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	$T_{2} = T_{1} * F_{s}$
$t_{h t}$	Time for half turn (s)
$t_{o t}$	Time for one turn (s)	240.00 s	$t_{o t} = 2 * t_{h t}$
$s_{2}$	Axis rotation speed (rpm)	0.25 rpm	$s_{2} = \frac{60}{t_{o t}}$
$P_{2}$	Power at axis (W)	308.19 W	$P_{2} = \frac{T_{2} * 2 * π}{t_{o t}}$
	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	$D_{w} = (Z_{w} + 2) * m_{w}$
$M a r g i n_{w}$	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	$Z_{r} = f (N_{w}, Z_{w}, M a r g i n_{w})$
$R_{r / w}$	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	$t_{3} = t_{o t} * R_{r / w}$
$s_{3}$	Gear-wheel rotation speed (rpm)	1.03 rpm	$s_{3} = \frac{60}{t_{3}}$
$P_{3}$	Power at gear-wheel (W)	24.08 W	$P_{3} = \frac{T_{3} * 2 * π}{t_{3}}$
	Reductor-1
$N_{r 1 p}$	Number of planets of reductor-1
$m_{r 1}$	Module of epicyclic of reductor-1 (mm)
$Z_{r 1 p}$	Number of teeth of planet-1
$D_{r 1 p}$	Diameter of planet-1 (mm)	50.00 mm	$D_{r 1 p} = (Z_{r 1 p} + 2) * m_{r 1}$
$D_{r 1 r}$	Diameter of ring of reductor-1 (mm)	198.00 mm	$D_{r 1 r} = (Z_{r 1 r} + 4) * m_{r 1}$
$Z_{r 1 r}$	Number of teeth of ring-1	95	$Z_{r 1 r} = f (N_{r 1 p}, Z_{r 1 p}, M a r g i n_{w})$
$Z_{r 1 s}$	Number of teeth of sun-1	49	$Z_{r 1 s} = Z_{r 1 r} - 2 * Z_{r 1 p}$
$R_{r 1 - 1}$	Ratio of one stage of reductor-1	1 : 2.94	$R_{r 1 - 1} = \frac{Z_{r 1 s}}{Z_{r 1 s} * Z_{r 1 r}}$
$N_{r 1}$	Number of stages of reductor-1
$R_{r 1}$	Ratio of reductor-1	1 : 25.38	$R_{r 1} = {R_{r 1 - 1}}^{N_{r 1}}$
$E_{r 1}$	Efficiency of reductor-1	51.20 %	$E_{r 1} = E^{N_{r 1}}$
$T_{4}$	Reductor-1 input torque (N.m)	17.13 N.m	$T_{4} = T_{3} * R_{r 1} * E_{r 1}$
$f_{4}$	Reductor-1 input rotation speed (Hz)	0.44 Hz	$f_{4} = \frac{1}{t_{3} * R_{r 1}}$
$s_{4}$	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	$P_{4} = T_{4} * 2 * π * f_{4}$
	From Reductor-1 input to axis
$R_{a / r 1 i}$	Ratio from reductor-1 input to axis	1 : 104.83
$E_{a / r 1 i}$	Efficiency from reductor-1 input to axis	40.96 %
	Reductor-2
$N_{r 2 p}$	Number of planets of reductor-2
$m_{r 2}$	Module of epicyclic of reductor-2 (mm)
$Z_{r 2 p}$	Number of teeth of planet-2
$D_{r 2 p}$	Diameter of planet-2 (mm)	25.00 mm
$D_{r 2 r}$	Diameter of ring of reductor-2 (mm)	99.00 mm
$Z_{r 2 r}$	Number of teeth of ring-2	95
$Z_{r 2 s}$	Number of teeth of sun-2	49
$R_{r 2}$	Ratio of one stage of reductor-2	1 : 2.94
$N_{r 2 - 1}$	Number of stages of reductor-2
$N_{r 2}$	Ratio of reductor-2	1 : 644.17
$E_{r 2}$	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
$R_{a / r 2 i}$	Ratio from reductor-2 input to axis	1 : 67529.49
$E_{a / r 2 i}$	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