CN103268378B - A kind of globoid cam curve movement discrimination method based on multistage correlation analysis - Google Patents

Abstract

The invention discloses a kind of globoid cam curve movement discrimination method based on multistage correlation analysis: the identification of (1) globoid cam curve movement; (2) the globoid cam motion pick data obtained carried out to correlation analysis and simulated actual motion curve, and then determining the similarity of globoid cam actual motion curve and the desirable characteristics of motion; (3) multistage correlation analysis, for carrying out multistage correlation analysis to the globoid cam motion pick data obtained, carry out the correlation analysis of the first order derivative of the globoid cam characteristics of motion, second derivative and pluriderivative and the desirable characteristics of motion, obtain globoid cam actual motion curve in the position of globoid cam, the related coefficient of speed and acceleration and similar morphology classification thereof, finally pick out globoid cam actual motion curve.The present invention is not only conducive to the positional precision improving mechanical motion mechanism in machinery industry, and is conducive to the speed and the acceleration precision that improve mechanical motion mechanism, and then improves robust motion.

Description

A kind of globoid cam curve movement discrimination method based on multistage correlation analysis

Technical field

The invention belongs to the design field of the process globoid cam characteristics of motion, relate to a kind of globoid cam curve movement discrimination method based on multistage correlation analysis.

Background technology

At mechanical engineering field, globoid cam is one of vital part realizing mechanical motion, its curve movement is the basis ensureing globoid cam kinematic accuracy and stationarity, and therefore, each globoid cam manufacturing enterprise and researcher are to this has been a large amount of theoretical researches and test.

The identification of globoid cam curve movement mainly carries out reverse to the characteristics of motion of globoid cam, obtains the mathematical expression of the characteristics of motion.But existing data fitting and curvilinear correlation analysis and research all concentrate on once fitting or the correlation analysis aspect of various curve, existing discrimination method adopts least square method directly to carry out curve fitting, the matched curve that such matching obtains is all very relevant with multi-motion curve, related coefficient, all close to 1, cannot be distinguished.Therefore, in order to avoid impacting, in the face of the design of globoid cam, need a kind of discrimination method of new curve movement, thus make globoid cam structure motion ground more steady.In the face of the processing of globoid cam, need a kind of discrimination method of curve movement, analyze the characteristics of motion of existing globoid cam, the kinematic error of the globoid cam that inspection manufactures.

Summary of the invention

The object of the present invention is to provide a kind of globoid cam curve movement discrimination method based on multistage correlation analysis.

For achieving the above object, present invention employs following technical scheme:

(1) least square fitting of globoid cam curve movement: to the globoid cam exercise data collected, adopts least square method to carry out curve fitting, obtains the actual motion curve of globoid cam;

(2) correlation analysis: according to actual motion curve and the desirable globoid cam curve movement of globoid cam, the correlation analysis carrying out the globoid cam characteristics of motion obtains related coefficient;

(3) identifying of the actual motion curve of globoid cam is completed according to the difference of related coefficient.

Described step (1) comprises following idiographic flow:

1. the actual motion curve supposing certain globoid cam comprises n collection point, then the actual motion curve of this globoid cam is expressed as C={y _t=f _c(x _t), t=1,2,3 ..., n; Desirable globoid cam curve movement is expressed as P _k={ y _kt=f _k(x _t), t=1,2,3 ..., n; K=1,2,3 ..., K, K are desirable globoid cam curve movement kind sum;

2. the polynomial fitting defining actual motion curve is:

f _C(x)=α ₀g ₀(x)+α ₁g ₁(x)+α ₂g ₂(x)+...α _mg _m(x)(1)

In formula (1), g _j(x)=x ^j, j=0,1,2 ..., m; M represents the exponent number of polynomial fitting;

3. by the actual motion curve collection point of globoid cam and the polynomial fitting error of calculation quadratic sum of actual motion curve:

$S_C=\underset{t=1}{\overset{n}{\begin{array}{c}\mathrm{\Σ}\end{array}}}{(y_t-f_c\left(x_t\right))}^2\→\min ---\left(2\right)$

