Post on 04-Jun-2018
Session: HUMS/CBM
Presented at the American Helicopter Society 66th
Annual Forum, Phoenix, Arizona, May 11-13, 2010.
Copyright 2010 by the American Helicopter Society International, Inc.
All rights reserved.
American Helicopter Society International, Inc.
Rotary Wing Dynamic Component Structural Life Tracking with Self-Powered Wireless Sensors
KCF Technologies, Inc. 112 W. Foster Ave.
State College, PA 16801
ABSTRACT
KCF Technologies has developed a novel wireless
load sensing technology that can be readily embedded
in existing rotorcraft parts located in critical load paths
for use in HUMS systems. An H-60 pitch link rod end
manufactured by Lord Corporation was chosen as the
development platform. The rod end has an existing
cavity within the threaded stem where components are
embedded. These components consist of a
piezoelectric stack for energy harvesting, a
magnetostrictive based load sensor, data acquisition
hardware, RF transmitter, and all accompanying circuitry. Experimental testing at Lord Corporation
demonstrated the system’s ability to harvest energy at
representative pitch link loading levels, continuously
sample load sensor data at 100 Hz, and wirelessly
transmit the data to a nearby location. Flash memory
can also be embedded within the rod end to store
critical parameters derived from pitch link loading
history. When not in service, the part could therefore
be interrogated to determine its individual fatigue
damage accumulation and remaining service life
leading to improved aircraft readiness and reduced
maintenance costs. KCF is working directly with partners Lord Corporation, Sikorsky Aircraft, and
Goodrich to develop the core technology subject to
critical performance and design constraints. KCF is
also collaborating with Technical Data Analysis, Inc.,
to address the essential objectives of tracking each
aircraft and its components in near real-time with a
system level approach.
INTRODUCTION
Basing rotorcraft component replacement on
individual component damage accumulation supports
the DoD objectives of improved aircraft readiness and
reduced maintenance costs. This concept requires
accurate and thorough sensing, automated diagnostics,
prognosis models to assess component condition and
system integrity, and a data management infrastructure
for directing appropriate maintenance activities. In
spite of the clear benefits of achieving this transition to
component damaged-based replacement, it is difficult
due to the large scope of the CBM infrastructure needed and the low tolerance for error in its
performance.
Although implementation of the data management
system requires a substantial effort to carry out, it has
a high likelihood of practically succeeding as a viable
commercial and military system. Similarly, the
diagnostics and prognostic models can be developed
with substantial work but low technical risk. Accurate
collection and supply of data to the data processing
and management system poses the greatest technical
risk since it must be a part of the rotorcraft structure
and most approaches will have many potential failure points. In addition, the rotorcraft sensor system weight
and robustness must ultimately be compared to simply
increasing component size/strength and factors of
safety.
The focus of this paper is the high technical risk
task of accurately monitoring component damage
accumulation. Zakrajsek, et al, indicate that there is a
strong case for implementing load monitoring on
helicopter rotor assemblies, if sensor system cost can
Jacob Loverich Jeremy Frank Joseph Szefi Edward C. Smith
Director of Research, KCF
Technologies, Inc.
President, KCF
Technologies, Inc.
President, Invercon, LLC Professor, Penn State
University
Member, AHS Member, AHS Member, AHS Member, AHS
Jacob Loverich Jeremy Frank Joseph Szefi Edward C. Smith
Director of Research, KCF
Technologies, Inc.
President, KCF
Technologies, Inc.
President, Invercon, LLC Professor, Penn State
University
Member, AHS Member, AHS Member, AHS Member, AHS
Zach Fuhrer
Product Engineer
LORD Corporation
Enrique Flores
Rotary Wing Str. Eng.
NAVAIR Struc 4.3.3.2
American Helicopter Society International, Inc.
be reduced and robustness increased1. This paper
builds on the substantial amount of work that has
already been done in this area. Since the scope of a
rotorcraft wide health monitoring system is
significantly larger than the project that is the basis for
this reporting, a strategic approach was taken to narrow the effort of monitoring the load transferred
through uniaxial load members that have rod ends.
This work supports the concept that data from a few
optimally placed load sensors will enable derivation of
a wide range of rotor component loads by using
advanced structural models like those being developed
by TDA (Technical Data Analysis, Inc.).
