A high-speed thin-webbed gear dangerous resonance frequency identification method

Abstract

The application provides a high-speed thin-web gear dangerous resonance frequency identification method. The method considers that gear damage is prone to occur under harmful working conditions of a transmission system, leading to failure, so that time domain diagrams and frequency spectrum diagrams of the gear under the working conditions are obtained by analyzing and processing vibration response data of the gear and fast Fourier transform (FFT). Further, a design life curve of the gear under the working conditions is drawn according to a material tensile curve and an S-N curve, and then data and images are combined to effectively find out a dangerous resonance point of the gear, and further obtain a dangerous resonance frequency of the gear. The method can realize determination of the dangerous resonance point and the dangerous resonance frequency of the gear vibration, and can well guarantee the precision of the extracted harmful resonance point. The method can be suitable for identifying dangerous resonance points and resonance frequencies under various working conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical resonance, in particular to a dangerous resonance frequency identification method for high-speed thin-web plate gears. BACKGROUND

[0002] In the field of aviation, the gear transmission system is widely used in the field due to the characteristics of high integration degree and multiple functions of the aero-engine accessory drive system. With the continuous improvement of the quality of aero-engine, the accessory drive system gear is designed to be lighter and thinner. At the same time, due to the service conditions of high speed, heavy load and high power density, the gear will produce severe vibration and impact during operation under severe conditions. At the same time, there are characteristics such as mode concentration, resonance band frequency domain width, high resonance peak, etc. Therefore, resonance structure damage and high cycle fatigue failure phenomena are prone to occur. Among them, the gear resonance caused by tooth fracture is the most hidden and destructive form of all gear failures. When the gear resonates, it will affect the vibration characteristics of the gear transmission system and even cause damage, which seriously threatens the safety of the system and may cause huge economic losses.

[0003] The traditional aero-engine gear resonance test method usually finds the resonance speed to prevent the resonance damage of the gear, but does not propose the dangerous resonance point and the dangerous resonance frequency. There is a method for obtaining the meshing resonance frequency band of the planetary gear train in the prior art. The method obtains the vibration signal of the planetary gear train in the target gear and the fault features contained in the vibration signal based on the meshing resonance distribution to obtain the resonance frequency band. The method finds the resonance frequency band of the gear, but is limited to finding the resonance frequency band, and does not predict the life of the gear at the dangerous resonance frequency.

[0004] Therefore, it is of great significance to develop a dangerous resonance frequency identification method for high-speed thin-web plate gears. SUMMARY

[0005] The purpose of the present application is to provide a dangerous resonance frequency identification method for high-speed thin-web plate gears to solve the problems in the prior art.

[0006] The technical solution adopted to achieve the purpose of the present application is as follows: a dangerous resonance frequency identification method for high-speed thin-web plate gears, comprising the following steps:

[0007] 1) Adopting a dynamic stress test system to collect the vibration response time domain signal of the measured high-speed thin-web plate gear.

[0008] 2) Dividing the time window, dividing the original signal data set into short time vectors, and calculating the strain mean value of a single time window

[0009] 3) Calculate the stress, stress mean value and stress amplitude of each time window. The fast Fourier transform is performed on the stress signal of each time window to obtain the frequency domain diagram of the gear under different working conditions.

[0010] 4) Draw the design life curve.

[0011] 5) Determine the dangerous resonance point and dangerous resonance frequency.

[0012] Further, in step 1), a strain gauge is installed on a designated position of the gear. The strain gauge is used to measure the vibration data of the gear during the speed sweep test.

[0013] Further, in step 2), time window division is performed according to the sweep time range.

[0014] Further, in step 2), the original vibration signal data set is divided into short-time vectors, as shown in the following expression:

[0015] {ε}→[ε1 ε2 … ε K … ε ns ] (1)

[0016] {ε} T →[ε1 ε2 … ε K … ε ns ] T (2)

[0017] Wherein: k = 1, 2…ns.

[0018] At the same time, the entire vibration signal data set is evenly divided into ns time windows, each containing nk points on average.

[0019] n k = len{ε} / ns (3)

[0020] And calculate the strain mean value of a single time window The calculation formula is as follows:

[0021]

[0022] Wherein: i = 1, 2…nk.

