Gear multi-fault signal decoupling and feature extraction method based on FSC and EMD

Abstract

The invention aims to provide a gear multi-fault signal decoupling and feature extraction method based on FSC and EMD, and belongs to the field of gear fault diagnos.The method comprises the steps that firstly, vibration signals are collected, then the impact frequency of each fault component is calculated, the corresponding relation between the impact frequency and the natural vibration frequency of fault signals is obtained from the original vibration signals, and the fault signals are obtained; therefore, the natural vibration frequency corresponding to the vibration excitation of each part is determined. Secondly, decomposing an original signal into a plurality of IMF components, performing spectrum analysis, identifying a spectrum envelope peak value, and determining the natural vibration frequency of each IMF component; iMF components reflecting fault information of different parts are determined by comparing the IMF natural vibration frequency with the natural vibration frequency of each part, and vibration signal decoupling of multiple fault information is achieved. And finally, calculating characteristic parameters of the fault signal of each part after decoupling to complete fault characteristic extraction. The method has high fault identification precision, and can accurately obtain the frequency information of the fault component.

Description

Technical Field

[0001] The invention relates to a gear fault diagnosis method, in particular to a gear coupling fault diagnosis method. Background Art

[0002] As an important component of mechanical transmission, gearboxes are widely used in ship power plants, vehicle transmission systems, chemical and machining equipment. Due to the heavy workload and changing working environment of gearboxes, various faults are prone to occur in gearboxes, which endanger equipment operation and personnel safety. Therefore, gearbox fault diagnosis is of great significance.

[0003] The vibration signal of the gearbox contains the status information of each component of the gearbox, and fault diagnosis based on vibration signals has been widely studied and applied. However, as the design of modern gearbox structures develops towards complexity, multi-function, and high power, the probability of simultaneous failure of the driving gear, driven gear, and bearing in the gearbox is gradually increasing. When multiple components of the gearbox fail at the same time, the fault features of each component extracted based on the vibration signal overlap with each other, making it difficult to distinguish the features of each component, which brings difficulties to the fault diagnosis of the gearbox. Summary of the invention

[0004] The purpose of the present invention is to provide a gear multi-fault signal decoupling and feature extraction method based on FSC and EMD, which can solve the problems of complex components of gearbox multi-component coupled fault signal and difficult feature extraction.

[0005] The object of the present invention is achieved in that:

[0006] The present invention provides a gear multi-fault signal decoupling and feature extraction method based on FSC and EMD, which is characterized by:

[0007] (1) Obtaining the gearbox coupling fault signal: placing the sensor on the surface of the gearbox, collecting the vibration signal generated during the operation of the gearbox, and storing the vibration signal in the form of a digital signal;

[0008] (2) Calculate the fault impact frequency of the faulty components of the gearbox;

[0009] (3) FSC transformation;

[0010] (4) Identify the natural frequency of each component;

[0011] (5) Perform EMD decomposition on the original signal;

[0012] (6) Identify fault signals;

[0013] (7) Extract fault features.

[0014] The present invention may also include:

[0015] 1. The faulty parts of the gearbox include the driving gear, the driven gear and the bearing. The calculation process of the fault impact frequency is as follows.

[0016] First, calculate the gear fault impact frequency. Assume that the speed of the shaft where the active gear is located is n1, and the active gear fault impact frequency α main for:

[0017]

[0018] Assume that the number of teeth on the driving gear is z1, the number of teeth on the driven gear is z2, and the transmission ratio between the driving and driven gears is g. r for:

[0019]

[0020] Fault impact frequency α of the driven gear slave for:

[0021]

[0022] Then calculate the bearing fault impact frequency. The bearing fault impact frequency is determined by its position and fault type. The bearing includes driving wheel bearing and driven wheel bearing according to its position. The bearing fault types include inner ring fault, outer ring fault, rolling element fault and cage fault.

[0023] Assume the number of rolling elements in the bearing is z b , the rolling element diameter is d, the diameter of the circle where the rolling element center is located is D, and the bearing contact angle is θ. The rotation frequency of the shaft where the bearing is located is α r , bearing inner ring fault impact frequency α bi for:

[0024]

[0025] Bearing outer ring fault impact frequency α bo for:

[0026]

[0027] Bearing rolling element fault impact frequency α br for:

[0028]

[0029] Bearing cage failure impact frequency α bc for:

[0030]

[0031] According to the above inner ring fault impact frequency, outer ring fault impact frequency, rolling element fault impact frequency, cage fault impact frequency, the impact frequency of different bearing faults is related to the rotation frequency α r For the driving wheel bearing, α r =α slave , the impact frequencies of the four faults of the driving wheel bearing are obtained: α main_bi , α main_bo , α main_br , α main_bc ; For the driven wheel bearing, α r =α slave , the impact frequency α of the four faults of the driven wheel bearing slave_bi , α slave_bo , α slave_br , α slave_bc ;

[0032] The impact frequency of each component is: driving gear impact frequency α main , driven gear impact frequency α slave , bearing impact frequency [α main_bi ,α main_bo ,α main_br ,α main_bc ,α slave_bi ,α slave_bo ,α slave_br ,α slave_bc ].