4. then local derviation is asked:

$\frac{\∂S_C}{\∂{\mathrm{\α}}_j}=0,j=\mathrm{0,1,2,3},...m---\left(3\right)$

Definition:

$A_{\mathrm{ij}}=\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{x}_t^{i+j},i=\mathrm{0,1,2},...,m;j=\mathrm{0,1},...m;---\left(4\right)$

$b_j=\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{y}_t\×x_t^j,j=\mathrm{0,1,2},...,m---\left(5\right)$

So have:

$\left[\begin{array}{cccc}{A}_{00}& A_{01}& ...& A_{0m}\\ A_{10}& & ...& A_{1m}\\ ...& ...& ...& ...\\ A_{m0}& A_{m1}& ...& A_{\mathrm{mm}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\α}}_0\\ {\mathrm{\α}}_1\\ ...\\ {\mathrm{\α}}_m\end{array}\right]=\left[\begin{array}{c}{b}_0\\ b_1\\ ...\\ b_m\end{array}\right]---\left(6\right)$

The factor alpha of polynomial fitting is obtained by solution formula (6) _j, by factor alpha _jcorrespondence brings the actual motion curvilinear equation that polynomial fitting obtains globoid cam into.

The correlation analysis of the described globoid cam characteristics of motion comprises the actual motion curve of globoid cam and the multistage correlation analysis of desirable globoid cam curve movement, described multistage correlation analysis comprises the actual motion curve of globoid cam and the desirable first order derivative of globoid cam curve movement or the correlation analysis of second derivative, and described related coefficient is the related coefficient of the globoid cam speed corresponding with correlation analysis or the related coefficient of globoid cam acceleration.

The correlation analysis of the described globoid cam characteristics of motion is further comprising the steps of: before multistage correlation analysis, the actual motion curve of globoid cam and desirable globoid cam curve movement is carried out correlation analysis, obtains related coefficient γ _xy.

Actual motion curve and the desirable globoid cam curve movement of described globoid cam carry out correlation analysis, comprise following idiographic flow:

Related coefficient γ is calculated by actual motion curve collection point and ideal movements curve point _xy:

${\mathrm{\γ}}_{\mathrm{xy}}=\frac{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}{y}_{\mathrm{ki}}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}}{\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_{\mathrm{ci}}}^2-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_{\mathrm{ki}}}^2-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}\right)}^2}}---\left(8\right)$

Wherein, y _cicorresponding x on the actual motion curve of expression matching _ivalue, y _kirepresent corresponding x on desirable globoid cam curve movement k _ivalue, n represents collection point number.

Described desirable globoid cam curve movement comprises cosine curve, sinusoidal curve, quintic algebra curve curve, revises curve of equal velocity, modified trapezoid curve and modified sinusoid, and described related coefficient is the related coefficient of globoid cam acceleration.

Described step (2) comprises following idiographic flow:

As the related coefficient γ of the actual motion curve of the desirable globoid cam curve movement of K kind and globoid cam _xy≈ 1, illustrate the actual motion curve of globoid cam and the desirable globoid cam curve movement of K kind very high at the similarity degree of position curve, need to carry out first order derivative or second derivative correlation analysis;

Related coefficient is calculated, if the related coefficient γ ' of actual motion rate curve and ideal movements rate curve by actual motion curve collection point and ideal movements curve point _xythe Speed attribute of the actual motion curve of globoid cam can't be distinguished, then carry out the related coefficient γ of second order differentiate and calculating acceleration " _xy, until the actual movement rule of identification out globoid cam:

${\mathrm{\γ}}_{\mathrm{xy}}^{\′}=\frac{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′}{y}_{\mathrm{ki}}^{\′}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′}}{\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′}\right)}^2}}---\left(11\right)$

${\mathrm{\γ}}_{\mathrm{xy}}^{\′\′}=\frac{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′}{y}_{\mathrm{ki}}^{\′\′}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′\′}}{\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′\′}\right)}^2}}---\left(12\right)$

Wherein, y ' _kirepresent corresponding x in desirable globoid cam curve movement k first order derivative _ivalue, y ' _cicorresponding x in the actual motion curve first order derivative of expression matching _ivalue, y " _cicorresponding x in the actual motion curve second derivative of expression matching _ivalue, y " _kirepresent corresponding x in desirable globoid cam curve movement k second derivative _ivalue, n represents collection point number.

