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ABSTRACTIn the noncircular sprocket designing process, drawing the teeth cannot be automatically performed using any function in the drawing software, and it needs complicated manual operations and adjustments. The accuracy and time waste are big problems here. This paper proposes a procedure to automatically generate a complete 3D sprocket design from a set of sprocket pitch coordinates. Japanese standard tooth profile (JIS B 1801) is used as an example model in the procedure development. First, the tooth profile equation is derived using the theory of gearing in a particular coordinate system. Subsequently, the coordinate transformation matrix is built to attach the tooth profile on every sprocket pitch coordinate in the correct direction, remove some coordinates surpassing the outer diameter limit, and build the complete 3D sprocket profile. The proposed procedure can be implemented into programming languages with the sprocket pitch coordinate file as the input and the set of sprocket teeth coordinate as the output. With the proposed procedure, a 3D design of any shape sprocket can be generated quickly and accurately.

ABSTRACTGrinding is the final step in machine tool processing; it affects the accuracy and surface roughness of the machined parts. This study aims to improve the static and dynamic performance of precision grinding machines and reduce their deformation and avoid resonance. Based on the static characteristic analysis, the maximum deformation of the spindle head was determined to be 134 μm, which was reduced to 40 μm by applying a counterweight to the design. The first two modal frequencies obtained from the modal analysis were 26.9 and 27.7 Hz. The vibration of the second mode directly affected the processing accuracy of the machine. The vibration frequency and vibration modes of the structure were verified using the simulation results. These experiments and simulations helped improve the performance of the precision grinding machines. A transient response analysis method was implemented to investigate the influence of applied force during the simulation process, and experiments were conducted to evaluate the performance of the machine. As the saddle was increased by 200 mm, the modal frequency of the machine increased by 26% and reached 35.0 Hz. Our redesigning helped increase the modal frequency and avoid resonance at 30 Hz.