[0033] 2. The process of FSC transformation is:

[0034] First, select the window function w = [w(1),w(2),…,w(p),…,w(N w )], where N w is the length of the window function;

[0035] According to the STFT theory, the window function is applied to the original signal multiple times to calculate the original signal x = [x(1), x(2), ..., x(L)] in the i-th window, the frequency point f k Energy at X STFT (i,f k ):

[0036]

[0037] In the formula, f k =(k-1)Δf, k=1,2,…,N w , Δf=F s / N w , F s is the sampling frequency; i=1,2,…,I w , I w=L / R, R is the step size of windowing;

[0038] Pair To perform phase correction, multiply it by

[0039]

[0040] Let q = p + i·R, substitute into the above formula, and get the Gabor form of the STFT transformation result X w (i,f k ):

[0041]

[0042] The signal is frequency shifted by α, then the signal is at frequency f k The energy at –α is:

[0043]

[0044] In the formula, α = k s / 2R,k s =1,2,…,F s ;

[0045] According to the FSC transformation principle, when the frequency shift is α, according to X w (i,f k ) and X w (i,f k -α), calculate the fault component with impulse frequency equal to α at frequency point f k Energy S x (f k ,α):

[0046]

[0047] In the formula, ||w|| 2 is the modulus length of the window function,

[0048] S x (f k ,α) is the result of FSC transformation, where α is the frequency shift and also the impact frequency of the periodic fault component. Set α=k s / 2R,k s =1,2,…,F s .

[0049] 3. Step (4) is as follows: α, f k and S x (f k ,α) is called the FSC diagram of the signal. For coupled fault signals, m Sx (f k ,α) frequency bands with higher values, read the α and f corresponding to these frequency bands k The signal contains natural frequency and impact frequency respectively [f k1 ,α1]、[f k2 ,α2],…,[f km ,α m ]; the signal impact frequency [α1,α2,…,α m ] are respectively related to the impact frequency [α main_g ,α slave_g ,α main_bi ,α main_bo ,α main_br ,α main_bc ,α slave_bi ,α slave_bo ,α slave_br ,α slave_bc ] to compare and determine [α1,α2,…,α m ] corresponding to the faulty component, and then determine the natural frequency [f k1 ,f k2 ,…,f km ] corresponds to the faulty component, and the total number of faulty components is m.

[0050] 4. The steps of EMD decomposition are as follows:

[0051] ① Input original signal x = [x(1), x(2), …, x(l), …, x(L)];

[0052] ② Identify all the maximum points of x, and use cubic spline interpolation to connect the maximum points so that the line between every two adjacent maximum points is a smooth cubic polynomial curve, thereby obtaining the upper envelope e max =[e max (1),e max (2),…,e max (l),…,e max (L)]; use the same method to obtain the lower envelope e min =[e min (1),e min (2),…,e min (l),…,e min (L)];

[0053] ③ Calculate the mean of the upper and lower envelopes m = [m(1), m(2), …, m(l), …, m(L)]:

[0054]

[0055] ④ Calculate the envelope difference h = [h(1), h(2), ..., h(l), ..., h(L)]:

[0056] h(l)=x(l)-m(l),l=1,2,...,L

[0057] ⑤ Determine whether h meets the conditions of the intrinsic mode: 1) In the entire signal length range, the number of maximum values ​​and the number of zero crossings must be equal or differ by one; 2) At any place on the time axis, the mean of the upper envelope spectrum formed by the signal maximum point and the lower envelope spectrum formed by the minimum point is zero;

[0058] If not satisfied, set x = h and repeat steps ① to ⑤;

[0059] If the conditions are met, let I1=h, and we get the first natural mode I1=[I1(1),I1(2),…,I1(l),…,I1(L)];

[0060] ⑥ Calculate the residual r1 = [r1(1), r1(2), …, r1(l), …r1(L)]:

[0061] r1(l)=x(l)-I1(l),l=1,2,...,L

[0062] Let x = r1, repeat steps ① to ⑥, and calculate the next natural mode I2, I3, ..., I n , where I n The corresponding residual is r n , r n =[r n (1),r n (2),…,r n (l),…,r n (L)];

[0063] When the modulus length of the residual signal is less than a given threshold, the signal decomposition terminates, that is:

[0064]

[0065] Where ε is the residual modulus length threshold;

[0066] A total of n IMF components I1, I2, ..., I n , and a residual signal r = r n ; During the signal decomposition process, by setting an appropriate threshold ε, the number of IMF components n> the total number of faulty components m.

