This page sizes the gears and motors for reaching the requirements of a motorized axis.

Symbol	Parameter	Value
	Motorized axis requirements
M	Mass of load (kg)
D1	Distance axis-load (m)
${T_1}$	Load torque (N.m)	2943.00 N.m	${T_1 = 9.81 * M * D_1}$
${F_s}$	Security factor
${T_2}$	Given torque (N.m)	11772.00 N.m	${T_2 = T_1 * F_s}$
${t_{ht}}$	Time for half turn (s)
${t_{ot}}$	Time for one turn (s)	240.00 s	${t_{ot} = 2 * t_{ht}}$
${s_2}$	Axis rotation speed (rpm)	0.25 rpm	${s_2 = \frac{60}{t_{ot}}}$
${P_2}$	Power at axis (W)	308.19 W	${P_2 = \frac{T_2 * 2 * \pi}{t_{ot}}}$
	Axis gear-rings and gear-wheels
${N_r}$	Number of gear-rings
${N_w}$	Number of gear-wheels
${m_w}$	Module of gear-wheel (mm)
${Z_w}$	Number of teeth of gear-wheel
${D_w}$	Diameter of gear-wheel (mm)	250.00 mm	${D_w = (Z_w + 2) * m_w}$
${Margin_w}$	Margin between gear-wheels (%)
${D_r}$	Diameter of gear-ring (mm)	990.00 mm	${D_r = (Z_r + 4) * m_w}$
${Z_r}$	Number of teeth of gear-ring	95	${Z_r = f(N_w, Z_w, Margin_w)}$
${R_{r/w}}$	Ratio ring / gear-wheel	1 : 4.13	${R_{r/w} = \frac{Z_w}{Z_r}}$
${E}$	Gear efficiency (%)
${T_3}$	Torque of gear-wheel (N.m)	222.66 N.m	${T_3 = \frac{T_2 * R_{r/w}}{N_r * N_w * E}}$
${t_3}$	Gear-wheel rotation time (s)	58.11 s	${t_3 = t_{ot} * R_{r/w}}$
${s_3}$	Gear-wheel rotation speed (rpm)	1.03 rpm	${s_3 = \frac{60}{t_3}}$
${P_3}$	Power at gear-wheel (W)	24.08 W	${P_3 = \frac{T_3 * 2 * \pi}{t_3}}$
	Reductor-1
${N_{r1p}}$	Number of planets of reductor-1
${m_{r1}}$	Module of epicyclic of reductor-1 (mm)
${Z_{r1p}}$	Number of teeth of planet-1
${D_{r1p}}$	Diameter of planet-1 (mm)	50.00 mm	${D_{r1p} = (Z_{r1p} + 2) * m_{r1}}$
${D_{r1r}}$	Diameter of ring of reductor-1 (mm)	198.00 mm	${D_{r1r} = (Z_{r1r} + 4) * m_{r1}}$
${Z_{r1r}}$	Number of teeth of ring-1	95	${Z_{r1r} = f(N_{r1p}, Z_{r1p}, Margin_w)}$
${Z_{r1s}}$	Number of teeth of sun-1	49	${Z_{r1s} = Z_{r1r} - 2 * Z_{r1p}}$
${R_{r1-1}}$	Ratio of one stage of reductor-1	1 : 2.94	${R_{r1-1} = \frac{Z_{r1s}}{Z_{r1s} * Z_{r1r}}}$
${N_{r1}}$	Number of stages of reductor-1
${R_{r1}}$	Ratio of reductor-1	1 : 25.38	${R_{r1} = {R_{r1-1}}^{N_{r1}}}$
${E_{r1}}$	Efficiency of reductor-1	51.20 %	${E_{r1} = E^{N_{r1}}}$
${T_4}$	Reductor-1 input torque (N.m)	17.13 N.m	${T_4 = T_3 * R_{r1} * E_{r1}}$
${f_4}$	Reductor-1 input rotation speed (Hz)	0.44 Hz	${f_4 = \frac{1}{t_3 * R_{r1}}}$
${s_4}$	Reductor-1 input rotation speed (rpm)	26.21 rpm	${s_4 = 60 * f_4}$
${P_4}$	Power at reductor-1 input (W)	47.03 W	${P_4 = T_4 * 2 * \pi * f_4}$
	From Reductor-1 input to axis
${R_{a/r1i}}$	Ratio from reductor-1 input to axis	1 : 104.83
${E_{a/r1i}}$	Efficiency from reductor-1 input to axis	40.96 %
	Reductor-2
${N_{r2p}}$	Number of planets of reductor-2
${m_{r2}}$	Module of epicyclic of reductor-2 (mm)
${Z_{r2p}}$	Number of teeth of planet-2
${D_{r2p}}$	Diameter of planet-2 (mm)	25.00 mm
${D_{r2r}}$	Diameter of ring of reductor-2 (mm)	99.00 mm
${Z_{r2r}}$	Number of teeth of ring-2	95
${Z_{r2s}}$	Number of teeth of sun-2	49
${R_{r2}}$	Ratio of one stage of reductor-2	1 : 2.94
${N_{r2-1}}$	Number of stages of reductor-2
${N_{r2}}$	Ratio of reductor-2	1 : 644.17
${E_{r2}}$	Efficiency of reductor-2	26.21 %
${T_5}$	Reductor-2 input torque (N.m)	0.10 N.m
${f_5}$	Reductor-2 input rotation speed (Hz)	281.37 Hz
${s_5}$	Reductor-2 input rotation speed (rpm)	16882.37 rpm
${P_5}$	Power at reductor-2 input (W)	179.39 W
	From Reductor-2 input to axis
${R_{a/r2i}}$	Ratio from reductor-2 input to axis	1 : 67529.49
${E_{a/r2i}}$	Efficiency from reductor-2 input to axis	10.74 %
	Electrical reluctance motor
${F_s}$	Force on one shuttle (N)
${D_s}$	Shuttle diameter (mm)	338.23 mm	${D_s = \frac{T_5}{F_s}}$

Parametrix

Motorized axis

Parameter description

Numerical application