[0023] Further, in step 3), the strain signal of a single time window is processed to obtain the stress of a single time window:

[0024] σ = ε·E (5)

[0025] {D}→[σ1 σ2 … σ K … σ ns ] (6)

[0026] where σ represents stress, and E is the elastic modulus of the gear material.

[0027] The average stress is calculated The stress signal of each time window is subjected to a fast Fourier transform to obtain a frequency spectrum of each time window and determine the stress amplitude and the corresponding frequency.

[0028]

[0029]

[0030] Further, in step 4), the number of cycles N of the gear under the vibration working condition s :

[0031] N s = f m × L m (9)

[0032] where f m is the vibration frequency of the gear under the vibration working condition, and L m is the design life length of the gear, in units of s.

[0033] The mapping relationship between the number of cycles N s and the corresponding design life stress value σ d is found through the S-N curve diagram. The mapping relationship of σ d on the S-N curve diagram can be expressed as:

[0034]

[0035] where L m is the design life of the gear, in units of s. SN(N S → S) is the mapping relationship between the maximum number of cycles N s and the sinusoidal alternating load S in the S-N curve of the gear material.

[0036] The average stress in step 3) is taken as the y-axis, the stress amplitude is taken as the z-axis, and the rotational speed n is taken as the x-axis to establish a coordinate system. The design life curve formula is expressed as:

[0037]

[0038] where σ s is the yield limit of the gear material.

[0039] Further, in step 5), the stress average and the stress amplitude As stress sampling point is marked as The sampling point is determined in the design life curve diagram, and the distance of the stress sampling point to the design life curve is defined as the safety margin, marked as Δk.

[0040]

[0041] If the safety margin Δk of the stress sampling point to the design life curve is ≤0, the sampling point is a harmful dangerous resonance point, and the sampling point frequency is a harmful dangerous resonance frequency. If the safety margin Δk of the stress sampling point to the design life curve is >0, the sampling point is a safe point, and the design life requirement can be met.

[0042] The technical effect of the present application is self-evident:

[0043] A. The dangerous resonance point and its dangerous resonance frequency in the working speed range can be found intuitively and effectively.

[0044] B. The safety margin Δk reflects the safety of the gear operation condition, and the smaller the value of Δk, the higher the danger of the operation condition;

[0045] C. Good practicability, convenient operation, and worth popularizing. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is constituted for the design life line;

[0047] Figure 2 is defined for the safety margin;

[0048] Figure 3 is a flow chart of the dangerous resonance frequency identification method of the high-speed thin-web plate gear;

[0049] Figure 4 is a front view of the test spur gear;

[0050] Figure 5 is the installation position of the strain gauge of the test spur gear

[0051] Figure 6 is a Campbell diagram for analyzing the traveling wave resonance characteristics of the test spur gear;

[0052] Figure 7 is the relationship between the stress mean value and the speed of the test spur gear under different operating conditions;

[0053] Figure 8 is the relationship between the stress amplitude and the speed of the test spur gear under different operating conditions;

[0054] Figure 9 is the safety margin Δk of the test spur gear under different operating conditions;

[0055] Figure 10 is a sectional view of the test driving bevel gear;

[0056] Figure 11 Strain gauge installation position for testing driving bevel gear

[0057] Figure 12 Sectional view of driving bevel gear for testing

[0058] Figure 13 Strain gauge installation position for testing driving bevel gear

[0059] Figure 14 Determination of harmful resonance points of driving bevel gear under different working conditions DETAILED DESCRIPTION

[0060] The application will be further described below in conjunction with examples, but should not be understood as limiting the above-mentioned subject matter of the application to the following examples. According to ordinary technical knowledge and common practice in the art, various substitutions and modifications can be made without departing from the above-mentioned technical idea of the application, and all of them should be included in the protection scope of the application.

[0061] Example 1

[0062] The example provides a method for identifying dangerous resonance frequency of high-speed thin-webbed gear, comprising the following steps:

[0063] 1) A dynamic stress testing system is used to collect time-domain vibration response signals of the measured high-speed thin-webbed gear. Strain gauges are installed at the tooth root and tooth surface of the gear. The strain gauges are used to measure vibration data of the gear during the speed-up sweep frequency test. The input torque is kept constant during the test, and the speed is uniformly increased with the sweep time.