[0067] 5. The process of identifying the fault signal in step (6) is as follows:

[0068] The I1,I2,…,I obtained by EMD decompositionn Perform spectrum analysis and obtain spectrum s1, s2, …s n , draw the envelope of each spectrum and find the frequency f at its maximum point w1 ,f w2 ,…,f wn , that is, I1,I2,…,I n The natural frequency of

[0069] [f w1 ,f w2 ,…,f wn ] is compared with the natural frequency of each component to obtain the IMF component corresponding to each component. The IMF component without corresponding component is the noise component.

[0070] 6. The process of extracting fault features in step (7) is as follows:

[0071] After determining the fault signal of each component, calculate the fault characteristics of each component respectively; the root mean square and kurtosis reflect the amplitude and impact characteristic of the signal respectively, and the root mean square and kurtosis are selected as features;

[0072] The signal RMS calculation formula is as follows:

[0073]

[0074] The calculation formula of signal kurtosis is as follows:

[0075]

[0076] The advantages of the present invention are:

[0077] 1. The present invention is simple to calculate and is applicable to vibration signals generated by coupling faults of multiple components in complex transmission systems.

[0078] 2. The present invention adopts the FSC algorithm to determine the periodic components in the signal, and determines the faulty parts of the gearbox according to the periodic characteristics of the signal. It has high fault identification accuracy and can accurately obtain the frequency information of the faulty parts.

[0079] 3. The present invention uses the EMD algorithm to adaptively decouple the fault signal, and by selecting the optimal IMF component to determine the signal component that best matches the faulty component, the recognition accuracy of the fault signal can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 is a flow chart of the present invention;

[0081] Figure 2 This is the gearbox coupling fault signal diagram;

[0082] Figure 3 It is the signal FSC diagram;

[0083] Figure 4 It is a local enlargement of the signal FSC graph;

[0084] Figure 5(a) is IMF1, Figure 5(b) is IMF2, Figure 5(c) is IMF3, Figure 5(d) is IMF4, Figure 5(e) is IMF5, Figure 5(f) is IMF6, Figure 5(g) is IMF7, Figure 5(h) is IMF8, Figure 5(i) is IMF9, and Figure 5(j) is the residual;

[0085] Figure 6(a) is the spectrum of IMF1, Figure 6(b) is the spectrum of IMF2, Figure 6(c) is the spectrum of IMF3, Figure 6(d) is the spectrum of IMF4, Figure 6(e) is the spectrum of IMF5, Figure 6(f) is the spectrum of IMF6, Figure 6(g) is the spectrum of IMF7, Figure 6(h) is the spectrum of IMF8, and Figure 6(i) is the spectrum of IMF9;

[0086] Figure 7(a) shows the wear-broken teeth-2000rpm-no-load sample, Figure 7(b) shows the fault signal of the driving gear, and Figure 7(c) shows the fault signal of the driven gear;

[0087] Figure 8(a) is a wear-wear-2000rpm-50% load sample, Figure 8(b) is a wear-wear-2000rpm-50% load sample driving gear fault signal, and Figure 8(c) is a wear-wear-2000rpm-50% load sample driven gear fault signal;

[0088] Figure 9(a) shows the characteristic distribution of the driving gear, and Figure 9(b) shows the characteristic distribution of the driven gear. DETAILED DESCRIPTION

[0089] The present invention is described in more detail below with reference to the accompanying drawings:

[0090] Combination Figure 1-Figure 9(b) , the present invention comprises the following steps:

[0091] 1. Obtain gearbox coupling fault signal

[0092] The sensor is placed on the surface of the gearbox to collect the vibration signal generated during the operation of the gearbox and store the vibration signal in the form of a digital signal.

[0093] 2. Calculate the impact frequency of each component failure

[0094] For ordinary speed gearboxes, the faulty parts of the gearbox mainly include the driving gear, the driven gear, and the bearing. The fault impact frequency of these parts can be calculated according to the speed and structural parameters of the gearbox. The calculation process is as follows.

[0095] First, calculate the gear fault impact frequency. Assume that the speed of the shaft where the active gear is located is n1, and the active gear fault impact frequency α main for:

[0096]

[0097] Assume that the number of teeth on the driving gear is z1 and the number of teeth on the driven gear is z2, then the transmission ratio between the driving and driven gears is g. r for:

[0098]

[0099] Fault impact frequency α of the driven gear slave for:

[0100]

[0101] Then calculate the bearing fault impact frequency. The bearing fault impact frequency is determined by its position and fault type. Bearings can be divided into two types according to their position: driving wheel bearings and driven wheel bearings. Common bearing fault types include inner ring fault, outer ring fault, rolling element fault, and cage fault.

[0102] Assume the number of rolling elements in the bearing is z b , the rolling element diameter is d, the diameter of the circle where the rolling element center is located is D, and the bearing contact angle is θ. The rotation frequency of the shaft where the bearing is located is α r , then the bearing inner ring fault impact frequency α bi for:

[0103]

[0104] Bearing outer ring fault impact frequency α bo for:

[0105]

[0106] Bearing rolling element fault impact frequency α br for:

[0107]

[0108] Bearing cage failure impact frequency α bc for:

[0109]

[0110] According to equations (4) to (7), the impact frequencies of different bearing faults are related to the rotation frequency α r For the driving wheel bearing, α r =α slave , the impact frequencies of the four faults of the driving wheel bearing are obtained: α main_bi , αmain_bo , α main_br , α main_bc ; For the driven wheel bearing, α r =α slave , the impact frequency α of the four faults of the driven wheel bearing slave_bi , α slave_bo , α slave_br , α slave_bc .

