ACHIEVING DESIRED STIFFNESS OF FLEX BEAM USING
SHAININ METHODOLOGY
1Shashikumar C B,
2Amaresh Kumar D, 3Shrishail Kakkeri,
4Syed Zain Ahmed
1Assistant Professor, Department of Mechanical Engineering, Sri Venkateshwara College of
Engineering,Bangalore, Karnataka, India
2Assistant Professor, Department of Mechanical Engineering, Sri Venkateshwara College of
Engineering, Bangalore, Karnataka, India
3Professor, Department of Mechanical Engineering, Sri Venkateshwara College of
Engineering,Bangalore, Karnataka, India
4Student, Department of Mechanical Engineering, Sri Venkateshwara College of
Engineering,Bangalore, Karnataka, India
Abstract
Main purpose of this paper is to observe the intensity of effectiveness of a modest but
not very habitually used method known as the Shainin Methodology for shorten the
implementing Six Sigma.Composite materials are created by combining two or more
constituent materials with a view to improve the properties or to create materials with the
desired properties. Composites due to their light weight, stiffness strength and high specific
thermal properties are widely used for aircrafts and aerospace applications. Recent
developments in this field have led to substantially improved fuel economy and extended
flight range.
The quality of composite parts mainly depends on the following:
1. Fiber volume ratio
2. Fiber resin properties
3. Fiber orientation
4. Curing parameters (Temperature, pressure, vacuum)
5. Processing techniques
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As the performance of the composite is shown to be dependent on the curing parameters
i.e. curing pressure, temperature, and vacuum, it is important to determine the best curing
temperature.
The cure cycle shown above is the standard cure cycle for monolithic components. The
temperatures and pressure shown in the above graph are standard used during the
manufacture of any component. This project studies the variation of the tensile and flexural
strength of parts manufactured by varying the curing temperatures.
In this work, five specimens or laminations have been taken and cured at different
temperatures including the standards curing temperatures (i.e.135°C)and the variation of
tensile and flexural strength of the laminates is studied.
The optimal curing temperature is sought to be determine by conducting these studies:
thereby saving time and energy for each cure cycle
Keywords:Shainin methodology, Composite materials, etc.
1.BASIC INTRODUCTION ON FLEX BEAM
A helicopter is a type of rotorcraft in which lift and thrust are supplied by rotors. This
allows the helicopters to take off and land vertically, to hover, and to fly forward, backward,
and laterally. These attributes allow helicopters to be used in congested or isolated areas
where fixed-wing aircraft and many forms of VTOL (Vertically takeoff and landing) aircraft
cannot perform
The tail rotor blade is a smaller rotor mounted so that it rotates vertically or near
vertically at the end of the tail of a traditional single-rotor helicopter. The tail rotor‟s position
and distance from the center of gravity allow it to develop thrust in the same direction as the
main rotor„s rotation, to counter the torque effect created by the main rotor.
The tail rotor drive system consists of a shaft powered from the main transmission and
a gearbox mounted at the end of the tail boom. The drive shaft may consist of one long shaft
or a series of shorter shafts connected at both ends with flexible couplings that allow the drive
shafts to flex with the tail boom. The gearbox at the end of the tail boom provides an angled
drive for the tail rotor and may also include gearing to adjust the output to the optimum
rotational speed for the tail rotor, measured in rotations per minute (rpm). The tail rotor pylon
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may also serve as a vertical stabilizing airfoil, to improve the power requirement for the tail
rotor in forward light. The tail rotor pylon may also serve to provide limited anti torque
within certain airspeed ranges, in the event that the tail rotor or the tail rotor flight controls
fail. About 10% of the engine power goes to the tail rotor.
Flex Beam is an integral part of tail rotor blade. The tail rotor blade(TBR) is
essentially is an un-ducted fan with blades that vary in pitch to vary the amount of thrust they
produce. The blade utilizes a composite material construction, such as a carbon and glass
fiber composite. The blades use a symmetrical airfoil and their pitch angle can be adjusted
both positive and negative to produce thrust in either direction.
