Investigation of the Dynamic Characterization of Aircraft Control Surface
Free Play
Jason C. Kiiskila, Matthew R. Duncan, Dale M. Pitt
The Boeing Company
P.O. Box 516
St. Louis, MO 63166-0516
Abstract
This paper puts forth a new technique for dynamically measuring the free play of an aircraft control surface. The
hypothesis is that the control surface acts as a pendulum in the free play zone and will poses a low frequency
pendulum mode that can be distinguished from the higher frequency control surface rotation mode. When the
control surface is driven or shaken hard enough it will vibrate both inside and outside the free play zone. The time
history response will contain two distinct frequencies. The lowest frequency amplitude is a measure of the time
spent within the free play range and the higher frequency is a measure of the time spent outside the free play
range. A numerical simulation was developed and conducted to verify the ability to both qualitatively and
quantitatively dynamically measure free play. Time history simulation responses allowed the spring stiffness to be
varied as a function of pendulum position. The spring stiffness was reduced when the pendulum was in free play.
The nonlinear time history responses were processed in the frequency domain using a linear FFT to obtain a
PSD of the response. The peaks of these responses were shown to directly relate/correlate with free play values.
Additionally, an experimental set-up of the simple pendulum simulation was constructed and tested. The
experimental apparatus was fabricated with a simple pendulum with accelerometer mounted to measure the
response. The apparatus had adjustable free play values. The experimental results reinforced the simulation
results. The new technique is faster and simpler than the standard force application method for measuring free
play.
Overview
Every joint inherently has a certain level of free play which is caused by slop in bolts, hinges and actuators. These
free play effects are inherently nonlinear and difficult to analyze and measure. Control surfaces on high speed
fighter aircraft, such as the one shown in Figure 1, typically exhibit free play and often display a unique challenge
for determining the mode shapes and resonant frequencies.
Figure 1: High Speed Fighter Aircraft
Control surface free play is an important test consideration and must be monitored throughout the life of an
aircraft. Excessive control surface free play can result in flutter, divergence, and other dynamic and aeroelastic
instabilities.1-2 Free play can also effect control surface vibrations and natural frequencies of a structure.
Increasing levels of free play can result in increased fatigue failure. For current testing practices, military
standards outline the amount of free play which is allowed on the different aircraft control surfaces for the service
life of an aircraft. Free play must often be tested and monitored at predetermined points throughout the service
life of an aircraft to document wear and assure that these specifications can be met.
The current industry standard for measuring control surface free play is applying a known load to the control
surface and measuring the corresponding deflection, either a linear measurement or angular displacement.
Figure 2 shows a typical free play measurement setup on the rudder. A Rotation Variable Differential
Transformer (RVDT) is used to measure the rotation between the rudder and the tail while a hydraulic actuator
and load cell are used to record the load. Currently the setup is very labor intensive and can take a considerable
amount of time. Larger aircraft require the tester to bring test equipment to great heights to measure rudder and
stabilator free play.
RVDT
Load Cell
Figure 2: Typical Free Play Setup
Load
Typically the static free play test is started at zero load and increased to some percentage of ultimate load. The
moment or applied load is then plotted versus displacement. For a surface with no free play and a linear spring
stiffness, this plot is a straight line. The slope of this measured line is the effective spring stiffness. As free play
is introduced into the system, a discontinuity in the curve occurs near the zero load range. For small
displacements, the effective slope is close to zero, indicating a low effective stiffness. For larger displacement
values the slope increases, and is more representative of the effective stiffness without the free play. As
hysteresis is introduced into the system, the load versus displacement curve looks similar to that in Figure 3.
Displacement (Degrees)
Figure 3: Typical Load Versus Displacement Plot For Free Play
Figure 4 shows an aileron attached to the wing with the hydraulic aileron actuator removed. This trailing edge
flap resembles a physical pendulum. Sometimes control surface rotational inertia is measured by allowing the
control surface to rotate about its hinge line and measuring the frequency or period of oscillation and calculate
inertia from its known weight and center-of-gravity (c.g.). This paper puts forth the hypothesis that the amount of
free play that the control surface has can be measured in a dynamic fashion. The dynamic test would consist of
exciting the control surface and using an accelerometer to measure the response. The response will have two
distinct frequencies. One frequency will be the control surface rotation frequency which is a function of the control
surface hydraulic actuator and rotation inertia. The second frequency is that associated with the control surface in
the free play range (where the actuator stiffness is assumed to be zero) and the frequency is that of the pendulum
mode.