[0111] In summary, the impact frequency of each component is: driving gear impact frequency α main , driven gear impact frequency α slave , bearing impact frequency [α main_bi ,α main_bo ,α main_br ,α main_bc ,α slave_bi ,α slave_bo ,α slave_br ,α slave_bc ].

[0112] 3. FSC transformation

[0113] First, select the window function w = [w(1),w(2),…,w(p),…,w(N w )], where N w is the length of the window function.

[0114] According to the STFT theory, the window function is applied to the original signal multiple times to calculate the original signal x = [x(1), x(2), ..., x(L)] in the i-th window, the frequency point f k Energy at X STFT (i,f k ):

[0115]

[0116] In the formula, f k =(k-1)Δf, k=1,2,…,N w , Δf=F s / N w , F s is the sampling frequency. i=1,2,…,I w , I w =L / R, R is the step size of windowing.

[0117] Perform phase correction on equation (8) and multiply it by

[0118]

[0119] Let q = p + i·R, substitute into equation (9), and we get the Gabor form of the STFT transformation result X w (i,f k ):

[0120]

[0121] The signal is frequency shifted by α, then the signal is at frequency f k The energy at –α is:

[0122]

[0123] In the formula, α = k s / 2R,k s =1,2,…,F s .

[0124] According to the FSC transformation principle, when the frequency shift is α, according to X w (i,f k ) and X w (i,f k -α), the fault component with impulse frequency equal to α can be calculated at frequency point f k Energy S x (f k ,α):

[0125]

[0126] In the formula, ||w|| 2 is the modulus length of the window function,

[0127] S x (f k ,α) is the result of FSC transformation. α is the frequency shift, which is also the impact frequency of the periodic fault component. By changing the value of α, different S x (f k ,α). The value of α can be freely selected, usually set α=k s / 2R,k s =1,2,…,F s , at this time, α has a higher resolution, the recognition accuracy of the fault component is higher, and α has a lower upper limit and the calculation complexity is lower. x (f k ,α) is large, the signal contains impulse frequency α and natural frequency f k The fault component, S x (f k ,α) is small, it does not contain the corresponding fault components.

[0128] 4. Identify the natural frequency of each component

[0129] α、f k and S x (f k ,α) is called the FSC diagram of the signal. For coupled fault signals, m S x (f k ,α) frequency bands with higher values, read the α and f corresponding to these frequency bands k The value shows that the signal contains natural frequency and impact frequency respectively [f k1 ,α1]、[f k2 ,α2],…,[f km ,α m ] of m fault components. m ] are respectively related to the impact frequency [α main_g ,α slave_g ,α main_bi ,α main_bo ,α main_br ,α main_bc ,α slave_bi ,α slave_bo ,α slave_br ,α slave_bc ] to compare and determine [α1,α2,…,α m ] corresponding to the faulty component, and then determine the natural frequency [f k1 ,f k2 ,…,f km ] corresponds to the faulty component, and the total number of faulty components is m.

[0130] 5. EMD decomposition

[0131] Perform EMD decomposition on the original signal. The steps are as follows:

[0132] ① Input original signal x = [x(1), x(2),…, x(l),…, x(L)].

[0133] ② Identify all the maximum points of x, and use cubic spline interpolation to connect the maximum points so that the line between every two adjacent maximum points is a smooth cubic polynomial curve, thereby obtaining the upper envelope e max =[e max (1),e max (2),…,e max (l),…,e max (L)]. Use the same method to get the lower envelope e min =[e min (1),e min (2),…,emin (l),…,e min (L)].

[0134] ③ Calculate the mean of the upper and lower envelopes m = [m(1), m(2), …, m(l), …, m(L)]:

[0135]

[0136] ④ Calculate the envelope difference h = [h(1), h(2), ..., h(l), ..., h(L)]:

[0137] h(l)=x(l)-m(l), l=1,2,...,L (14)

[0138] ⑤ Determine whether h meets the conditions of the inherent mode: 1) Within the entire signal length range, the number of maximum values ​​and the number of zero crossings must be equal or differ by one; 2) At any place on the time axis, the mean of the upper envelope spectrum formed by the signal maximum points and the lower envelope spectrum formed by the minimum points is zero.

[0139] If not satisfied, set x=h and repeat steps ①~⑤.

[0140] If the conditions are met, let I1 = h and obtain the first natural mode I1 = [I1(1), I1(2),…, I1(l),…, I1(L)].