Fig. 1.1: 3D view of tail rotor drive system
Fig. 1.2: Fiberglass-Epoxy Flex Beam
A fiberglass-epoxy flex beam extends from tip to tip of each opposed blade pair, carrying the
blade centrifugal forces so that none of the centrifugal loading is carried by the hub. Two
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pairs of opposed rotor blades are used, and the opposed blades are interconnected by the flex
beams. These flex beams are bolted to the hub. The flex beam is clamped between the hub
plates and the bolts are tightened.
2. LITERATURE REVIEW
Stefan Steiner and Jock MacKay are both Associate Professors in the Statistics and
Actuarial Science Department of the University of Waterloo. They are also active consultants
who have worked with organizations from a wide range of Industriesincluding Automotive,
Telecommunications, Aerospace, govt. and more.
John S. Ramberg, Professor Emeritus, University of Arizona and quality consultant, is
a fellow of ASQ, ASA and IIE. He holds a B Electrical Engineering (Industrial Engineering).
His work experience includes Procter & Gamble, Motorola, and Hughes Space Systems. He
is editor emeritus of The Journal of Quality Technology, and member of the editorial board.
The selected details about constituent materials are shown in table.
Table 2.3 Properties of constituent materials.
Parameter Carbon Fiber
(Fabric) Epoxy Resin
Density 1.65 g/cm3 1.13 g/cm3
Areal weight 240 Grms/m2 ----
Thermal
conductivity
coefficient
15.0 W/mK 0.22W/mK
Carbon fiber reinforced epoxy composites were fabricated by hand lay – up with a
variation of carbon content, the variation of fiber contents was achieved using different
number of carbons layers with the same total thickness of the specimen. The epoxy resin was
cold – cured under ambient conditions (-21degree C) and after curing process was thermally
hardened at 50degC for 24hrs. The specimens were 100mm by 100mm square and ~ 6.2mm
thick.
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3. METHODOLOGY FOR QUALITY IMPROVEMENT
3.1 Introduction on Shainin methodology for Quality Improvement.
The Shainin methodology is the name given to a problem solving system, with its
associated strategies and tools, developed by Dorian Shainin, and widely used and promoted
in the manufacturing sector. The Shainin System was developed for and is best suited to
problem solving on operating, medium to high volume processes where data are cheaply
available, statistical methods are widely used.In any problem, there is a dominant cause of
variation in the process output that defines the problem. This presumption is based on an
application of the Pareto principle to the causes of variation. There is a risk that multiple
failure modes contribute to a problem, and hence result in different dominant causes for each
mode Shainin methodology uses a process of elimination called progressive search, to
identify the dominant causes.
FIGURE-3.1.1The Shainin system for quality improvement.
3.2The problem solving algorithm
The Shainin methodology steps for problem solving are given in Figure3.1.1the
algorithm is divided into two parts, the Diagnostic and Remedial Journeys. In the diagnostic
journey, the problem is defined, the measurement system is assessed, and the dominant cause
of variation is identified and verified. In the remedial journey, the effect of the dominant
cause is eliminated or reduced by changing the product design, the process, or the control
plan.
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The purpose of the first stage of the algorithm is to quantify the magnitude ofthe
selected problem. To do this, we monitor the output of the process using an appropriate
sampling scheme.
The second stage in the Shainin methodology algorithm (see Figure 3.1.1) involves
the quantification and establishment of an effective measurement system. Without a good
measurement system, it is difficult to learn about and improve the process, and the
measurement system itself may be home to the dominant cause of the problem.
The goal of the third stage of the Shainin algorithm is to generate clues about the dominant
cause. This is the progressive search. At this stage, another key emphasis in Shainin is to
„„talk to the parts‟‟ we use observational rather than experimental plans as much as possible.
Shainin methodology makes heavy use of observational plans such as
a) Multivari investigations
b) Stratification
c) Group comparasion
d) Scatter
e) Isoplot
The basic concept of Shainin Red X can be summarized by 6 statements:
• Variation exists in all processes.