[0064] 2) Time window division is performed to divide the original signal data set into short-time vectors, and the strain average value ε of each time window is calculated. In step 2), the time window is divided according to the sweep time range.

[0065] The original vibration signal data set is divided into short-time vectors, and the expression is as follows:

[0066] {ε}→[ε1 ε2 … ε K … ε ns ] (1)

[0067] {ε} T →[ε1 ε2 … ε K … ε ns ] T (2)

[0068] Wherein, k=1, 2…ns.

[0069] At the same time, the whole vibration signal data set is evenly divided into ns time windows, each of which contains nk points on average.

[0070] n k = len{ε} / ns (3)

[0071] And the average strain of a single time window is calculated The calculation formula is as follows:

[0072]

[0073] Where: i = 1, 2… nk.

[0074] 3) Calculate the stress, stress average and stress amplitude of each time window. The stress signal of each time window is subjected to fast Fourier transform to obtain the frequency domain graph of the gear under different working conditions. In step 3), the strain signal of a single time window is subjected to data processing to obtain the stress of a single time window:

[0075] σ = ε · E (5)

[0076] {D}→[σ1 σ2 … σ K … σ ns ] (6)

[0077] In the formula, σ represents stress, and E is the elastic modulus of the gear material.

[0078] Calculate the average stress At the same time, the stress signal of each time window is subjected to fast Fourier transform to obtain the frequency spectrum graph of each time window and determine its stress amplitude And the corresponding frequency.

[0079]

[0080]

[0081] 4) Draw the design life curve graph. In step 4), the cycle number N s of the gear under the vibration working condition:

[0082] N s = f m × L m (9)

[0083] Where f m is the vibration frequency of the gear under the vibration working condition. L m is the design life length of the gear, unit: s.

[0084] Through the S-N curve graph, find the cycle number N s and its corresponding design life stress value σd The mapping relationship of the S-N curve can be expressed as: d The mapping relationship of the S-N curve can be expressed as:

[0085]

[0086] The mapping relationship of the S-N curve can be expressed as: S The mapping relationship of the S-N curve can be expressed as: s The mapping relationship of the S-N curve can be expressed as:

[0087] The average stress in step 3) is taken as the y-axis, The average stress in step 3) is taken as the y-axis, The average stress in step 3) is taken as the y-axis,

[0088]

[0089] The mapping relationship of the S-N curve can be expressed as: s The mapping relationship of the S-N curve can be expressed as:

[0090] 5) Determine the dangerous resonance point and the dangerous resonance frequency. In step 5), the stress average and the stress amplitude of each time window corresponding to different rotating speeds n are defined as stress sampling points, denoted as The sampling points are determined in the design life curve diagram, and the distance from the stress sampling point to the design life curve is defined as the safety margin, denoted as Δk.

[0091]

[0092] If the safety margin Δk of the stress sampling point to the design life curve is less than or equal to 0, the sampling point is a harmful dangerous resonance point, and the sampling point frequency is a harmful dangerous resonance frequency. If the safety margin Δk of the stress sampling point to the design life curve is greater than 0, the sampling point is a safe point and can meet the design life requirement.

[0093] The present embodiment considers that gear failure is prone to occur under harmful working conditions of the transmission system, so that the time domain diagram and the frequency spectrum diagram of the gear under the working condition are obtained by analyzing and processing the gear vibration response data and fast Fourier transform (FFT). Further, the design life curve of the gear under the working condition is drawn according to the material tensile curve and the S-N curve, and then the data and the image are combined to effectively find out the dangerous resonance point of the gear, and further obtain the dangerous resonance frequency of the gear. The method can realize the determination of the harmful dangerous resonance point of the gear vibration, and can well guarantee the precision of the extracted harmful resonance point. The method can be applied to identify the dangerous resonance point and the resonance frequency under various working conditions.

[0094] Example 2:

[0095] The embodiment provides a high-speed thin-web plate gear dangerous resonance frequency identification method, which comprises the following steps.

[0096] 1) A dynamic stress test system is used to collect vibration response time domain signals of the measured high-speed thin-web plate gear.

