Bulletin of the JSME Transactions of the JSME (in Japanese) 日本機械学会論文集 [DOI: 10.1299/transjsme.22-00192] この記事は   [ 表示 - 非営利 - 改変禁止 4.0 国際 ] の下に提供さていす。 (https://creativecommons.org/licenses/by-nc-nd/4.0/deed.ja) Vol.88, No.916, 2022 © 2022 The Japan Society of Mechanical Engineers 1. 緒 言 回転しながら移動する物体は，多くの製品中にみられ，その動を記述する基礎を確立しておくことは重要で ある．物理の科書（原島，1970；藤原，1991；Berkley Physics，1973；Timoshenko and Young，1956，渡 辺他訳，1967）では，円柱がすべることなくころがる問題が取り上げられている．そこでは，円柱も面も，表 面は凹凸のない剛体として扱い，並と回転の立微分程式を解く．しかし，水平面上でのその解は，空気抵 抗を無視すると，等速動となり，永久に転がり続けるものとなる．これは非現実的である．この現実との矛盾 をけるために，これまでは，回転動との立を無視して，並動の式に，ころがり摩擦力を導入してきた． 1 Keywords : Rolling friction, Friction torque, Rolling friction coefficient, Elastic histeresis, High-speed train ころがり摩擦トルクを基礎とした円柱の回転運動の分析 Analysis of rotational motion of cylinder based on rolling friction torque Shosuke SASAKI *1 , Yohe NAMBA *2 , Tadao IWANARI *3 and Yasuyuki KITANO *4 *1 Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University. Osaka, Japan *2 Izumo Shimane Prefectural Senior High School, 1800 Imaichi-cho, Izumo, 693-0001, Japan *3 Matsue Minami High School Supplementary Course. Yakumodai 1-1-1, Matsue, Shimane, 690-8519, Japan *4 Professor Emeritus, Shimane University, Maeguma Nishiwaki 20-1, Nagakute, Aichi 480-1102, Japan Abstract In the problem of cylinder rolling without slipping on a horizontal floor, both the cylinder and floor are generally treated as rigid bodies in normal textbooks. When the air resistance is ignored, the equation of motion has a solution with a constant velocity. However, in the real world, permanent motion does not occur. The difficulty can be solved by taking account of vertical force. Two main origins of vertical force are described. 1) Both a cylinder and a floor are not perfect circle and not perfect plane, but have uneven surfaces. The micro bumps on the surface yield small collisions in the direction perpendicular to the floor. The collisions generate rolling friction torque around the center. 2) A strong force acts on the contact part which is deformed. The high-speed deformation produces a history effect on the relationship between stress and strain, because the compressed wave in the contact part diffuses to the outside at the speed of sound. Then rolling friction torque is also generated. Both are originated by the forces perpendicular to the floor. The rolling friction torque derives velocity decrease of the cylinder. To solve the simultaneous differential equations of rotation and translation is important. This method is useful for studying rolling systems such as trains and cars. Received: 22 June 2022; Revised: 28 August 2022; Accepted: 6 November 2022 佐々木 祥介 *1 ，南波 陽平 *2 ，岩成 唯夫 *3 ，北野 保行 *4 No.22-00192 [DOI:10.1299/transjsme.22-00192], J-STAGE Advance Publication date : 15 November, 2022 *1 正員，大阪大学大学院理学研究科先端強磁場科学研究センター 招聘教員（自宅〒664-0856 兵庫県伊丹市梅ノ木 5-4-20） *2 島根県立出雲高等学校（〒693-0001 島根県出雲市今市町 1800） *3 松江南高等学校 補習科（〒690-8519 島根県松江市八雲台 1—1-1） *4 正員，島根大学 名誉教授（自宅〒480-1102 愛知県長久手市前熊西脇 20-1） E-mail of corresponding author: zazensou@gmail.com