• Understanding and reducing variation are keys to success.
• In the real world nothing happens without a mason.
• There is always a Red X
• Finding and controlling the Red X is the only way to reduce variation.
• Executing a progressive search by “talking to the parts” is the best way to find the Red X.
The Shainin Red X methodology consists of about 30 techniques and tools. They are
known as well as newly developed techniques which create the comprehensive stepwise
system for process improvement.
Shainin problem solving roadmap is called
FACTUAL
F-Focus
A-Approach
C-Converge
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T-Test
U-Understand
A-Apply
L-Leverage
No problem can be solved without knowledge of the output and related processes,
symptoms of the failure as well as difference between good and bad parts. This is ensured by
approach which is described as “talking to parts”, set of techniques used to converge the
problem as elimination of suspects, comparison between good and bad parts, finding
extremes.
Focus
Leverage probable events
Project Definition
Estimate the impact
Approach
Green Y Identification and
Description
Developmentof Investigation
Strategy
Measurement System
Verification
Converge
Converging on the Red X
Compare best and worst case
Red X Candidate
Identification
Test
Risk Assessment
Red X Confirmed by Trial
Understand
Green Y to Red X
Relationship Understood
Optimization of interactions
Customer needs translated to
limits
Appropriate Tolerance Limits
Established
Apply Corrective Action
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Implemented and Verified
Procedures updated
Green Y monitoring
Project Benefits and Cost
Savings
Leverage
Read Across Red X Control
Savings Calculated
Lessons Learned
3.3selections of Shainin Tools
By tool, both the plan of the investigation and the recommended analysis method.
Shainin system tools are generally statistically simple plans with small sample sizes that
make extensive use of graphical displays and non-parametric tests that can be performed by
hand.However, that the non- parametric analysis methods are weak and non- intuitive. While
we are strongly in favour of graphical approaches, with today‟s widespread availability of
statistical software, ease of calculation is not an issue and we recommend supplementing the
graphs with straightforward standard analyses. For some of the Shainin tools,
a) Isoplot
b) Multivari
c) Component searchand variable search
d) Group comparison
e) B v/s Cand factorial experiments
f) Tolerance parallelogram
g) Precontrol
4. Design, fabrication and testing of the helicopter tail rotor blade from composite
laminated materials
4.1Design and Fabrication
A development of a tail rotor blade is performed in four phases:
(a) The blades design on the working station using designing system
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(b) Preparation and cutting of blade components on the cutting system
(c) Blade manufacturing in a two-section metal die
(d) Final verification testing.
In the blade manufacturing procedure, the conventional composite materials with
epoxy resin matrix, a fiberglass filament spar, an eighteen-section skin of laminated fabrics,
some carbon filament embedded along the trailing edge, a core, leading edge protection strips
of polyurethane and stainless steel etc. were used. All the used materials are standard
products
Fig. 4.1.1 Automated composite garment cutting facility.
The trailing edge contour of the airfoil is formed by a continuous structural pocket
which has a polyurethane foam core and a fiberglass skin. The upper and lower skins are
fabricated from woven fiberglass that is laid up with the fibers oriented at ±45° and 0°/90° to
the blade longitudinal axis. On the blades, the in plane blade natural frequency is tuned by
stiffening the trailing edge of lower skin with some carbon filaments In assembly, the first
process is to cut the fiberglass fabrics to the require shape and stacking it to build up the
required shapes
Next stage is woven wrap and placed it in a matched metal tool, together with the
fiberglass filament spar, uncured trailing edge skins, polyurethane foam core and tool
transferred to heated pattern press.
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Fig.4.1.2 Matched aluminium die.
The TRB consists of spar, tail section, Anti Icing System,Blade Root, Blade Tipare
the main structure components.
Some of the salient specifications of Tail Rotor Blades (TRB) are –
(a) Blade Length - 1719 mm
(b) Blade weight (single) - 10 KG Appx.
(c) Flex beam weight- 2.7KG Appx.