[0141] ⑥ Calculate the residual r1 = [r1(1), r1(2), …, r1(l), …r1(L)]:

[0142] r1(l)=x(l)-I1(l), l=1,2,...,L (15)

[0143] Then, let x = r1, repeat steps ① to ⑥, and calculate the next natural mode I2, I3, ..., I n , where I n The corresponding residual is r n , r n =[r n (1),r n (2),…,r n (l),…,r n (L)].

[0144] When the modulus length of the residual signal is less than a given threshold, the signal decomposition terminates, that is:

[0145]

[0146] Where ε is the residual modulus length threshold.

[0147] Finally, a total of n IMF components I1, I2, ..., I n , and a residual signal r = r n During the signal decomposition process, by setting a suitable threshold ε, the number of IMF components n> the total number of faulty components m.

[0148] 6. Identify fault signals

[0149] The I1,I2,…,I obtained by EMD decomposition n Perform spectrum analysis and obtain spectrum s1, s2, …s n , draw the envelope of each spectrum and find the frequency f at its maximum point w1 ,f w2 ,…,f wn , that is, I1,I2,…,I n The natural frequency of .

[0150] [f w1 ,f w2 ,…,f wn ] is compared with the natural frequency of each component to obtain the IMF component corresponding to each component. The IMF component without a corresponding component is the noise component.

[0151] 7. Extract fault features

[0152] After determining the fault signals of each component, the fault characteristics of each component are calculated. The root mean square and kurtosis reflect the amplitude and impact characteristics of the signal respectively, and are more sensitive to bearing and gear faults, so the root mean square and kurtosis are selected as features.

[0153] The root mean square can reflect the overall amplitude of the signal and is usually used to measure the intensity of the object's vibration. The signal root mean square calculation formula is as follows:

[0154]

[0155] Kurtosis is a statistic that describes the steepness of a frequency distribution curve. The calculation formula for signal kurtosis is as follows:

[0156]

[0157] Example:

[0158] The process of the present invention is as follows Figure 1 As shown in the figure, firstly, the gear fault signal is obtained, and then the impact frequency of each faulty component is calculated according to the speed and structural parameters of the gearbox [α main_g ,α slave_g ,α main_bi ,α main_bo ,α main_br ,α main_bc ,αslave_bi ,α slave_bo ,α slave_br ,α slave_bc ], and then use the FSC algorithm to extract the corresponding relationship between the impulse frequency and the natural frequency of the fault signal [f k1 ,α1]、[f k2 ,α2],…,[f km ,α m Then, the natural frequency of each component is determined by comparing the impact frequency. Then, the EMD algorithm is used to decouple the original signal into multiple IMF components [I1, I2, …, I n ]. Then, the natural frequency [f w1 ,f w2 ,…,f wn ], by comparing the IMF self-oscillation frequency with the self-oscillation frequency of each component, the component corresponding to each IMF is determined, and the fault signal identification is completed. Finally, the characteristics of the fault signal of each component after decoupling are calculated to complete the fault feature extraction. The details are as follows:

[0159] Step 1: Get the gearbox coupling fault signal

[0160] In order to verify the effectiveness of the present invention, it is assumed that the gearbox has three faults, namely, the driving gear broken tooth, the driven gear broken tooth, and the driven wheel bearing rolling element fault, and a multi-fault coupling simulation signal x∈R is generated. 20480×1 , the analog signal waveform is as follows Figure 2 . Signal length L = 20480, sampling frequency F s =20.48kHz, the signal duration is 1s, and the structural parameters of the gearbox components are shown in Table 1.

[0161] Table 1 Gearbox structural parameters

[0162] Structural parameters Value Structural parameters Value Driving shaft speed 1200rpm Number of teeth on driving gear 17 Driven gear teeth number 20 Number of bearing rolling elements 9 Bearing contact angle 0° Rolling element diameter 27mm Rolling element center diameter 60mm

[0163] The specific steps of coupling fault signal decoupling and feature extraction are as follows:

[0164] Step 2: Calculate the fault impulse frequency

[0165] It is known that the speed of the shaft where the driving gear is located is n1 = 1200rpm. When the driving gear fails, its fault impact frequency α main_g for:

[0166]

[0167] Get α main_g =20Hz.

[0168] It is known that the number of teeth on the driving gear is z1=17 and the number of teeth on the driven gear is z2=20, so the transmission ratio between the driving and driven gears is g. r for:

[0169]

[0170] Get g r =17 / 20.

[0171] Fault impact frequency α of the driven gear slave_g for:

[0172]

[0173] Get α slave_g =17Hz.

[0174] Bearing structural parameters z b =9, d=27mm, D=60mm, cosθ=1. Bearing inner ring fault impact frequency α bi for:

[0175]

[0176] Bearing outer ring fault impact frequency α bo for:

[0177]

[0178] Bearing rolling element fault impact frequency α br for:

[0179]

[0180] Bearing cage failure impact frequency α bc for:

[0181]

[0182] The impact frequency of different bearing faults is related to the rotation frequency α r For the driving wheel bearing, α r =α slave_g ; For the driven wheel bearing, α r =α main_g According to equations (22) to (25), the impact frequencies of the four faults of the driving wheel bearing are obtained: α main_bi , α main_bo , α main_br , α main_bc ; Impact frequency α of four faults of driven wheel bearing slave_bi , α slave_bo , α slave_br , α slave_bc .

