CN103778339A - Method for forecasting abrasion life of honing processing honing strip - Google Patents

Abstract

The invention relates to a method for forecasting abrasion life of a honing processing honing strip. The method comprises the following steps of firstly collecting measured abrasion numerical values of the honing strip in different honing processing times, accumulating a time series of the abrasion numerical values, obtaining a new series, establishing a whitening-form differential equation of a GM (Gray Model) (1, 1), obtaining a data array B of the GM (1, 1), further obtaining a parameter vector (img file='DDA0000462533150000011.TIF' wi='33' he='60'/) by utilizing the least square method according to the data array B and a data vector YN, and finally obtaining a time response function and a time series form of abrasion of the honing processing honing strip according to the whitening-form differential equation of the GM, wherein an abrasion critical value of the honing processing honing strip can be supposed, the honing processing honing strip needs to be replaced when an abrasion value of the honing processing honing strip is larger than the abrasion critical value, and the abrasion life of the honing processing honing strip can be obtained by substituting the abrasion critical value into the time response function of the honing processing honing strip. According to the method disclosed by the invention, the forecasting on the abrasion life of the honing processing honing strip can be realized, and thus the honing processing accuracy and the surface smoothness can be ensured.

Description

Hone processing hone bar wear-out life Forecasting Methodology

Technical field

What the present invention relates to is the hone stone wear-out life Forecasting Methodology of the field of machining in a kind of mechanical engineering, specifically a kind of honing processing hone stone wear-out life Forecasting Methodology.

Background technology

Along with the gentle car industrial expansion of space flight and aviation, the endoporus machining precision to precision pair and the requirement of surface smoothness are more and more higher, and 1) circularity: 0.4 μ m, 2) linearity: 1 μ m, 3) surfaceness: in Ra0.04 μ m.To fulfill this requirement, must adopt honing processing, and therefore hone stone wear-out life particularly important to machining precision and the surface smoothness of honing processing, guarantee good honing machining precision and surface smoothness, must process hone stone wear-out life to honing and predict that this gordian technique carries out innovative research.

Do not find by prior art documents the report of relevant honing processing hone stone wear-out life Forecasting Methodology.Therefore be necessary that research invention can guarantee the honing processing hone stone wear-out life Forecasting Methodology of good honing machining precision and surface smoothness.

Summary of the invention

The technical scheme that the present invention adopted is for achieving the above object: honing processing hone stone wear-out life Forecasting Methodology, first gather and measure not hone stone wearing and tearing numerical value in the same time of honing processing, and this wearing and tearing numerical value time series is carried out to one-accumulate, obtain a new ordered series of numbers; Then, to this new ordered series of numbers, set up the differential equation of GM (1,1) gray model albefaction form, try to achieve the data matrix B of GM (1,1) model; Further according to data matrix B and data vector Y _n, adopt least square method can obtain parameter vector

finally, by the differential equation of gray model albefaction form, the time response function that can process hone stone wearing and tearing in the hope of honing is with sequence form at that time, suppose the wearing and tearing critical value of honing processing hone stone, in the time that the attrition value of honing processing hone stone is greater than this critical value, honing processing hone stone will be changed, and the time response function of wearing and tearing critical value substitution honing processing hone stone wearing and tearing just can be obtained to honing processing hone stone wear-out life.

Described honing processing hone stone wearing and tearing numerical value time series is:

VB ⁽⁰⁾=(VB ⁽⁰⁾(1),VB ⁽⁰⁾(2).......VB ⁽⁰⁾(m))

After its one-accumulate, obtain a new ordered series of numbers and be:

VB ⁽¹⁾=(VB ⁽¹⁾(1),VB ⁽¹⁾(2).......VB ⁽¹⁾(m))。

The formula that described one-accumulate utilizes is:

${\mathrm{VB}}^{\left(1\right)}\left(k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{\mathrm{VB}}^{\left(1\right)}\left(i\right),i=\mathrm{1,2}.....m.$

The described described differential equation of setting up GM (1,1) gray model albefaction form is:

$\frac{{\mathrm{dVB}}^{\left(1\right)}}{\mathrm{dt}}+{\mathrm{AVB}}^{\left(1\right)}=\mathrm{\θ}.$

The formula that the data matrix B of the differential equation of calculating albefaction form utilizes is:

$B=\left[\begin{array}{cc}-\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(1\right)+{\mathrm{VB}}^{\left(1\right)}\left(2\right)]& 1\\ -\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(3\right)+{\mathrm{VB}}^{\left(1\right)}\left(4\right)& 1\\ \·& \\ \·& \\ \·& \\ -\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(m\right)+{\mathrm{VB}}^{\left(1\right)}(m+1)]& 1\end{array}\right].$

