ボールスプラインの負荷分布と寿命に関する研究（第1報）

—Type AII の理論解析—

抄録

Ball splines were standardized by JIS in 2004 and now they are examined in ISO / TC39 as power transmitting components. In this paper the ball load distribution and basic dynamic load rating for ball spline type AII are discussed theoretically by considering the re-circulation of balls in each row including a spline shaft bending deformation with radial load and the crownings of nut raceway both end portions. The ball load distributions in case of even arrangement, condition I for the effective number of balls, Z_t = Z_{t I} = 9 and uneven arrangement, condition II for the effective number of balls, also Z_t = Z_{t II} = 8 are discussed with ball re-circulation. The results are as follows. (1) Under the application of pure torque, the ball load distributions for each condition I and II are even except the crowning portions and the shaft deformation does not occur, and maximum ball load in condition II is shown P_{max II} ≤ 1.03P_{max I} in accordance with ball re-circulation. (2) Under the application of pure radial load, the ball load fluctuation is P_{max II} ≤ 1.19P_{max I} without shaft deformation and further P_{max II} ≤ 1.15P_{max I} with shaft deformation. (3) Under the application of combined radial load and torque, the ball load fluctuation is P_{max II} ≤ 1.07P_{max I} in case of without shaft deformation and further P_{max II} ≤ 1.07P_{max I} with shaft deformation. (4) The basic dynamic load rating C_F* for ball spline can be classified into pure torque C_Mx, pure radial load C_Fy, combined radial load and torque C_Fy+Mx etc. In case of pure torque, the C_Mx value by this report is agreed with ISO's load rating for condition I theoretically. (5) In case of combined radial load and torque, it is made clear that the load rating for C_Fy is remarkably decreased in accordance with the increase in load eccentricity and C_Fy+Mx value approaches to the basic dynamic load rating for pure torque C_Mx.