WO2010029204A1

WO2010029204A1 - Method and system for detecting, in real time, the imbalance of the head in a high-precision rotary mechanism

Info

Publication number: WO2010029204A1
Application number: PCT/ES2009/070374
Authority: WO
Inventors: Raúl Mario DEL TORO MATAMOROS; Michael Charles Schmittdiel; Rodolfo Elias Haber Guerra
Original assignee: Consejo Superior De Investigaciones Científicas (Csic)
Priority date: 2008-09-15
Filing date: 2009-09-10
Publication date: 2010-03-18
Also published as: ES2337432B2; ES2337432A1; ES2337432B8

Abstract

The invention relates to a method for detecting, in real time, an imbalance of the head in a high-precision rotary mechanism, and to the system for carrying out said method. The method comprises the following steps: a) the signal X(t) corresponding to the acceleration of the vibrations of the head is acquired by means of an acquisition means at a sampling rate FS; and b) it is determined, from the signal X(t) obtained, whether the head is imbalanced.

Description

PROCEDURE AND SYSTEM FOR TIME DETECTION

HEAD UNBALANCING REAL IN A MECHANISM

HIGH PRECISION ROTARY

D E S C R I P C I Ó N

OBJECT OF THE INVENTION

The main object of the present invention is a method for detecting in real time an imbalance of the head in a high precision rotary mechanism, as well as the system for carrying out said procedure.

BACKGROUND OF THE INVENTION

It is known that small imbalances of the head of a rotary mechanism of high precision can lead to serious losses of quality in the result of the process in question.

For example, in the field of ultra-precision machining, sometimes the objective is to achieve surfaces with low roughness, suitable for applications where surface quality is a key factor. An unbalanced head produces vibrations that have a direct influence on the precision of the cut, and therefore on the quality of the surface finish. Therefore, the study of vibrations in machining processes is of great importance for the detection of anomalies.

The real-time machining monitoring is known in the art. In particular, documents US 4131837, US 5917726, US 6161055, US 6549869 and US 6947800 claim devices or methods for

Ia real-time monitoring of different variables or events in the conventional machining using different types of sensors, whether piezoelectric or opto-electronic. US Patent 7024063 also describes a method and apparatus for real-time monitoring of the operation of polishing layers of semiconductor wafers.

The vibrations in rotary elements of mechanical bearings, either in centrifugal machines or in conventional machine tools, have also been thoroughly studied, developing different methods and devices for their detection and subsequent analysis. In particular, patents US 3908444, EP 0011101, US 5537182, EP 1140405, US 6323943, US 6694213, US 7043376, US 7073384 and US 7386401 describe different methods for measuring or detecting vibrations in the axes of rotating machines using different sensors opto-electronic or piezoelectric.

US Patent 4432253 describes the design of a self-compensating system of mass imbalance for centrifugal heads and high speed lathes, among others, by means of the automatic injection of fluids in the shaft bearing system.

Also related to the imbalance of engine heads, the application US 2007/0263321 describes a system for controlling the mass imbalance in the head of the hard disk engine.

US 5356225 patent presents a system to control the air flow in hydrostatic bearings of mechanisms with a high level of rigidity, maintaining a low level of presence of vibrations.

Finally, for tasks of superficial finishing of optical lenses through ultra-precision machining, it has been developed in the US patent

5861114 a method for the automatic suppression of vibrations that are produced in the cutting tool. Patents US 7036408 and US 7178433 describe devices for milling or turning using diamond-tipped tools for the manufacture of optical lenses.

DESCRIPTION OF THE INVENTION

In this document, the term "high precision rotary mechanism" is intended to refer to all types of processes where there is a head that rotates at high speed, including for example rotary mechanisms with hydrostatic bearings. In particular, special reference is made to ultra-precision machining processes aimed at obtaining surface roughnesses in the nano-scale, and more particularly to diamond-tip turning and other similar processes.

