CN103234748B - Klingelnberg bevel gear fault diagnosis method based on sensitive IMF (instinct mode function) components - Google Patents

Abstract

The invention discloses a Klingelnberg bevel gear fault diagnosis method based on sensitive IMF (instinct mode function) components. The method includes 1, measuring a Klingelnberg bevel gear box by an acceleration sensor, collecting acceleration vibration signals, 2, importing the collected signals into Matlab to acquire initial signals, performing EMD (empirical mode decomposition) on the initial signals to acquire a series of IMF components, 3, calculating sensitiveness of each IMF component according to the sensitiveness evaluation algorithm, selecting the sensitive IMF component, 4, calculating instant energy spectrum of the sensitive IMF component, drawing a instant energy spectrogram, and accurately extracting fault characteristics according to the amplitude distribution of the spectrogram. The method is an effective fault characteristic extracting method, and can be applied to fault diagnosis on a Klingelnberg bevel gear; fault information can be quickly and accurately extracted; and a significant theoretical basis is provided for the fault diagnosis and the characteristic extraction of the Klingelnberg bevel gear.

Description

A kind of crin Gen Beierge bevel gear method for diagnosing faults based on responsive IMF

Technical field

The invention belongs to fault diagnosis technology field, relate to a kind of crin Gen Beierge bevel gear method for diagnosing faults, more specifically relate to a kind of crin Gen Beierge bevel gear method for diagnosing faults based on responsive IMF.

Background technology

Crin Gen Beierge bevel gear (Klingelnberg Spiral Bevel Gear) is as one of two canine tooths of spiral bevel gear, there is the features such as stable drive, load-bearing capacity are high, hard surface skiving technology, thus be specially adapted to high-power and high pulling torque heavy load transmission field, be the core transmission component in the key areas such as heavy high-grade, digitally controlled machine tools, car transmissions, Aero-Space equipment.This kind of gear works usually under the complex working conditions such as heavy duty, impact, variable load, often produces spot corrosion, glues together, the even phenomenon such as broken teeth of bursting apart, and causes gear to break down.If fail Timeliness coverage and fixing a breakdown, whole plant equipment may be caused to break down or interrupt, also may bring huge potential safety hazard and great economic loss.Therefore, study the fault signature extracting method of this gear, find as early as possible and eliminate in time fault for guarantee plant equipment safely, avoid accident and great economic loss and improve equipment use performance, tool is of great significance.

Domestic and international many scholars have carried out more extensive and deep research to Gear Fault Diagnosis technology, but majority is all consider the fault diagnosis technology of straight spur gear, and the research that crin Gen Beierge bevel gear fault signature extracts and method little.For the fault diagnosis of crin Gen Beierge bevel gear, available diagnostic message is a lot, comprises temperature, vibration, noise etc., but vibration signal directly can react its state, and implementation method also simple and fast, therefore, using the state response of the feature of vibration signal as this kind of gear.But how from the vibration signal of crin Gen Beierge bevel gear, effectively to extract failure message, current mechanical fault diagnosis technology is well positioned to meet actual demand not yet, still there is very large research potential, explore and study new diagnostic method, technology, one of important research content being still this field.Realize the diagnosis of this kind of gear distress, the object of crin Gen Beierge bevel gear condition monitoring and fault diagnosis can not only be reached, also for the fault diagnosis of this kind of gear provides theoretical foundation.

Summary of the invention

The object of this invention is to provide a kind of crin Gen Beierge bevel gear method for diagnosing faults based on responsive IMF, by carrying out treatment and analysis to vibration signal, extract gear distress feature quickly and accurately, for the fault diagnosis of crin Gen Beierge bevel gear and feature extraction provide important theoretical foundation, the fault diagnosis technology for gear provides effective reference.

The present invention adopts following technological means to realize:

1, utilize acceleration transducer to measure crin Gen Beierge bevel gear housing, gather gear acceleration vibration signal as signal to be analyzed;

2, the signal to be analyzed gathered is imported in Matlab software, obtain original signal x (t), EMD(Empirical Mode Decomposition is carried out to original signal) decompose, obtain a series of IMF(Intrinsic Mode Function) component;

Each IMF component should meet two conditions: (1), in whole time series signal, the number of extreme point is equal with the number of zero crossing, or differs one at the most; (2), on a time point in office, the envelope formed by the Local modulus maxima of signal and the mean value of envelope formed by local minizing point are zero, and namely signal is about time shaft Local Symmetric.