Elastomeric rod ends are ideal platforms for load
monitoring because they are located on critical load
links on main rotor dampers and pitch link assemblies,
as pictured in Figure 1. KCF Technologies, Inc. and
LORD Corporation have developed a rod end load monitoring system that improves upon work in the
area of wireless load monitoring on aircraft by
addressing issues related to system level robustness
and component level integration. The rod end system
is intended to supplement existing HUMS systems by
providing real time load data on the rotor assembly.
Since the rod end is a common aircraft component, the
sensor system is applicable to other locations
including landing gear.
Figure 1 Potential application of KCF’s embedded
load monitoring technology on rotorcraft
KCF is integrating energy harvesting, load sensing, and wireless communication for enabling the
rod end’s autonomous and real time load monitoring.
The new load sensor addresses the need for low
power, EMI robustness, and calibration free sensing.
The energy harvester enables battery-free operation of
the sensor system with 0.3 inch package size. The
wireless RF communication uses recent advances in
low-power wireless radio communication. The
complete system is self-contained inside the threaded
stem of the rod end, rendering a durable and
maintenance–free sensor.
OBJECTIVES
The overall goal of this work is to develop
fundamental tools for wireless load sensing
technology for rotorcraft that can locally harvest
energy using embedded components. The primary objectives pursued to reach this goal are the following:
1) Identify appropriate energy harvesting and load sensing methodologies.
2) Develop custom, ultralow power data acquisition and wireless transmission
components.
1) Experimentally validate the performance of
the embedded components in an H-60 pitch
link rod end undergoing representative
loading conditions.
BACKGROUND
Rotorcraft Health Monitoring
Energy harvesters and wireless sensors enable
complete elimination of liabilities relating to
hardwiring of health monitoring sensors. Because
batteries require periodic replacement and are sensitive
to extreme temperature environments, energy harvesters are an ideal solution for many applications.
The combination of wireless data transmission and
energy harvesting provides a cost effective and robust
approach to implementing sensor systems.
In such systems, sensors measure various health
indicators such as strain, temperature, pressure, and
vibration (acceleration). Each sensor node in this case
is autonomous and maintenance free in that the energy
required to acquire and transmit sensor measurements
will be harvested, rather than supplied by a wired
power source.
One such existing approach to wirelessly monitor rotor loads has been developed by Microstrain, Inc2,3.
This approach measures rotor loads with a
piezoresistive sensor applied to the exterior of the
pitch link. Exterior piezoelectric patches provide
energy harvesting for load sensing and wireless
transmission power requirements. The system was
flight tested on a Bell 412 helicopter and was capable
of sampling and wirelessly transmitting data at a rate
of 64 Hz in flight. Because the load monitoring and
energy harvesting components are located on the pitch
link’s exterior, however, this system may be readily subject to damaging impacts during helicopter
American Helicopter Society International, Inc.
operation or routine maintenance. A more robust
solution would be to package these components into
existing parts in critical load paths. KCF has
accomplished this by embedding both harvesting and
load sensing components within a pitch link rod end
stem. To provide a clear path to commercialization, KCF is collaborating directly with the rod end
manufacturer, Lord Corporation, to incorporate the
components during the manufacturing process.
Embedded Component Load Monitoring
Measuring the structural response of mechanical
systems subject to loading provides a fundamental
means for characterizing the local response of
components or the global inputs to systems or
components. For example, strain gauges on helicopter
pitch links are used to measure loads being transmitted through the pitch links to the rotor assembly.
Alternatively, strain gauges on rotor blades could be
used to determine the actual stress state of the blade
for estimating its damage accumulation during use.
Use of bondable metal foil strain gauges have
been by far the most prominent strain and load
measurement technique for the past half century. Foil
strain gauges have a network of thin wires embedded
in a thin plastic film. When subject to strain, the metal
foil stretches, which in turn changes the length to
cross-sectional area ratio of the metal wire. The geometric changes of the wire alter the electrical
resistance of the gauge. Because the changes in
resistance are small, Wheatstone bridge circuits are
used to amplify the electrical response.
