CN104156516B - Meshing phase difference-based phenomenological modeling method for normal single-stage epicyclic gear train - Google Patents
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Abstract
Disclosed is a meshing phase difference-based phenomenological modeling method for a normal single-stage epicyclic gear train. The meshing phase difference-based phenomenological modeling method includes calculating meshing phase differences between a plurality of planet gears and a central gear, namely a sun gear as well as the planet gears and a gear ring, and the meshing phase differences between one planet gear and the sun gear as well as the gear ring; analyzing influences of different transferring paths to signals during multiple meshing processes; establishing a simulation model of a vibration signal in the normal state of a planet gear train to achieve a vibration response expression. The meshing phase difference-based phenomenological modeling method breaks the limits that vibration influence of just one pair of meshing in the gear system is considered and comprehensively considers phase relations between multiple pairs of meshing in the epicyclic gear train and time-varying transferring path caused by revolution of the planet gears. According to the phenomenological model, the vibration response signal of the normal single-stage epicyclic gear train is achieved and verified by experiments, providing the basis for fault diagnosis of the single-stage epicyclic gear train.
Description
Technical Field
The invention belongs to the technical field of early fault diagnosis of mechanical equipment, and particularly relates to a normal single-stage epicyclic gear train phenomenological modeling method considering meshing phase difference.
Background
The epicyclic gear train is always a strand-arm beam in a gear transmission system, so that the epicyclic gear train can be widely applied to mechanical transmission in various industries such as wind power generation, aviation, ships, metallurgy, petrifaction, mines, hoisting and transportation and the like, and unique advantages of the epicyclic gear train have indispensable important functions, such as compact structure, large transmission ratio, high bearing efficiency and the like. However, the harsh operating environment of these devices causes the epicyclic gear train to normally operate under the conditions of low-speed heavy load or transient and large variation of load and rotating speed, so that the critical parts of the epicyclic gear train are firstly brought into the rush and faults occur.
The epicyclic gear train generally consists of a central wheel (i.e. a sun wheel), a planet wheel, an inner gear ring, a planet carrier and the like. Unlike an ordinary gear train, the structure inside thereof is relatively complicated. In general, the ring gear is stationary, the sun or planet carrier serves as the input, and correspondingly, the planet or sun gear serves as the output. The sun wheel rotates around the central shaft of the sun wheel, and the planet wheels not only rotate around the respective central shaft, but also revolve around the central shaft of the sun wheel and are simultaneously meshed with the sun wheel and the inner gear ring, so that the sun wheel is simultaneously meshed with the planet wheels, the planet wheels and the inner gear ring and other pairs of gears. The vibrations caused by the multiple pairs of meshing have phase differences and are mutually superposed, so that the vibration response of the epicyclic gear train is more complicated than that of the ordinary gear train.
The vibration signal time domain and frequency domain analysis method formsThe main theoretical basis of the fault diagnosis of the epicyclic gear train. Ideally, the planet gears in the epicyclic gear train are identical, so that the vibration frequency generated by each planet gear meshing with the inner gear ring and the sun gear is identical, i.e. the vibration frequency is the meshing frequency fm，fm＝Nrfc，NrNumber of teeth of ring gear, fcThe planet carrier rotates at a frequency, and only a certain phase difference exists between the meshing vibration. Furthermore, the sensor is usually mounted on a case connected to a fixed ring gear. Due to the revolution of the planet wheels, transmission paths between each meshing point and the sensor change periodically, and the transmission paths changing periodically can modulate the amplitude of meshing vibration signals. Therefore, even in a normal case, a plurality of side bands appear in the frequency spectrum of the epicyclic gear train vibration signal. The above factors make fault diagnosis of the epicyclic gear train more difficult than that of the ordinary gear train.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a normal single-stage epicyclic gear train phenomenological modeling method considering the meshing phase difference, which breaks through the limitation of only considering the influence of certain meshing vibration in a gear train and can comprehensively consider the phase relation between a plurality of pairs of meshes in the epicyclic gear train and a time-varying transmission path caused by the revolution of a planet wheel. From this phenomenological model, the vibration response signal of a normal single-stage epicyclic gear train is obtained.
