A mathematical model for simulating and manufacturing ball end mill
The performance of ball end mill cutters in cutting operations is influenced by the configuration of the rake and clearance faces in the ball component. From the mathematical design of a cutting edge curve, the rake face can be defined by the rake angle and the width of the rake face at each cross section along the cutting edge. We propose the fundamental conditions that must govern the engagement between the grinding wheel and the designed rake face in order to avoid interference while machining a ball end mill. As a result, a new mathematical model for determining the wheel location and a software program for simulating the generation of the rake face of a ball end mill are proposed. In addition, methods for grinding the clearance face in both concave and flat-shapes are introduced. The flute surface generated by a disk wheel during the grinding process is determined on the basis of a tangency condition. The results of the experiment and the simulation are compared to validate the proposed model.
Modeling and analysis of variable-core groove for integral cutting tools
With good stiffness, the helical groove with variable-core radius has been widely used for end mills, drills and other integral cutting tools. However, ground by five-axis grinder, its machining process is high cost and time consuming. Thus, this paper reports a graphical analysis method to obtain the structure parameters and geometric shapes of variable-core grooves with the known wheel geometry and position before the practical machining. The wheel movement during the machining process is firstly decomposed into three simple motions and modeled as a translation matrix. Then, a family of wheel surfaces is calculated and the groove cross section line is deduced by splitting the surfaces with a cross section plane. Accordingly, the normal section line of the groove is expressed by a series of scattered points, which are the intersections of the normal section plane and the helical curves generated by the points on the groove cross section line which moves along the wheel trajectory. All the mathematic models are programed by Matlab and verified by experiment. Finally, the key parameters of the variable-core groove, including the rake angle, groove width on the cross and normal sections and the departure distance between the cross and normal groove section lines, are analyzed from the tool bit to the hilt.
Effect of superficial gas velocity on the particle temperature distribution in a fluidized bed with heat production
The heat transfer behavior of particles and gas in an olefin polymerization fluidized bed was numerically analyzed using an in-house developed 3-D computational fluid dynamics discrete element model (CFD-DEM). First the implementation of the model was verified by comparing simulation results with analytical results. A constant volumetric heat production rate was implemented in the particle energy equation to mimic the heat production due to the polymerization reaction. It was found that the probability density function (PDF) of the particle temperature becomes more homogeneous with increasing superficial gas velocity. Furthermore, instantaneous snapshots of the thermal driving force (the difference between the single particle temperature and bed-average gas temperature, Tp− ) for different heat production rates provide detailed insight in the particle temperature distribution inside the fluidized bed. The time- and bed-averaged particle convective heat transfer coefficient, which was calculated by Gunn׳s correlation, was found to be independent of the superficial gas velocity. This is explained by the fact that the relative velocity of gas and particles in the emulsion phase, where most of the particles and gas interact, is hardly influenced when increasing the gas superficial velocity. From the spatial distribution of Nusselt number, it becomes apparent that the high heat transfer regions are found in the wake of rising bubbles, whereas low heat transfer rates are found in the clouds of the bubbles.