Page 119 - DMcatalogue2017

Useful engineering information

Reference information and explanation of abbreviations

Time to acelerate a rotating mass Solid cylinder rotating about axis XX
M(acc) = Accelerate torque, Nm J = (mR )/2
2
J(tot) = Total inertia, kgm 2
J(mot) = Motor inertia, kgm 2 Hollow cylinder rotating about axis XX
2
2
J(load) = Load Inertia, kgm 2 J = m(R + r )/2
Z = Gearbox ratio (speed reducing)
t(acc) = Acceleration time, sec Equivalent inertia of slide mass on a ballscrew
a = Angular acceleration, rad.sec -2 J = m(s/2p) 2
= Angular speed, rad.sec -1
n = Angular speed, rpm Effect of gear ratio on reflected inertia
J = J(load)/Z 2
M(acc) = J(tot) x a or a = M(acc)/J(tot)
Torque required to produce a force on a leadscrew
a = v/t(acc) or t(acc) = v/a M = Required torque, Nm
F = Linear force, N
v = (n/60) x 2p Z = Gearbox ratio (speed reducing)
(Z = 1 for direct drive)
2
J(tot) = J(mot) + (J(load)/Z ) s = Ballscrew pitch, m
h = Efficiency
Example M = Fs/2pRh
J(load) = 0.05 kgm 2
J(mot) = 5.0 kgcm (= 0.00050kgm ) Example 9
2
2
Z = 30:1 F = 10,000 N
n = 1500 rpm s = 10 mm (0.01m)
M(acc) = 15 Nm Z = 2:1
h = 0.9
J(tot) = 0.00050 + (0.5/30 )
2
J(tot) = 0.00106 kgm 2 Required motor torque M = (10,000 x 0.01)/
(2p x 2 x 0.9)
a = M(acc)/J(tot) = 8.85 Nm

a = 15/0.00106 NB: The required force is often provided in kg’s or kgf.
a = 14,150 rad.sec -2 This implies the force exerted on the mass by gravity
(g) and must be multiplied by 9.81 to obtain the force
v = (1500/60) x 2p in N (newtons); eg A “force” of 100 kg is 981 N.
v = 157 rad.sec -1

t(acc) = v/a
t(acc) = 157/14,150
t(acc) = 0.0111 sec (11.1mS)

Useful inertia formula
Servo drives are often employed in highly dynamic applications
where rapid and accurate positioning is required. To obtain the
ultimate performance in any system, the reflected load inertia
(taking into account any gearbox or pulley ratios) should equal
the motor inertia. This is often not possible, but ratio mismatches
of typically 5:1 are not normally significant. The greater this
mismatch between reflected load inertia and motor inertia, the
lower will be the dynamic performance of the system.

Drives and controls, motors and mechanical power transmission catalogue 119