In order to achieve the purpose, the invention adopts the technical scheme that:
a normal single-stage epicyclic gear train phenomenological modeling method considering meshing phase difference comprises the following steps:
1) respectively calculating phase differences between a plurality of planet wheels and a central wheel, namely a sun wheel, a plurality of planet wheels and a gear ring, and between the same planet wheel and the sun wheel and the gear ring in the epicyclic gear train;
2) analyzing the influence of different transmission paths of a plurality of meshing processes on signals on the basis of the step 1);
3) and (3) integrating the calculation results of the steps 1) and 2), establishing a vibration signal simulation model in the normal state of the epicyclic gear train, and giving a vibration response expression.
The calculation process of the step 1) is as follows:
1.1) respectively calculating the initial phase when the ith planet wheel is meshed with the inner gear ring according to the initial installation position of the planet wheel
Wherein Z isrRepresents the number of teeth of the ring gear; psiiRepresents the initial installation position of the ith planet wheel, namely the anticlockwise central angle from a fixed reference position;
1.2) similarly, calculating to obtain the initial phase when the ith planet wheel is meshed with the sun wheel
Wherein Z issRepresents the number of teeth of the sun gear; psiiRepresents the initial installation position of the ith planet wheel, namely the anticlockwise central angle from a fixed reference position;
1.3) phase difference gamma also exists between two groups of vibrations generated by the engagement of the same planet wheel with the sun wheel and the inner gear ring respectivelyrsAnd calculating to obtain:
wherein,representing the phase when the ith planet gear is engaged with the inner gear ring and the sun gear respectively.
The analysis process of the step 2) comprises the following steps:
2.1) analyzing all transmission paths of the vibration, besides, the vibration is transmitted to the sensor through oil, a box body and the like, but the vibration of other paths is obviously attenuated and does not dominate in a vibration signal, so that the vibration sensor does not consider,
2.2) ignoring the time-invariant transfer path, only considering the effect of the time-variant transfer path,
2.3) giving a functional expression of the transfer path.
The specific process of the step 3) is as follows:
analyzing each vibration one by one, then superposing the vibrations to obtain a vibration signal simulation model of the epicyclic gear train under normal conditions,
in the formula, N is the number of planet wheels;andrespectively represents the vibration caused by the meshing of the ith planet wheel and the inner gear ring and the ith planet wheel and the sun wheel, f represents the meshing frequency,representing engagement of the i-th planet with the internal-gear ringAt the initial phase, the phase of the phase-locked loop,representing the initial phase of the engagement of the ith planet wheel and the sun wheel; a. ther(t)、AsAnd (t) represents the transfer path function of meshing vibration of the planet wheels with the inner gear ring and the sun wheel respectively.
The core of the invention is to establish a vibration signal simulation model in the normal state of the epicyclic gear train and provide a response expression of the vibration signal. The method starts from an internal meshing transmission mechanism of the epicyclic gear train, comprehensively considers the phase difference among all meshing components, analyzes the transmission path of each meshing component, and establishes a vibration signal simulation model of the epicyclic gear train in a normal state. The model has the advantages that the limitation that only the influence of a certain pair of meshing vibration inside the gearbox is considered is broken through, the phase relation among multiple pairs of meshing inside the epicyclic gear train and the time-varying transmission path caused by the revolution of the planet wheel can be comprehensively considered. According to the phenomenological model, a vibration response signal of a normal single-stage epicyclic gear train is obtained, and experimental verification proves that the phenomenological model can provide a basis for fault diagnosis of the single-stage epicyclic gear train.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic structural diagram of a planetary gear train with three planetary gears.
FIG. 3 is a schematic view of the planetary gear mesh of FIG. 2.
Fig. 4 is a schematic diagram of a vibration transmission path of the planetary gear train in fig. 2.
FIG. 5 is a simulated signal waveform of a normal gear and its order spectrum.
FIG. 6 shows experimental signal waveforms and their order spectra for normal gears.
