Due to the development of high-performance engineering plastics, the application process of replacing steel with plastic has been accelerated, so that the proportion of plastics in the field of mechanical engineering has been increasing, and the materials for making gears are no longer limited to metal materials, and have developed to plastic gears.
Many applications and theoretical studies on plastic gears have been carried out at home and abroad, but compared with steel gears, the appearance time is late, the research time is shorter, and the experimental research on plastic gears, especially planetary gears, is rarely reported.
Moreover, researchers at home and abroad have a very immature understanding of the performance and application of plastic gears, but imitate and improve on the basis of steel gears, so it is necessary and significant to conduct experimental research on plastic gears.
From a general point of view, it is generally believed that because plastic materials have viscoelastic properties, they should have more obvious noise and vibration reduction properties.
In fact, for gears that transmit power, when the natural frequency and meshing frequency of the gear body are very close, even viscoplastic material gears will produce resonance and large noise, so the vibration and noise testing is also a very important aspect when designing plastic gears.
Moreover, compared with steel gears, when plastic gears are subjected to larger loads, the elastic deformation will increase, which will inevitably affect the stability and reliability of the entire mechanism, which shows that it is very necessary to study the vibration characteristics of plastic gears under different loads.
Meshing impact of gears
1. Gear noise generation mechanism
For gears with a standard involute profile, there is a single-tooth meshing near the knotline, and a double tooth meshing at a certain part on both sides of the knotline (the exact position is determined by the overlap factor) to the top and root of the tooth.
Therefore, the distribution of the load of each gear tooth during the meshing process is changed, and the change of load will cause the change of the gear tooth rigidity, thereby causing the vibration of the gear tooth, coupled with the manufacturing error and installation error of the gear, so that the collision between the tooth and the tooth will occur during meshing and produce shock vibration, which is called the meshing vibration of the gear.
Due to the excitation generated by the meshing vibration, the gear must generate forced vibration with the frequency of meshing frequency and its higher harmonics on the one hand, and transient self-excited vibration with a frequency of natural frequency on the other hand. Strong resonances can occur when the meshing frequency and natural frequency are integer multiples of each other.
Therefore, gear noise has two manifestations: one is the noise of the meshing frequency, and the other is the noise generated by the vibration of the entire gear at its natural frequency, so studying the vibration characteristics in these frequency bands is the key to designing plastic gears.
2. Meshing frequency and stiffness analysis
In this experiment, the vibration signal of the 2K-H plastic planetary gear was acquired, and the three-dimensional model and finite element model were shown in Figure 1.
Figure 1 Three-dimensional model and finite element model of 2K-H planetary gear
The gear pair's gear tooth stiffness alternating with the rotation of the gear, single and double pairs.
For the convenience of numerical theoretical analysis, most studies of gear dynamics expand it into Fourier series:
In this article, the circumferential frequency of meshing when the inner ring gear is fixed is a certain value, and its value can be expressed as
Using the finite element model in Figure 1, the meshing stiffness at 20 meshing points on the gear teeth is calculated according to the multi-meshing point calculation method, and the time-varying meshing stiffness is obtained by curve fitting as shown in Figure 2.
It can be seen from Figure 2 that when a plastic planetary gear is used instead of a steel planetary gear, its meshing stiffness changes greatly, and its vibration characteristics must change significantly compared with steel gears when operating under different loads.
Fig. 2 Meshing stiffness of a planetary gear pair
Fig. 2 Meshing stiffness of a planetary gear pair
Fig. 2 Meshing stiffness of planetary gear pair Figure 2 Meshing stiffness of planetary gear pair
Fig. 2: Meshing stiffness of a planetary gear pair
experiment
As shown in Figure 3, this experimental device is mainly composed of AC motor, planetary gear reducer, magnetic powder brake, frequency conversion speed governor, sensor and a set of signal collector.
Figure 3 Experimental equipment
In this experiment, the eddy-current sensor is used to calibrate the speed, and the vibration signal of the reducer is measured by the acceleration sensor, and 20 measurement points at different positions are selected in this experiment, and 4 are marked in Figure 3, and the 4 different measurement points are marked in Figure 3, and the vibration signal collected at 1 is found to be the most obvious, so the place is used as the best measurement point of this experiment for data collection.
The parameters of the plastic planetary gear for the test are shown in Table 1.
During the load operation of mechanical equipment, the periodic vibration signal measured by the sensor is sometimes difficult to distinguish on the time domain map, because it is overwhelmed by a strong random signal, in this case, if the signal measured by the sensor is analyzed by the power spectrum, it can be found that the measured signal not only has a periodic signal component of shaft or gear rotation frequency, but also has a periodic signal component of other frequencies.
Therefore, in this experiment, the method of self-power spectrum will be mainly used when processing the vibration signal of plastic planetary gear, and in order to avoid the influence of noise signal on the results to effectively extract the signal of each frequency band, filtering processing must be carried out, and the FIR digital filter will be selected in this experiment, and the window function-based tool function provided by the Matlab Signal Processing Toolbox will be used to achieve this function.
