Static and dynamic performance evaluation of a 3-DOF spindle head using CAD–CAE integration methodology

Accurate and rapid modeling and performance evaluation over the entire workspace is a crucially important issue in the design optimization of parallel kinematic machines (PKMs), especially for those dedicated for high-speed machining where high rigidity and high dynamics are the essential requirements. By taking a 3-DOF spindle head named A3 head as an example, this paper presents a feature-based CAD–CAE integration methodology for the static and dynamic analyses of PKMs. The approach can be implemented by four steps: (1) creation of a parameterized geometric (CAD) model with analysis features in SolidWorks; (2) extraction of the features from the CAD model using the Application Programming Interface (API) available in SolidWorks; (3) formulation of a CAD model in SAMCEF by mapping the configuration features from SolidWorks to SAMCEF; and (4) conversion of the analysis features into a scripting language named Bacon for Finite Element Analysis (FEA). The merit of this approach lies in that the FE model at different configurations can be updated automatically in batch mode, and PKMs having different topologies can be modeled with ease thanks to the down to link/joint level featuring. The experiment is also carried out to verify the effectiveness of the proposed approach

Ship Pipe Routing Design Using NSGA-II and Coevolutionary Algorithm

Pipe route design plays a prominent role in ship design. Due to the complex configuration in layout space with numerous pipelines, diverse design constraints, and obstacles, it is a complicated and time-consuming process to obtain the optimal route of ship pipes. In this article, an optimized design method for branch pipe routing is proposed to improve design efficiency and to reduce human errors. By simplifying equipment and ship hull models and dividing workspace into three-dimensional grid cells, the mathematic model of layout space is constructed. Based on the proposed concept of pipe grading method, the optimization model of pipe routing is established. Then an optimization procedure is presented to deal with pipe route planning problem by combining maze algorithm (MA), nondominated sorting genetic algorithm II (NSGA-II), and cooperative coevolutionary nondominated sorting genetic algorithm II (CCNSGA-II). To improve the performance in genetic algorithm procedure, a fixed-length encoding method is presented based on improved maze algorithm and adaptive region strategy. Fuzzy set theory is employed to extract the best compromise pipeline from Pareto optimal solutions. Simulation test of branch pipe and design optimization of a fuel piping system were carried out to illustrate the design optimization procedure in detail and to verify the feasibility and effectiveness of the proposed methodology

An Improved Algorithm for Calculating Friction Force and Torque in Involute Helical Gears

Time varying frictional force and torque are one of the main exciting sources of vibration in helical gears. This paper presents an approach to determine the friction force and torque in involute helical gears considering nonuniform load distribution along contact lines. An analytical load distribution model is employed and extended to obtain the load per unit of length along contact lines. Friction force and torque models under nonuniform assumption are derived. Comparisons of the determined friction force and torque with the results from uniform assumption are made. In addition, the differences between constant friction coefficient and varying coefficient are revealed. Moreover, two typical design cases of helical gears are studied. Results show that the fluctuations of friction force and torque under uniform assumption are more significant than those under nonuniform assumption in sample I for a single tooth, but less significant for the sum of those of the three teeth, while in sample II, the fluctuations under uniform assumption are less significant than those under nonuniform assumption. The friction coefficient induced difference is negligible compared with the difference induced by load distribution assumptions

COMPARATIVE STUDY ON FREQUENCY DOMAIN FATIGUE ANALYSIS METHODS FOR HALF AXLE OF COMBINE HARVESTER

The calculation models of frequency domain fatigue analysis method are various and their accuracy is different. In order to solve the above problems, based on the time domain analysis results of the half axle, the accuracy comparison of frequency domain fatigue analysis methods is carried out. Firstly, the load signals of the half axle under different working conditions are obtained, and the stationarity, Gaussianity and bandwidth were investigated to obtain the basic properties of the load signal. Secondly, the static analysis of the half axle was carried out, and the transfer coefficients of stress and torque at the dangerous node of the walking half axle were obtained. Meanwhile, the stress time histories of the dangerous node of the half axle under various working conditions were obtained. Based on the above stress time histories, the comparative study of fatigue life in time-frequency domain was carried out, in which the average stress and non-Gaussian correction model were introduced to modify the traditional frequency domain method. The results showed that the accuracy of the modified frequency domain method was significantly better than that of the traditional frequency domain method. In the modified frequency domain method, TB2ms+nG and DKms+nG had the highest accuracy. When the above two methods were applied to the stationary load signals, the reliability was high. Nevertheless, when they were applied to the non-stationary load signals, the reliability was low