2.1. all Local Extremum of signal x (t) are determined, with cubic spline curve all maximum points are coupled together the coenvelope line forming x (t), the all minimum point of same connection forms the lower envelope line of x (t), and upper and lower envelope should all data point of envelope.Remember that the mean value of upper and lower envelope is m ₁(t), and calculate x (t) and m ₁t the difference of (), obtains:

h ₁(t)=x(t)-m ₁(t)。

2.2. for different x (t), h ₁t () may meet the condition of IMF, also may not meet.If do not meet IMF condition, now by h ₁t (), as original signal, repeats to obtain h ₁t the decomposition step of (), obtains:

h ₁₁(t)=h ₁(t)-m ₁₁(t)

Wherein, m ₁₁t () is h ₁the upper and lower envelope average of (t).

If 2.3. h ₁₁t () does not meet the condition of IMF, then decompose continuation, the decomposition in repetition above-mentioned steps 2.1 k time:

h _1k(t)=h _1(k-1)(t)-m _1k(t)

2.4. h is judged _1kt whether () be an IMF component, must have decomposition stop criterion, and it can be defined as the standard deviation SD value between continuous two decomposition result:

$\mathrm{SD}=\frac{\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{|h_{1(k-1)}\left(t\right)-h_{1k}\left(t\right)|}^2}{\underset{t=0}{\overset{T}{\mathrm{\Σ}}}{h}_{1(k-1)}^2\left(t\right)}$

2.5. h is worked as _1kt conditioned disjunction SD value that () meets IMF is less than a certain setting value, namely thinks h _1kt () is an IMF component, note C ₁(t)=h _1kt (), obtains first IMF component.

2.6. r is made ₁(t)=x (t)-C ₁t (), by r ₁t () repeats the step of 2.1 to 2.5 as new signal to be analyzed, to obtain second IMF component, be designated as C ₂(t), repetitive cycling n time, so far, obtains n IMF component of signal x (t),

$\left\{\begin{array}{c}{r}_1\left(t\right)-C_2\left(t\right)=r_2\left(t\right)\\ r_2\left(t\right)-C_3\left(t\right)=r_3\left(t\right)\\ .\\ .\\ .\\ r_{n-1}\left(t\right)-C_n\left(t\right)=r_n\left(t\right)\end{array}\right.$

Work as r _nwhen () becomes a monotonic quantity or therefrom can not extract the component meeting IMF condition again t, decompose and terminate.So far, signal x (t) is broken down into:

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{C}_i\left(t\right)+r_n\left(t\right)$

3, calculate the susceptibility of each IMF component according to susceptibility assessment algorithm, reject and have nothing to do or the IMF component of noise with fault, select responsive IMF component;

3.1. signal x (t) and each IMF component C is calculated _ilikeness coefficient between (t), and be designated as α _i, wherein

${\mathrm{\α}}_i=\frac{{\∫}_{-\∞}^{+\∞}x\left(t\right)C_i\left(t\right)\mathrm{dt}}{\sqrt{{\∫}_{-\∞}^{+\∞}{x}^2\left(t\right)\mathrm{dt}\·{\∫}_{-\∞}^{+\∞}{C}_i^2\left(t\right)\mathrm{dt}}},i=\mathrm{1,2,3},...,n$

3.2. normal signal x is calculated _nor(t) and each IMF component C _ilikeness coefficient between (t), and be designated as β _i, wherein

${\mathrm{\β}}_i=\frac{{\∫}_{-\∞}^{+\∞}{x}_{\mathrm{nor}}\left(t\right)C_i\left(t\right)\mathrm{dt}}{\sqrt{{\∫}_{-\∞}^{+\∞}{x}_{\mathrm{nor}}^2\left(t\right)\mathrm{dt}\·{\∫}_{-\∞}^{+\∞}{C}_i^2\left(t\right)\mathrm{dt}}},i=\mathrm{1,2,3},...,n$

3.3. define Sensitivity Factor ξ, and calculate each IMF component C _ithe susceptibility of (t);

${\mathrm{\ξ}}_i=\frac{|{\mathrm{\α}}_i-{\mathrm{\β}}_i|}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|{\mathrm{\α}}_i-{\mathrm{\β}}_i|}\×100\%,i=\mathrm{1,2,3},...,n$

3.4. select the IMF component that can react fault characteristic information according to the size of ξ value, be defined as responsive IMF component.ξ value the greater is selected to be responsive IMF component under normal circumstances.