[0097] 2) Time window division is performed, the original signal data set is divided into short-time vectors, and strain mean values of individual time windows are calculated

[0098] 3) Stress, stress mean value and stress amplitude of each time window are calculated. Fast Fourier transform is performed on the stress signals of each time window, and frequency domain diagrams of the gear under different working conditions are obtained.

[0099] 4) A design life curve diagram is drawn.

[0100] 5) Dangerous resonance points and dangerous resonance frequencies are determined.

[0101] The embodiment provides a simple and accurate method for effectively finding dangerous resonance points of a high-speed thin-web plate gear and effectively finding dangerous resonance points possibly occurring in a working speed range of the gear and resonance frequencies corresponding to the dangerous resonance points.

[0102] Embodiment 3

[0103] The embodiment mainly comprises the same content as the embodiment 2, wherein a strain gauge is installed on a specified position of the gear. The strain gauge is used to measure vibration data of the gear in the process of the speed-up sweep frequency test.

[0104] Embodiment 4

[0105] The embodiment mainly comprises the same content as the embodiment 2 or 3, wherein in step 2), time window division is performed according to a sweep frequency time range. In step 2), the original vibration signal data set is divided into short-time vectors, and the expression is as follows:

[0106] {ε}→[ε1 ε2 … ε K … ε ns ] (1)

[0107] {ε} T →[ε1 ε2 … ε K … ε ns ] T (2)

[0108] Wherein, k=1, 2, …, ns.

[0109] Meanwhile, the entire vibration signal data set is evenly divided into ns time windows, and each time window contains nk points on average.

[0110] n k = len{ε} / ns (3)

[0111] And the average strain of a single time window is calculated, and the calculation formula is as follows:

[0112]

[0113] Wherein: i = 1, 2… nk.

[0114] Example 5:

[0115] The main content of this embodiment is the same as any one of examples 2-4, wherein in step 3), the stress of a single time window is obtained by data processing of the strain signal of a single time window:

[0116] σ = ε · E (5)

[0117] {D}→[σ1 σ2 … σ K … σ ns ] (6)

[0118] In the formula, σ represents stress, and E is the elastic modulus of the gear material.

[0119] Calculate the average stress At the same time, the stress signal of each time window is subjected to fast Fourier transform to obtain the frequency spectrum of each time window and determine the stress amplitude and the corresponding frequency.

[0120]

[0121]

[0122] Example 6:

[0123] The main content of this embodiment is the same as any one of examples 2-5, wherein in step 4), the cycle number N s of the gear under the vibration working condition is:

[0124] N s = f m × L m (9)

[0125] Wherein, f m is the vibration frequency of the gear under the vibration working condition. L m is the design life length of the gear, unit: s.

[0126] Through the S-N curve diagram, the mapping relationship between the cycle number N s and the corresponding design life stress value σ d is found. Then σ dThe mapping relationship in the SN curve can be represented as:

[0127]

[0128] In the formula, SN(N) S →S) represents the maximum number of cycles N in the SN curve of the gear material. s The mapping relationship between the sinusoidal alternating load S and the load S.

[0129] The average stress in step 3) As the y-axis, Establish a coordinate system with the z-axis as the z-axis and the rotational speed n as the x-axis. The design life curve formula is then expressed as:

[0130]

[0131] Where, σ s This represents the yield strength of the gear material.

[0132] Example 7:

[0133] The main content of this embodiment is the same as any one of embodiments 2 to 6, wherein, in step 5), the average stress value corresponding to different rotational speeds n is defined for each time window. and stress amplitude The stress sampling point is denoted as The sampling points are determined on the design life curve diagram, and the distance from the stress sampling point to the design life curve is defined as the safety margin, denoted as Δk.

[0134]

[0135] If the safety margin Δk from the stress sampling point to the design life curve is less than or equal to 0, the sampling point is a hazardous resonance point, and the sampling point frequency is the hazardous resonance frequency. If the safety margin Δk from the stress sampling point to the design life curve is greater than or equal to 0, the sampling point is a safe point and can meet the design life requirements.

