HEIDENHAIN TNC 410 M Technical Manual page 155

Data
Moment of inertia of
the table J
T
Moment of inertia of
the ball screw J
S
Moment of inertia of
the gearwheel on the
ball screw J
GS
Moment of inertia of
the gearwheel on the
motor J
GM
External moment of
inertia J
F
Total moment of
inertia of the machine
slide with motor J
tot
Ratio of external
moment of inertia to
the moment of inertia
of the motor
3 – 6
Formulas
2
⎛ ⎞
h
⋅
------------ -
J = m
⎝ ⎠
⋅ π
T
2
4
⋅ π ⋅ ⋅ ρ
d l
S
J = ------------------------------------- -
S
32
4
⋅ π ⋅ ⋅
d l
GS
=
J ----------------------------------------- -
GS
32
4
⋅ π ⋅
d l
GM
J = -------------------------------------------
GM
32
+ +
J J J
T S GS
=
J ------------------------------- -
F
2
i
+ +
J J J
T S GS
=
J tot ------------------------------- -
2
i
J
≤ ≤
F
------ 2
0.5
J
M
HEIDENHAIN Technical Manual for Inverter Systems and Motors
Variable
m: Table mass [kg]
h: Ball screw pitch [m]
d : Diameter of the ball screw [m]
S
l: Length of the ball screw [m]
ρ: Density of the ball screw material
3
[kg/m
d : Diameter of the gearwheel on the
GS
ball screw [m]
ρ
l: Length of the gearwheel on the ball
screw [m]
ρ: Density of the gearwheel material
3
[kg/m
d = Diameter of the gearwheel on the
GM
ball screw [m]
⋅ ρ
l = Length of the gearwheel on the ball
screw [m]
ρ: Density of the gearwheel material
3
[kg/m
J : Moment of inertia of the table [kgm
T
J : Moment of inertia of the ball screw
S
2
[kgm ]
+ J
J : Moment of inertia of the gearwheel
GM
GS
on the ball screw [kgm
i = Gear ratio
(n
motor
J : Moment of inertia of the gearwheel
GM
on the motor [kgm
J : Moment of inertia of the table [kgm
T
J : Moment of inertia of the ball screw
S
2
[kgm ]
+ +
J J
GM M
J : Moment of inertia of the gearwheel
GS
on the ball screw [kgm
i = Gear ratio
(n
motor
J : Moment of inertia of the gearwheel
GM
on the motor [kgm
J : Moment of inertia of the motor
M
2
[kgm ]
J : External moment of inertia [kgm
F
J : Moment of inertia of the motor
M
2
[kgm ]
This ratio ensures a stable control
response!
]
]
]
2
]
/n )
ball screw
2
]
2
]
/n )
ball screw
2
]
2
]
2
]
2
]