4, calculate the Instantaneous energy spectrum of responsive IMF component, adopt Matlab Software on Drawing to go out instantaneous energy spectrogram, according to the distribution of amplitude in instantaneous energy spectrogram, extract fault signature exactly.

Feature of the present invention is based on EMD theoretical, proposes a kind of gear failure diagnosing method, can extract crin Gen Beierge bevel gear fault signature rapidly and accurately, reach the object of this kind of Gear Fault Diagnosis by the method.Summary of the invention comprises four parts.In a first portion, mainly utilize acceleration transducer to measure crin Gen Beierge bevel gear housing, gather gear acceleration vibration signal as signal to be analyzed; In the second portion, the signal gathered is imported in Matlab software, obtains original signal x (t), EMD decomposition is carried out to original signal, obtain a series of IMF component; In Part III, mainly calculate the susceptibility of each IMF component according to sensitivity assessment algorithm, reject and have nothing to do or the IMF component of noise with fault, select responsive IMF component; In Part IV, by calculating the Instantaneous energy spectrum of responsive IMF component, adopting Matlab Software on Drawing to go out instantaneous energy spectrogram, according to the distribution of amplitude in instantaneous energy spectrogram, extracting fault signature exactly.The method of the present invention's proposition is demonstrated finally by example.

By description below and accompanying drawings, the present invention can be more clear, and accompanying drawing illustrates for explaining the inventive method and embodiment.

Accompanying drawing explanation

Fig. 1 is based on the crin Gen Beierge bevel gear method for diagnosing faults process flow diagram of responsive IMF

Fig. 2 signal acquiring system structure diagram of the present invention

Fig. 3 embodiment of the present invention normal signal time domain waveform

Fig. 4 embodiment of the present invention fault-signal time domain waveform

The IMF component (front four IMF) that Fig. 5 embodiment of the present invention fault-signal obtains after EMD decomposes

Fig. 6 embodiment of the present invention responsive IMF component time domain waveform

The IE spectrum of the responsive IMF component of Fig. 7 embodiment of the present invention

Embodiment

A kind of crin Gen Beierge bevel gear method for diagnosing faults process flow diagram based on responsive IMF of the embodiment of the present invention as shown in Figure 1, elaborates to step of the present invention below in conjunction with process flow diagram.Concrete implementation step is as follows:

The first step: utilize acceleration transducer to measure crin Gen Beierge bevel gear housing, gathers gear acceleration vibration signal as signal to be analyzed;

Step (1): the layout of signal acquiring system and correlation parameter

Fig. 2 is signal acquiring system arrangement sketch.As shown in Figure 2, acquisition system mainly comprises three parts, and Part I is for system provides the motor M of power, and the speed of motor is controlled by speed control, to ensure the rotation speed requirements of system middle gear; Part II is motivation transfer motion part, and be a pair crin Gen Beierge bevel gear Z1, Z2, ratio of gear is 1:2.5, and contact ratio and overlap ratio is between 2 and 3; Last part is an AC motor G, provides the load torque in system.Gear pair is driven by motor, and gear Z1 is arranged on axle I(input shaft) on, gear Z2 is arranged on axle II(output shaft) on, acceleration transducer is arranged in bearing cover, input shaft place, gathers gear vibration acceleration signal.This adopts centralized control axle I(input shaft) rotating speed is 1440r/min, by the various parameter of gear and meshing frequency computing formula can calculate each axle rotating speed, turn frequently and meshing frequency as shown in table 1.

Table 1 gear pair relevant parameters

Step (2): the collection of vibration acceleration signal

First gather the vibration acceleration signal of orthodont wheel set as reference signal x _nor(t), then simulated failure on gear Z2, and simulated failure type is wearing and tearing.Acceleration transducer collection now again by being arranged on input shaft place break down after gear pair vibration acceleration signal, as the original signal x (t) of fault signature extraction and analysis.Experiment sample frequency is 10240Hz, and under identical operating mode, collect the vibration acceleration signal in two kinds of situations, partial vibration signal amplitude is as shown in table 2.Fig. 3 and Fig. 4 is respectively the normal signal of collection and the time domain waveform of fault-signal.

