Gear dynamics analysis based on time-varying meshing stiffness (TMS) is an important means to understand the gear fault mechanism. Based on Jones bearing theory, a bearing statics model was established and introduced into a gear system. The lateral–torsion coupling vibration model of the gear shaft was built by using a Timoshenko beam element. The lumped parameter method was used to build the dynamic model of a gear pair. The dynamic model of a spur gear system was formed by integrating the component model mentioned above. The influence of rectangular and elliptical spalling on TMS was analyzed by the potential energy method (PEM). The fault feature of tooth spalling was studied by dynamic simulation and verified by experiments. It is found that the gear system will produce a periodic shock response owing to the periodic change of the number of meshing gear teeth. Due to the contact loss and the decrease of TMS, a stronger shock response will be generated when the spalling area is engaged. In the spectrum, some sidebands will appear in the resonance region. The results can provide a theoretical guide for the health monitoring and diagnosis of gear systems.
Wellbore instabilities frequently occur in mudstone formation with weak plane bedding because of strong anisotropies. The mechanics parameters of weak plane bedding are of vital significance to the wellbore stability analysis for mudstone formations. The conventional method for determining the mechanics parameters is to fit lots of triaxial test data due to the blindness of coring. In this paper, an evaluation method of the mechanics parameters of weak plane bedding is proposed to improve the accuracy of weak plane bedding mechanical properties. The mechanics parameters of weak plane bedding are obtained by combing the single-weak plane failure criterion with the compressive strength of rock obtained by the triaxial test of cores with different coring angles. It is seen that the new evaluation method is simple and convenient. On the other hand, a validation method of the mechanics parameters of weak plane bedding is proposed to ensure their accuracy. The compressive strength obtained from the core with the special coring angle is compared with the theoretical compressive strength for verifying the accuracy of weak plane bedding mechanical properties. It is observed that the proposed evaluation and validation methods can be used to measure the value of weak plane bedding mechanical properties precisely. The proposed methods are general and can be used for measuring the mechanical properties of fracture weak-plane and joint weak-plane.
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