4.1.2 Ground Resonance

The provision of individual blade lag hinges means that the rotor head will now become more complicated, will require extra maintenance and will add to the weight and drag of the rotor

Figure 4.28 shows the basic features governing the natural frequency of the aircraft on the ground and the forcing derived from uneven blade lag motion. Should the forcing frequency at the rotor head be close to the natural frequency of the fuselage rocking on its undercarriage, a resonant condition can occur.

The undercarriage of a helicopter can be of many forms and Figure 4.28 shows an example. The strut consists of a spring and damper, and this is directly connected to the wheel and tyre unit. The latter has spring and damping properties due to the tyre inflation. The spring contributes to the fuselage frequency while the damping is present to suppress any potential ground resonance. The suppression of ground resonance is crucial and will be discussed later in this chapter.  Figure 4.29 Simple model of ground resonance 4.4.6.1 Simple Analysis of the Problem – Rotor Only

The analysis of ground resonance can encompass a wide degree of complexity. The simplest model is to concentrate on the rotor alone and focus on the position of the CG. A further simplification is made where each blade is modelled by a concentrated mass joined to the lag hinge by a weightless rod. This is effectively viewing the individual blade mass centres.

The rotor/blade layout is shown in Figure 4.29.

The figure shows a single blade (of index k) where the rotor head (and the appropriate lag hinge) itself is at an azimuth angle of Ck. The blade itself is placed in a leading (forward lag) position with angle zk.

The blade lag motion is then defined by:

Zk = Cocos IzCk (4-12)

which represents simple harmonic motion (SHM) of maximum amplitude z0 and circular frequency Af, relative to the rotor speed.

Substituting this lag behaviour into the position of the blade masses, the centre of mass of the N blades can be calculated. The analysis is relatively straightforward and produces a result which, if interpreted as a single mass, shows a motion which can be described as tracing the petals of a flower – see Figure 4.30.

While this explains the CG motion, it is not helpful, so rather than the motion of one specific mass, the result can be interpreted as the motion of two equal masses. The values of radial location and circular frequency is shown in the following table:

 Mass 1 Mass 2 Mass mN mN Radial location rgf0 S 2N’S +1 rgf0 S 2N’S-1 Circular frequency (Af + 1)O (AC-1)Q S = sin[(1z ± 1)p]

±! sin[(1c ± 1)n/N

The variation of the S terms with non-dimensional lag frequency is shown in Figure 4.31. The frequency which is greater than the rotor speed is known as progressive, indicating that the mass is rotating, relative to the rotor, in the direction of rotor rotation. The other is known as regressive since it moves against the rotor direction.

Figure 4.32 shows the result for the case of a normalized lag hinge offset of 0.1. The rotor has four blades and the two masses are circles at 2 and 8 o’clock. The overall rotor CG is the circle in between and, since the two masses are equal, it lies at their mid-point.