Time?variant excitations in planetary gear trains can cause excessive noise and vibration and even damage the system on a permanent basis. This paper focuses on the elastic vibrations of a helical planetary ring gear subjected to mesh and planet?pass excitations. Motivated by the structure, excitation and deformation symmetries, this paper proposes dual?frequency superposition and modulation methods to capture the mesh and sideband vibrations. The transi?tion between ring gear tooth and planet is introduced to address the excitations and vibrations. The phasing e ect of ring gear tooth and planet on various deformations is formulated. The inherent connections between the two types of vibrations are identified. The vibrations share identical exciting rules and the wavenumber and modulating signal order both equal the linear combination of tooth and planet counts. The results cover in?plane bending and extensional, out?of?plane bending and torsional deformations. Main findings are verified by numerical calculation and comparisons with the open literature. The analytical expressions can be used to determine whether the sideband is caused by component fault or only by elastic vibration. The methods can be extended to other power?transmission systems because little restriction is imposed during the analysis.
Full face rock tunnel boring machine(TBM) has been widely used in hard rock tunnels, however, there are few published theory about cutter-head design, and the design criteria of cutter-head under complex geological is not clear yet. To deal with the complex relationship among geological parameters, cutter parameters, and operating parameters during tunneling processes, a cutter-head load model is established by using CSM(Colorado school of mines) prediction model. Force distribution on cutter-head under a certain geology is calculated with the new established load model, and result shows that inner cutters bear more force than outer cutters, combining with disc cutters abrasion; a general principle of disc cutters' layout design is proposed. Within the model, the relationship among rock uniaxial compressive strength(UCS), penetration and thrust on cutter-head are analyzed, and the results shows that with increasing penetration, cutter thrust increases, but the growth rate slows and higher penetration makes lower special energy(SE). Finally, a fitting mathematical model of ZT(ratio of cutter-head torque and thrust) and penetration is established, and verified by TB880 E, which can be used to direct how to set thrust and torque on cutter-head. When penetration is small, the cutter-head thrust is the main limiting factor in tunneling; when the penetration is large, cutter-head torque is the major limiting factor in tunneling. Based on the new cutter-head load model, thrust and torque characteristics of TBM further are researched and a new way for cutter-head layout design and TBM tunneling operations is proposed.
