Natural Frequency Of The Hydraulic Drive - Siemens Sinumerik 840D Series Function Manual

2 Configuration
2.3 Configuring the hydraulic drive
2.3.4

Natural frequency of the hydraulic drive

Servo gain
Natural frequency
Possible
dynamic response
2-42
The possible servo gain is essentially determined by the natural frequency of
the cylinder and its load ω
ω
.
v
The cylinder and its load constitute a spring/mass attenuation system whose
natural frequency is calculated using the following formula:
4 @ E @ A
X
w
o
m @ h
Where: E=modulus of elasticity (N/m
A=piston area (m
A =ring surface (m
R
h=stroke (m)
α=surface ratio A
m=mass (kg)
Oil volumes in the cylinder pipes must also be taken into account.
The minimum natural frequency occurs only at a particular mid-position about
the middle and increases as the end positions are approached.
The natural frequency of the hydraulic drive is automatically calculated by the
HLA module and applied in the controller once the corresponding data parame-
ters have been set. See machine data, Sections 4.8 and 4.9:
S
MD 5131: CYLINDER_PISTON_DIAMETER
...
MD 5136: CYLINDER_DEAD_VOLUME_B
S
MD 5140: VALVE_CYLINDER_CONNECTION
...
MD 5143: PIPE_INNER_ DIAMETER_A_B
S
MD 5150: DRIVE_MASS
...
MD 5152: CYLINDER_FASTENING
S
MD 5160: PISTON_POS_MIN_NAT_FREQ
...
MD 5163: DRIVE_NATURAL_FREQUENCY
The dynamic response of the servo solenoid valves thus depends on the ampli-
tude of the valve modulation. For valves that are used in controlled axes, the
natural frequency is typically determined for a modulation amplitude of "10%
and a phase offset of -180°. The relevant information is given in the valve
manufacturer's catalog, e.g. /BR1/.
For pilot-controlled servo solenoid valves, the dynamic response is determined
by the pilot pressure p
pilot
f ~ p
0
The Rexroth catalog data relates to a pilot pressure of 100 bar.
Servo valves can reach corner frequencies of up to 1000 Hz, but are very sensi-
tive to contamination.
SINUMERIK 840D/SIMODRIVE 611 digital, HLA Module (FBHLA) - 10.03 Edition
and the limit frequency of the servo solenoid valve
0
O
1 + α
( )
2
2
2
)
2
)
/A
R
, in addition to the valve type:
before
 Siemens AG, 2003. All rights reserved
10.03
A
R
m
h
)