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

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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 All 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>.
2008-08-05

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

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