In the past, family of elliptic gears with closed pitch curve includes elliptic gears, high-order elliptic gears, modified elliptic gears, and high-order and two-segment modified elliptic gears. On this basis, this article expands their connotation and unifies them into high-order and multi-segment modified elliptical helical gear (HOMSMEHG), and puts forward the expression of pitch curve. In order to obtain a physical model with real tooth flanks, this article proposed a parametric design approach on the HOMSMEHG based on virtual gear shaping, including decoupling basic parameters, parametric design based on the shaping cutter, and design of shaping linkage models, which had laid a theoretical foundation for designing the HOMSMEHG. Moreover, the realization technology of parametric design was also offered, which had solved the key problem of engineering implementation. Finally, two cases of designing internal and external gears are provided based on virtual gear shaping, which shows that the design approach of the HOMSMEHG and the virtual shaping method proposed in this article are feasible. The tooth flanks of the gears obtained has obvious cutting marks, and conforms to the real ones, which can ensure the reliability of the dynamic or kinematic analysis.

The condition of the drilling of a roof bolter for mine support system is complex, and the existing analytical approaches for the vibration of the drilling for oil wells cannot be fully applicable to it. In order to reveal the vibration mechanism of bolt drilling, some models for longitudinal, bending, and torsional coupled vibration were established based on the energy method and finite element method. A global matrix was assembled in the order of units. Taking the drilling condition as the boundary conditions, a reduced-order model was constructed. The simulations for drilling mudstone show that the order of mode shape is positively correlated with the corresponding natural frequency, and the low-order mode shape plays a decisive role in the vibration characteristics of a drill string. The order of causing drill string displacement from large to small is as follows: longitudinal vibration, torsional vibration, and bending vibration. Compared with the bit, the displacements of longitudinal and torsional vibration of the tail of the drill string are decreased by 93.2% and 84.7%, respectively. The perturbed force and reaction torque are the main reasons for inducing the coupled vibration of it. This research provides a theoretical basis for analysing the vibration characteristics of the drilling of roof bolters for mine support systems and developing their absorbers.

Due to the influence of uncertain external disturbance and model error, the trajectory tracking of manipulators has some problems such as inaccuracy, low speed and severe chattering. To solve the problems mentioned, a sliding mode control method combined fuzzy controller and Radial Basis Function Neural Network (RBFNN) was proposed. The RBFNN was used to approximate the equivalent system model of manipulators, and the weights of their hidden layers were updated adaptively online. The robust item with the form of sliding mode had been set to compensate the uncertain external disturbances or the approximation errors of the RBFNN. A fuzzy controller was used to adjust the switching gain online adaptively and to solve the chattering of the sliding mode control. The stability and finite time convergence of the closed-loop system had been analyzed by using Lyapunov method. Finally, simulation experiments about trajectory tracking were implemented by MATLAB/SIMULINK, which shows that the proposed method can improve the position-tracking accuracy by more than 40%, the speed-tracking accuracy by more than 70%, and the cumulative-error accuracy by more than 40% compared with the comparison method. Moreover, there is no chattering. The proposed method has been proved to be efficient.