Thus, by means of an intelligent monitoring of the balancing of the head of a rotating mechanism of high precision, it can be guaranteed that the rotation of the head is carried out in the ideal conditions and that balances that affect the quality of the process in question do not occur. .

A first aspect of the invention is directed to a method for the real-time detection of the imbalance of the head in a high precision rotary mechanism, where the head rotates at an RPM speed, which comprises the following operations:

a) Acquire, by means of acquisition at a sampling frequency FS, the signal X (t) corresponding to the acceleration of the spindle vibrations.

The X (t) signal is acquired using a suitable acquisition means, in particular an accelerometer connected to a card acquisition. The accelerometer is located in any radial line to the axis of rotation, preferably on the X axis of the head, since the closer it is to the head, the greater the power of the signal obtained, but always without interfering with the process in question.

b) Determine, from the signal X (t) obtained, if the spindle is unbalanced.

In this second operation, the data obtained in the previous operation are used to determine if the vibrations obtained are due to an imbalance of said spindle. To do this, the following operations are performed:

b1) Eliminate the DC component of the signal X (t) and apply a transformation to X (t) to pass the frequency domain, obtaining the transformed T [X (t)].

The transform can be any that serves to pass the data of X (t) to the frequency domain. In particular embodiments of the invention the algorithm of Ia is used

Fast Fourier Transform (FFT).

In addition, to calculate the transform that is applied to X (t) a number of points proportional to the relationship between the sampling frequency FS and the rotation frequency of the RPM head is used.

b2) Find the maximum of the transformed T [X (t)] and its corresponding frequency, obtaining MAX (T [X (t)]) and f _{MAX (τ [X (m} . Once the acceleration signal has been passed to the frequency domain, the peak or harmonic of the maximum value of the spectrum and its corresponding frequency is searched.

b3) Search, within the analysis range (1 ± p) • / ^^^ _j , those harmonics whose value exceeds a threshold value TH.

From the maximum value harmonic located in the previous operation, harmonics whose value exceeds a threshold value TH are searched in its surroundings. In a preferred embodiment of the invention, p takes values between 0.05 and 0.20, and in an even more preferred embodiment of the invention, p takes values between 0.08 and 0.12.

The threshold value TH can be determined as a percentage of the noise value in the entire spectrum, as a percentage value of the main harmonic of the spectrum, as a geometric mean of both values, or as the arithmetic mean of the spectrum in the entire frequency range In analysis. Selecting an appropriate value of this threshold can greatly improve the efficiency of the described procedure.

b4) Search, among the harmonics located in the previous operation, harmonic groups separated from each other by distances corresponding to the frequency of rotation of the spindle.

In this operation the position in frequency of each of the harmonics located in the previous operation is analyzed, determining if there is another harmonic at a distance approximately equivalent to the frequency of rotation of the spindle, that is, at the distance (RPM / 60) Hz. By saying that harmonics are separated a distance equivalent to the frequency of rotation of the head is understood that it is not necessary for said distance to be exact, but rather a range or window is determined around (RPM / 60). At the end of this operation, it is discovered if the harmonics are independent of each other, or they form separate groups that distance of approximately (RPM / 60) Hz from each other. Preferably, it is considered that a minimum group is formed by at least two harmonics.

b5) Determine, if there is at least one group of harmonics separated from each other by distances corresponding to the frequency of rotation of the head, that the head is unbalanced.

Finally, if at least one harmonic group is located, then it can be determined that the spindle is unbalanced to a greater or lesser extent. In other words, this procedure could detect both large balances harmful to the outcome of the process in question and small balances whose consequences could be neglected.

Additionally, another particular embodiment of the process of the invention further comprises the operation of:

c) Estimate the degree of unbalance of the head.

