corresponding node value into the above formula to obtain a linear equation set consisting of n+1 vector equations, wherein the equation is as follows:
two additional equations given by boundary conditions are additionally complemented:
C 0 '，C n ' is the tangent vector at the end point, resulting in the following system of equations:
wherein,
the interpolation spline curve output result comprises the following sampling modes, wherein the first type is a result obtained by taking any section of waveform on a cycloid disc line as an example for uniform sampling; the second class takes half of waveforms at any two ends of a cycloid disc line as an example to uniformly sample the obtained result; taking half waveforms at any two ends of a cycloid disc line as an example to uniformly sample and increase the number of control points;
the fitting accuracy error verification includes the steps of,
calculating the distance of the data point to the curve, including calculating an average distance and a maximum distance;
performing accuracy error analysis on curve fitting results by two fitting curve error analysis methods referring to MATLAB tools, wherein the accuracy error analysis comprises calculation, variance and determination coefficients;
wherein the sum variance is SSE:the method calculates the square sum of errors of corresponding points of the fitting data and the original data, and when SSE is closer to 0, the model selection and fitting are better, and the data prediction is successful;
the determination coefficient is R-square:it features that a fitting is performed by the variation of data, and the normal range of coefficient is 0,1]When the model is closer to 1, the interpretation capability of the variable of the equation to y is stronger, and the model is better in fitting the data;
the sampling mode of the interpolation spline curve output result is respectively corresponding to three fitting precision errors for verification;
the first type is a fitting precision error of a fitting curve obtained by taking any section of waveform on a cycloid disc line as an example to uniformly sample the first sampling method; the second type is a fitting precision error of a fitting curve obtained by taking half waveforms at any two ends of a cycloid disc line as an example for uniform sampling; the third class is to take half of waveforms at any two ends of the cycloid disc line as examples for uniform sampling and increase the accuracy error of the fitting curve obtained by the number of control points; wherein the third class of errors reaches 0.1 microns and the determined coefficient reaches 0.999.
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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 |
| 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 |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
-
2019
- 2019-05-31 CN CN201910469105.4A patent/CN110377932B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
Non-Patent Citations (3)
| Title |
|---|
| 基于NURBS的双螺杆转子型线正反构型的研究;施国江;《中国优秀硕士学位论文全文数据库》;20190131;第8-81页 * |
| 施国江.基于NURBS的双螺杆转子型线正反构型的研究.《中国优秀硕士学位论文全文数据库》.2019,第8-81页. * |
| 面向有限测点的弯扭叶片曲线/曲面重构方法研究;吴佳露;《中国优秀硕士学位论文全文数据库》;20170228;第26-33页 * |
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