Figure 4: Trailing Edge Flap Free Play
The dynamic measuring of free play was readily demonstrated with a simple simulation. A schematic for the
physical pendulum with free play is shown in Figure 5. The modeled pendulum consisted of a point mass at the
bottom, which was allowed to swing freely for a certain free play value.
Free play
Figure 5: Schematic Of Modeled Free Play Simulation
Once the free play value was exceeded, the pendulum impacted the springs. The two springs were connected to
each other and allowed the pendulum to swing freely in between. In the free play zone gravity acts as the
stiffness term and the control surface frequency is that of a simple pendulum. When the free play zone is reduced
to zero the pendulum is in contact with the spring and the system poses a higher frequency due to the stiffness
effect of the spring and gravity.
Simulation Of Control Surface Free Play
The simple pendulum with free play, as shown in Figure 5, was simulated using Matlab® Simulink. The simulation
integrated the second order differential equation in time. The free play was simulated using a “Dead Zone” in
Simulink. The amount of free play in the “Dead Zone” block was adjustable. The Simulink model is shown in
Figure 6. As the equation of motion was integrated the stiffness was changed as a function of the pendulum
position. If the pendulum was within the free play or dead zone the spring stiffnesses was reduced to zero. The
time history accelerations of the pendulum were stored for post processing in MATLAB® files. Simulation time
steps were 0.01 seconds or 100 sample per second. The stiffness values were adjusted with gain blocks to yield
two distinct frequencies for inside and outside the free play zone. The frequency in the free play zone was 1 Hz
for the free pendulum mode. The frequency for the pendulum with the springs attached was 5 Hz. Simulations
were conducted utilizing a variety of different inputs. The inputs were: step inputs, sine sweeps and random input.
Only results for random inputs are discussed in this paper. The simulations were run for 20 seconds, and all
output data was recorded. Damping values were assumed to insure a damped response inside and outside the
free play zone.
Figure 6. Free Play Simulation
The results of three representative simulations are shown in Figure 7. The top plot is the random input force time
history. Three acceleration plots are presented in Figure 7 for the same random inputs. The three cases
considered were: a) the case of zero free play, b) the case of ± 0.15 free play and c) the case of ± ∞ free play.
The time history plots for case “a” no free play response was at a higher frequency due to engagement of the
springs. The bottom curve “c” of Figure 7 is for the dead zone infinitely large. For this case the system was always
in free play (the springs were not engaged and system acted as a simple pendulum). The frequency of the time
history response for infinite free play was obviously less than the first case of zero free play. The middle curve “b”
of Figure 7 was the response for a system with typical value of free play ± 0.15 in the simulation. The middle
curve posses both frequency characteristics of the other two systems, no free play and infinite free play.
(a)
(b)
(c)
Figure 7. Representative Free Play Simulation – Time History
The time history data from the MATLAB® Simulink simulations were processed using the MATLAB® Signal
Process Tool Box. The Power Spectral Densities (PSD) of the three time histories shown in Figure 7 is presented
in Figure 8. The infinite free play time history resulted in a PSD with a peak frequency of 1 Hz. The peak PSD
response for the no free play case is shown in Figure 8 at 5 Hz. The PSD of the time history response for ± 0.15
free play is shown to have a peak response of 3.5 Hz. This peak response was perplexing because the simulation
had only two paths: a 1 Hz path and a 5 Hz path. The nonlinear time history response with free play when
processed in the frequency domain using a Fast Fourier Transformation (FFT) yields an apparent peak between
1 Hz and 5 Hz. In actuality the time history contains only two frequencies 1 Hz and 5 Hz. The authors feel that a
nonlinear frequency response process would actually show the two distinct frequency responses at 1 Hz and
5Hz. The relative magnitude of the 1 Hz and 5 Hz frequency response would be a direct indication of the amount
of time spent in and out of free play. The nonlinear time history simulations when processed using the linear FFT
yield a peak response at an apparent frequency between the 1Hz and 5Hz boundaries.
Figure 8. Representative Free Play Simulation – PSD
Multiple simulations were conducted with varying values of free play from zero to ± 0.8 inches in ± 0.05 inch
increments. All simulations had the same random input to the system. The MATLAB® Signal Process Tool Box
SPTOOL was used to transform the nonlinear time history simulation into the linear frequency domain. The PSD
responses were recorded at both 1 Hz and 5 Hz to determine the amount of energy for each of the two distinct
systems: free play and no free play. Figure 9 is a plot of both the 1 Hz and 5 Hz response levels as they varied
with different amounts of free play. This is really a plot of the relative energy of the 1 Hz and 5 Hz systems.