In order to measure the vibration characteristics of plastic planetary gears under different loads, this experiment uses magnetic powder brakes to apply 0N.m, 6N.m, 10N.m loads, starting from a frequency of 20Hz (1155r/min) every 1Hz interval to collect a set of data until 68Hz (3896r/min), the following is an example of the data measured with a load of 6N.m and a frequency of 40Hz (2274r/min), and the following is explained as follows:
To facilitate comparison, we performed cubic spline fitting of the acquired data at different loads and at different frequency bands, as shown in Figures 11 to 14.
In this study, the original time-domain signal collected was analyzed by self-power spectrum, time-domain filtering, and dimensionless, and it can be seen from the figure that the vibration signal of the reducer picked up in the test mainly includes: meshing frequency and its harmonics; On both sides of the meshing frequency and some other high-frequency components, the edge band due to the modulation effect; the shaft speed frequency and its low-order harmonics, which are caused by additional pulses generated repeatedly with each rotation of the gear shaft; Cross-modulation components and implicit components, etc.
From Figure 3, it can be seen that the vibration of plastic planetary gear is mainly distributed in the gear meshing base frequency band, 2 times frequency band, 3 times frequency band and 1/3, 1.5 times harmonic band and rotor unbalanced frequency band, etc., from Figure 4, Figure 5 can be clearly seen that the frequency band has obvious shock signal, the main reason for vibration is the influence of rotor imbalance.
Figure 6 ~ Figure 9 also reflects that in the plastic planetary meshing base band (/= 719Hz), meshing 2 times (/= 1392.8Hz) has a significant impact signal, which is mainly generated by the meshing impact of the plastic planetary gear itself, Figure 10 clearly reflects that the increase of load and speed can well suppress the rotor imbalance caused by shadow pool.
In Figure 11, it can be found that the increase of speed and load will significantly aggravate the vibration intensity of the base band of the plastic planetary gear meshing, and with the increase of load, its resonance peak will appear at a lower speed earlier than that of lower load, (when the load is 6N.m, it occurs at a speed of 3600r/min, and the load is 10N.m, and it appears at a speed of 3000r/min).
It can be seen from Figure 12 that in the 2 octave band, when the planetary gear mechanism is subjected to a small load (6N-m), a vibration peak occurs at a speed of 2300r/min, but as the speed continues to increase, the shock signal of this frequency band will be suppressed; As the load continues to increase, the vibration intensity at 2 times the meshing frequency is suppressed regardless of the change in speed (as shown in the 10N.m curve in the figure).
From Figure 13, it can be found that the vibration signal in the gear meshing 1/3 harmonic band is very complex, but it is similar to the situation of the meshing base band, and the vibration of the frequency band will increase as the load increases, and the large load will cause the vibration peak to appear earlier (when the load is 6N.m, it occurs at a speed of 2000r/min, and the load is 10N.m, and it appears at a speed of 2800r/min).
2. Analysis of experimental results
The transmission error of the gear mainly includes the following errors:
Tangential comprehensive error + tangential one tooth comprehensive error + tooth shape error + pitch error and pitch cumulative error + basal section deviation
Instrument and installation error:
Scale error = error when dividing the scale at the time of manufacture
Systematic error = scale error + subdivision error
Post-installation error = systematic error + effect of installation differences
In fact, the error curve is the result of a combination of factors, and sometimes it is necessary to deliberately change a certain factor to observe the change of the error curve in order to determine the nature and magnitude of the error.
Herringbone gears have a large degree of overlap, so their meshing stiffness is high and the stiffness change fluctuation is small, so the transmission error is also small.
It can be seen from Figure 3 and Table 1 that the amplitude of the tooth frequency transmission error before and after the modification is very small, and the amplitude of the tooth frequency transmission error after the modification is significantly reduced, and the measurement results verify that the analysis predicts that the tooth frequency error data are within the range of ±1arcsec, which also reflects the high accuracy and feasibility of the detection and analysis system.
Of course, the meshing frequency analysis also has shortcomings: it is the average of the vibration energy of many gears, so the amplitude increase is not very significant in the event of local gear damage or machining errors.
conclusion
My team proposed a method to detect the actual gear transmission error with high accuracy, and wrote the corresponding acquisition and analysis software. The measured results verify the feasibility and accuracy of the method, provide an experimental basis for further improving the design and processing of gears, and also provide a practical and effective means for the accurate detection of gear pairs required by high transmission accuracy.
(1) The vibration energy of plastic planetary gears is mainly distributed in the gear meshing base band, 2 times the frequency band, 3 times the frequency band, 1/3 and 1.5 times the harmonic frequency band and the rotor unbalance band.
(2) The increase in load significantly increases the vibration of the plastic planetary gear system in the meshing base band, especially the vibration at the resonance peak.
(3) The load and speed increase inhibits the vibration of the plastic planetary gear transmission in the meshing 2 frequency band.
(4) The increase in load aggravates the vibration of the plastic planetary gear in the 1/3 harmonic band, which makes the nonlinear behavior of the frequency band more complicated.
(5) The increase of load and speed effectively suppresses the vibration at the harmonic frequency of the shaft speed.
Our team's research will be of great significance to further understand the dynamic behavior of plastic planetary gears, improve transmission accuracy, reduce vibration and noise, and enrich and improve the design methods of planetary gear transmission, but the complex vibration signals of plastic planetary gear transmission need to be further analyzed.