Their small size, minimal influence on the host
structure’s mechanical properties, and ease with which
they can be added to a structure have made them
useful for many applications particularly in temporary
installations or in diagnostic implementations on
existing structures. Significant drawbacks of these
sensors, which typically do not limit their application
in light of other traditional strain measurement technology, include temperature sensitivity, change in
performance over time due, and the power electronics
needed to operate them. The temperature sensitivity is
minimized using low thermal expansion metals alloys
such as nickel-copper.
For some applications, the mentioned drawbacks
make their use particularly unattractive. For example,
strain measurement accuracy on helicopters is critical
due to the small safety factors. Changes in the
sensitivity over time are unacceptable, especially
because these strain gauges are often used for updating component retirement times to reduce operating cost,
and a strain gauge that requires frequent calibration
would add cost and maintenance. With advances in
ultra low power wireless sensors, the power
requirements and electronic circuit required for foil
gauges are further limiting their applicability for some
applications.
Of the alternative and innovative strain sensing
technologies, including optical fiber Bragg, piezoresistive, and capacitive, the inverse
magnetostrictive sensors are the most promising for
discrete low power sensor nodes. Fiber Bragg sensors
are particularly well suited for applications where
large power electronics are acceptable, cost is not a
concern, and many measurement locations along a
single fiber are needed. Piezoresistive sensors suffer
from strong temperature sensitivity, and capacitive
sensors typically require complicated power
electronics and signal processing.
The strain sensor developed by KCF utilizes the
inverse magnetostrictive effect. This effect characterizes the change of domain magnetization
when a stress is applied to a material, which is also
known as the Villari effect. On a micro scale,
application of a magnetic field causes boundaries
between the domains to shift and the material's
dimensions to change. A Hall effect sensor is used to
measure changes in the magnetic permeability of the
magnetostrictive material. The sensor voltage output
can then be calibrated to actual load levels. The
advantages of this approach include very low power
requirements and the ability to put the sensor in sleep mode when data is not acquired.
In the current work, KCF has seamlessly embedded
this sensor in a pitch link rod end’s interior so that
information recorded about the rod end’s health remains
with the rod end. In this case, removing the rod end from
its assembly will not disassociate the health data from the
rod end. This is important for air and land vehicle
components that are periodically removed and may
remain in storage for a period of time. Since retrieval of
health data from the sensor depends on the operation of
the energy harvesting power supply, the power harvester
must be subject to its intended environment. When a component with an embedded sensor and power
harvester is in storage or removed from its assembly, the
energy harvester is likely to be completely inert and it
would not be possible to extract health data from the
component. This is an issue because one of the main
purposes of embedded health sensors is to evaluate if a
component can be returned to service. KCF is currently
developing technologies that will allow for local
interrogation of uninstalled components that rely on
embedded energy harvesters for power. Current designs
consist of connectionless interrogation wands that can quickly provide wireless power and communicate with
the component to assess its health when not in use.
American Helicopter Society International, Inc.
Energy Harvesting
To harvest energy from a host object’s mechanical
strain, piezoelectric transducers are directly attached
or embedded in the host component, where the
piezoelectric material strains with the host component. This strain on the piezoelectric element in turn induces
charge at its electrodes. The charge is then extracted
by the circuit so that it can be delivered to the health
monitoring device.
This strain-based harvester is implemented by
placing the piezoelectric material in the load path.
Since the electric field generated in the piezoelectric
material is proportional to the strain, the voltage at the
electrodes is minimized by using thin layers of
material. In this configuration, the d33 piezoelectric
constant defines the relationship between strain and
electric field. To increase the power output of the harvester while still minimizing voltage, the
piezoelectric material is layered to form a piezoelectric
stack. The piezoelectric element is coupled
mechanically to the host structure by placing it under a
preload using the host structure’s surrounding
structure. In this way, the element is in parallel with
the primary stiffness of the host structure.
Energy is harvested from the electromechanical
transducer using a circuit that consists of a diode
bridge, a DC-DC converter, energy storage element,
and voltage regulator. Input voltage protection and overvoltage protection for the storage element are also
included in the circuit. The bridge provides
rectification of the voltage waveform from the energy
harvester transducer. The uni-polar rectified
waveform is fed into an input capacitor that acts as a
voltage filter so that a steady DC voltage is available
for the DC-DC converter. The DC-DC converter
optimally transfers energy from the input capacitor(s)
which are at variable voltages to a much larger sized
energy storage element that is typically used within a
narrow voltage range4. The energy storage element
provides an energy reservoir so that the load can draw power that is much higher than that supplied by the
harvester for short durations. This is needed because
the electrical load is generally determined by its
specific application and it is often much higher than
that which is available directly from the energy
transducer.