Fig. 4.1.3 Cross sectional view of a tail rotar blade
4.2 Testing
The verification test program for the helicopter blade encompassed static and dynamic
testing. The static tests of the tail blade involved experimental evaluation of Torsional and
flexional blade stiffness and its elastic axis position.
Dynamic tests involved testing of vibratory characteristics and verification testing of
blade fatigue properties. The purpose of the static tests was to evaluate experimentally
Torsional and flexional stiffness and elastic axis position of the blades. To fit the blade
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model, a robust
Facility frame made of steel L and U-profiles was employed. For load application, i.e.
for force and torque, an airfoil clamp and system of wheels and cables mounted on a special
frame made of steel profiles were used. For displacement measurement, comparators with an
accuracy of 0.01 mm were used.
Fig.4.1.4 Load-introduction airfoil clamp in static testing.
5. EXPERIMENTAL RESULTS
With the help of different experimental techniques we found the results which are tabulated
below.
Table 5.1. Resin content in the flex beam
AREA
WT
RESIN
CONTENT
VOLATILE
CONTENT
DSC
TEST
(Ts)
DSC
TEST
(Tp)
ILSS
TEST
402.14
g/m2 31.99% 0.65% 139.68 151.87
99.15
&
1451.87
N/mm2
434.58
g/m2 31.39% 0.29% 139.95 151.31
93.65
&
1390.69
N/mm2
418.56
g/m2 34.15% 0.34% 143.14 153.78
90.28
&
1292.57
N/MM2
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Table 5.2. Stiffness vale of each flex beam
Sl.
No.
Mean
Hub
Thickness
Stiffness
Value in
Kg/Mm WT. in kg
1 13.4925 0.67 2.69
2 13.481 0.67 2.698
3 13.495 0.71 2.758
4 13.482 0.67 2.696
5 13.487 0.66 2.694
6 13.494 0.67 2.692
7 13.487 0.68 2.693
8 13.4855 0.67 2.696
9 13.4875 0.66 2.679
10 13.476 0.66 2.69
11 13.4915 0.67 2.701
12 13.488 0.67 2.693
13 13.4885 0.67 2.7
14 13.483 0.67 2.702
15 13.494 0.67 2.701
16 13.4825 0.68 2.746
17 13.489 0.68 2.695
18 13.487 0.67 2.701
19 13.486 0.67 2.698
20 13.489 0.68 2.7
21 13.488 0.7 2.71
22 13.486 0.7 2.696
23 13.4875 0.7 2.708
24 13.486 0.67 2.693
25 13.4 0.68 2.692
26 13.4845 0.68 2.696
27 13.493 0.68 2.69
28 13.487 0.68 2.704
29 13.4855 0.68 2.701
30 13.4445 0.73 2.691
31 13.498 0.67 2.698
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32 13.481 0.68 2.69
33 13.487 0.7 2.7
34 13.4625 0.66 2.698
35 13.4695 0.68 2.699
36 13.489 0.68 2.704
37 13.488 0.67 2.712
38 13.4765 0.67 2.712
39 13.476 0.68 2.685
40 13.483 0.67 2.69
41 13.4805 0.68 2.7
42 13.4825 0.68 2.7
43 13.4955 0.68 2.7
44 13.495 0.68 2.705
45 13.4685 0.68 2.697
46 13.478 0.67 2.704
47 13.487 0.66 2.708
48 13.461 0.68 2.701
49 13.4935 0.682 2.702
50 13.4945 0.68 2.701
51 13.466 0.66 2.682
52 13.478 0.66 2.682
53 13.469 0.66 2.68
54 13.4765 0.67 2.68
55 13.476 0.66 2.692
56 13.4745 0.64 2.701
57 13.48 0.68 2.683
58 13.486 0.66 2.686
59 13.478 0.67 2.684
60 13.475 0.65 2.68
Table 5.3 show the data of Bests of best and worst of worst
Sl
No
ARM
THICKNESS
HUB
THICKNESS
WT
IN
KG
1 8.778 8.811 13.498 2.698
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2 8.777 8.814 13.48/13.491 2.701
3 8.874 8.814 13.483/13.491 2.704
4 8.832 8.84 13.474/13.491 2.7
5 8.81 8.842 13.475/13.486 2.69
6 8.98 8.989 13.474/13.478 2.712
7 8.705 8.715 13.479/13.487 2.685
8 8.994 8.892 13.484/13.494 2.704
9 8.769 8.812 13.492/13.497 2.701