Compared with prior art, its advantage is in the present invention:

1) the present invention is that the identification of globoid cam curve movement provides complete reference solution and control flow clearly.

2) the present invention proposes a kind of globoid cam curve movement discrimination method based on multistage correlation analysis, and be applied to the identification of globoid cam curve movement first.The identification of globoid cam actual motion curve comprises: the 1. data acquisition of globoid cam actual motion curve; 2. the correlation analysis of globoid cam actual motion curve data; 3. globoid cam actual motion curve is in the correlation analysis of first order derivative, second derivative and more higher derivative.

3) the present invention is not only conducive to the positional precision improving mechanical motion mechanism in machinery industry, and is conducive to the speed and the acceleration precision that improve mechanical motion mechanism, and then improves the stationarity of mechanical motion.

Accompanying drawing explanation

Fig. 1 is modificatory sine motion curve; Wherein, the displacement curve that (a) is modificatory sine motion, the rate curve that (b) is modificatory sine motion, the accelerating curve that (c) is modificatory sine motion, the acceleration change curve that (d) is modificatory sine motion;

Fig. 2 is acceleration theoretical curve and matched curve figure; Wherein, solid line is actual acceleration curve, a in (), dotted line is for revising constant speed acceleration theoretical curve, b in (), dotted line is modified trapezoid acceleration theoretical curve, c in (), dotted line is for revising sinusoidal acceleration theoretical curve, d in (), dotted line is cosine acceleration theoretical curve, in (e), dotted line is quintic algebra curve acceleration theoretical curve, and in (f), dotted line is sinusoidal acceleration theoretical curve;

Fig. 3 is displacement curve identification program FB(flow block).

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described:

Based on a globoid cam curve movement discrimination method for multistage correlation analysis, comprise three steps: the least square fitting of globoid cam curve movement, the correlation analysis of globoid cam actual motion curve data and multistage correlation analysis.

The least square fitting of step (1) globoid cam curve movement

In order to the actual movement rule with identification globoid cam can be identified, the machining precision of further raising globoid cam, by carrying out data acquisition to the actual motion curve of globoid cam, on this basis, carry out least square curve fitting, obtain the mathematical expression of the actual movement rule of globoid cam.Therefore, in globoid cam curve movement identification process, after collecting globoid cam exercise data, adopt least square method to carry out curve fitting, obtain actual motion curve; Specifically comprise the following steps:

1. suppose certain globoid cam actual motion curve comprises n collection point, then this globoid cam actual motion curve is expressed as C={y _t=f _c(x _t) (t=1,2,3 ..., n); Desirable globoid cam curve movement is expressed as P _k={ y _kt=f _k(x _t) (t=1,2,3 ..., n; K=1,2,3 ..., K), wherein: K is the ideal movements curve kind sum that globoid cam may occur, has P _k={ P ₁, P ₂... P _kplant; P _k={ y _kt=f _k(x _t) represent t point on kth kind ideal movements curve;

2. the polynomial fitting defining actual motion curve is:

f _C(x)=α ₀g ₀(x)+α ₁g ₁(x)+α ₂g ₂(x)+...α _mg _m(x)(1)

In reality, simple in order to calculate, generally define: g _j(x)=x ^jfor conventional power function.J=0,1,2 ..., m; M represents the exponent number of polynomial fitting, and exponent number is higher, and precision is higher, for mechanical motion, through conventional 5 ~ 10.

3. by actual motion curve collection point and polynomial fitting error of calculation quadratic sum:

$S_C=\underset{t=1}{\overset{n}{\begin{array}{c}\mathrm{\Σ}\end{array}}}{(y_t-f_c\left(x_t\right))}^2\→\min ---\left(2\right)$

This error sum of squares represents the departure degree of actual motion curve and polynomial fitting.

