To limit velocity fluctuations and to achieve a controllable jerk value in a glass polishing process, a new velocity control algorithm is proposed based on nonuniform rational B-splines (NURBS). The key of this algorithm is replacing the traditional linear acceleration–deceleration with flexible NURBS acceleration–deceleration. Based on the linear acceleration–deceleration algorithm, the control points of the NURBS curve are confirmed, and the final velocity of the polishing wheel center is solved using the Preston equation. With jerk continuity and limitations of the servo system, nonlinear equations are constructed, and the weighting factors corresponding to the control points are obtained. Cubic velocity control equations can be derived from the obtained feature parameters, which include the final velocity, control points, weighting factors and knot vectors. Based on the proposed NURBS acceleration–deceleration algorithm, a fourth-order Runge–Kutta formula was used to obtain the initial points, and the Milne–Hamming equation was used to predict and correct the next point. The predictor-corrector interpolation algorithm for parametric trajectory was implemented during the polishing process. The experimental results indicate that the proposed approach guarantees limited fluctuations of the relative velocity at contact points and ensure smoother velocity changes at dangerous points.
Wear of runner blades is a common problem affecting the operational reliability of turbines with high head and high sediment content. In order to accurately predict the wear of the turbine runner blade, based on the solid-liquid two-phase flow equation and turbulence model, the full channel numerical simulation of the internal water and sediment flow was carried out, and the sediment volume distribution and sand water velocity on the turbine runner blade were obtained. Then, according to the digital simulation results and the operating parameters of the turbine runner, the sediment wear test scheme for the turbine blade material specimen is designed, and the sediment wear test is carried out on the runner material. According to the test results, the sediment wear curve of runner blade material is obtained and applied to numerical simulation, and the main position and wear degree of turbine blade sediment erosion are predicted. The inspection results of the runner blade wear after the unit has operated for a flood season show that obvious wear can be seen at the outlet edge of the lower band of the runner blade, and the wear position and wear amount are basically consistent with the simulation values. The study is of great importance for predicting the wear of turbine runner blades with high drop height and high sediment content, and for turbine maintenance under complex conditions.
To deal with a new-developed ferrite and pearlite wheel material named D1, an alternative ordinary state-based peridynamic model for fatigue cracking is introduced due to cyclic loading. The proposed damage model communicates across the microcrack initiation to the macrocrack growth and does not require additional criteria. Model parameters are verified from experimental data. Each bond in the deformed material configuration is built as a fatigue specimen subjected to variable amplitude loading. Fatigue crack initiation and crack growth developed naturally over many loading cycles, which is controlled by the parameter “node damage” within a region of finite radius. Critical damage factors are also imposed to improve efficiency and stability for the fatigue model. Based on the improved adaptive dynamic relaxation method, the static solution is obtained in every loading cycle. Convergence analysis is presented in smooth fatigue specimens at different loading levels. Experimental results show that the proposed peridynamic fatigue model captures the crack sensitive location well without extra criteria and the fatigue life obtained from the simulation has a good correlation with the experimental results.
To address flexural fractures and predict fatigue life, an ordinary state-based peridynamic (PD) fatigue model is proposed for the initiation and propagation of flexural fractures. The key to this model is to replace the traditional partial differential fracture model with a spatially integral peridynamic model. Based on the contact and slip theory, the nonlocal peridynamic contact algorithm is confirmed and the load transfer is through the contact area. With the 3D peridynamic J-integration and the energy-based bond failure criterion, the peridynamic fatigue model for flexural cracks’ initiation and propagation is constructed. The peridynamic solid consists of a pair of gear contact surfaces and the formation and growth of flexural fatigue cracks evolved naturally over many loading cycles. The repeated load is transferred from the drive gear to the follower gear using the nonlocal peridynamic contact algorithm. The improved adaptive dynamic relaxation approach is used to determine the static solution for each load cycle. The fatigue bending crack angle errors are within 2.92% and the cycle number errors are within 10%. According to the experimental results, the proposed peridynamic fatigue model accurately predicts the location of the crack without the need for additional criteria and the fatigue life predicted by the simulation agrees quite well with the experimental results.
In this work, we have developed a non-ordinary state-based peridynamic model for multiple crack initiation and propagation due to compression-compression fatigue load. In each loading cycle, the fatigue loading is redistributed among the peridynamic solid body, leading to the progressive fatigue damage initiation and propagation in an autonomous fashion. The proposed fatigue model parameters are firstly validated by 3D numerical benchmark tests, and then it is applied to simulate widespread fatigue damage evolution of the aircraft wing corner box. The modified constitutive damage model has been implemented into the peridynamics framework at finite strain. Furthermore, the criterion algorithm from multiple initiation to propagation is discussed. It is shown that the numerical results obtained from peridynamics simulations are in general agreement with those from the experiment data. The comparison of experimental and numerical results indicates that the proposed non-ordinary state-based peridynamics fatigue model has the ability to capture the multiple crack initiation and propagation and other features of the aluminium alloy material.
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