To estimate the degree of unbalance of the head, the following operations are carried out:

d) Select, from among the groups of harmonics located, the main group, which is the group that has the highest number of harmonics with the greatest power. For each group of harmonics its total number is taken, the one with the highest value and the sum of its values, so that there is a notion of the number that compose it and the power of each one of them. Next, the groups are sorted first according to the amount of harmonics they contain, and secondly by the sum of their values, selecting as the main group the one that contains the highest number of harmonics with the greatest power.

c2) Calculate a PR parameter that measures the relative power of the harmonics of the main group with respect to the main harmonic of said main group.

The PR parameter could be calculated in any way, provided that it was fundamentally a measure of the relationship between the value of the main harmonic of the main group and the sum of the values of all the harmonics of the group. However, in a particular embodiment of the invention, the PR parameter is defined as:

BPG + BP

PR = I -

HSPG + BP

where: BPG is the power of the main harmonic of the group;

BP is the frequency component with the greatest power in the range of the analyzed spectrum; HSPG is the sum of the powers of the harmonics of the main group.

c3) Estimate, from parameter PR, the degree of spindle unbalance (UL). The expression that relates the PR parameter and the degree of imbalance of the UL head is determined empirically from a set of experimental data, and therefore different expressions could be used to adjust the empirical data obtained. The present patent application claims protection for any of the expressions used. In a particular embodiment of the invention, however, the following equation is used:

where: UL is the degree of unbalance of the head; n and m are experimentally adjusted coefficients.

In a second aspect of the invention, a system for real time detection of unbalance of the head in a high precision rotary mechanism is described, comprising the following elements:

- An accelerometer, located on the X axis of the head, which acquires the signal corresponding to the accelerations of the head vibrations;

A processing means, connected to the acquisition means, that receives said signal and determines if the measured vibrations are caused by an imbalance of the head.

DESCRIPTION OF THE DRAWINGS

To complement the description that is being made and in order To help a better understanding of the characteristics of the invention, according to a preferred example of practical realization thereof, is accompanied as an integral part of said description, a set of drawings in which with an illustrative and non-limiting nature, it has been represented as follows:

Figure 1.- Shows a block diagram of the process according to the present invention.

Figures 2 to 6.- They show the frequency spectrum of the spindle acceleration signal, for different speeds of rotation and degree of spindle imbalance. For each figure, the graph named with the letter a) shows the entire spectrum in frequencies, while the one named with the letter b) shows a detail corresponding to the range of analysis selected.

Figure 7.- Shows the relative power between peaks against the degree of imbalance of the head and the adjustment curve.

Figure 8.- Shows the experimental data of the degree of imbalance against the relative power between harmonics and the curve corresponding to the inverse model developed.

Figure 9.- Shows the relative absolute error, calculated from the application of the model to the experimental validation data.

PREFERRED EMBODIMENT OF THE INVENTION

An example of carrying out the described procedure specifically directed to an ultra-precision machining process is described below, referring to the attached figures. In this example, a system comprising:

a piezoelectric accelerometer with a resolution of 10 mV / g, amplifier and signal conditioner;

an industrial computer with data acquisition card;

a computer program embedded in the computer for the digital processing of the signal (data acquisition and filtering), implementation of the procedure of the invention and implementation of the graphical user interface for the sample of results.

The procedure is mainly based on the search for separate harmonic sequences according to the frequency of rotation of the spindle, around a range of ± 10% (that is, p = 0.1) of the frequency of the main component of the spectrum. This component can be adjusted automatically in advance, since it corresponds to the main harmonic of the signal with the spindle without turning. This determined in advance allows to improve the calculation time of the algorithm. If there are sequences of components with more than a minimum of elements, it follows that the spindle is unbalanced. Fig. 1 shows an algorithm of the described procedure.