4. ask the local derviation of polynomial fitting and solve an equation, obtaining polynomial coefficient:

$\frac{\∂S_C}{\∂{\mathrm{\α}}_j}=0,j=\mathrm{0,1,2,3},...m---\left(3\right)$

Wherein, define:

$A_{\mathrm{ij}}=\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{x}_t^{i+j},i=\mathrm{0,1,2},...,m;j=\mathrm{0,1},...m;---\left(4\right)$

$b_j=\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{y}_t\×x_t^j,j=\mathrm{0,1,2},...,m---\left(5\right)$

So have:

$\left[\begin{array}{cccc}{A}_{00}& A_{01}& ...& A_{0m}\\ A_{10}& & ...& A_{1m}\\ ...& ...& ...& ...\\ A_{m0}& A_{m1}& ...& A_{\mathrm{mm}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\α}}_0\\ {\mathrm{\α}}_1\\ ...\\ {\mathrm{\α}}_m\end{array}\right]=\left[\begin{array}{c}{b}_0\\ b_1\\ ...\\ b_m\end{array}\right]---\left(6\right)$

So, just can obtain the actual motion curvilinear equation of globoid cam by solving this equation, and then the actual motion curvilinear correlation analysis of globoid cam can be carried out.

Step (2) correlation analysis

By calculating the actual motion curve of globoid cam and the related coefficient of desirable curve movement, carrying out the actual motion curve of globoid cam and the correlation analysis of desirable curve movement, specifically comprising:

1. by actual motion curve collection point and ideal movements curve point error of calculation quadratic sum:

$S_k=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_{\mathrm{ci}}-y_{\mathrm{ki}})}^2,k=\mathrm{1,2,3}...,K---\left(7\right)$

Above formula medial error quadratic sum is one of foundation distinguishing relative motion curve, and this error sum of squares represents the departure degree of actual motion curve and kth kind ideal movements curve, can be used in combination with normalized related coefficient.

2. related coefficient is calculated by actual motion curve collection point and ideal movements curve point:

${\mathrm{\γ}}_{\mathrm{xy}}=\frac{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}{y}_{\mathrm{ki}}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}}{\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_{\mathrm{ci}}}^2-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y_{\mathrm{ki}}}^2-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}\right)}^2}}---\left(8\right)$

This related coefficient represents the similarity degree of actual motion curve and kth kind ideal movements curve.Wherein, y _cicorresponding x on the actual motion curve of expression matching _ivalue, y _kirepresent corresponding x on ideal movements curve k _ivalue, n represents collection point number.

Step (3) multistage correlation analysis

On the closely related basis of globoid cam actual motion curve and the desirable characteristics of motion, carry out the correlation analysis of the first order derivative of the globoid cam characteristics of motion, second derivative and more higher derivative, obtain globoid cam actual motion curve in the related coefficient of globoid cam speed, acceleration etc. and similar morphology classification thereof, complete the identifying of globoid cam actual motion curve, specifically comprise:

1. as the related coefficient γ of K kind ideal movements curve and actual motion curve _cP≈ 1, illustrate actual motion curve and K kind ideal movements curve very high at the similarity degree of position curve, need to carry out the correlation analysis of first order derivative, second derivative and more higher derivative.

2. actual motion curve and K kind ideal movements curve are carried out differentiate respectively, calculate actual motion curve and the single order of K kind ideal movements curve and the Derivative Error quadratic sum of second order:

$S_k^{\′}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_{\mathrm{ci}}^{\′}-y_{\mathrm{ki}}^{\′})}^2,---\left(9\right)$

$S_k^{\′\′}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(y_{\mathrm{ci}}^{\′\′}-y_{\mathrm{ki}}^{\′\′})}^2,---\left(10\right)$

k=1,2,3…,K；

Above formula medial error quadratic sum be distinguish relative motion curve according to one of, represent the degree that actual curve and ideal curve depart from, be used in combination with normalized related coefficient.For mechanical motion mechanism, the error sum of squares of this first order derivative represents the speed deviations degree of actual motion curve and ideal movements curve, and the error sum of squares of second derivative represents the acceleration of globoid cam and the acceleration offset degree of ideal movements.

