Design of an optimal damper to minimize the vibration of machine tool structures subject to random excitation
The vibration of machine tools during machining adversely affects machining accuracy and tool life, and therefore must be minimized. The cutting forces for stable turning are generally known to be random, and hence excite all the resonance modes. Of all these modes, those that generate relative motions between a cutting tool and a workpiece are of concern.This paper presents a new approach for designing an optimal damper to minimize the relative vibration between the cutting tool and workpiece during stable machining. An approximate normal mode method is employed to calculate the response of a machine tool system with nonproportional damping subject to random excitation. The major advantage of this method is that it reduces the amount of computation greatly for higher-order systems when responses have to be calculated repeatedly in the process of optimization. An optimal design procedure is presented based on a representative lumped parameter model that can be constructed by using existing experimental or analytical techniques. The two-step optimization procedure based on the modified pattern search and univariate search effectively leads the numerical solution to the global minimun irrespectively of initial values even under the existence of many local minima.
The static and dynamic analysis of machine tools using dynamic matrix reduction technique
Abstract An approach, for condensing the system matrices of machine-tool structures, based on dynamiccondensation, is presented. The selection of the number of degrees of freedom to be retained in the condensed system, is based on the accurate representation of the first five modes of the original system. This is illustrated by an example of a lathe spindle-workpiece system. In this example, the system inertia, the damping and the stiffness matrices, which are orginally of the dimension 25×25, are condensed to a dimension of 12×12. Thus economy in the computation time and computer memory storage is realized. It is shown that this condensation technique is valid for the static case also.
Joint strength of aluminum ultrasonic soldered under liquidus temperature of Sn–Zn hypereutectic solder
Abstract In order to obtain high-strength aluminum joints, ultrasonic soldering of 1070 aluminum was conducted under liquidus temperature of Sn–Zn hypereutectic solder. A device for ultrasonic soldering was assembled, which propagated ultrasonic vibrations in a direction perpendicular to joining surfaces. This device joined 1070-Al using quasi-melting Sn–Zn hypereutectic solder without using any artificial spacers. The strength of the solder joints was evaluated by tensile tests. The optimum joining conditions were determined, and the effects of solder compositions and soldering temperature on the joint strength and the solder layer thickness were examined. In this ultrasonic soldering process, the highest tensile strength was obtained for the solder joints fabricated at 220 °C for the Sn–23Zn and Sn–40Zn solder compositions. The joint strength was equivalent to that of 1070-Al heat treated at 220 °C. The sound joints were obtained at 300 °C using Sn–82Zn solder, the liquid phase volume fraction of which was theoretically only 0.24. The present work also revealed that the thickness of retained solder layer in the joint after ultrasonic soldering could be estimated. Accordingly, ultrasonic soldering under the liquidus temperature of Sn–Zn hypereutectic solder could be a spacer-free soldering method to obtain high-strength aluminum joints.