Search for harmonic groups

As explained previously, in a first part of the procedure, harmonic groups are sought, which are indicative of an imbalance of the head. The steps that are followed are the following: 1) From the measured signal, the DC component is eliminated by subtracting its average value. Next, in this example the Fast Fourier Transform is calculated (X _FFT = FFT (X))

2) The maximum spectrum (MAX_X _FFT ) and its corresponding frequency (f _MA χ_x _FFT ) are searched for -

3) The analysis range is calculated, which in this example is between 0.9 and 1, 1 of f _{MAX XFFτ} , since p = 0.1

4) Harmonics are detected by calculating the slope of the spectrum of the signal, if there is a change of sign from positive to negative on the slope, there is a maximum in the original signal. If the value of the spectrum at this point exceeds a threshold and also the tendency of the slope before and after this point changes sign, then it is considered that the maximum found is a harmonic of the spectrum.

5) The harmonic frequency distance is calculated, looking for those that are separated by a distance within a window centered on the frequency of rotation (RPM / 60) ± a tolerance, which in this case is obtained as a percentage of the speed rotation.

6) If harmonics are separated a frequency within said window, then they are counted and grouped according to the order of the sequences that exist.

For the calculation of the Fourier transform, a number of points (N_fft) proportional to the relationship between the sampling frequency (FS) and the spindle rotation frequency must be used, 60

N _fft = NxRPM - FS

RPM

where, NxRPM is the number of points, in the spectrum of the signal, between consecutive harmonics of the frequency of rotation.

In addition, the threshold value (TH) for the detection of harmonics, can be determined either as a fixed value, or from the level of noise in the spectrum, as a percentage value of the main harmonic of the spectrum, as a geometric mean of both values or as the arithmetic mean of the spectrum in the entire frequency range under analysis. By selecting an appropriate threshold value, the efficiency of the algorithm will be greatly improved.

Thus, if a group of harmonics with more than two elements is detected, it can be deduced that the spindle is unbalanced. Next, the procedure to estimate the degree of head imbalance is continued.

Harmonic group analysis

For each localized harmonic sequence group, its total number, the one with the highest value and the sum of its values are stored. So that there is a notion of the number that compose it and the power of each one of them.

Next, the groups are sorted first according to the amount of harmonics they contain and also by the sum of their values, leaving as the main group the one that contains the highest number of harmonics with the greatest power. The ratio between the main harmonic and the rest of the group (Peak Ratio) is calculated from the main group obtained, obtaining a measure of the relative power of the rest of the harmonics with respect to the main one. In this example, the coefficient used is defined by the following expression:

BPG + BP

PR = 1 -

HSPG + BP

where:

PR - Peak Ratio BPG - Main harmonic of the group (Biggest Peak in the Group)

BP - Higher peak frequency component in the spectrum range analyzed (Biggest Peak)

HSPG - Sum of the harmonic powers of the chosen group (Highest Sum Peaks in a Group)

The following table shows the results obtained for different spindle speeds, where UL represents the degree or level of head imbalance measured experimentally and the "number of peaks" represents the highest number of peaks or harmonics obtained in sequence. The degree of unbalance of the spindle is measured using the unit of measurement provided by the CNC measuring system of the lathe used before the cutting process. The displacement in microns produced by the axis of rotation due to the imbalance of the head is measured. Thus, there are 4 different levels of imbalance and the experiment was repeated three times for each level.

For the calculation of the Fourier transform, 20 points (NxRPM) were used between harmonics of the rotation frequency. The sampling frequency used is 50 kHz.

In Figs. 2, 3, 4, 5 and 6 the spectra of some of the experiments are shown: Fig. 2a and 2b: 1000RPM and degree of imbalance 0.044 μm Fig. 3a and 3b: 2000RPM and degree of imbalance 0.149 μm Fig. 4a and 4b: 3000RPM and degree of imbalance 0.304 μm Fig. 5a and 5b: 4000RPM and degree of imbalance 0.478 μm Fig. 6a and 6b: 5000RPM and degree of unbalance 0.665 μm

They show the detected peaks and the TH thresholds used. In a broken line the threshold calculated for harmonics is shown, which in this example was determined as the arithmetic mean of the spectrum in the entire frequency range under analysis.