[0136] Example 8:

[0137] This embodiment provides a method for identifying the dangerous resonance frequency of high-speed thin-spread gears, including the following steps:

[0138] 1) Strain gauges are installed at designated positions on the gear for measuring its dynamic stress. Further, a speed-sweep frequency method is used, where the output torque of the test gear is fixed while the rotational speed of the tested high-speed thin-spoke gear is increased uniformly over a time range. This allows the vibration response data, i.e., the strain signal, of the tested high-speed thin-spoke gear to be extracted from the dynamic stress testing system.

[0139] 2) The strain signal extracted by the dynamic stress measurement system is time windowed according to the sweep time range, and the original vibration signal dataset is divided into short time vectors, as shown in the following expression:

[0140] {ε}→[ε1 ε2 … ε K … ε ns ] (1)

[0141] {ε} T →[ε1 ε2 … ε K … ε ns ] T (2)

[0142] wherein k = 1, 2, …, ns.

[0143] Meanwhile, the entire vibration signal dataset is evenly divided into ns time windows, each containing nk points on average.

[0144] n k = len{ε} / ns (3)

[0145] The average strain of a single time window is calculated as The calculation formula is shown below:

[0146]

[0147] wherein i = 1, 2, …, nk.

[0148] 3) The stress of a single time window is obtained by data processing of the strain signal of the single time window.

[0149] σ = ε·E (5)

[0150] {D}→[σ1 σ2 … σ K … σ ns ] (6)

[0151] In the formula, σ represents stress, and E is the elastic modulus of the gear material.

[0152] The average stress is further calculated as Meanwhile, the stress signal of each time window is subjected to fast Fourier transform (FFT) to obtain the frequency spectrum of each time window and determine the stress amplitude and the corresponding frequency.

[0153]

[0154]

[0155] 4) Draw the design life curve, as shown in Figure 1 . The specific process is as follows:

[0156] Assuming the gear in the vibration working condition, the vibration frequency is f m , the design life is L m , unit: s. Then the cycle number N s :

[0157] N s = f m × L m (9)

[0158] Further through the S-N curve diagram, find the cycle number N s and the corresponding design life stress value σ d mapping relationship. Then σ d in the S-N curve diagram of the mapping relationship can be expressed as:

[0159]

[0160] In the formula, SN(N S →S) is the mapping relationship between the maximum cycle number N s and the sinusoidal alternating load S in the S-N curve of the gear material.

[0161] Further, the average stress in step 3 is taken as the y-axis, the z-axis is taken as the z-axis, and the speed n is taken as the x-axis to establish the coordinate system. Then the design life curve formula is expressed as:

[0162]

[0163] Where σ s is the yield limit of the gear material.

[0164] 5) Determine the dangerous resonance point and the dangerous resonance frequency. Define the stress average and the stress amplitude corresponding to different speeds n of each time window as the stress sampling point, that is Determine the sampling point in the design life curve diagram, and define the distance from the stress sampling point to the design life curve as the safety margin, denoted as Δk.

[0165]

[0166] The safety margin is defined as shown in Figure 2 . When the safety margin Δk of the stress sampling point to the design life curve is ≤0, the sampling point at this time is a harmful dangerous resonance point, and the sampling point frequency at this time is a harmful dangerous resonance frequency; when the safety margin Δk of the stress sampling point to the design life curve is >0, it is a safe point and can meet the design life requirement.

[0167] Example 9:

[0168] Referring to Figure 3 , the embodiment provides a high-speed thin-web gear dangerous resonance frequency identification method, comprising the following steps.

[0169] 1) A strain gauge is installed on the fixed position of the gear for measuring the vibration data of the gear during the speed-up sweep frequency test. The measured high-speed thin-web gear is as shown in Figure 4 , and the strain gauge installation position is as shown in Figure 5 . The test spur gear parameters are shown in Table 1, and the speed-up sweep frequency test parameters are shown in Table 2.

[0170] Table 1

[0171]

[0172] Table 2

[0173]

[0174] The modal analysis is performed on the measured high-speed thin-web gear, the low-order modal frequency of the measured high-speed thin-web gear is extracted, the corresponding test spur gear traveling wave resonance speed and resonance frequency are shown in Table 3, and the Campbell diagram is drawn as shown in Figure 6 .

