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8. CALCULATION METHODS FOR DESIGNING
8. CALCULATION METHODS FOR DESIGNING
8.1 Specification symbol list
The following symbols are required for selecting the proper servo:
Ta : Acceleration torque [N m]
Td : Deceleration torque [N m]
TMa : Servo motor torque necessary for [N m]
acceleration
T
Md : Servo motor torque necessary for [N m]
deceleration
T
LH : Torque applied during servo motor stop [N m]
T
L : Load torque converted into equivalent [N m]
value on servo motor shaft
T
U : Unbalance torque [N m]
T
F : Load friction torque [N m]
TL0 : Load torque on load shaft [N m]
T
rms : Continuous effective load torque [N m]
converted into equivalent value
on servo motor shaft
J
L : Load inertia moment converted [kg cm
2
]
into equivalent value on servo
motor shaft
J
L0 : Load inertia moment on load shaft [kg cm
2
]
JM : Servo motor's rotor inertia moment [kg cm
2
]
N : Servo motor speed [r/min]
N
0 : Servo motor speed during fast feed [r/min]
NL0 : Load shaft speed during fast feed [r/min]
V : Moving part speed [mm/min]
V
0 : Moving part speed during fast feed [mm/min]
P
b : Ball screw lead [mm]
Z1 : Number of gear teeth on servo motor shaft
Z
2 : Number of gear teeth on load gear
n: Gear ratio
n
Z1
Z2
Speed reduced when n 1,
Speed increased when n
1
: Drive system efficiency
g : Gravitational acceleration (9.8[m/s
2
])
: Friction coefficient
: Circle ratio (3.14)
P
t : Number of feedback pulses in [pulse/rev]
position control mode
f : Input pulse frequency in [pps]
position control mode
f
0 : Input pulse frequency during fast [pps]
feed in position control mode
t
psa : Acceleration time constant of [s]
pulse frequency command in
position control mode
t
psd : Deceleration time constant of [s]
pulse frequency command in
position control mode
K
p : Position control gain 1 [rad/s]
T
p : Position control time constant (Tp 1/Kp) [s]
: Feed per feedback pulse
in position control mode [mm/pulse]
0 : Feed per command pulse
in position control mode [mm/pulse]
: Feed [mm]
P : Number of internal command pulses [pulse]
t
s : Internal settling time [s]
t
0 : Positioning time [s]
t
c : Time at constant speed of servo [s]
motor in 1 cycle
t
: Stopping time in 1 cycle [s]
: Positioning accuracy [mm]
: Number of droop pulses [pulse]
S : Feed per servo motor revolution [mm/rev]
W: Mass [kg]