10 8.832 8.864 13.490/13.497 2.702
11 8.934 8.856 13.456/13.466 2.701
12 8.894 8.872 13.480/13.492 2.698
13 8.848 8.866 13.482/13.492 2.701
14 8.824 8.884 13.486/13.492 2.695
15 8.964 8.832 13.479/13.486 2.746
16 8.843 8.812 13.491/13.497 2.701
17 8.915 8.924 13.480/13.486 2.702
18 8.812 8.82 13.484/13.493 2.7
19 8.842 8.864 13.496/13.493 2.692
20 8.864 8.873 13.478/13.486 2.696
Table 5.4 experimental final results
6. Conclusions
This work has been undertaken, with an objective to explore the stiffness of the flex
beam and hence achieve six sigma through shanin methodology and to study the mechanical
properties of the composite materials used in manufacturing of the flex beam. The present
Expt.
No. Pre.
Cooling
rate
2nd
heating
rate
Precom
paction
temp
1st dwell Resin
content
1 660 1.6 1.1 78 38 Low
2 660 1.6 1.1 80 44 High
3 660 2 1.3 78 38 High
4 660 2 1.3 80 44 Low
5 664 1.6 1.3 78 44 Low
6 664 1.6 1.3 80 38 High
7 664 2 1.1 78 44 High
8 664 2 1.1 80 38 Low
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work reports the use of failure of flex beam due to high stiffness. This work focused at
providing knowledge to enhance further research in improving the mechanical properties of
the flex beam and improving the stiffness of the flex beam by undergoing certain procedures.
However, more work is needed to demonstrate the full potential of these techniques. The
present study does not include the possibly major effect of failure of flex beam. This can be
another strong contributor to the unsteady loading fluctuation on a tail rotor blade.
SCOPE OF FUTURE WORK
The present scope in research and development field is to produce flex beams under
the required stiffness criteria. This work provides for exploration in finding out the main
cause of over stiffness of flex beam and finding the problem through root cause analysis
using shanin methodology. Researchers can consider other aspects such as using of fish-bone
diagram, 7 quality control technique, six sigma methodology etc. Also varying the input data
that can contribute to good amount of work in future. One of the other important aspects
would be to develop composites using different grades and making use of new techniques
REFERENCES
1. Guyett, R.P. and Cardrick, A.W., The Certification of Composite Airframe Structures,
Symposium on large scale composite structures, Aeronautical Journal, The Royal
Aeronautical Society, London, July 1980, 84.
2. Rasuo, B., Full-Scale Fatigue Testing of Helicopter Blades from Composite Laminated
Materials, ECCM-9, 4-7 June 2000, Brighton, UK
3. Adams, D. O. and Kearney, H. L., Full-Scale Fatigue Testing of Advanced Fiber
Composite Components, Journal of the American Helicopter Society, Vol. 31, April 1986
4. Rasuo, B., Aircraft Production Technology, Faculty of Mechanical Engineering, University
of Belgrade, Belgrade, 1995
5. Lemanski, S. L. Weaver, P. M. and Hill, G. F. J., Design of Composite Helicopter Rotor
Blades to Meet Given Gross- Sectional Properties, Aeronautical Journal, the Royal
Aeronautical Society, London, Oct. 2005.
6.P.Priyanka,Deivanai Kathiresan,” A Machine Learning Approach To Mainframe Analysis”,
International Journal Of Innovations In Scientific And Engineeringresearch,Vol.4,Issue.1,18-
24,2017.
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