Infrastructure for Dynamic Component Life
Tracking
For effective component tracking and life assessment, it is imperative that up-to-date history and
remaining life of components be readily available
through a sophisticated system architecture that
smoothly integrates all pertinent data management
systems. KCF is collaborating with technology partner
TDA to address the essential objectives of tracking
each aircraft and its components in near real-time with
a system level approach, gathering complete
component usage history and thereby accurately predicting the life of each component, and
subsequently eliminating penalties imposed due to
unknown usage histories. KCF’s sensor development
supplements this system with accurate and near real-
time load data on the rotor assembly.
TDA envisions one comprehensive and integrated
dynamic component tracking system. This vision
brings together rotorcraft data in one open architecture
framework to provide near real-time component health
and fatigue life expended (FLE) values. The fleet
management tool envisioned in this framework will
promote the development of safety strategies through asset management via prognostics, scheduling fleet
maintenance actions, and future acquisitions.
TECHNOLOGY DEVELOPMENT
Load Monitoring H-60 Rod End with Embedded
Components
An elastomeric H-60 pitch link rod end was
chosen as the development platform for KCF’s
rotorcraft load monitoring technology. The rod end,
pictured in Figure 2, was provided by the Lord
Corporation. As indicated in the figure, the energy
harvester, load sensor, data acquisition circuit board,
harvester circuit board, and RF communication circuit
board are all embedded within an existing cavity that is approximately three quarters of an inch in diameter
and four inches deep. The loads applied to the rod end
in flight cause dynamic straining of the part, which in
turn cause straining of the piezoelectric harvesting
element. The dynamic voltage created in the
piezoelectric element is collected by the harvester
circuit. The harvested power is then delivered to the
load sensor and the data acquisition and RF
communication boards. The magnitude of the
dynamic flight loads is sufficient to power all of the
embedded electrical components and RF communication devices.
American Helicopter Society International, Inc.
Figure 2 Load monitoring H-60 rod end with
embedded KCF components
Magnetostrictive Load Sensor
The magnetostrictive load sensor currently in
development at KCF consists primarily of a magnetostrictive material, a Hall effect sensor, and
permanent magnets located at either end of the
magnetostricive material. A change in stress to the
load sensor results in a change in the magnetic
permeability of the magnetostricive material. This
change in permeability alters the amount of magnetic
flux that is passing perpendicularly through the Hall
effect sensor. This change in magnetic flux
corresponds to a change in the Hall voltage output,
which can then be calibrated to the load. The Hall
effect sensor is ultra low power and compact, with a
geometry of 2.0 x 3.0 x 0.75 mm, and is capable of being put into sleep mode when not being
interrogated.
Figure 3 Magnetostrictive load sensor and
piezoelectric energy harvesting stack
Energy Harvesting
The embedded energy harvesting element consists
of a piezoelectric stack element that generates a
voltage in proportion to the level of strain it
undergoes. The piezoelectric stack within the rod end
is capable of providing in excess of 5 mW of power
while the rod end is subject to representative pitch link
loading.
A comparison of the harvester power generation
and the power used by the sensor for various operation
modes is plotted in Figure 4. The power generation
depends directly on the magnitude of load applied to the rod end, and the power consumed is approximately
proportional to the data sampling rate.
Data Acquisition and Wireless Transmission
An ultra low power microprocessor is employed
to sample the load sensor data. The microprocessor
has a 12 bit A/D for high resolution conversions, a
DMA engine for efficient and power sensitive
transferring of data, multiple timers for
synchronization, and large amounts of on-board RAM
for larger transfers of data packets. The data acquisition code is interrupt driven to take advantage
of the different low power modes of the processor.
The RF link has over the air data rates of up
to 2Mbits/sec, which halves the duty cycle over
traditional 1Mbits/sec RF radio. This in turn reduces
the number of over the air data packet collisions that
could occur. The radio also has the capability of auto-
acknowledging receptions of data packets, up to three
times, without any microprocessor involvement. Flash
memory components ranging from 4 – 128 Mb can
also be added to store sensor history and rainflow counting.
