A lumped mass gear-rattling model with backlash is established by considering the time varying mesh stiffness, composite transmission error and the torque fluctuation. Based on the principle that no separation will oc...A lumped mass gear-rattling model with backlash is established by considering the time varying mesh stiffness, composite transmission error and the torque fluctuation. Based on the principle that no separation will occur if the response amplitude is not larger than the static response, the threshold is obtained by theoretical derivation. The validity of the theoretical derivation is verified by the numerical method. The results show that the time-varying mesh stiffness has little effect on the threshold. When the exciting frequency is less than the system natural frequency, the theoretical agrees well with the numerical one. The higher the exciting frequency or the smaller the average input torque is, the easier the separation will occur. When the exciting frequency is larger than the natural frequency by a certain value, the theoretical threshold does not agree with the numerical results. The numerical results show that the motion state will change from the meshing state to the separating state directly. The phenomenon that the gear pair sometimes separates and sometimes meshes occurs only when the exciting frequency is smaller.展开更多
Rattling vibration is an important noise source of gear-box. To controlthat noise, it is necessary to elaborate a mathematics-mechanical model on rattlinggears. In this paper, a rattling system modulated by noise was ...Rattling vibration is an important noise source of gear-box. To controlthat noise, it is necessary to elaborate a mathematics-mechanical model on rattlinggears. In this paper, a rattling system modulated by noise was investigated. Insteadof performing the very tedious numerical calculation, a discrete stochastic modeldescribed by three dimensional mean mapping was established by means of the NonGaussian closure technique. Through the example, the chaotic stochastic behaviormay be revealed. In comparison with deterministic model, the model developed inthis paper is more approximate to practice adn more available for acousticinvestigation, so that it is suggested to be applied to modeling on rattling vibration.展开更多
We prepared (1-x)CaTiO3-xLaAlO3 (0 ≤x≤ 1) microwave dielectric ceramics using a conventional two-step solid-state reaction method,and investigated microwave dielectric properties of the ceramics in terms of A/B-site...We prepared (1-x)CaTiO3-xLaAlO3 (0 ≤x≤ 1) microwave dielectric ceramics using a conventional two-step solid-state reaction method,and investigated microwave dielectric properties of the ceramics in terms of A/B-site ionic-parameters.Ionic-parameters such as ionic polarizability,A-site bond valence,and ionic rattling were linked to the microwave dielectric properties.As the LaAlO3 content x in the (1-x)CaTiO3-xLaAlO3 ceramics increased from 0.3 to 0.7,the dielectric constant gradually decreased,which was attributed to the decrease of polarizability deviation and suppression of the cation rattling.The temperature coefficient of the resonant frequency decreased as the content of LaAlO3 increased because of the increase of A-site cation bond valence.The quality factor value (Q × f) increased as LaAlO3 content increased because of the enhancement of the order degree of B-site cation.A significant deterioration of the temperature coefficient of the resonant frequency and Q ×fvalue was observed at the composition x =0.5.These decreases were attributed to a phase transition from orthorhombic crystal (for x ≤ 0.5) to rhombohedral crystal (for x ＞ 0.5).展开更多
基金This project is supported by National Natural Science Foundation of China(No.50075070).
文摘A lumped mass gear-rattling model with backlash is established by considering the time varying mesh stiffness, composite transmission error and the torque fluctuation. Based on the principle that no separation will occur if the response amplitude is not larger than the static response, the threshold is obtained by theoretical derivation. The validity of the theoretical derivation is verified by the numerical method. The results show that the time-varying mesh stiffness has little effect on the threshold. When the exciting frequency is less than the system natural frequency, the theoretical agrees well with the numerical one. The higher the exciting frequency or the smaller the average input torque is, the easier the separation will occur. When the exciting frequency is larger than the natural frequency by a certain value, the theoretical threshold does not agree with the numerical results. The numerical results show that the motion state will change from the meshing state to the separating state directly. The phenomenon that the gear pair sometimes separates and sometimes meshes occurs only when the exciting frequency is smaller.
文摘Rattling vibration is an important noise source of gear-box. To controlthat noise, it is necessary to elaborate a mathematics-mechanical model on rattlinggears. In this paper, a rattling system modulated by noise was investigated. Insteadof performing the very tedious numerical calculation, a discrete stochastic modeldescribed by three dimensional mean mapping was established by means of the NonGaussian closure technique. Through the example, the chaotic stochastic behaviormay be revealed. In comparison with deterministic model, the model developed inthis paper is more approximate to practice adn more available for acousticinvestigation, so that it is suggested to be applied to modeling on rattling vibration.
文摘We prepared (1-x)CaTiO3-xLaAlO3 (0 ≤x≤ 1) microwave dielectric ceramics using a conventional two-step solid-state reaction method,and investigated microwave dielectric properties of the ceramics in terms of A/B-site ionic-parameters.Ionic-parameters such as ionic polarizability,A-site bond valence,and ionic rattling were linked to the microwave dielectric properties.As the LaAlO3 content x in the (1-x)CaTiO3-xLaAlO3 ceramics increased from 0.3 to 0.7,the dielectric constant gradually decreased,which was attributed to the decrease of polarizability deviation and suppression of the cation rattling.The temperature coefficient of the resonant frequency decreased as the content of LaAlO3 increased because of the increase of A-site cation bond valence.The quality factor value (Q × f) increased as LaAlO3 content increased because of the enhancement of the order degree of B-site cation.A significant deterioration of the temperature coefficient of the resonant frequency and Q ×fvalue was observed at the composition x =0.5.These decreases were attributed to a phase transition from orthorhombic crystal (for x ≤ 0.5) to rhombohedral crystal (for x ＞ 0.5).
