【正文】 International Journal of Machine Tools amp。 Manufacture 42 (2020) 467–472Damping capacity improvement of machine structures by closepacking with ballsYasunori Wakasawaa,*, Masatoshi Hashimotoa, Etsuo MaruibaDepartment of Mechanical Engineering, Toyota National College of Technology, 21 Eiseicho, Toyotashi 4718525, JapanbFaculty of Engineering, Gifu University, 11 Yanagido, Gifushi 5011193, JapanReceived 12 February 2020。 accepted 3 October 2020AbstractThis paper deals with an experimental investigation on damping characteristics of structures packed with balls. The structuresfor testing are square pipes packed with glass balls. The effects of impulse magnitude, square pipe dimensions, ball size andexcitation directions on damping characteristics are investigated. The experiments show that the damping characteristics are markedlyaffected by the ball size, and the damping capacity is improved by the ball packing. It is also shown that the damping capacity isaffected by the packing arrangements, packing ratio and repulsion coefficient. Dramatic improvement in damping capacity is achieved by leaving only a small space between the packed balls and the inner surface of the square pipe. This fact is confirmedexperimentally. ? 2020 Elsevier Science Ltd. All rights reserved.Keywords: Damping capacity。 Vibration。 Damping energy。 Glass ball。 Machine structure1. IntroductionAn outstanding design criterion for machine toolstructure with an effective damping capacity is requiredto achieve high accuracy and highefficiency cuttingoperations, since even a small vibration generated in amachine tool seriously affects machining accuracy.Some papers have reported damping capacityimprovement, including those dealing with steel–resinconcrete posite structure [1], overlaid with fiberreinforced plastics [2] which are a laminated positeof steel and high damping capacity material, and sandwich beam [3] in which a viscoelastic core is insertedbetween two steel plates. Moreover, various techniqueswere devised. In the nonobstructive particle damping(NOPD) technique [4], smalldiameter holes are drilledat appropriate locations inside the vibrating structuresand filled to the optimum level with a layer of particles,and the maximum damping capacity is attained for thedesired mode (or modes). An impact damper with granular materials [5] packed and movable in a container fixed* Corresponding author. Fax: +81565365924.Email address: (Y. Wakasawa).08906955/02/$ see front matter ? 2020 Elsevier Science Ltd. All rights reserved.PII: S08906955(01)001432to the primary vibrating system and a powder positedamper [6] packed with powder in a steel container witha high packing ratio, have also been reported. However,when packed materials were inserted in the structurecavity, the effects of impulsive excitation magnitude, thekinds of packed material, cavity shape etc. on the damping capacity were not made sufficiently clear in suchreports.In a precision machine tool, measures must be considered against the impulsive force from surroundingmachines in the light of many uncertain and unknownfactors. Many practical vibration isolation systems [7]for machinery and tools and for floor and building havebeen developed. However, when these plicated isolation systems are applied to machine tools, machiningcosts may be increased. If the damping capacity of themachine structure can be improved without anyadditional apparatus, it is more practical for machinetool operation.In the present study, the damping characteristics ofmachine structures packed with glass balls were investigated experimentally. Experiments were carried out forvarious impulsive forces, sizes of model structure andpacked ball. When balls were closely packed by excitation, the packing ratio of the balls was determined by468 Y. Wakasawa et al. / International Journal of Machine Tools amp。 Manufacture 42 (2020) 467–472Fig. 1. Experimental apparatus.the relation between the shape and size of the modelstructure and the packed balls. The ball arrangement andpacking ratio were obtained for various ball sizes. Theeffects of these factors on damping characteristics werealso exam