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(Fig. 8.8).
For example, a possible design criterion for such a system could be the
minimisation of the total bΩ frequency pitching moment at the helicopter
centre of gravity. The attenuation efficiency of such a system would only be
optimal for a specific flight condition having a particular relationship between
the rotor hub forces and moments.
(iii) Systems employing the Dynamic Anti-Resonant Vibration Isolator (DAVI)1.
Originally developed for the isolation of crew seats by the Kaman company,
this principle has been applied very successfully to the mounting of the gearbox2.
Fig. 8.8 Flexibly mounted gearbox and engine system
Fig. 8.7 Westland W-30 raft mounting system
Elastomeric mounts
M
F
C.G.
Main Gearbox Engine
Rotor induced vibration 299
Figure 8.9 illustrates its use and response characteristics. An appreciation of
how the vibration reduction is achieved may be obtained by study of the
simplified but equivalent model shown in Fig. 8.10. In this, the upper mass M1
represents the gearbox and rotor, and M2 the helicopter fuselage, and between
them is mounted a rigid arm, as shown, which carries a small mass mbob (the
‘bobweight’) at its tip.
The equations of motion when there is no damping are easily obtained as
– [ + (1+ ) ] + (1+ ) –
(1 + ) – – [ + (1+ ) ]+
2
1 bob b
2 2
bob b b
2
bob b
2
2 bob b
2
1
2
ω Λ ω Λ Λ
ω Λ Λ ω Λ
M m K m K
m K M m K
x
x b

 

 

 

 
=
0
0
F eiωt
 

 
DAVI unit
Blade passing frequency
Fuselage
response
Fig. 8.9 The DAVI gearbox mounting system
F0eiωt
X1
d1 d2
X2
Bobweight
m
M1
M2
Spring
K
Fig. 8.10 Simplified DAVI model
300 Bramwell’s Helicopter Dynamics
where F0 is the amplitude of the exciting force and Λb = d2/d1 is the ratio of
lengths of the rigid arm either side of the mounting point on M1. The system
is seen to be ‘free-free’ so the net linear momentum is zero at all instants of
time. This leads to a relationship between x1 and x2 which is used to eliminate
x1 from one of the equations, allowing the following expression for x2K/F0
(the normalised fuselage response) to be formed.
x K
F 2
0
2
b b b
2
b b b
2 2
b b
2 2
m b b
2 =
[ (1 + ) – 1]
[ (1+ ) –1] –[1– (1+ )][1– ( + (1+ ) )]
˜
˜ ˜ ˜
ω μ Λ Λ
ω μ Λ Λ ω μ Λ ω ρ μ Λ
The main parameters of the system are the fuselage to gearbox and rotor mass
ratio ρm = M2/M1, the bobweight mass ratio μb = mbob/M1, the bobweight arm
length ratio Λb, and the normalised excitation frequency ω˜ = ω(K/M1)–1/2.
The denominator of the response expression is the characteristic equation for
the system, the roots of which provide the natural frequencies (one of which
is zero, since the system is ‘free-free’), and the numerator similarly provides
the zero response frequency. The latter shows that the bobweight mass is
reduced as Λb is increased. However, there is a practical upper limit, since the
greater the ratio is, the stiffer, and hence the heavier, the arm becomes. Figure
8.11 shows the variation of the response amplitude with excitation frequency
for the simple undamped DAVI model for a particular set of chosen parameters.
The DAVI unit can provide a very high attenuation over a narrow frequency
range, whilst utilising a value of spring stiffness which overcomes the problem
of excessive quasi-static deflections. The system is also relatively insensitive
to variations in the isolated mass. The balance between the degree of attenuation
0.6
0.4
0.2
0.5 1.0 1.5 2.0
X10
Normalised fuselage response | x2K/F0 |
ω˜
Normalised excitation frequency
Fig. 8.11 Response amplitude of simplified DAVI model as a function of excitation frequency
(Λb = ρm = 10, μb = 0.01). Note: amplitudes on right-hand section of curve are multiplied by ten.
Rotor induced vibration 301
Fig. 8.12 Principle of the nodal beam mounting system
　
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本文鏈接地址：Bramwell’s Helicopter Dynamics(150)