Detailed Description
The invention is described in further detail below with reference to the figures and examples.
In the planetary gear box on the test bed of the embodiment, an inner gear ring is fixed, a sun gear is used as an input end, and a planet carrier is used as an output end; specific parameters are shown in table 1.
TABLE 1 planetary gearbox parameters
Referring to fig. 1, a normal single-stage epicyclic gear train phenomenological modeling method considering meshing phase differences includes the steps of:
1) calculate the inside a plurality of planet wheels of epicyclic train and the meshing of sun gear, a plurality of planet wheels and the meshing of ring gear, same planet wheel and sun gear and the phase difference between the ring gear meshing respectively, the process of calculating the phase difference specifically as follows:
1.1) calculating initial phases of the ith planet wheel engaged with the inner gear ring respectively according to the initial installation positions of the planet wheels as shown in figure 2
Wherein Z isrRepresents the number of teeth of the ring gear; psiiRepresents the initial installation position of the ith planet wheel, namely the anticlockwise central angle from a fixed reference position;
1.2) similarly, calculating to obtain the initial phase when the ith planet wheel is meshed with the sun wheel
Wherein Z issRepresents the number of teeth of the sun gear; psiiRepresents the initial installation position of the ith planet wheel, namely the anticlockwise central angle from a fixed reference position;
1.3) phase difference gamma also exists between two groups of vibrations generated by the engagement of the same planet wheel with the sun wheel and the inner gear ring respectivelyrsFrom fig. 3, it can be seen that:
wherein p is a base segment, R in FIG. 3so、RsbRespectively representing the addendum circle radius and the base circle radius of the sun gear; rpo、RpbRespectively representing the radius of an addendum circle and the radius of a base circle of the planet wheel; rro、RrbRespectively representing the addendum circle radius and the base circle radius of the inner gear ring; p1Representing the node at which the sun wheel meshes with the planet wheels, Q1Is P1Corresponding to a point on the base circle of the planet, Q2And Q1By one tooth width. Q3When the sun wheel-planet wheel meshing pair is in P1When the points are meshed, the meshing points of the inner gear ring and the planet gears are located. P2Is a node of the planet gear engaged with the inner gear ring, B2For the engagement point of the planet wheel with the inner ring gear, E2Is the disengaging point of the planet wheel and the inner gear ring. Because the planet gear meshes with the sun gear and the inner gear ring respectively on different tooth surfaces, one tooth width needs to be reduced when the phase difference between the sun gear-planet gear meshing pair and the inner gear ring-planet gear meshing pair is calculated.
2) On the basis of the step 1), analyzing the influence of different transmission paths of a plurality of meshing processes on signals, wherein the specific process is as follows:
the meshing vibrations are transmitted to the sensor through a plurality of paths, and furthermore, the transmission paths between the meshing points and the sensor periodically change due to the revolution of the planetary gear, and fig. 4 shows six possible transmission paths.