The data vector Y of described GM (1,1) model _nfor:

Y _N=[VB ⁽⁰⁾(2),VB ⁽⁰⁾(3),.....VB ⁽⁰⁾(m)] ^T。

Described described employing least square method is asked parameter vector

the formula utilizing is respectively:

$\widehat{\mathrm{\α}}={\left[B^{T}B\right]}^{-1}{B}^T{Y}_N.$

From the differential equation of gray model albefaction form, the time response function of the honing processing hone stone wearing and tearing of trying to achieve is:

$\hat{V}{B}^{\left(1\right)}\left(t\right)=[{\mathrm{VB}}^{\left(1\right)}\left(0\right)-\frac{\mathrm{\θ}}{a}]e^{-\mathrm{at}}+\frac{\mathrm{\θ}}{a}.$

The time series form of the time response function of described honing processing hone stone wearing and tearing is:

$\hat{V}{B}^{\left(1\right)}(i+1)=[{\mathrm{VB}}^{\left(1\right)}\left(0\right)-\frac{\mathrm{\θ}}{a}]e^{-\mathrm{ai}}+\frac{\mathrm{\θ}}{a}.$

Feature of the present invention: utilize GM (1,1) whitening approach of grey forecasting model, the wearing and tearing of prediction honing processing hone stone, compared with method in the past, precision of prediction, can save human and material resources, be specially adapted to the prediction of honing processing hone stone wear-out life.

Embodiment

Below in conjunction with embodiment, the present invention is described in further detail, but is not limited to concrete embodiment.

Honing processing hone stone wear-out life Forecasting Methodology, concrete implementation step is as follows:

(1) gathering the honing processing hone stone wearing-in period sequence having measured is:

VB ⁽⁰⁾=(VB ⁽⁰⁾(1),VB ⁽⁰⁾(2).......VB ⁽⁰⁾(m))

(2) this ordered series of numbers is carried out to one-accumulate, obtains a new ordered series of numbers:

VB ⁽¹⁾=(VB ⁽¹⁾(1),VB ⁽¹⁾(2).......VB ⁽¹⁾(m))

Wherein, ${\mathrm{VB}}^{\left(1\right)}\left(k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{\mathrm{VB}}^{\left(1\right)}\left(i\right),i=\mathrm{1,2}.....m.$

(3) to VB ⁽¹⁾, the differential equation of setting up GM (1,1) gray model albefaction form is:

$\frac{{\mathrm{dVB}}^{\left(1\right)}}{\mathrm{dt}}+{\mathrm{AVB}}^{\left(1\right)}=\mathrm{\θ}$

In formula: A, θ-parameter to be identified.VB ⁽¹⁾-raw data one-accumulate generates.

(4), by after original data processing, obtain the data matrix B of GM (1,1) model:

$B=\left[\begin{array}{cc}-\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(1\right)+{\mathrm{VB}}^{\left(1\right)}\left(2\right)]& 1\\ -\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(3\right)+{\mathrm{VB}}^{\left(1\right)}\left(4\right)& 1\\ \·& \\ \·& \\ \·& \\ -\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(m\right)+{\mathrm{VB}}^{\left(1\right)}(m+1)]& 1\end{array}\right].$

(5) based on least square method, can be in the hope of parameter vector

$\widehat{\mathrm{\α}}={\left[B^{T}B\right]}^{-1}{B}^T{Y}_N$

In formula: $\widehat{\mathrm{\α}}=\left[\begin{array}{c}a\\ \mathrm{\θ}\end{array}\right]$

Wherein, Y _ndata vector for GM (1,1) model:

Y _N=[VB ⁽⁰⁾(2),VB ⁽⁰⁾(3),.....VB ⁽⁰⁾(m)] ^T。

(6) after parameter a, θ determine, set up the differential equation of GM (1,1) gray model albefaction form, can obtain its time response function:

$\hat{V}{B}^{\left(1\right)}\left(t\right)=[{\mathrm{VB}}^{\left(1\right)}\left(0\right)-\frac{\mathrm{\θ}}{a}]e^{-\mathrm{at}}+\frac{\mathrm{\θ}}{a}.$

(7) for response function service time easily, conventionally it is become to time series form:

$\hat{V}{B}^{\left(1\right)}(i+1)=[{\mathrm{VB}}^{\left(1\right)}\left(0\right)-\frac{\mathrm{\θ}}{a}]e^{-\mathrm{ai}}+\frac{\mathrm{\θ}}{a}$

In formula: i=2,3......n.

