| With the progress of the Industrial Revolution and the development of manufacturing industry,automatic mechanical equipment has occupied an irreplaceable position in human production and life.Gear transmission has undoubtedly become the preferred high-precision transmission mechanism for mechanical equipment,especially for large highprecision equipment.Under the condition of meeting the basic requirements of gear transmission,gear transmission error(TE)and vibration has become an important guiding target of gear system performance.Therefore,the measurement and analysis of TE and vibration characteristics of cylindrical gears are carried out in this paper.The aim of this paper is to discuss and utilize the meshing frequency modulation characteristics caused by gear errors,to construct a general method of extracting and separating the modulation sideband.In addition,considering the importance of TE measurement in gear design,manufacture and evaluation.The precision of TE measurement based on magnetic method is modeled and analyzed.The main contents of this paper are as follows:(1)A dynamic model considering the modulation characteristics caused by excitation error was established.On this basis,the dynamic model of spur gear was established by using lumped parameter method,and the geometric transmission error(GTE)and time-varying mesh stiffness(TVMS)in Fourier series form are introduced.The results of dynamic transmission error(DTE)and vibration response of the model show that the error excitation can modulate the meshing frequency components of the two signals.(2)A measurement accuracy analysis model of transmission error measurement method based on magnetic encoder is established.Based on the basic principle of magnetic grating,the calculation model of magnetic field distribution outside magnetic ring is derived,and the angle of magnetic ring encoder and transmission error measurement model are constructed.The angle measurement errors and its frequency distribution caused by installation height(0.1 ≤ h ≤ 0.7)and eccentric distance(0.02 ≤e ≤ 0.08)is quantitative analysed.At the same time,the influence of different installation height and eccentricity distance on the frequency distribution of transmission error is analyzed.(3)A method of sideband extraction and separation based on VMD,envelope demodulation(HED)and time domain synchronous average(TSA)is proposed.The validity of the method is verified by measured vibration signals.Using the method mentioned above,the distrubution characteristic of the sideband components of each gear corresponding to different constant rotational speed is analyzed and studied.(4)A testing and precision analysis platform of TE based on magnetic encoder is established.Using this mechanical enclosed cylindrical gear test-bed,the experimental research on the fault gears is carried out.The DTE of gears at different speeds are tested.The analysis of the test results shows that the magnetic method model is effective to explain the actual measurement.In addition,the sideband components of fault gears are analyzed by the sideband separation method,and the distribution characteristics of sideband components are given by observing statistics and estimating reconstruction.Finally,the general gear condition monitoring indexes are applied to the extracted sideband signals to determine the feasibility of the existing monitoring indexes on the sideband signals. |
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