24.1 Introduction

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Helicopter rotor tuning (track and balance) is the process of adjusting the rotor blades so as to reduce the

aircraft vibration and the spread of rotors. Rotor tuning as applied to Sikorsky’s Black Hawk (H-60)

helicopters is performed as follows. For initial measurements, the aircraft is flown through six different

regimes, during which measurements of rotor track and vibration (balance) are recorded. Rotor track is

measured by optical sensors, which detect the vertical position of the blades (see Chapter 15). Vibration is

measured at the frequency of once per blade revolution ( per rev) by two accelerometers, A and B,

attached to the sides of the cockpit (see Figure 24.1, detail B). The vibration data are vectorially combined

into two components: A þ B, representing the vertical vibration of the aircraft, and A 2 B, representing

its roll vibration. A sample of peak vibration levels for the six flight regimes, as well as the peak angular

positions relative to a reference blade, are given in Table 24.1, along with a sample of track data.

24-1

© 2005 by Taylor & Francis Group, LLC

FIGURE 24.1 Illustration of the position of accelerometers A and B on the aircraft, and the rotor blade adjustments

(push rod, trim tab, and hub weights).

TABLE 24.1 Typical Track and Balance Data Recorded during a Flight

Flight Regime Vibration

A þB A2 B

Magnitude (ips) Phase (8) Magnitude (ips) Phase (8)

fpm 0.19 332 0.38 272

hov 0.07 247 0.10 217

80 0.02 86 0.04 236

120 0.04 28 0.04 333

145 0.02 104 0.07 162

vh 0.10 312 0.12 211

Track (mm)

Blade #

1 2 3 4

fpm 22 3 1 2 2

hov 21 3 0 2 2

80 1 11 1 2 13

120 2 13 2 1 2 14

145 5 18 2 3 2 20

vh 2 13 2 1 2 14

24-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

The six flight regimes in Table 24.1 are: ground ( fpm), hover (hov), 80 knots (80), 120 knots (120), 145

knots (145), and maximum horizontal speed (vh). The track data indicate the vertical position of each

blade relative to a mean position.

In order to bring track and one per rev vibration within specification, three types of adjustments can be

made to the rotor system: pitch control rod adjustments, trim tab adjustments, and balance weight

adjustments (see Figure 24.1). Pitch control rods can be extended or contracted by a certain number of

notches to alter the pitch of the rotor blades. Positive push rod adjustments indicate extension. Trim tabs,

which are adjustable surfaces on the trailing edge of the rotor blades, affect the aerodynamic pitch

moment of the air foils and consequently their vibration characteristics. Tab adjustments are measured in

thousandths of an inch, with positive and negative changes representing upward and downward tabbing,

respectively. Finally, balance weights can be either added to or removed from the rotor hub to tune

vibrations through changes in the blade mass. Balance weights are measured in ounces, with positive

adjustments representing the addition of weight. In the case of the Sikorsky H-60 helicopter, which has

four main rotor blades, a total of 12 adjustments can be made to tune the rotors (i.e., three adjustments

per blade). Among them, balance weights primarily affect the ground vibration, so they are not

commonly used for in-flight tuning. Furthermore, since the symmetry of rotor blades in four-bladed

aircraft produces identical effects for adjustments to opposite blades, the combined form of blade

adjustments to opposite blade pairs can be used as inputs. Accordingly, the input vector can be defined as

Dx ¼ ½Dx1; Dx2; Dx3; Dx4􀀉T ð24:1Þ

where Dx1 and Dx3 denote the combined (condensed) trim tab adjustments ðDT Þ to blade combinations

one/three and two/four, respectively, and Dx2 and Dx4 represent the combined pitch control rod

adjustments ðDPÞ to blade combinations one/three and two/four, respectively. The relationships between

the combined and individual adjustments are in the form:

Dx1 ¼ DT3 2 DT1 ð24:2Þ

Dx2 ¼ DP3 2 DP1 ð24:3Þ

Dx3 ¼ DT4 2 DT2 ð24:4Þ

Dx4 ¼ DP4 2 DP2 ð24:5Þ

Ideally, identical adjustments made to any two aircraft with different tail numbers should result in

identical changes in vibration. In reality, however, significant inconsistencies in vibration changes may be

present for identical adjustments to different tail numbers. This is perhaps due more to nonuniformity of

flight conditions from weather or error in implementing the blade adjustments than factors such as

dissimilarities between aircraft and rotor blades.