The some experimental data that table 2 gathers

Second step: the signal gathered is imported in Matlab software, obtains original signal x (t), EMD decomposition is carried out to original signal, obtain a series of IMF component;

1), remember that fault-signal is x (t), find out all extreme points of this signal, with cubic spline curve all maximum points are coupled together the coenvelope line forming x (t), the all minimum point of same connection forms the lower envelope line of x (t), and upper and lower envelope should all data point of envelope.Remember that the mean value of upper and lower envelope is m ₁t (), calculates x (t) and m ₁t the difference of () obtains:

h ₁(t)=x(t)-m ₁(t)

2), h is used ₁t () replaces original signal x (t) to repeat 1) in process, obtain:

h _1k(t)=h _1(k-1)(t)-m _1k(t)

Definition standard deviation SD, $\mathrm{SD}=\frac{\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{|h_{1(k-1)}\left(t\right)-h_{1k}\left(t\right)|}^2}{\underset{t=0}{\overset{T}{\mathrm{\Σ}}}{h}_{1(k-1)}^2\left(t\right)};$ Experience shows that SD generally gets 0.2-0.3.Work as h _1kt conditioned disjunction SD value that () meets IMF is less than a certain setting value, namely thinks h _1kt () is an IMF component, note C ₁(t)=h _1kt (), obtains first IMF component.

3), r is made ₁(t)=x (t)-C ₁t (), to r ₁t () repeats above two steps, obtain r _i(t)=r _i-1(t)-C _i(t) (i=1,2 ..., n) until r _nt () becomes a monotonic quantity or till can not decomposing again.So far, signal x (t) is broken down into:

$x\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{C}_i\left(t\right)+r_n\left(t\right)$

Embodiment of the present invention fault-signal obtains 10 rank IMF components through EMD decomposition, and wherein the time domain waveform of front four IMF components as shown in Figure 5.

3rd step: the susceptibility calculating each IMF component according to susceptibility assessment algorithm, rejects and fault has nothing to do or the IMF component of noise, selects responsive IMF component;

Calculate signal x (t) and C _ilikeness coefficient α between (t) _i; And calculate normal signal x _nor(t) and C _ilikeness coefficient β between (t) _i.Each rank C is calculated by susceptibility assessment algorithm _it the susceptibility of (), obtains result as shown in table 3.IMF1 component and IMF2 component is finally selected to be responsive IMF component according to the value of ξ in table 3.

α, β and ξ value of each IMF component of table 3 fault-signal

4th step: crin Gen Beierge bevel gear fault signature extracts

1), to the responsive IMF component selected do Hilbert conversion, obtain:

$Y_i\left(t\right)=H\left[C_i\left(t\right)\right]=\frac{1}{\mathrm{\π}}{\∫}_{-\∞}^{+\∞}\frac{C_i\left(\mathrm{\τ}\right)}{t-\mathrm{\τ}}\mathrm{d\τ},i=\mathrm{1,2}$

2), analytic signal Z is built _i(t), as follows:

$Z_i\left(t\right)=C_i\left(t\right)+j{Y}_i\left(t\right)=a_i\left(t\right)e^{j{\mathrm{\θ}}_i\left(t\right)},i=\mathrm{1,2}.$

In formula, a _i(t) and θ _it () is respectively magnitude function and phase function, and defined by equation;

$a_i\left(t\right)=\sqrt{C_i^2\left(t\right)+Y_i^2\left(t\right)},i=\mathrm{1,2}$

${\mathrm{\θ}}_i\left(t\right)=\arctan \left[\frac{Y_i\left(t\right)}{C_i\left(t\right)}\right],i=\mathrm{1,2}$

3), calculate responsive IMF Hilbert spectrum, be designated as H (f, t), wherein f is instantaneous frequency, then:

$H(f,t)=\mathrm{Re}\left\{\underset{i=1}{\overset{2}{\mathrm{\Σ}}}{a}_i\left(t\right)e^{[j\∫f_i\left(t\right)\mathrm{dt}]}\right\}$

4), by the squared magnitude of H (f, t) carry out integration to frequency, obtain Instantaneous energy spectrum, its reaction signal is in the energy summation of certain various frequency content in local.Definition Instantaneous energy spectrum IE (t), namely;

$\mathrm{IE}\left(t\right)={\∫}_0^f{H}^2(f,t)\mathrm{df}$

Fig. 7 is the IE spectrogram of responsive IMF component.From Fig. 7, find out to there is periodic peaks point significantly, and the time interval between adjacent two peak values is approximately 0.104s, close to the swing circle (1/9.6=0.10417s) of system middle gear axle II.Thus, extracted gear distress feature exactly, can infer that the gear 2 on shaft II there occurs fault, diagnosis is out of order and position is occurred exactly, achieves the fault diagnosis of crin Gen Beierge bevel gear.