Response level of the 1 Hz frequency variation increased with increasing free play levels. Conversely, the
amplitude of 5 Hz responses in the PSD was shown to decrease as the free play increased. For values above ±
0.15 the 5 Hz response is flat and does not change with increasing free play. The 1 Hz amplitude response in
Figure 9 is somewhat linear and can serve as a correlation of dynamic response of the system to asses the
magnitude of the free play.
20
15
10
Response - dB
5
0
-5
-10
-15
-20
1 Hz Amplitude
5 Hz Amplitude
-25
-30
-35
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
Free Play - Inches
Figure 9. PSD Response At Discrete Frequencies For Free Play Simulation
6
Peak Response Frequency - Hz
5
4
3
2
1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Free Play - Inches
Figure 10. Frequency Of PSD Pseudo Peak Response For Free Play Simulation
The PSD pseudo peak response varied as the free play values were varied in the simulations. Figure 10 displays
the variation in the pseudo peak response as free play is varied from zero to ± 0.8 inches. The Pseudo peak
response frequency approaches 1 Hz at a free play value of ± 0.8 inches. The frequency at zero free play is 5 Hz
and appears to vary linearly in Figure 10 with increasing free play to the 1 Hz total free play frequency. The linear
frequency decrease variation with free play does not hold for free play values greater than ± 0.20 and less than ±
0.45 inches.
Experimental Dynamic Measurements of Free Play
Figure 11 shows the simple pendulum test structure that was fabricated. The structure consisted of a wood frame
with a 14 inch pendulum that was free to rotate. Two springs were fixed to each side of the wood frame and
connected together by a threaded rod, which ran through a throughput hole in the pendulum. Nuts were utilized
on the threaded rod to vary the amount of free play in the system.
To quantify the response of the pendulum two similar accels were located at the bottom of the pendulum. One
accelerometer was utilized to measure the response and the other for mass balance. For varying amounts of free
play, the accelerometer measuring the pendulum response had difficulty pulling the pendulum resonance out of
the response. It was theorized that the accelerometer measurement was at zero or near zero acceleration in the
free play zone and due to the lowness in energy of the pendulum mode its acceleration signals were low.
Therefore, a laser vibrometer was also utilized to measure the response of the pendulum. To measure the base
excitation applied to the system a reference accelerometer was attached to the wood frame.
The system level input excitation was obtained by mounting the wood base of the pendulum structure to the slip
table of a fixed base shaker. Random, Sine sweeps and Sine dwells were all used to excite the structure, though
only sine results are presented in this paper.
For sine sweep testing the adjustment nuts were utilized to vary the amount of free play in 1/16 inch increments
from the no free play condition to 3/8 inches of free play. Total free play was also measured by removing the nuts
and allowing the pendulum to swing freely. Sine dwells were utilized to find the pendulum and pendulum/spring
resonant frequencies. The amplitude of the excitation was adjusted to give a reasonable amount of response at
both the pendulum and pendulum/spring resonance frequencies for the sine sweeps.
Free Play Adjustment
Stops
Pendulum Accel
Pendulum (Mass
Balance) Accel
Reference (Base) Accel
Slip Table
Figure 11. Photograph Of Experiment
Figure 12 shows spectrums of the response of the pendulum measured by the laser vibrometer. The response
amplitude remained constant, while free play was adjusted from the no free play case to the total free play case.
For no free play the pendulum/spring resonance is very apparent around 5.2 Hz. As free play is increased the
non-typical looking resonance shifts down (lower frequencies) in frequency. Once at total free play, the 1 Hz
mode is very apparent. These results agree with the simulation results previously reported but are contrary to
what was expected. With different amounts of free play the energy is expected to be concentrated at 1 Hz and
5.2 Hz. With more energy at 1 Hz for larger values of free play and more energy at 5 Hz for lesser values of free
play.
