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APPENDIX
App. - 9
App. 5 Calculation methods for designing
5.1 Specification symbol list
The following symbols are required for selecting the proper servo.
T
a
: Acceleration torque [N•m] g: Gravitational acceleration (9.8 [m/s
2
])
T
d
: Deceleration torque [N•m] µ: Friction coefficient
T
Ma
: Torque necessary for acceleration [N•m] π: Pi constant (3.14)
T
Md
: Torque necessary for deceleration [N•m] P
f
: Number of feedback pulses in position control mode [pulse/rev]
T
LH
: Load torque converted into equivalent value
on servo motor shaft during stop
[N•m] f: Input pulse frequency in position control mode [pulse/s]
[N•m] f
0
: Input pulse frequency during fast feed in position control
mode
[pulse/s]
T
L
: Load torque converted into equivalent value
on servo motor shaft
[N•m] t
psa
: Acceleration time constant of pulse frequency
command in position control mode
[s]
T
U
: Unbalanced torque [N•m] t
psd
: Deceleration time constant of pulse frequency
command in position control mode
[s]
T
F
: Load friction torque [N•m]
T
B
: Brake static friction torque [N•m] K
p
: Position loop gain 1 [rad/s]
T
L0
: Load torque on load shaft [N•m] T
p
: Position control time constant (Tp = 1/Kp) [s]
T
rms
: Continuous effective load torque converted
into equivalent value on servo motor shaft
[N•m] ∆l: Feed per feedback pulses in position control mode
Travel distance per pulse
[mm/pulse]
J
L
: Load inertia moment converted into
equivalent value on servo motor shaft
[× 10
-4
kg•m
2
] ∆l
0
: Feed per command pulse in position control mode
Travel distance per command pulse
[mm/pulse]
J
L0
: Load inertia moment on load shaft [× 10
-4
kg•m
2
] l: Feed [mm]
J
M
: Servo motor's rotor inertia moment [× 10
-4
kg•m
2
] P: Number of internal command pulses [pulse]
N: Servo motor speed [r/min] t
s
: Internal settling time [s]
N
0
: Servo motor speed during fast feed [r/min] t
0
: Positioning time [s]
N
L0
: Load shaft speed during fast feed [r/min] t
c
: Time at constant speed of servo motor in one cycle [s]
V: Moving part speed [mm/min] tl: Stopping time in one cycle [s]
V
0
: Moving part speed during fast feed [mm/min] ∆
ε
: Positioning accuracy [mm]
P
B
: Ball screw lead [mm] ε: Number of droop pulses [pulse]
Z
1
: Number of gear teeth on servo motor shaft ∆S: Travel distance per servo motor revolution [mm/rev]
Z
2
: Number of gear teeth on load gear W: Mass [kg]
n: Gear ratio n =
Z
1
Z
2
L
max
: Maximum coasting distance [mm]
Speed reduced when n > 1, Speed increased when n < 1
η: Drive system efficiency