Standard IEEE 802.15.4 protocols such as
Bluetooth® and Zigbee® are designed for specific
applications that are different enough from rotorcraft
low power sensor applications that a proprietary RF
communication is required. The wireless solution
presented herein addresses the need for a lower
payload overhead and high data transmission rate
while maintaining a high level of robustness. In
addition, KCF’s wireless communication system will
comply with the US government’s FIPS 140 security
standard. Antenna design is a critical feature for highly
reliable data transmission and in terms of optimal
mechanical packaging. A few antenna designs were
evaluated for application to the rod end sensor. Patch
style antennas provided a balance between size and
attenuation. Chip antennas for direct implementation
on a PCB and helical whip antennas were also
characterized. A summary of preliminary antenna
testing is shown in Figure 6.
RF Antenna
Harvester
Load Sensor
Harvester Circuit, Microprocessor, and RF
Transmitter
1.5”
0.7”
Energy Harvester
Load Sensor
American Helicopter Society International, Inc.
Figure 4 Power requirements for varying operating conditions and different flight conditions versus
sampling frequency
Figure 5 Antenna dBm relative to receiver
detection lower threshold for 0°, 90°, 180°, and
270° orientations around the rod end stem at an
eight foot radius
Experimental Demonstration under Representative
Loading
An experimental demonstration of the wireless
load monitoring technology was conducted at the Lord
Corporation. The test set up is pictured in Figure 6. It was demonstrated that the wireless sensor system
reports the uni-axial rod end load time history in near
real time. The system consists of the piezoelectric
stack energy harvester, a 2.4 GHz wireless RF link,
and the magnetostrictive strain sensor to measure and
report the component load. Proper operation of all
three subsystems and their interoperability was tested.
The demonstration showed that for nine of twelve
typical loading conditions, the harvester provided
sufficient power to sample and transmit load data
wirelessly at a continuous rate of 100 Hz. Proper
operation of the wireless RF link was confirmed by the
receipt of full and coherent data sets. The strain sensor
operation was confirmed by registration of the rod end’s static and dynamic load levels. In Figure 7 and
Figure 8, force time histories are plotted as measured
by a calibrated load cell and KCF’s embedded load
cell for both sinusoidal and triangular force inputs. It
was observed that the two load cells agreed well over a
range of loading conditions.
On-going development work includes strain
sensor signal conditioning, increased strain sensor
sensitivity, data acquisition synchronization, storage of
data locally at the rod end, energy transmission to the
component when it is not loaded, wireless security,
improved energy harvester performance, and calibration modes of operation.
ACKNOWLEDGEMENTS
KCF would like to thank our technology
development partners, Lord Corporation, Sikorsky,
and Goodrich, for their continued support in this
development work.
American Helicopter Society International, Inc.
Figure 6 Experimental testing of rod end with embedded components at Lord Corporation for varying
loading conditions at 4.3 Hz
7.1 7. 2 7.3 7. 4 7.5 7.6 7.7 7.8
-3000
-2000
-1000
0
1000
2000
3000
4000
Time (sec)
Ro
d E
nd F
orc
e (
lb.)
Lord Load Cell
KCF Rod End Load Sens or
Figure 7 Force time history of Lord load cell and
KCF’s embedded load cell for a sinusoidal force
input at 4.3 Hz
1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2. 2
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
5000
Tim e (sec)
Fo
rce
(lb
.)
Lord Load Cell
KCF Rod End Load Sensor
Figure 8 Force time history of Lord load cell and
KCF’s embedded load cell for a triangular force
input at 5 Hz
American Helicopter Society International, Inc.
REFERENCES
1 Zakrajsek, J., et al, 2006. Rotorcraft Health
Management Issues and Challenges, NASA/TM—
2006-214022.
2 Arms, S. W., Moon, S.M., Phan, N., “Energy
Harvesting Wireless Sensors for Helicopter Damage
Tracking,” 62nd
Annual Forum Proceedings of the
American Helicopter Society, May 11, 2006, Phoenix,
AZ, USA, 2006.
3 Arms, S.W., Townsend, C.P., Churchill, D.L.,
Augustin, M., Yeary, D., Darden, P.,“Tracking Pitch
Link Dynamic Loads with Energy Harvesting
Wireless Sensors,” 63rd
Annual Forum Proceedings
of the American Helicopter Society, May 1-3, 2007,
Virginia Beach, VA, USA, 2007.