Spectrum
100k
No Freeplay
1/16" Freeplay
1/8" Freeplay
3/16" Freeplay
1/4" Freeplay
5/16" Freeplay
3/8" Freeplay
Total Freeplay
Log in/s
10k
1k
100
10
500m
2
4
Frequency - Hz
6
Figure 12. Measured Response Spectrums for Varying Free Play levels
7
Figure 13 shows the relative energies measured at 1Hz and 5Hz for different values of free play. The plots show
the same general trends as the Simulink simulation results previously discussed and reported in Figure 9. At 1
Hz there was a large increase in amplitude at first and then a gradual increase there after. At 5 Hz there was a
large decrease in amplitude and then the response remains relatively constant.
.
18
16
Response - Magnitude
14
12
10
8
6
4
1 Hz Amplitude Experimental
2
0
-2
0
0.1
0.2
0.3
0.4
Free Play - Inches
45
40
Response - Magnitude
35
30
25
20
15
10
5
5 Hz Amplitude Experimental
0
-5
-10
0
0.1
0.2
0.3
0.4
Free Play - Inches
Figure 13. Measured Frequency Response Amplitudes For The 1 Hz And 5 Hz Modes
With 3/8 inches of free play sine dwells for five different force levels were recorded. The sine dwells were
performed at 1 Hz for a time period of 5 minutes. The first force level was set so that the pendulum was not
impacting the free play stops. The force was then increased for each of the remaining dwells to have an
increasing interaction with the springs. The thought was that with an increasing interaction with the springs there
would be a peak developing around the pendulum/spring mode at 5.2 Hz. From Figure 14 it was apparent that
there was a difference in the frequency content between the first force level (purple curve), which, does not
impact the stops, and the other force levels that do impact the stops. Absent though was the peak that was
expected to be developing at 5.2 Hz.
Spectrum
100k
3/8" Freeplay Dwell Force 5
3/8" Freeplay Dwell Force 2
3/8" Freeplay Dwell Force 3
3/8" Freeplay Dwell Force 4
3/8" Freeplay Dwell Force 1
Log in/s
10k
1k
100
10
500m
2
4
Frequency - Hz
6
7
Figure 14. Measured Frequency Response For 1 Hz Sine Dwells Of Increasing Amplitude
Conclusions
This paper puts forth a new technique for dynamically measuring the free play of an aircraft control surface. The
hypothesis was that the control surface acts as a pendulum in the free play zone and will poses a low frequency
pendulum mode that can be distinguished from the higher frequency control surface rotation mode. When the
control surface is driven or shaken hard enough it will vibrate both inside and outside the free play zone. The time
history response will contain two distinct frequencies. The lowest frequency amplitude is a measure of the time
spent within the free play range and the higher frequency is a measure of the time spent outside the free play
range.
A numerical simulation was developed and conducted to verify the ability to qualitatively and quantitatively
dynamically measure free play. The simulation studies were conducted using a time simulation using MATLAB®
Simulink. Random inputs were applied to the simple pendulum system that represented the aircraft control
system in free play. Time history simulation responses allowed the spring stiffness to be varied as a function of
pendulum position. The spring stiffness was reduced when the pendulum was in free play. The nonlinear time
history responses were processed in the frequency domain using a linear FFT to obtain a PSD of the response.
The peaks of these two different frequency responses were shown to be directly related/correlate with free play
values.
Additionally, an experimental set-up of the simple pendulum simulation was constructed and tested. The
experimental apparatus was fabricated with a simple pendulum with accelerometer mounted to measure the
response. The apparatus had adjustable free play values. The apparatus was subjected to base excitation and
the measured time history responses were processed using standard FFT techniques. Additionally, a laser
vibrometer was also utilized to measure the response of the pendulum. The pendulum acceleration levels were
noted to be very small in the free pay range where the pendulum displacement is nearly zero.
The experimental results reinforced the simulation results. This new technique is faster and simpler than the force
application method. More work is required in employing “Higher Order Spectral” techniques to distinguish the two
frequencies which are smeared together in a “pseudo peak” using standard linear FFT techniques.
References
1. Pitt, D.M., “A Physical Explanation of Free Play Effects On The Flutter Response of an All-Movable
Control Surface”, AIAA Paper 95-1387, Presented at the 36th AIAA/ASME/ASCE/AHS/ASC Structures,
Structural Dynamics, and Materials Conference, April 10-13, 1995.
2. Pitt, D.M., “Further Physical Explanations of Free Play Effects on Chaotic Flutter Response of AllMovable Control Surfaces”, 2nd International Conference on Nonlinearities in Aerospace, Volume 2, page
617-631, Embry-Riddle Aeronautical University, Daytona Beach, FL, April 29 – May 1, 1998