Obtaining the relationship between the PR and the imbalance of the UL head

From the experimental data obtained, the behavior of the Peak Ratio is obtained for each experiment according to the level of spindle balancing (Fig. 7), and it is also observed that with the increase of the spindle balancing also increases the relative power between the peaks

Fig. 7 also illustrates an adjustment curve for which a hyperbolic tangent mathematical function obtained by linear regression techniques with a correlation coefficient R ² equal to 0.98 has been used in this example. The general form of the equation of the fitted curve is the following:

PR = - [tanh (/ w - UL + n) + \]

where:

PR is the Peak Ratio; UL is the degree of head imbalance (Unbalance Level); m, n are linear adjustment coefficients.

The coefficients m and n are initially adjusted in 2,220126 and - 1, 59696, respectively.

Once the mathematical model that relates the level of imbalance of the head has been obtained, by means of measurements prior to the cutting operation, and the Peak Ratio or power ratio between harmonics, it is possible to develop an inverse model, which estimates the degree of unbalance of the head from the PR. This inverse model allows estimating the imbalance of the head, both before the cut and during the operation of the cut, measuring only the vibrations in the head. In this way, possible vibrations can be detected in real time that are harmful to the head or that may affect the quality of the cut.

From the direct model, described previously, it is possible to obtain the inverse model, which has in this example the following general equation:

The model outlined above must meet the condition that UL is greater than 0, so PR must comply with the following:

PR> - [tanh (n) + l]

But regardless of the latter condition, it is possible to define a minimum value condition for UL (UL _m¡n ) of a practical nature. According to the experiments performed, on which the model has been based developed, we can set this minimum value, initially, at 0.010 μm. Given the value of UL _m¡n set, then Ia general equation for calculating UL, Ia is as follows:

^V h _* . ^, PR ≤ PR

UL =; PR _mm = - [t _a nh (m - UL _mm + n) + \]

-In PR

- n PR> PR, m 2 [l - PR

Figure 8 shows the experimental data of UL vs. PR and also the UL values obtained from the inverse model, for the same relative power values between harmonics or peaks.

Analysis of the errors of the described procedure.

The following table shows the result of the evaluation of the procedure described using another set of experimental data.

When evaluating the procedure according to the new PR data set, the absolute error was obtained between the degree of imbalance of the modeled head and the experimental one. In Fig. 9 it can be seen how the error decreases dramatically as the PR increases, which means that the model is more precise as the head imbalance increases. Decision making for the detection of vibrations in the head due to its degree of imbalance.

Taking into account the analysis performed in the previous section, it is possible to make decisions regarding the influence of the degree of imbalance in the appearance of vibrations that could damage the machine head or the quality of the cut during the cutting operation itself. If a minimum limit value for PR (PR-UM) 'Q ^ue ' is defined, given the experimentally obtained data, it can be initially set to 0.055, the monitoring system can make the following decisions:

If PR <PR _LIM , then: VIBRATIONS ARE NOT DETECTED

HARMFUL IN THE HEAD DUE TO ITS UNBALANCE.

Otherwise: VIBRATIONS ARE DETECTED IN THE HEAD THAT CAN DAMAGE THE QUALITY OF THE COURT

Although the described embodiments of the invention with reference to the drawings also comprise computer systems and processes performed in computer systems, the invention also extends to computer programs, more particularly to computer programs in or on carrier media , adapted to put the invention into practice. The computer program may be in the form of source code, object code or an intermediate code between source code and object code, such as partially compiled form, or in any other form suitable for use in the implementation of the agreement processes. with the invention. The carrier medium can be any entity or device capable of carrying the program.

For example, the carrier means may comprise a means of storage, such as a ROM, for example a CD ROM or a semiconductor ROM, or a magnetic recording medium, for example a floppy disc or a hard disk. In addition, the carrier means may be a transmissible carrier medium such as an electrical or optical signal that can be transmitted via electrical or optical cable or by radio or other means.

