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Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.

This article proposes the application of a profile-shifted grinding disc to generate an offset, non-orthogonal and profile-shifted face gear. A detailed investigation of the modelling, tooth geometry and contact characteristics of the offset, non-orthogonal and profile-shifted face gear has been conducted. The mathematical models of the profile-shifted shaper cutter, profile-shifted pinion, profile-shifted grinding disc and offset, non-orthogonal and profile-shifted face gear are established. Considering the topological modification, the tooth surface equation of the offset, non-orthogonal and profile-shifted face gear is deduced. Based on the undercutting and pointing of the tooth surface, the limiting tooth width of the offset, non-orthogonal and profile-shifted face gear is determined, and a mathematical model of tooth contact analysis of the offset, non-orthogonal and profile-shifted face gear drive is established with the alignment errors. Using the approach presented in this article, an example of an offset, non-orthogonal and profile-shifted face gear drive and analytical results are presented.

In this paper, a mathematical model for large deformation of a cantilever beam subjected to tip-concentrated load is presented. The model is governed by nonlinear differential equations. Large deformation of a cantilever beam has number of applications is structural engineering. Since finding an exact solution to such nonlinear models is difficult task, this paper focuses on developing soft computing technique based on artificial neural networks (ANNs), generalized normal distribution optimization (GNDO) algorithm, and sequential quadratic programming (SQP). The strength of ANN modeling for governing the equation of cantilever beam is exploited by the global search ability of GNDO and further explored by the local search mechanism of SQP. Design scheme is evaluated for different cases depending on variations in dimensionless end-point load ρ . Furthermore, to validate the effectiveness and convergence of algorithm proposed technique, the results of the differential transformation method (DTM) and exact solutions are compared. The statistical analysis of performance indicators in terms of mean, median, and standard deviations further establishes the worth of ANN-GNDO-SQP algorithm.

Quality control is considered a critical aspect of plastic materials in the injection molding process. Two types of deformations occur during the injection molding process, namely, volumetric shrinkage and warpage. This study aims to optimize the warpage of the polyethylene terephthalate preform (PET) used for the packing of carbonated drinks. PET warpage results in an uneven distribution of material over the wall surface of the preform and causes variation in wall thickness. During the filling operation of carbonated drinks, the preforms are subjected to high pressure at the points where the wall thickness is at a minimum, which induces a high-stress concentration. Under high pressure, the preforms are ruptured at the points where the warpage is at a maximum (stress concentration area), causing wastage of the beverage as well as the preform. In this study, the Taguchi method and analysis of variance (ANOVA) are used to determine the most significant parameters to induce warpage during the molding process. Then, we optimize the process parameters in order to reduce warpage through a numerical approach using Solid Works Plastics. The result shows that the ambient temperature and melting temperature are the most critical parameters that contribute to the warpage, yielding 42.115% and 41.278%, respectively. Among the 6 parameters considered for this study, the pressure holding time contributes a minimum of 0.5961% to the yielding of the warpage. Overall, by optimizing the process parameters, warpage of the PET preform is minimized by 7.7202%, which helps to reduce wastage of the carbonated drink as well as the rejection rate of the preform during the filling operation. In a nutshell, the quality of the preform is improved.