HEIDENHAIN TNC 410 M Technical Manual page 154

Mathematical
formulas for
calculation
Data
Frictional moment M
Moment for
overcoming the force
of gravity M
G
Machining moment
M
B
Static moment M
Stat
Desired speed of the
motor n
S
Selection of the
motor
Modular inverter:
Selection of the
power module
Compact inverter:
Selection of the axis
unit
April 2007
Formulas
R
⋅ ⋅ μ ⋅
m g
M R = ------------------------------------------------------
⋅ π ⋅
2
⋅ ⋅ ⋅
m g h
M = ------------------------------------------ -
⋅ π ⋅
G
2 i
⋅
F h
B
M = ------------------------------ -
⋅ π ⋅
B
2 i
M = M +
Stat R
⋅
v i
max
n = ------------------- -
S
h
≥
M M
0Motor Stat
≥
n n
NMotor S
≥
I I
NU 0Motor
Selection of the Axis Motor
Variable
m: Mass [kg]
g: Acceleration of gravity [m/s
⋅ α
h cos
μ: Coefficient of friction [-]
⋅ η
i
h: Ball screw pitch [m]
α: Axis angle [°]
(0° = horizontal axis)
i: Gear ratio [-]
(n
motor
η : Efficiency [-]
m: Mass [kg]
g: Acceleration of gravity [m/s
α
sin
h: Ball screw pitch [m]
⋅ η
α: Axis angle [°]
(90° = vertical axis)
i: Gear ratio [-]
(n
motor
η : Efficiency [-]
F : Machining force [N]
B
h: Ball screw pitch [m]
i: Gear ratio [-]
⋅ η
(n
motor
η : Efficiency [-]
M : Frictional moment [Nm]
R
M
G
M + M
gravity [Nm]
G B
M : Machining moment [Nm]
B
v
max
i: Gear ratio [-]
(n
motor
h: Ball screw pitch [m]
M
0Motor
M
Stat
n
NMotor
n : Desired speed of the motor
S
I : Rated current of the inverter
NU
I
0Motor
motor
/n )
ball screw
/n )
ball screw
/n )
ball screw
: Moment for overcoming the force of
: Rapid traverse [m/min]
/n )
ball screw
: Stall torque of the motor
: Static moment
: Rated speed of the motor
: Continuous stall current of the
2
]
2
]
3 – 5