There is due to crin Gen Beierge bevel gear the features such as registration is high, stable drive, bring certain difficulty to the extraction of the fault signature of this kind of gear and fault diagnosis.And a series of IMF components that fault-signal obtains after EMD decomposes, usually minority component and fault signature is only had to be closely related (claiming the IMF component be closely related with fault to be responsive IMF component), other are then irrelevant with fault or noise composition, and this brings certain difficulty to feature extraction equally.And the inventive method accurately can select responsive IMF component, weaken and to have nothing to do with fault or the interference of noise composition, strengthen the extraction of fault characteristic information, result directly reacts fault signature.

Summed up by above instance analysis: the inventive method can apply in the fault diagnosis of crin Gen Beierge bevel gear, and fault characteristic information can be extracted rapidly and accurately, finally realize the fault diagnosis of this kind of gear.The inventive method is not only the fault diagnosis of crin Gen Beierge bevel gear and feature extraction provides important theoretical foundation, and provides effective reference for the fault diagnosis technology of gear.

Claims (1)

1., based on a crin Gen Beierge bevel gear method for diagnosing faults of responsive IMF, it is characterized in that, the method comprises the following steps:

1) utilize acceleration transducer to measure crin Gen Beierge bevel gear housing, gather gear acceleration vibration signal as signal to be analyzed; Wherein gather the vibration acceleration signal of normal crin Gen Beierge bevel gear gear pair respectively as reference signal x _nor(t), signal x (t) to be analyzed that the gear pair vibration acceleration signal after breaking down extracts as fault signature;

2) signal x (t) to be analyzed gathered is imported in Matlab software, obtain original signal, carry out EMD (Empirical ModeDecomposition) to original signal to decompose, obtain a series of IMF (Intrinsic Mode Function) component, wherein, each IMF component should meet two conditions:

A (), in whole time series signal, the number of extreme point is equal with the number of zero crossing, or differ one at the most,

B, on () time point in office, the envelope formed by the Local modulus maxima of signal and the mean value of envelope formed by local minizing point are zero, and namely signal is about time shaft Local Symmetric;

2.1) all Local Extremum of signal x (t) to be analyzed are determined, with cubic spline curve all maximum points are coupled together the coenvelope line forming x (t), the all minimum point of same connection forms the lower envelope line of signal x (t) to be analyzed, upper and lower envelope should all data point of envelope, remembers that the mean value of upper and lower envelope is m ₁(t), and calculate signal x (t) to be analyzed and m ₁t the difference of (), obtains:

h ₁(t)＝x(t)-m ₁(t)

2.2) for different signals x (t) to be analyzed, h ₁t () may meet the condition of IMF, if do not meet the condition of IMF component, now by h ₁t (), as original signal, calculates h ₁(t) and m ₁₁t the difference of (), obtains:

h ₁₁(t)＝h ₁(t)-m ₁₁(t)

Wherein, m ₁₁t () is h ₁the upper and lower envelope average of (t),

If now h ₁₁t () does not meet the condition of IMF component, then repeat said process k time, obtain h _1k(t)=h _{1 (k-1)}(t)-m _1kt (), until h _1kt () meets the condition of IMF component, or the standard deviation SD value between continuous two decomposition result is less than a certain setting value, obtains an IMF component, is designated as:

C ₁(t)＝h _1k(t)

Wherein, standard deviation SD is:

2.3) r is made ₁(t)=x (t)-C ₁t (), by r ₁t () repeats 2.1 as new signal to be analyzed), 2.2) step, obtain n IMF component of signal x (t), until r _nt () becomes a monotonic quantity or till can not decomposing, so far, signal x (t) is broken down into again:

3) calculate the susceptibility of each IMF component according to sensitivity assessment algorithm, reject and have nothing to do or the IMF component of noise with fault, select responsive IMF component;

3.1) signal x (t) and each IMF component C is calculated _ilikeness coefficient between (t), and be designated as α _i, wherein,

3.2) normal signal x is calculated _nor(t) and each IMF component C _ilikeness coefficient between (t), and be designated as β _i, wherein,

3.3) define Sensitivity Factor ξ, and calculate each IMF component C _ithe susceptibility of (t);

3.4) select the IMF component that can react fault characteristic information according to the size of ξ value, be defined as responsive IMF component, wherein, select ξ value the greater to be responsive IMF component;

4) calculate the Instantaneous energy spectrum of responsive IMF component, adopt Matlab Software on Drawing to go out instantaneous energy spectrogram, according to the distribution of amplitude in instantaneous energy spectrogram, extract fault signature exactly.