Aeroflex Incorporated: Products | Motion Control Products

Motion Control

Motors & Elect Control

Gimbal Systems

Actuators & Mechanisms

Optical Scanners

Brushless DC Motors

Useful Conversions and Relationships

Multiply:	By	To Obtain
in-oz/amp	.00706	Volts/rad/sec or Nm/amp

volts/rad/sec	141.6	in-oz/amp or Nm/amp

Volt/krpm	.009549	Volts/rad/sec

Volt/rad/sec	104.72	Volts/krpm

Oz-in/rad/sec	.00706	Nm/rad/sec

Nm	.7375 141.6 8.85	Ft-Lb in-oz in-lb

oz-in	.00706 72.01	Nm gm-cm

Ft-Lb	192 1.356	oz-in Nm

gm-cm²	10^-7.005468	Kgm-m²oz-in²

oz-in-sec²	.00706	Kgm-m²

RPM	.01666 6 .1047	RPS deg/sec rad/sec

Hp	746	watts

Torque vs Speed
F = BIL
E = BLwV
T = Fr = BILr = KI
E = BLr = Kw

K = T/I = torque constant
K = E/w = Bemf constant

Apply a voltage to a wire in a magnetic field:

V = E + IR = Kw + (T/K)R

Current
V = E + IR = Kw + (T/K)R
I = (V - Kw) / R = V/R - Kw/R
I = 0 when Kw/R = V/R
or when V = Kw

Power
V = E + IR = Kw + (T/K)R

TR = VK - K²w

T = (V/R)K - K²w/R

T = I_stK - (K²/R)w

T = I_stK - Dw

P_mechanical = Tw = (I_st K - Dw)w

P = (T_st - Dw) w

P = T_st w - Dw²

dP/dw = T_st - 2Dw = 0

T_st = 2Dw w_max = T_st / 2D = w_nl /2

…·max power occurs at w_nl /2

P_max = T_st (w_nl /2) - D (w_nl /2) ²

P_max = T_st (w_nl /2) - (T_st / w_nl ) w_nl²(1/4)

P_max = 1/4 T_st w_nl

P_{mech max} = 1.4 (VK/R)V/K = 1.4 V²/R = 1/4 P_st

P_st = T_st w_nl = 4 P_max

1) Let K=V/w ; Tst = KV/R N= turns	2) Reduce turns by 1/2 results in: K/2; N/2; R/2; 2w	3) Add wire cross sect results in: K/2; N/2; R/4; 2w
R = Resistance w = speed	T_st = ((K/2)V) / (R/2) = KV/R	T_st = ((K/2)V)/ (R/4) =2 KV/RTst = ((K/2)V)/ (R/4) =2 KV/R
P_st = T_st w_nl	P_st = 2T_st w_nl	P_st = 4T_st w_nl

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	Phone:	(631) 231-9100
	Fax:	(631) 231-8375
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