3. related coefficient is calculated by actual motion curve collection point and ideal movements curve point, if the related coefficient of actual motion rate curve and ideal movements rate curve can't distinguish the Speed attribute of the actual motion curve of globoid cam, then repeat second order differentiate and calculate the related coefficient of acceleration, until the actual movement rule of identification out globoid cam:

${\mathrm{\γ}}_{\mathrm{xy}}^{\′}=\frac{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′}{y}_{\mathrm{ki}}^{\′}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′}}{\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′}\right)}^2}}---\left(11\right)$

${\mathrm{\γ}}_{\mathrm{xy}}^{\′\′}=\frac{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′}{y}_{\mathrm{ki}}^{\′\′}-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′}\·\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′\′}}{\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ci}}^{\′\′}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′\′2}-{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{y}_{\mathrm{ki}}^{\′\′}\right)}^2}}---\left(12\right)$

Wherein, y ' _kirepresent corresponding x in ideal movements curve k first order derivative _ivalue, y ' _cicorresponding x in the actual motion curve first order derivative of expression matching _ivalue, y " _cicorresponding x in the actual motion curve second derivative of expression matching _ivalue, y " _kirepresent corresponding x in ideal movements curve k second derivative _ivalue.

Based on the globoid cam curve movement discrimination method application example of multistage correlation analysis

Conventional globoid cam curve movement has: six kinds of versions such as cosine accelerating curve, sinusoidal acceleration curve, quintic algebra curve curve, correction curve of equal velocity, modified trapezoid curve and modified sinusoid.Wherein, the displacement curve (0 rank) of modified sinusoid, rate curve (1 rank), accelerating curve (2 rank) and acceleration change curve (3 rank) is illustrated in figure 1.

The identification of these curve movements mainly carries out reverse to the characteristics of motion of globoid cam, obtains the mathematical expression of the characteristics of motion.Therefore, in order to verify correctness of the present invention, carrying out the data acquisition of actual arc face cam, obtaining the data of one group of globoid cam.

1) least square fitting of globoid cam curve movement

Carry out least square fitting according to above-mentioned steps (1), the actual motion curve polynomial expression obtaining globoid cam is:

p(x)=91.4645×x ¹⁰-448.3554×x ⁹+934.9087×x ⁸-1.078×10 ³×x ⁷

+746.8583×x ⁶-312.223×x ⁵+70.0229×x ⁴-5.7668×x ³+2.156×x ²

-0.1052×x ¹+0.0011

2) correlation analysis

Carry out correlation analysis according to above-mentioned steps (2), the related coefficient obtaining the actual motion curve of globoid cam and ideal movements curve is as shown in table 1:

Table 1matlab program runs displacement curve six kinds of errors and related coefficient of obtaining

Theoretical curve

Cosine

Sinusoidal

Quintic algebra curve

Revise constant speed

Modified trapezoid

Revise sinusoidal

Displacement error

2.151×10 -7

8.687×10 -8

8.1775×10 -8

5.9926×10 -6

3.0269×10 -6

4.8481×10 -9

Related coefficient

1

1

1

1

1

1

3) multistage correlation analysis

Shown in above table 1, because the actual motion curve of globoid cam and the related coefficient of ideal movements curve all equal 1, this globoid cam curve movement and six kinds of ideal movements curves all strong correlations are described, therefore, need to carry out multistage correlation analysis further, carry out multistage correlation analysis according to above-mentioned steps (3), the related coefficient obtaining the actual motion curve of globoid cam and the second derivative of ideal movements curve is as shown in table 2:

Table 2matlab program runs accelerating curve six kinds of errors and related coefficient of obtaining

4) effect

Identification effect as shown in Figure 2, the result that the accelerating curve of actual cam and six kinds of theoretical acceleration curves are compared, wherein solid line is actual acceleration curve, dotted line is various theoretical acceleration curves, can find out, actual acceleration curve only and in Fig. 2 c accelerating curve overlapped, all the other are not overlapping.Visible, when carrying out identification to the characteristics of motion of globoid cam, because the displacement law of various cam is extremely similar, and acceleration law has very big difference, and it is more directly perceived to carry out identification with accelerating curve to globoid cam curve movement, therefore, through correlation analysis and figure display, actual globoid cam curve is for revising cam curve, and its program flow diagram as shown in Figure 3.