[0183] The fault impact frequencies of each component calculated above are shown in Table 2.

[0184] Table 2 Fault impact frequency of each component

[0185]

[0186] Step 3: FSC transformation

[0187] Select the window function w as length N w = 256 Kaiser window, according to STFT theory, calculate the original signal x in the i-th window, frequency point f k Energy at X STFT (i,f k ):

[0188]

[0189] In the formula, f k =(k-1)Δf, k=1,2,…,N w , Δf=F s / N w =20480 / 256=80, that is, f1=0, f2=80, f3=160,…, f 256 =20480. i = 1, 2, ..., I w , I w =L / R, take the windowing step size R = 40, then I w =L / R=512, that is, i=1,2,…,512.

[0190] get:

[0191]

[0192] Perform phase correction on equation (26) and multiply it by

[0193]

[0194] Let q = p + i·R and substitute it into equation (27) to obtain the Gabor form of the STFT transformation result X w (i,f k ):

[0195]

[0196] The signal is frequency shifted by α, then the signal is at frequency f k The energy at –α is:

[0197]

[0198] In the formula, α = k s / 2R,k s =1,2,…,20480, that is, α=0.0125,0.025,…256.

[0199] According to X w (i,f k ) and X w (i,f k -α), perform FSC transformation on the signal:

[0200]

[0201] In the formula, ||w|| 2 is the modulus length of the window function,

[0202] get:

[0203]

[0204] S x (f k ,α) is shown in the FSC diagram Figure 3 As shown, its local enlargement is as follows Figure 4 shown.

[0205] Step 4: Identify the natural frequency of each component

[0206] According to the FSC transformation results of the signal, m = 3 fault signal components are extracted, and their natural frequency and impact frequency are [f k1 =400Hz,α1=20Hz],[f k2 =880Hz,α2=17Hz],[f k3 =1440Hz,α3=30Hz].

[0207] Compare the fault impulse frequencies of each component in Table 2 with the signal impulse frequencies [α1=20Hz, α2=17Hz, α3=30Hz]. main_g , the driving gear fails. α2=α slave_g , the driven gear fails. α3=α slave_bc , the driven wheel bearing fails. Finally, we get: [the self-vibration frequency of the driving gear is f k1 =400Hz, the self-vibration frequency of the driven gear is f k2 =880Hz, the natural frequency of the driven wheel bearing is f k3 =1440Hz].

[0208] Step 5: EMD decomposition

[0209] The signal decomposition termination threshold is set to ε = 8, and the original signal is decomposed by EMD, and a total of n = 9 IMF components I1, I2, ..., I9 and a residual signal r are decomposed. The time domain waveforms of each IMF component and the residual are shown in Figure 5.

[0210] Step 6: Identify fault signs

[0211] The I1,I2,…,I obtained by EMD decomposition n Perform spectrum analysis and draw the envelope of each spectrum, and obtain each spectrum and its envelope as shown in Figure 6.

[0212] The natural frequency of each IMF component is obtained from its spectrum and envelope as shown in Table 3, and it is compared with the natural frequency of the driving gear f k1 =500Hz, self-vibration frequency of driven gear f k2 =1000Hz, driven wheel bearing natural frequency f k3 =1400Hz] for comparison, it can be obtained that I1 corresponds to the bearing fault signal, I2 corresponds to the driven gear and bearing fault signal, I3 corresponds to the driving gear and driven gear fault signal, I4 corresponds to the driving gear fault signal, and [I5, I6, I7, I8, I9] are noise components.

[0213] Table 3 Natural frequency of each IMF component

[0214]

[0215] The bearing has a unique IMF component I1 corresponding to it, the driving gear has a unique IMF component I4 corresponding to it, and I2 and I3 containing the fault components of the driven gear respectively contain the fault components of other components. I2 with a relatively high IMF amplitude is selected as the fault signal of the driven gear. Finally, the driving gear fault signal I4, the driven gear fault signal I2, and the bearing fault signal I1 are obtained.

[0216] Step 7: Fault feature extraction

[0217] Calculate the RMS value of a signal:

[0218]

[0219] Substituting I1, I2, and I4 into equation (31), we get the bearing fault signal root mean square of 0.32 m / s 2 , the root mean square of the fault signal of the driving gear is 0.35m / s 2 , the RMS of the driven gear fault signal is 0.21m / s 2 .

[0220] Calculate the signal kurtosis:

[0221]

[0222] Substituting I1, I2, and I4 into equation (32), we can obtain the average kurtosis of the bearing fault signal is 43.20, the kurtosis of the driving gear fault signal is 13.28, and the kurtosis of the driven gear fault signal is 6.86 m / s. 2 .