(8), based on above formula, can try to achieve the honing hone stone wear extent in processing i moment:

$\hat{V}{B}^{\left(0\right)}\left(i\right)=\hat{V}{B}^{\left(1\right)}\left(i\right)-\hat{V}{B}^{\left(1\right)}(i-1)$

In formula: i=2,3......n.

(9) supposition honing processing hone stone wear extent reaches VB _cas honing processing hone stone wearing and tearing critical value, when

time, mill processing hone stone will be changed, VB _csubstitution wear extent time series, just can obtain honing processing hone stone wear-out life.

Feature of the present invention: utilize GM (1,1) whitening approach of grey forecasting model, the wearing and tearing of prediction honing processing hone stone, compared with method in the past, precision of prediction, can save human and material resources, be specially adapted to the prediction of honing processing hone stone wear-out life.

Claims (9)

1. honing processing hone stone wear-out life Forecasting Methodology, is characterized in that: first gather and measure not hone stone wearing and tearing numerical value in the same time of honing processing, and this wearing and tearing numerical value time series is carried out to one-accumulate, obtain a new ordered series of numbers; Then, to this new ordered series of numbers, set up the differential equation of GM (1,1) gray model albefaction form, try to achieve the data matrix B of GM (1,1) model; Further according to data matrix B and data vector Y _n, adopt least square method can obtain parameter vector finally, by the differential equation of gray model albefaction form, the time response function that can process hone stone wearing and tearing in the hope of honing is with sequence form at that time, suppose the wearing and tearing critical value of honing processing hone stone, in the time that the attrition value of honing processing hone stone is greater than this critical value, honing processing hone stone will be changed, and the time response function of wearing and tearing critical value substitution honing processing hone stone wearing and tearing just can be obtained to honing processing hone stone wear-out life.

2. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, described honing processing hone stone wearing and tearing numerical value time series is:

VB ⁽⁰⁾=(VB ⁽⁰⁾(1),VB ⁽⁰⁾(2).......VB ⁽⁰⁾(m))

After its one-accumulate, obtain a new ordered series of numbers and be:

VB ⁽¹⁾=(VB ⁽¹⁾(1),VB ⁽¹⁾(2).......VB ⁽¹⁾(m))。

3. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, the formula that described one-accumulate utilizes is:

${\mathrm{VB}}^{\left(1\right)}\left(k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{\mathrm{VB}}^{\left(1\right)}\left(i\right),i=\mathrm{1,2}.....m.$

4. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, the described described differential equation of setting up GM (1,1) gray model albefaction form is:

$\frac{{\mathrm{dVB}}^{\left(1\right)}}{\mathrm{dt}}+{\mathrm{AVB}}^{\left(1\right)}=\mathrm{\θ}.$

5. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, the formula that the data matrix B of the differential equation of calculating albefaction form utilizes is:

$B=\left[\begin{array}{cc}-\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(1\right)+{\mathrm{VB}}^{\left(1\right)}\left(2\right)]& 1\\ -\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(3\right)+{\mathrm{VB}}^{\left(1\right)}\left(4\right)& 1\\ \·& \\ \·& \\ \·& \\ -\frac{1}{2}[{\mathrm{VB}}^{\left(1\right)}\left(m\right)+{\mathrm{VB}}^{\left(1\right)}(m+1)]& 1\end{array}\right].$

6. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that the data vector Y of described GM (1,1) model _nfor:

Y _N=[VB ⁽⁰⁾(2),VB ⁽⁰⁾(3),.....VB ⁽⁰⁾(m)] ^T。

7. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, described described employing least square method is asked parameter vector

the formula utilizing is respectively:

$\widehat{\mathrm{\α}}={\left[B^{T}B\right]}^{-1}{B}^T{Y}_N.$

8. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, from the differential equation of gray model albefaction form, the time response function of the honing processing hone stone wearing and tearing of trying to achieve is:

$\hat{V}{B}^{\left(1\right)}\left(t\right)=[{\mathrm{VB}}^{\left(1\right)}\left(0\right)-\frac{\mathrm{\θ}}{a}]e^{-\mathrm{at}}+\frac{\mathrm{\θ}}{a}.$

9. honing processing hone stone wear-out life Forecasting Methodology according to claim 1, is characterized in that, the time series form of the time response function of described honing processing hone stone wearing and tearing is:

$\hat{V}{B}^{\left(1\right)}(i+1)=[{\mathrm{VB}}^{\left(1\right)}\left(0\right)-\frac{\mathrm{\θ}}{a}]e^{-\mathrm{ai}}+\frac{\mathrm{\θ}}{a}.$