Modified sinusoid is improving cosine curve, it had both overcome the discontinuous shortcoming of cosine curve, remain again maximal rate and the less advantage of peak acceleration, the balance of this curve is fabulous, use dangerous least in the unclear situation of load character, and there is good absorbing, can easy motion be realized.Modified sinusoid is applied to the heavy duty beyond high-speed motion, has special superiority.

For globoid cam curve movement, prior art only carries out the matching of position curve movement, and do not consider the curvilinear correlation analysis that the higher derivative such as the speed that curve is corresponding and acceleration is corresponding, for the mechanical motion mechanism that curve movement is corresponding, do not consider the correlation analysis result of speed continuity and flatness like this, the impact of motion can be brought to machinery.The result of above-mentioned application example demonstrates the accuracy of the proposed globoid cam curve movement discrimination method based on multistage correlation analysis, also demonstrates the feasibility and necessity that the globoid cam curve movement discrimination method based on multistage correlation analysis is implemented in globoid cam process.

Claims (4)

1., based on a globoid cam curve movement discrimination method for multistage correlation analysis, it is characterized in that, this discrimination method comprises the following steps:

(1) least square fitting of globoid cam curve movement: to the globoid cam exercise data collected, adopts least square method to carry out curve fitting, obtains the actual motion curve of globoid cam;

(2) correlation analysis: according to actual motion curve and the desirable globoid cam curve movement of globoid cam, the correlation analysis carrying out the globoid cam characteristics of motion obtains related coefficient;

Actual motion curve and the desirable globoid cam curve movement of globoid cam carry out correlation analysis, comprise following idiographic flow:

Related coefficient γ is calculated by actual motion curve collection point and ideal movements curve point _xy:

${\mathrm{\γ}}_{xy}=\frac{n\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}{y}_{ki}-\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}\·\underset{i=1}{\overset{n}{\Σ}}{y}_{ki}}{\sqrt{n\underset{i=1}{\overset{n}{\Σ}}{y_{ci}}^2-{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\Σ}}{y_{ki}}^2-{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_{ki}\right)}^2}}---\left(8\right)$

Wherein, y _cirepresent corresponding x on actual motion curve _ivalue, y _kirepresent corresponding x on desirable globoid cam curve movement k _ivalue, n represents collection point number;

As the related coefficient γ of the actual motion curve of the desirable globoid cam curve movement of K kind and globoid cam _xy≈ 1, illustrate the actual motion curve of globoid cam and the desirable globoid cam curve movement of K kind very high at the similarity degree of position curve, need to carry out first order derivative or second derivative correlation analysis;

Related coefficient is calculated, if the related coefficient γ ' of actual motion rate curve and ideal movements rate curve by actual motion curve collection point and ideal movements curve point _xythe Speed attribute of the actual motion curve of globoid cam can't be distinguished, then carry out the related coefficient γ of second order differentiate and calculating acceleration " _xy, until the actual movement rule of identification out globoid cam:

${\mathrm{\γ}}_{xy}^{\′}=\frac{n\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}^{\′}{y}_{ki}^{\′}-\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}^{\′}\·\underset{i=1}{\overset{n}{\Σ}}{y}_{ki}^{\′}}{\sqrt{n\underset{i=1}{\overset{n}{\Σ}}{y_{ci}^{\′}}^2-{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}^{\′}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\Σ}}{y_{ki}^{\′}}^2-{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_{ki}^{\′}\right)}^2}}---\left(11\right)$