Virtually all of the current systems of rotor track and balance rely on the strategy shown in Figure 24.2,

whereby the measurements of the flight just completed are used as the basis of search for the new blade

adjustments. The search for blade adjustments is

guided by the “process model” (see Figure 24.2),

which represents the relationship between

vibration changes and blade adjustments.

A difficulty of rotor tuning is the excess of

equations compared to degrees of freedom (four

inputs to control 24 outputs), which translates

into one-to-many mapping. Another difficulty is

caused by the high level of noise present in the

vibration measurements.

The traditional approach to rotor tuning uses

linear relationships to define the process model

Process

Model

Helicopter

Search

aircraft vibration

blade

modifications

FIGURE 24.2 Tuning strategy of the current methods.

Helicopter Rotor Tuning 24-3

© 2005 by Taylor & Francis Group, LLC

and uses model inversion to streamline the search. The drawback of the traditional approach, therefore, is

its neglect of the potential nonlinearity of track and balance, and the vibration noise, as well as its limited

capacity to produce comprehensive solutions to facilitate model inversion due to its consideration of the

most extreme vibration components. In an attempt to include the potential nonlinearity of the process,

Taitel et al. (1995) trained a set of neural networks with actual track and balance data to map vibration

measurements to blade adjustments as well as to evaluate the goodness of the solution. In effect, they

developed an inverse model based on the solutions available in the historical track and balance data, and

provided a forward model to evaluate the solution. The potential advantage of this method is that it can

interpolate among the historical solutions to address potential nonlinearity and vibration noise. Its

disadvantages are that it is only applicable to helicopters with extensive track and balance history, and

that its solutions are constrained by those contained in the historical data.

Another deviation from the traditional approach is introduced by Ventres and Hayden (2000), who

define the relationships between blade adjustments and vibration in frequency domain, and provide an

extension of these relationships to higher order vibrations. They use an optimization method to search

for the adjustments to reduce per rev vibration as well as higher-order vibrations. Accordingly, this

approach has the capacity to provide a comprehensive solution, but it too neglects the potential

nonlinearity between the blade adjustments and aircraft vibration as well as the noise in the

measurements.

The most recent solutions to rotor tuning are those by Wang et al. (2005a, 2005b), which are designed

to address both the stochastics of vibration and the potential nonlinearity of the tuning process. In the

first solution, which is a probability-based method, the underlying model comprises two components: a

deterministic component and a probability component. The method relies on the probability model to

estimate the likelihood of the measured vibration satisfying the specifications and to search for blade

adjustments that will maximize this likelihood. The likelihood measures in the probability model are

computed according to the probability distribution of vibration derived from historical track and balance

data. The second solution is an adaptive method that uses an interval model to cope with the potential

nonlinearity of the process and to account for vibration noise. This method, which also incorporates

learning to provide adaptation to the rotor tuning process, initializes the coefficients of the interval

model according to the sensitivity coefficients between the blade adjustments and helicopter vibration.

However, it modifies these coefficients after the first iteration to better represent the vibration

measurements acquired. This method takes into account vibration data from all of the flight regimes

during the search for the appropriate blade adjustments; therefore, it has the capacity to provide

comprehensive solutions. The remainder of this chapter describes three of the methods discussed above

to provide a representation of various solutions proposed for rotor tuning, followed by a case study to

demonstrate the application of the adaptive method.

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