[0175] Table 3

[0176]

[0177] 2) The strain signal extracted from the dynamic stress measurement system is time windowed according to the sweep frequency time range, the original vibration signal is divided into short time vectors, and then the vibration signal is divided into ns time windows. In this embodiment, the collected gear vibration signal is divided into ns time windows, ns = 300, and each time window contains nk points on average.

[0178] n k = len{ε} / ns (1)

[0179] Further calculation of the strain average of a single time window

[0180]

[0181] 3) The strain signal of a single time window is processed to obtain the stress of a single time window.

[0182] σ = ε·E (3)

[0183] {D}→[σ1 σ2 … σ K … σ ns ] (4)

[0184] In the formula, σ represents stress, and E is the elastic modulus of the gear material.

[0185] Further calculation of mean stress Simultaneously, a Fast Fourier Transform (FFT) is performed on the stress signal of each time window to obtain the spectrum of each time window and determine its stress amplitude. and the corresponding frequency;

[0186]

[0187]

[0188] The stress, mean stress, and stress amplitude for each time window can be obtained from equations (3) to (6). The relationship between the mean stress and rotational speed under different working conditions is shown below. Figure 7 As shown, the relationship between stress amplitude and rotational speed under different working conditions is as follows: Figure 8 As shown. Simultaneously, a Fast Fourier Transform (FFT) is performed to obtain the frequency domain diagrams of the gear under different operating conditions.

[0189] 4) Draw the design life curve. In this embodiment, it is assumed that the gear is under vibration conditions, and the vibration frequency is the natural frequency f. m Lifespan not less than L m =1000h, i.e., L m =3.6×10 6 s.

[0190] N s =f m ×L m (7)

[0191] For a rotating high-speed thin-spoke gear under test, it possesses two rotating vibration waves. When the pitch line rotates in the same direction as the gear's rotation, it is a forward traveling wave; when the pitch line rotates in the opposite direction, it is a backward traveling wave. When the gear experiences N-pitch diameter vibration, its forward / backward traveling wave resonant frequencies are:

[0192] f (f / b) =f m ±Nf m / (zN) (8)

[0193] The number of alternating sinusoidal loads that a single particle of the gear will experience within its theoretical design life under resonant conditions is:

[0194] N s =L m [f m ±Nf m / (zN)] (9)

[0195] Further analysis using the SN curve reveals the number of iterations N.s and the corresponding design life stress value σ d of the mapping relationship. For the forward wave, the backward wave, then σ d The mapping relationship of the S-N curve diagram can be expressed as:

[0196]

[0197] The design life stress value σ d of the forward wave and the backward wave can be obtained from equation (10) as 36 MPa and 41 MPa, respectively.

[0198] The average stress σ in step 3) is taken as the y-axis, the rotational speed n is taken as the x-axis, and a coordinate system is established. Then the design life curve formula is expressed as:

[0199]

[0200] The design life curve equation is determined from equation (11).

[0201] The forward wave design life line equation is:

[0202]

[0203] The backward wave design life line equation is:

[0204]

[0205] 5) Determine the dangerous resonance point and the dangerous resonance frequency. Define the stress average σ and the stress amplitude σ of each time window corresponding to different rotational speeds n as the stress sampling points, that is, Determine the stress sampling points in the design life curve diagram, and define the distance from the stress sampling points to the design life curve as the safety margin, denoted as Δk.

[0206]

[0207] The stress average σ and the stress amplitude σ Figure 9The corresponding rotational speed and safety margin Δk of the back wave resonance point and the front wave resonance point of the test spur gear are 2972.8 r / min and Δk = 40.28 MPa, respectively, when the torque Ti = 10 N·m; the corresponding rotational speed and safety margin Δk of the back wave resonance point and the front wave resonance point of the test spur gear are 3026.2 r / min and Δk = 37.61 MPa, respectively, when the torque Ti = 20 N·m; the corresponding rotational speed and safety margin Δk of the back wave resonance point and the front wave resonance point of the test spur gear are 3013.4 r / min and Δk = 38.43 MPa, respectively, when the torque Ti = 30 N·m. Through comparative analysis of the results, it can be concluded that the safety margin Δk of the stress sampling point of each time window to the design life curve is greater than zero at the resonance rotational speed under different working conditions, and is a safe point. At this time, the resonance point frequency is the safe working resonance frequency. The resonance point and the corresponding resonance frequency of the test spur gear are shown in Table 4.