${\mathrm{\γ}}_{xy}^{\′\′}=\frac{n\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}^{\′\′}{y}_{ki}^{\′\′}-\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}^{\′\′}\·\underset{i=1}{\overset{n}{\Σ}}{y}_{ki}^{\′\′}}{\sqrt{n\underset{i=1}{\overset{n}{\Σ}}{y_{ci}^{\′\′}}^2-{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_{ci}^{\′\′}\right)}^2}\·\sqrt{n\underset{i=1}{\overset{n}{\Σ}}{y_{ki}^{\′\′}}^2-{\left(\underset{i=1}{\overset{n}{\Σ}}{y}_{ki}^{\′\′}\right)}^2}}---\left(12\right)$

Wherein, y ' _kirepresent corresponding x in desirable globoid cam curve movement k first order derivative _ivalue, y ' _cirepresent corresponding x in actual motion curve first order derivative _ivalue, y " _cirepresent corresponding x in actual motion curve second derivative _ivalue, y " _kirepresent corresponding x in desirable globoid cam curve movement k second derivative _ivalue, n represents collection point number;

(3) identifying of the actual motion curve of globoid cam is completed according to the difference of related coefficient.

2. a kind of globoid cam curve movement discrimination method based on multistage correlation analysis according to claim 1, is characterized in that: described step (1) comprises following idiographic flow:

1. the actual motion curve supposing certain globoid cam comprises n collection point, then the actual motion curve of this globoid cam is expressed as C={y _t=f _c(x _t), t=1,2,3 ..., n; Desirable globoid cam curve movement is expressed as P _k={ y _kt=f _k(x _t), t=1,2,3 ..., n; K=1,2,3 ..., K, K are desirable globoid cam curve movement kind sum;

2. the polynomial fitting defining actual motion curve is:

f _C(x)＝α ₀g ₀(x)+α ₁g ₁(x)+α ₂g ₂(x)+...α _mg _m(x)(1)

In formula (1), g _j(x)=x ^j, j=0,1,2 ..., m; M represents the exponent number of polynomial fitting;

3. by the actual motion curve collection point of globoid cam and the polynomial fitting error of calculation quadratic sum of actual motion curve:

$S_C=\underset{t=1}{\overset{n}{\Σ}}{(y_t-f_c(x_t\left)\right)}^2\→min---\left(2\right)$

4. then local derviation is asked:

$\frac{\∂S_C}{\∂{\mathrm{\α}}_j}=0,j=0,1,2,3,...m---\left(3\right)$

Definition:

$A_{ij}=\underset{t=1}{\overset{n}{\Σ}}{x}_t^{i+j},i=0,1,2,...,m;j=0,1,...m;---\left(4\right)$

$b_j=\underset{t=1}{\overset{n}{\Σ}}{y}_t\×x_t^j,j=0,1,2,...,m---\left(5\right)$

So have:

$\left[\begin{array}{cccc}{A}_{00}& A_{01}& ...& A_{0m}\\ A_{10}& & ...& A_{1m}\\ ...& ...& ...& ...\\ A_{m0}& A_{m1}& ...& A_{mm}\end{array}\right]\left[\begin{array}{c}{\mathrm{\α}}_0\\ {\mathrm{\α}}_1\\ ...\\ {\mathrm{\α}}_m\end{array}\right]=\left[\begin{array}{c}{b}_0\\ b_1\\ ...\\ b_m\end{array}\right]---\left(6\right)$

The factor alpha of polynomial fitting is obtained by solution formula (6) _j, by factor alpha _jcorrespondence brings the actual motion curvilinear equation that polynomial fitting obtains globoid cam into.

3. a kind of globoid cam curve movement discrimination method based on multistage correlation analysis according to claim 1, it is characterized in that: described multistage correlation analysis comprises the actual motion curve of globoid cam and the desirable first order derivative of globoid cam curve movement or the correlation analysis of second derivative, and described related coefficient is the related coefficient of the globoid cam speed corresponding with correlation analysis or the related coefficient of globoid cam acceleration.

4. a kind of globoid cam curve movement discrimination method based on multistage correlation analysis according to claim 1, it is characterized in that: described desirable globoid cam curve movement comprises cosine curve, sinusoidal curve, quintic algebra curve curve, revises curve of equal velocity, modified trapezoid curve and modified sinusoid, and described related coefficient is the related coefficient of globoid cam acceleration.