Iranian Journal of Mechanical Engineering Transactions of ISME
Volume:10 Issue: 1, Mar 2009

The equations governing the motion of steel balls and their impact onto shell liners in industrial Semi-Autogenous Grinding (SAG) mills are derived in full details by the authors and are used in order to determine the effective design variables for optimizing the working conditions of the mill and to avoid severe impacts which lead to the breakage of SAG mill shell liners. These design variables are the lifter height H, the working coefficient of friction μ, lifter face inclination angle φ, steel ball size rB, mill rotational velocity ω, and mill size R. In order to optimize the operating conditions and avoid severe impacts to its shell liners, the effect of these parameters need to be studied. The effect of lifter height (H) and the coefficient of friction (μ) on some of the main impact characteristics are simultaneously investigated for a SAG mill in Sarcheshmeh Copper Complex. It was shown that as the lifter height or the coefficient of friction increases, the impact position tends to move upward, but the maximum impact force and the absolute value of the maximum principal stress decreases, reducing the impact severity.

The growth of a two-phase cloud of a liquid fuel in a stagnant atmosphere is studied using computational fluid dynamic techniques. In order to predict the danger and hazard of such cloud in open atmosphere it is very important to determine the fuel concentration in the cloud, especially in the far field region from the fuel reservoir. The results show that with omission of droplets break up, the vaporization rate becomes very low due to large droplets and vapor cloud would be highly elongated. If the collision of droplets is neglected, vapor volume is higher. The results also show that when the height of device is increased, the cloud will have more symmetry. Any decrease in injection velocity leads to lower radial expansion of cloud. Reduction of injection time duration decreases the dangerous part of cloud slightly.

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approximation obtained by these approaches are valid uniformly even for very large parameters and are more accurate than straightforward expansion solution. The methods, which are proved to be mathematically powerful tools for solving the nonlinear oscillators, can be easily extended to any nonlinear equation, and the present paper can be used as paradigms for many other applications in searching for periodic solutions, limit cycles or other approximate solutions for real-life physics and engineering problems.

In the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. The cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axisymmetrically on the boundary surfaces. Material properties of the cylinder are assumed to vary through the thickness according to a power law function. In contrast to many previous researches, the FGM cylinder is not divided into isotropic sub-cylinders. A solution approach associated with the expansion of the transient wave functions in terms of a series of the Eigen functions is employed. The dynamic radial displacement expression is divided into quasi-static and dynamic parts and for each part, an analytical solution is presented. By this method, radial displacement and stress distributions in the functionally graded thick-walled cylinders are obtained for various values of the exponent of the power law function, various radius ratios, and various dynamic loads. Finally, advantages of the proposed method are discussed.