Multiobjective Optimization of Steering Mechanism for Rotary Steering System Using Modified NSGA-II and Fuzzy Set Theory

Due to the complicated design process of gear train, optimization is a significant approach to improve design efficiency. However, the design of gear train is a complex multiobjective optimization with mixed continuous-discrete variables under numerous nonlinear constraints, and conventional optimization algorithms are not suitable to deal with such optimization problems. In this paper, based on the established dynamic model of steering mechanism for rotary steering system, the key component of which is a planetary gear set with teeth number difference, the optimization problem of steering mechanism is formulated to achieve minimum dynamic responses and outer diameter by optimizing structural parameters under geometric, kinematic, and strength constraints. An optimization procedure based on modified NSGA-II by incorporating dynamic crowding distance strategies and fuzzy set theory is applied to the multiobjective optimization. For comparative purpose, NSGA-II is also employed to obtain Pareto optimal set, and dynamic responses of original and optimized designs are compared. The results show the optimized design has better dynamic responses with minimum outer diameter and the response decay decreases faster. The optimization procedure is feasible to the design of gear train, and this study can provide guidance for designer at the preliminary design phase of mechanical structures with gear train

Effect of modification coefficient on nonlinear dynamic characteristics of planetary drive with small teeth number difference

Planetary Drive with Small Teeth Number Difference (PDSTND) is widely utilized in industry for its advantages including large transmission ratio, huge torque and high efficiency. However, interference can easily occur due to the small teeth number difference between annulus and planetary gear, which can be solved by modification. Besides, noise and vibration are still the remained problems to influence its working performance. In order to discover the interaction of modification coefficient and vibration, a nonlinear dynamic model is established by using Lagrange equation and solved by the fourth-order Runge-Kutta method. Modification coefficient, backlash and transmission error are used as the control parameters to investigate their effects on the dynamic characteristics of the system, by means of bifurcation diagrams, Poincaré maps, trajectories and frequency spectrums. The results show that the system turns into quasi‑periodic motion, and then alternates between period‑ ( 5, 6) and chaotic motion as modification coefficient increases. Moreover, the responses of backlash and transmission error to the system get more complex with increasing modification coefficient. The results can provide new theoretical basis for the design, manufacture and fault diagnosis of PDSTND

An Improved VMD-Based Denoising Method for Time Domain Load Signal Combining Wavelet with Singular Spectrum Analysis

Measured load data play a crucial role in the fatigue durability analysis of mechanical structures. However, in the process of signal acquisition, time domain load signals are easily contaminated by noise. In this paper, a signal denoising method based on variational mode decomposition (VMD), wavelet threshold denoising (WTD), and singular spectrum analysis (SSA) is proposed. Firstly, a simple criterion based on mutual information entropy (MIE) is designed to select the proper mode number for VMD. Detrended fluctuation analysis (DFA) is adopted to obtain the noise level of the noisy signal, which can optimize the selection of MIE threshold. Meanwhile, the noisy signal is adaptively decomposed into band-limited intrinsic mode functions (BLIMFs) by using VMD. In addition, weighted-permutation entropy (WPE) is applied to divide the BLIMFs into signal-dominant BLIMFs and noise-dominant BLIMFs. Then, the signal-dominant BLIMFs are reconstructed with the noise-dominant BLIMFs processed by WTD. Finally, SSA is implemented for the reconstructed signal. Experimental results of synthetic signals demonstrate that the presented method outperforms the conventional digital signal denoising methods and the related methods proposed recently. Effectiveness of the proposed method is verified through experiments of the measured load signals