[0208] Table 4

[0209]

[0210] Through the above test conclusion and analysis in the Campbell diagram, it can be concluded that the gear will produce front wave and back wave resonance near the three-pitch rotational speed. Further analysis of the sweep test data shows that the gear rotational speed will resonate near the three-pitch rotational speed range under different working conditions. The specific analysis is as follows:

[0211] a. When the torque is 10 N / m, 2972.8 r / min may occur three-pitch back wave resonance, and 3159.5 r / min may occur three-pitch front wave resonance.

[0212] b. When the torque is 20 N / m, 3026.2 r / min may occur three-pitch back wave resonance, and 3200.1 r / min may occur three-pitch front wave resonance.

[0213] c. When the torque is 30 N / m, 3013.4 r / min may occur three-pitch back wave resonance, and 3212.8 r / min may occur three-pitch front wave resonance.

[0214] According to the comparison of the data obtained by analysis, the maximum frequency error of the front wave is 3.75%, and the maximum frequency error of the back wave is 3.56%. Therefore, it can be further concluded that the test results are highly consistent with the simulation calculation results. This method can be used to identify the dangerous resonance point and the dangerous resonance frequency of the gear.

[0215] Example 10:

[0216] This embodiment provides a method for determining the harmful resonance point of high-speed gears according to any one of the methods in Embodiments 1 to 8, for testing the driving and driven bevel gears (such as...). Figure 10 12), the installation positions of the strain gauges of the driving and driven bevel gears are as follows: Figure 11 13. Determine the critical resonance point. The driving and driven bevel gears undergo speed-up frequency sweep tests under torque conditions Ti = 10 N·m, Ti = 20 N·m, and Ti = 30 N·m. Analyze and calculate the measured dynamic stress data to obtain the safety margin Δk from each stress sampling point to the design life curve. Figure 14 Generally, the traveling wave resonance of gears has resonance points for the forward and backward traveling waves.

[0217] Depend on Figure 14 It can be obtained that: for the driving bevel gear, when the torque Ti = 10 N·m, the speed and stress amplitude corresponding to the rear traveling wave resonance point are 6301 r / min and 1.68 MPa, respectively, and the speed and stress amplitude corresponding to the front traveling wave resonance point are 6718 r / min and 1.50 MPa, respectively. The safety margins to the design life line are Δk = 38.93 MPa and Δk = 38.85 MPa, respectively. When the torque Ti = 20 N·m, the speed and stress amplitude corresponding to the rear traveling wave resonance point are 6177 r / min and 2.52 MPa, respectively, and the front traveling wave resonance point... The corresponding rotational speed and stress amplitude are 6598 r / min and 3.06 MPa, respectively, and the safety margins to the design life line are Δk = 37.76 MPa and Δk = 37.01 MPa, respectively. When the torque Ti = 30 N·m, the corresponding rotational speed and stress amplitude at the rear traveling wave resonance point are 6357 r / min and 3.76 MPa, respectively, and the corresponding rotational speed and stress amplitude at the front traveling wave resonance point are 6361 r / min and 4.01 MPa, respectively, and the safety margins to the design life line are Δk = 36.39 MPa and Δk = 37.12 MPa, respectively.

[0218] For the driven bevel gear, when the torque Ti = 10 N·m, the corresponding rotational speed and stress amplitude of the back wave resonance point are 5758 r / min and 1.72 MPa, respectively, and the corresponding rotational speed and stress amplitude of the front wave resonance point are 6260 r / min and 1.55 MPa, respectively, and the safety margin to the design life line is Δk = 38.15 MPa and Δk = 38.16 MPa, respectively; when the torque Ti = 20 N·m, the corresponding rotational speed and stress amplitude of the back wave resonance point are 5600 r / min and 3.51 MPa, respectively, and the corresponding rotational speed and stress amplitude of the front wave resonance point are 6093 r / min and 3.61 MPa, respectively, and the safety margin to the design life line is Δk = 36.50 MPa and Δk = 36.25 MPa, respectively; when the torque Ti = 30 N·m, the corresponding rotational speed and stress amplitude of the back wave resonance point are 5806 r / min and 4.70 MPa, respectively, and the corresponding rotational speed and stress amplitude of the front wave resonance point are 6261 r / min and 5.82 MPa, respectively, and the safety margin to the design life line is Δk = 35.33 MPa and Δk = 33.90 MPa, respectively.