[0223] In order to further verify the effectiveness of the present invention, a gear coupling fault test bench was built to collect coupling fault vibration signals for decoupling and feature extraction. The working conditions and fault types of the vibration signals are shown in Table 2, and 10 samples were collected in each group.

[0224] Table 2 Experimental sample working conditions and fault types

[0225] Driving gear failure Driven gear failure Speed load Wear Broken Teeth 2000rpm No load Wear Wear 2000rpm 50% load Broken Teeth Broken Teeth 2000rpm 100% load Wear Broken Teeth 1200rpm 50% load

[0226] According to the method proposed in the present invention, each signal sample is decoupled to obtain the driving gear fault signal and the driven gear fault signal of each sample. Among them, the decoupling signal of the "wear-broken tooth-2000rpm-no-load" sample is shown in Figure 7, and the decoupling signal of the "wear-wear-2000rpm-50% load" sample is shown in Figure 8. It can be seen from Figures 7 and 8 that the original sample is decomposed into two signal components with different vibration characteristics, indicating that the method proposed in the present invention can effectively realize the decoupling of fault signals.

[0227] According to the method of the present invention, the characteristics of each driving gear fault signal and driven gear fault signal obtained by decoupling are calculated, and the characteristic distribution of the driving gear and the driven gear is obtained as shown in Figure 9. As can be seen from Figure 9, the characteristics of the decoupling signals of the driving gear and the driven gear of different fault types are significantly different, indicating that the coupling fault feature extraction method proposed in the present invention can accurately extract the characteristics of each fault component.

[0228] In summary, the present invention proposes a gear multi-fault coupled signal decoupling and feature extraction method based on FSC transformation and EMD decomposition. For coupled fault signals of driving gears, driven gears, bearings and other components, signal component decoupling is achieved, and the features of each fault component are extracted respectively.

Claims

1. A gear multi-fault signal decoupling and feature extraction method based on FSC and EMD, characterized by: (1) Obtaining the gearbox coupling fault signal: placing the sensor on the surface of the gearbox, collecting the vibration signal generated during the operation of the gearbox, and storing the vibration signal in the form of a digital signal; (2) Calculate the fault impact frequency of the faulty components of the gearbox; (3) FSC transformation; (4) Identify the natural frequency of each component; (5) Perform EMD decomposition on the original signal; (6) Identify fault signals; (7) Extract fault features.

2. The gear multi-fault signal decoupling and feature extraction method based on FSC and EMD according to claim 1 is characterized in that: The faulty parts of the gearbox include the driving gear, the driven gear, and the bearings. The fault impact frequency calculation process is as follows. First, calculate the gear fault impact frequency. Assume that the speed of the shaft where the active gear is located is n1, and the active gear fault impact frequency α main for: Assume that the number of teeth on the driving gear is z1, the number of teeth on the driven gear is z2, and the transmission ratio between the driving and driven gears is g. r for: Fault impact frequency α of the driven gear slave for: Then calculate the bearing fault impact frequency. The bearing fault impact frequency is determined by its position and fault type. The bearing includes driving wheel bearing and driven wheel bearing according to its position. The bearing fault types include inner ring fault, outer ring fault, rolling element fault and cage fault. Assume the number of rolling elements in the bearing is z b , the rolling element diameter is d, the diameter of the circle where the rolling element center is located is D, and the bearing contact angle is θ. The rotation frequency of the shaft where the bearing is located is α r , bearing inner ring fault impact frequency α bi for: Bearing outer ring fault impact frequency α bo for: Bearing rolling element fault impact frequency α br for: Bearing cage failure impact frequency α bc for: According to the above inner ring fault impact frequency, outer ring fault impact frequency, rolling element fault impact frequency, cage fault impact frequency, the impact frequency of different bearing faults is related to the rotation frequency α r For the driving wheel bearing, α r =α slave , the impact frequencies of the four faults of the driving wheel bearing are obtained: α main_bi , α main_bo , α main_br , α main_bc ;for The driven wheel bearing, then α r =α slave , the impact frequency α of the four faults of the driven wheel bearing slave_bi , α slave_bo , α slave_br , α slave_bc ; The impact frequency of each component is: driving gear impact frequency α main , driven gear impact frequency α slave , bearing impact frequency [α main_bi ,α main_bo ,α main_br ,α main_bc ,α slave_bi ,α slave_bo ,α slave_br ,α slave_bc ].