When the computer program is contained in a signal that can be transmitted directly by means of a cable or other device or medium, the carrier means may be constituted by said cable or other device or medium.

Alternatively, the carrier means can be an integrated circuit in which the computer program is encapsulated {embedded), said integrated circuit being adapted to perform, or to be used in the realization of, the relevant processes.

Claims

1. Procedure for real-time detection of head imbalance in a high precision rotary mechanism, where the head rotates at an RPM speed, characterized in that it comprises the following operations:

a) Acquire, by means of acquisition at a sampling frequency FS, the signal X (t) corresponding to the acceleration of the spindle vibrations;

b) Determine, from the signal X (t) obtained, if the spindle is unbalanced.

2. Procedure according to claim 1, characterized in that it further comprises the operation of:

c) Estimate the degree of unbalance of the head.

3. Method according to claim 1, characterized in that the acquisition means that acquires the signal X (t) is placed on the X axis of the head.

4. Method according to claim 1, characterized in that the operation of determining if the head is unbalanced comprises the following operations:

b1) Eliminate the DC component of the signal X (t) and apply a transformation to X (t) to pass the frequency domain, obtaining the transformed T [X (t)]. b2) Find the maximum of the transformed T [X (Jt)] and its corresponding frequency, obtaining MAX (T [X (t)]) and f _{MAX (τ [X (m} .

b3) Search, within the analysis range (l í ^ '/ ^ _η ^ ₎ , those harmonics whose value exceeds a threshold value TH.

b5) Determine, if there is at least one group of said harmonics separated from each other by distances corresponding to the frequency of rotation of the head, that the head is unbalanced.

5. Method according to claim 4, characterized in that the parameter p is within the range [0.05, 0.20].

6. Method according to claim 5, characterized in that the parameter p is within the range [0.08, 0.12].

7. Method according to claim 4, characterized in that the transformation that is applied to X (t) is the Fast Fourier Transform (FFT).

8. Method according to claim 4, characterized in that the number of points used to calculate the transform that is applied to X (t) is proportional to the relationship between the sampling frequency FS and the rotation frequency of the RPM head.

9. Method according to claim 4, characterized in that the threshold value TH is proportional to the arithmetic mean of the spectrum in the analysis range.

10. Method according to claim 4, characterized in that the threshold value TH is proportional to the geometric mean of the noise level of the spectrum and the level of the main harmonic of the spectrum.

11. Method according to claim 4, characterized in that the threshold value TH is proportional to the main harmonic within the range under analysis.

12. Method according to claim 4, characterized in that the threshold value TH is fixed.

13. Method according to claim 1, characterized in that the operation of estimating the degree of imbalance of the head comprises the following operations:

d) Select, from among the groups of harmonics located, the main group that has the highest number of harmonics with the greatest power.

c3) Estimate, from parameter PR, the degree of spindle unbalance.

14. Method according to claim 13, characterized in that the PR parameter is calculated by means of the following expression:

BPG ₊ BP

HSPG + BP

where: BPG is the power of the main harmonic of the group;

BP is the frequency component with the highest power in the range of analysis;

HSPG is the sum of the powers of the harmonics of the main group.

15. Procedure according to claim 13, characterized in that the operation of estimating the degree of imbalance of the head is performed by means of the following equation:

16. Computer program characterized in that it comprises program instructions to cause a computer system to perform the procedure according to any one of claims 1 to 15.

17. Computer program according to claim 16, characterized in that it is stored in recording media.

18. Computer program according to claim 16, characterized in that it is carried by an electrical carrier signal.

19. System for real-time detection of head imbalance in a high precision rotary mechanism by means of the method described in any of the preceding claims, which comprises the following elements:

An accelerometer, located on the X axis of the head, which acquires the signal corresponding to the accelerations of the head vibrations;

- A processing means, connected to the acquisition means, that receives said signal and determines if the measured vibrations are caused by an imbalance of the head.