[0219] The resonance point corresponding rotational speed and stress amplitude of the main and driven bevel gears under different working conditions are shown in Table 5.

[0220] Table 5

[0221]

[0222] From the result analysis of the present embodiment, it can be obtained that since the test working condition is small and no dangerous resonance frequency appears, all resonance points are safe points. The method has high precision for picking up dangerous resonance points, can accurately and independently separate out dangerous resonance points, and thus obtain dangerous resonance frequency, which is beneficial to the prediction and prevention of gear dangerous resonance.

Claims

1. A method for identifying dangerous resonance frequencies of a high-speed thin-webbed gear, characterized by, The method comprises the following steps: 1) collecting the time domain signal of the vibration response of the measured high-speed thin-web plate gear by using a dynamic stress testing system; 2) Perform time windowing, segmenting the raw signal dataset into short time vectors and calculating the strain mean for individual time windows 3) calculating the stress σ, the stress mean value and the stress amplitude for each time window performing a fast Fourier transform on the stress signal for each time window to obtain a frequency domain diagram of the gear under different working conditions; 4) Draw the design life curve; the number of cycles N of the gear under the vibration condition s : N s = f m x L m (1) Wherein, f m is the vibration frequency of the gear under the vibration working condition; L m is the gear design life length, unit: s; The mapping relationship between the cycle number N and the corresponding design life stress value σ is found through the S-N curve diagram. s d The mapping relationship in the S-N curve diagram can be expressed as:​ where SN(N S represents the maximum number of cycles N s for the gear material S-N curve and the mapping relationship between the sinusoidal alternating load S. with the stress mean value in step 3) as the y-axis, the stress amplitude as the z-axis, the rotational speed n as the x-axis; the design life curve formula is expressed as: where σ s is the yield limit of the gear material; 5) Determine dangerous resonance points and dangerous resonance frequencies; define the stress mean value corresponding to different rotating speeds n for each time window and stress amplitude as stress sampling points Determine the sampling points in the design life curve diagram, and define the distance from the stress sampling point to the design life curve as the safety margin, denoted as Δk; If the safety margin Δk of the stress sampling point to the design life curve is less than or equal to 0, the sampling point is a harmful dangerous resonance point, and the sampling point frequency is a harmful dangerous resonance frequency; if the safety margin Δk of the stress sampling point to the design life curve is greater than 0, the sampling point is a safe point and can meet the design life requirement.

2. The dangerous resonance frequency identification method of a high-speed thin-webbed plate gear according to claim 1, characterized in that: In step 1), a strain gauge is installed on a specified position of the measured high-speed thin-web plate gear; the strain gauge is used to measure the vibration data of the measured high-speed thin-web plate gear during the speed-up sweep frequency test.

3. The method of claim 1, wherein: In step 2), time window division is performed according to the sweep frequency time range.

4. The dangerous resonance frequency identification method of a high-speed thin-webbed plate gear according to claim 3, characterized in that, In step 2), the original vibration signal data set is divided into short-time vectors, and the expression is as follows: {ε}→[ε1 ε2…ε K …ε ns ] (5) {ε} T →[ε1 ε2…ε K …ε ns ] T (6) Wherein, k = 1, 2…ns; At the same time, the whole vibration signal dataset is evenly divided into ns time windows, each of which contains an average of n k points. n k = len{ε) / ns (7) and the average strain of a single time window is calculated The calculation formula is shown as follows: Wherein, i = 1, 2…nk.

5. The method of claim 1, wherein, In step 3), the stress of a single time window is obtained by performing data processing on the strain signal of the single time window: σ = ε·E (9) {D}→[σ1 σ2…σ K …σ ns ] (10) Computing the stress mean value Simultaneously performing a fast Fourier transform on the stress signal of each time window to obtain a frequency spectrum of each time window and determine the stress amplitude value thereof and the corresponding frequency: In the formula, σ represents stress, and E is the elastic modulus of the gear material.

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