3. The gear multi-fault signal decoupling and feature extraction method based on FSC and EMD according to claim 1 is characterized in that: The process of FSC transformation is: First, select the window function w = [w(1),w(2),…,w(p),…,w(N w )], where N w is the length of the window function; According to the STFT theory, the window function is applied to the original signal multiple times to calculate the original signal x = [x(1), x(2), ..., x(L)] in the i-th window, the frequency point f k Energy at X STFT (i,f k ): In the formula, f k =(k-1)Δf, k=1,2,…,N w , Δf=F s / N w , F s is the sampling frequency; i=1,2,…,I w , I w =L / R, R is the step size of windowing; Pair To perform phase correction, multiply it by Let q = p + i·R, substitute into the above formula, and get the Gabor form of the STFT transformation result X w (i,f k ): The signal is frequency shifted by α, then the signal is at frequency f k The energy at –α is: In the formula, α = k s / 2R,k s =1,2,…,F s ; According to the FSC transformation principle, when the frequency shift is α, according to X w (i,f k ) and X w (i,f k -α), calculate the fault component with impulse frequency equal to α at frequency point f k Energy S x (f k ,α): In the formula, ||w|| 2 is the modulus length of the window function, S x (f k ,α) is the result of FSC transformation, where α is the frequency shift and also the impact frequency of the periodic fault component. Set α=k s / 2R,k s =1,2,…,F s .

4. The gear multi-fault signal decoupling and feature extraction method based on FSC and EMD according to claim 1 is characterized in that: Step (4) is as follows: α, f k and S x (f k ,α) is called the FSC diagram of the signal. For coupled fault signals, m S x (f k ,α) frequency bands with higher values, read the α and f corresponding to these frequency bands k The signal contains natural frequency and impact frequency respectively [f k1 ,α1]、[f k2 ,α2],…,[f km ,α m ]; the signal impact frequency [α1,α2,…,α m ] are respectively related to the impact frequency [α main_g ,α slave_g ,α main_bi ,α main_bo ,α main_br ,α main_bc ,α slave_bi ,α slave_bo ,α slave_br ,α slave_bc ] to compare and determine [α1,α2,…,α m ] corresponding to the faulty component, and then determine the natural frequency [f k1 ,f k2 ,…,f km ] corresponds to the faulty component, and the total number of faulty components is m.

5. The gear multi-fault signal decoupling and feature extraction method based on FSC and EMD according to claim 1 is characterized by: EMD The decomposition steps are as follows: ① Input original signal x = [x(1), x(2), …, x(l), …, x(L)]; ② Identify all the maximum points of x, and use cubic spline interpolation to connect the maximum points so that the line between every two adjacent maximum points is a smooth cubic polynomial curve, thereby obtaining the upper envelope e max =[e max (1),e max (2),…,e max (l),…,e max (L)]; use the same method to obtain the lower envelope e min =[e min (1),e min (2),…,e min (l),…,e min (L)]; ③ Calculate the mean of the upper and lower envelopes m = [m(1), m(2), …, m(l), …, m(L)]: ④ Calculate the envelope difference h = [h(1), h(2), ..., h(l), ..., h(L)]: h(l)=x(l)-m(l),l=1,2,...,L ⑤ Determine whether h meets the conditions of the intrinsic mode: 1) In the entire signal length range, the number of maximum values ​​and the number of zero crossings must be equal or differ by one; 2) At any place on the time axis, the mean of the upper envelope spectrum formed by the signal maximum point and the lower envelope spectrum formed by the minimum point is zero; If not satisfied, set x = h and repeat steps ① to ⑤; If the conditions are met, let I1=h, and we get the first natural mode I1=[I1(1),I1(2),…,I1(l),…,I1(L)]; ⑥ Calculate the residual r1 = [r1(1), r1(2), …, r1(l), …r1(L)]: r1(l)=x(l)-I1(l),l=1,2,...,L Let x = r1, repeat steps ① to ⑥, and calculate the next natural mode I2, I3, ..., I n , where I n The corresponding residual is r n , r n =[r n (1),r n (2),…,r n (l),…,r n (L)]; When the modulus length of the residual signal is less than a given threshold, the signal decomposition terminates, that is: Where ε is the residual modulus length threshold; A total of n IMF components I1, I2, ..., I n , and a residual signal r = r n ; During the signal decomposition process, by setting an appropriate threshold ε, the number of IMF components n> the total number of faulty components m.

6. The gear multi-fault signal decoupling and feature extraction method based on FSC and EMD according to claim 1 is characterized by: The process of identifying the fault signal in step (6) is as follows: The I1,I2,…,I obtained by EMD decomposition n Perform spectrum analysis and obtain spectrum s1, s2, …s n , draw the envelope of each spectrum and find the frequency f at its maximum point w1 ,f w2 ,…,f wn , that is, I1,I2,…,I n The natural frequency of [f w1 ,f w2 ,…,f wn ] is compared with the natural frequency of each component to obtain the IMF component corresponding to each component. The IMF component without corresponding component is the noise component.

7. The gear multi-fault signal decoupling and feature extraction method based on FSC and EMD according to claim 1 is characterized by: The process of extracting fault features in step (7) is as follows: After determining the fault signal of each component, the fault characteristics of each component are calculated respectively; the root mean square and kurtosis reflect the amplitude and impact characteristic of the signal respectively, and the root mean square and kurtosis are selected as features; The signal RMS calculation formula is as follows: The calculation formula of signal kurtosis is as follows:

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