2.1) analysis of all Transmission paths of vibrations
The transmission path of the meshing vibration of the single planet wheel and the sun wheel to the sensor is as follows: sun gear → sun gear central axis → case → sensor, sun gear → planet gear → inner gear → case → sensor, sun gear → planet gear central axis → planet carrier → case → sensor, as shown by the 1, 2, 3 routes in fig. 4; transmission path of meshing vibration with the ring gear to the sensor: planet wheel → sun wheel → central axis of sun wheel → box → sensor, planet wheel → central axis of planet wheel → planet carrier → sensor, planet wheel → inner gear ring → box → sensor, as shown in 4, 5, 6 in figure 4,
in addition, vibration can be transmitted to the sensor through oil, a box body and the like, but vibration of other paths is obviously attenuated and does not dominate in a vibration signal, so that only the six transmission paths are considered,
2.2) ignoring time-invariant transfer paths, taking into account only the effects of time-variant transfer paths
For the transmission paths 2 and 6, namely the sun wheel → the planet wheel → the inner gear ring → the box → the sensor and the planet wheel → the inner gear ring → the box → the sensor, the time-varying meshing point enables the distance between the vibration source and the sensor to be periodically changed, and further causes the amplitude of a signal received by the sensor to be periodically changed; the other four transmission paths can not change due to the revolution of the planet wheel, and only the whole energy of the vibration signal picked up by the sensor can change, so that when the model is established, the time-invariant transmission paths are ignored, and only the influence of the time-variant transmission paths 2 and 6 is considered;
2.3) giving a functional expression of the transfer path,
representing the transmission path by a Hanning Window function, denoted by Ar1(t) Representing the transfer path function 6 of the engagement of the first planet with the internal gear ring, denoted As1(t) represents the transfer path function 2 of the first planet-to-sun meshing, which can be expressed as
As1(t)＝kAr1(t)
Where k represents the attenuation due to the longer transmission path of the planet gears in mesh with the annulus gear than the transmission path of the planet gears in mesh with the sun gear, k <1,
for the transfer path 6: the transfer path functions of the meshing vibration of the other i planet gears and the inner gear ring are as follows:
Ari(t)＝Ar1[t+(i-1)T/3]
similarly, for the transfer path 2: the sun wheel → the planet wheel → the inner gear ring → the box → the sensor, and the transfer path function of the meshing vibration of the other i planet wheels and the sun wheel is as follows:
Asi(t)＝As1[t+(i-1)T/3]
3) integrating the calculation results of the steps 1) and 2), establishing a vibration signal simulation model in a normal state of the planetary gear train, and giving a vibration response expression, wherein the specific process is as follows:
analyzing each vibration one by one, then superposing the vibrations to obtain a vibration signal simulation model of the planetary gear train under normal conditions,
in the formula, N is the number of the planet wheels,andrespectively representThe vibration caused by the engagement of the i planet gears and the inner gear ring and the i planet gears and the sun gear, f represents the engagement frequency,represents the initial phase of the engagement of the ith planet wheel and the inner gear ring,representing the initial phase of the engagement of the ith planet wheel and the sun wheel; a. ther(t)、AsAnd (t) represents the transfer path function of meshing vibration of the planet wheels with the inner gear ring and the sun wheel respectively.
Fig. 5 shows a simulation signal obtained according to the model proposed by the method and an order spectrum thereof, a data length corresponding to a time domain waveform is twice of a revolution period T of the planet wheel, and 100 orders in the order spectrum correspond to the meshing frequency. As can be seen in the figure, there are three equally spaced envelopes within one revolution of the planet. This is because the planetary gear revolves for one cycle, and three planetary gears pass right below the sensor in sequence. Further, around the meshing frequency, a plurality of side bands appear in the order spectrum. This is caused by the modulation of the vibration signal by the time-varying transmission path due to the revolution of the planetary gear. But the side-band asymmetry phenomenon (mainly represented by higher amplitudes at 96, 99 and 102 orders) also appears in the order spectrogram of the simulation signal. The reason is that the amplitudes at the 96, 99 and 102 orders are enhanced after the calculated multiple pairs of meshing vibration of the three planet wheels and the inner gear ring are superposed due to the phase difference, and the amplitudes at other orders are weakened or even cancelled. In conclusion, the three equally-spaced envelopes are reasonably distributed, the meshing frequency in the order spectrogram is correct correspondingly, and the correctness of the established meshing vibration model is preliminarily verified.
In order to further verify the reasonability of the method, the method is applied to the analysis of the experimental data of the test bed. The vibration sensor is fixed on the planetary gearbox, the sampling frequency is 5120Hz, and the sampling length is 100 s. The waveforms and order spectra of the experimental data are shown in fig. 6. As can be seen from the time domain waveform diagram, the time domain waveform of the experimental data signal also has the phenomenon of time-varying transmission path modulation meshing vibration caused by the revolution of the planet wheel, and three envelopes with equal intervals appear in one revolution period of the planet wheel, and the amplitudes of the envelopes are almost equal. From the order spectrum, it can be found that the amplitudes of 96, 99 and 102 orders are larger, and the amplitudes of other orders are smaller, so that the two orders are well matched. However, the order spectrum of the measured signal contains many components which are not ideally "clean", because the measured signal is relatively complex and contains a lot of noise, and the laboratory bench inevitably has manufacturing errors, installation errors, and the like. In summary, compared with the simulation signal, the time domain waveform and the order spectrum of the two are consistent, and the correctness of the established meshing vibration model is further verified.