4 Ottman, G.K., Hofmann, H. F., Lesieutre, G.A.
(2003). “Optimized Piezoelectric Energy Harvesting
Using Step-Down Converter in Discontinuous
Conduction Mode”, IEEE Transactions on Power
Electronics, March 2003, vol. 18, issue 2, pp. 696-
703.
5 Global Security Online Documents http://www.
globalsecurity.org/military/systems/ship/ddg-51.htm,
accessed April 2007
6 Mokole, E. L., M. Parent, T. T. Street, and E. Tomas.
RF Propagation on Ex-USS SHADWELL. Naval Research Laboratory. Washington, DC. 153-156. 20
Apr. 2007 <http://ieeexplore.ieee.org/
iel5/7225/19474/00900165.pdf>.
7 Scholtz, Dr. Robert, Dr. Keith Chugg, Mr. Robert
Weaver, Mr. Joon-Yong Lee, Mr. Carlos Corrada,
Mr. Eric Homier, and Mr. Robert Wilson. Naval
Total Asset Visibility (NTAV) Tests on the SS
Curtiss, Port Hueneme, CA. Naval Facilities
Engineering Service Center. University of Southern
California: Steven J. Gunderson, 2002. 1-15. 20 Apr. 2007 <http://www.uwblab.net
/Publications/NTAV_Appendix_A_USC.pdf>.
8 Robinson, Brian. "Antenna Considerations for
ZigBee Hardware." ZigBee Alliance Developer's
Conference. Held in Conjunction with Embedded
Systems Conference, Silicon Valley. McEnery
Convention Center, San Jose, CA. 5 Apr. 2007.
9 U.S. Army Aviation & Missile Life-Cycle
Management Command, G-3 CBM,- DoD
Maintenance Symposium 13 Nov t07 (Nenninger) –
10/16/2007
10 Ferris D H, “Large Transverse Deflections of
Circular Plates Loaded Symmetrically,” Computers
and Structures 33 4 709-724 (1986).
11 Bechhoefer, E. and Bernhard, A. 2003. Setting
HUMS Condition Indicator Thresholds by Modeling
Aircraft and Torque Band Variance. IEEEAC
paper#1104, Version 3, Updated December 2, 2003.
12 Benoit, J., Dreitlein, K., Zepke, B., Morgan, R., Bayt,
R. (2000), “UTC wireless sensor applications
requiring energy harvesting”, Presented at the
DARPA Energy Harvesting Review,
http://www.darpa.mil/dso/trans/energy /ab_utrc.html.
13 Romero, R., Summers, H. and Cronkhite, J. 1996.
Feasibility Study of a Rotorcraft Health and Usage
Monitoring System (HUMS): Results of Operator's
Evaluation, NASA CR-198446, February.
14 Johnny Wright, “Emerging Results Using IMD-
HUMS in a Black Hawk Assault Battalion”
American Helicopter Society 61st Annual Forum,
Grapevine, TX, June 1-3, 2005.
15 Peter J. Jones, Donald D. Russell, and Dennis P.
McGuire, Latest Developments in Fluidlastic Lead-
Lag Dampers for Vibration Control in Helicopters,
American Helicopter Society 59th Annual Forum,
Phoenix, Arizona, May 6 – 8, 2003.
16 Ray Dora, Johnny Wright, Robert Hess. “Utility of
the IMD HUMS in an Operational Setting on the
UH-60LBlackhawk”American Helicopter Society
60th Annual Forum, Baltimore, Maryland, May7-10,
2004.
17 Ray Dora, Treven Baker, Robert Hess, “Application
of the IMD HUMS to the UH-60A Blackhawk”
American Helicopter Society 58th Annual Forum,
Montréal, Canada, June 11-13, 2002
18 Scott Maley, “Overview of Fatigue Life
Management Enabled Through CAMEO
Integration.” Post Seattle-JCDT, Jun 2007.
19 Thang, Bui Quoc, Dubuc, Julien, Bazergui, Andre,
and Biron, Andre. “Cumulative Fatigue Damage
under Strain Controlled Conditions.” Journal of
Materials, JMLSA, Vol. 6, No. 3, Sept. 1971, pp.
718 - 737.