Evaluation of drag force on a nonuniform particle distribution with a meshless method

A meshless Element-Free Galerkin （EFG） method was used to directly simulate the fluidization process in two dimensions. The drag force on particles was obtained by integrating the stress and shear forces on the particle surfaces. The results show that meshless methods are capable of dealing with real particle collisions, thus are superior to most mesh-based methods in reflecting the fluidization process with frequent particle collisions and suitable void fractions. Particle distribution greatly influences the drag coefficients even for the same voidage, that is, there are large differences in the average drag coefficients between nonuniform and uniform particle distributions. Different compacting directions also have different regu- larities, so conventional formulas such as ＇Wen and Yu＇ and ＇Felice＇ models have some deviations in such nonuniform distributions. To evaluate the influence of the nonuniformity, the drag force in multiple particle systems was simulated by using nonuniformity coefficients, Cvx and Cvy, to quantitatively describe the nonuniform distribution in different directions. Drag force during fluidization can be successfully evaluated by the use of Cvx alone.

Working Principle and Error Analysis for Hemispherical Resonator Gyro under Force-rebalance Mode

The two control methods, namely the general-control and the quadrature-control modes for HRG under force-rebalance mode were introduced firstly. Then the azimuth of antinode on the hemispherical resonator was deduced. The dynamics equations of resonator under the nonuniformity of density distribution were established by way of Bubonov-Galerkin method which is commonly used for solution of differential equations, and the state equation was established through the dynamics equations. The analytic solutions of the vibration displacement and the velocity were achieved by solving the state equation, and then the ratio of rebalance excitation to primary excitation was derived under the two working modes, thus the estimation of input angular rate of HRG were obtained. By comparing and calculating these two modes, the error caused by resonator's machining defects can be greatly inhibited under quadrature-control, and the fourth harmonic density error's tolerance were calculated to ensure the accuracy of HRG under these two modes.

A comparative study of surface waviness models for predicting vibrations of a ball bearing

Surface waviness models utilized to describe the excitation events in the ball bearings(BABs) play an important role in predicting the vibrations of the ball bearing systems. This work proposes a comparative study on the most relevant existing surface waviness models. One model is named as time-varying displacement(TVD) model, which can only describe the time-varying displacement excitation(TDIE). Another model is named as TVDS model, which can describe the TDIE and time-varying contact stiffness coefficient excitation(TCSE). The influences of the wave number, maximum amplitude, nonuniform distribution on the contact stiffness coefficients are studied, as well as vibrations of the BAB. The comparative results demonstrate that the time-varying displacement and stiffness(TVDS) model can provide a more accurate impulses caused by the uniform and nonuniform surface waviness on the races of the BABs. It also seems that the surface waviness distribution has a significantly influence on vibrations of the BABs.