Therefore, the phenomenological modeling method can comprehensively consider factors such as a plurality of pairs of meshes in the epicyclic gear train, the phase relation between the pairs of meshes, the time-varying transmission path caused by the revolution of the planet wheel and the like, and is reasonable and comprehensive; the model has the advantages that the limitation that only one pair of meshing vibration influences in the gear system is considered is broken through, the phase relation among multiple pairs of meshing in the epicyclic gear system and the time-varying transmission path caused by the revolution of the planet wheel are comprehensively considered, the basis can be provided for effective diagnosis of early faults of the epicyclic gear system, and the model has good innovation.
While the invention has been described in further detail in connection with specific embodiments thereof, it will be understood that the invention is not limited thereto, and that various other modifications and substitutions may be made by those skilled in the art without departing from the spirit of the invention, which should be considered to fall within the scope of the invention as defined by the appended claims.
Claims (2)
1. A normal single-stage epicyclic gear train phenomenological modeling method considering meshing phase difference is characterized by comprising the following steps:
1) respectively calculating phase differences between a plurality of planet wheels and a central wheel, namely a sun wheel, a plurality of planet wheels and a gear ring, and between the same planet wheel and the sun wheel and the gear ring in the epicyclic gear train;
2) analyzing the influence of different transmission paths of a plurality of meshing processes on signals on the basis of the step 1); the analysis process of the step 2) is as follows:
2.1) analyzing all transmission paths of the vibration, in addition, the vibration is transmitted to the sensor through oil and a box body, but the vibration of other paths is obviously attenuated and does not dominate in a vibration signal, so that the vibration signal is not considered,
2.2) ignoring the time-invariant transfer path, only considering the effect of the time-variant transfer path,
2.3) giving a function expression of the transfer path;
3) integrating the calculation results of the steps 1) and 2), establishing a vibration signal simulation model in a normal state of the epicyclic gear train, and giving a vibration response expression; the specific process of the step 3) is as follows:
analyzing each vibration one by one, then superposing the vibrations to obtain a vibration signal simulation model of the epicyclic gear train under normal conditions,
in the formula, N is the number of planet wheels;andrespectively represents the vibration caused by the meshing of the ith planet wheel and the inner gear ring and the ith planet wheel and the sun wheel, f represents the meshing frequency,represents the initial phase of the engagement of the ith planet wheel and the inner gear ring,representing the initial phase of the engagement of the ith planet wheel and the sun wheel; a. ther(t)、AsAnd (T) represents a transfer path function of meshing vibration of the planet wheel with the inner gear ring and the sun wheel respectively, and T is the revolution period of the planet wheel.
2. A normal single-stage epicyclic gear train phenomenological modeling method taking into account meshing phase differences according to claim 1, wherein the calculation process of step 1) is:
1.1) respectively calculating the initial phase when the ith planet wheel is meshed with the inner gear ring according to the initial installation position of the planet wheel
Wherein Z isrRepresents the number of teeth of the ring gear; psiiRepresents the initial installation position of the ith planet wheel, namely the anticlockwise central angle from a fixed reference position;
1.2) similarly, calculating to obtain the initial phase when the ith planet wheel is meshed with the sun wheel
Wherein Z issRepresents the number of teeth of the sun gear; psiiRepresents the initial installation position of the ith planet wheel, namely the anticlockwise central angle from a fixed reference position;
1.3) phase difference gamma also exists between two groups of vibrations generated by the engagement of the same planet wheel with the sun wheel and the inner gear ring respectivelyrsAnd calculating to obtain:
wherein,representing the phase when the ith planet gear is engaged with the inner gear ring and the sun gear respectively.
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