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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Das vorliegende Buch ist ein umfassendes grundlegendes Kompendium über Dehnungsmessstreifen (DMS) und ihre Anwendung in der Materialwissenschaft und Werkstofftechnik sowie in allen Bereichen des Ingenieurwesens. Es deckt sowohl die theoretischen als auch die praktischen Aspekte der Spannungsanalyse mithilfe von Dehnungsmessstreifen ab. Ein historischer Rückblick auf die Erfindung und Entwicklung von DMS fasst das "Wer, Wann und Wie" zusammen. Die umfassende Bibliographie führt zu zusätzlichen Hintergrundinformationen. Besonderes Augenmerk gilt der Spannungsanalyse zur Bestimmung der mechanischen Eigenschaften, der Tragfähigkeit und der Gebrauchstauglichkeit von Bauteilen sowie zur Planung von Monitoring und Inspektionen. Die richtige Planung und Auswertung von Messungen und die Algorithmen zur Ermittlung von Spannungen werden aufgezeigt und die Interpretation von Ergebnissen erläutert. Dabei schöpft der Autor für die praxisorientierten Beschreibungen der Messprinzipien, der Messanordnungen und der Versuchsreihen aus seinem reichen Erfahrungsschatz. Das Buch enthält eine Anzahl realer Anwendungsbeispiele mit detaillierten Anleitungen, die als Vorbilder für die Lösung ähnlicher Aufgaben betrachtet werden können. Kommentare helfen, typische Fehler und Fehlversuche zu vermeiden. Das Buch ist ein unverzichtbares Nachschlagewerk für Fachleute, die Bauteile analysieren und Messungen planen müssen, die zu zuverlässigen Ergebnissen führen. Das Buch ist lehrreich für Praktiker, die zuverlässige Messkreise installieren und die Ergebnisse beurteilen müssen. Das Buch empfiehlt sich auch für Anfänger, um sich mit den Problemen vertraut zu machen und die Möglichkeiten und Grenzen der Dehnungsmesstechnik kennen zu lernen.
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Contents
Cover
Title Page
Copyright
Preface
Chapter 1: Historical Review
References
Chapter 2: Fundamentals of Strain Gage Technology
2.1 Measurement Principle and Structure
2.2 Sensitivity
2.3 Transverse Sensitivity
2.4 Temperature Effects
2.5 Mechanics of the Strain Gage
2.6 Influence of Pressure
2.7 Dynamic Behaviour
2.8 Heat Dissipation
2.9 Measuring at Elevated Temperatures
2.10 Stress Gages
References
Chapter 3: Installation of Strain Gages
3.1 Preparatory Work
3.2 Methods of Fastening
3.3 Different Measurement Object Materials
3.4 Measurement Point Protection
3.5 Quality Tests of the Strain Gage Installation
References
Chapter 4: The Wheatstone Bridge Circuit
4.1 Circuit Principle
4.2 Basic Equation of the Bridge Circuit
4.3 Temperature Compensation
4.4 Limit of the Bridge Signal Resolution
4.5 Examples of Some Elementary Bridge Circuits
References
Chapter 5: Adjustment and Compensation Circuits
5.1 General
5.2 Compensation of Zero Shift with Temperature Change and Zero Adjustment
5.3 Compensation of Temperature Effects on the Sensitivity and Linearity Measures
5.4 Adjustment of the Characteristic Value
5.5 Creep Compensation
5.6 Full-Bridge Circuits Connected in Parallel
References
Chapter 6: Cable Between the Strain Gage Bridge Circuit and Measuring Instrument
6.1 Basic
6.2 Ohmic Resistance of the Cable
6.3 Influence of Cable Capacitance
6.4 Full-Bridge Connection in Four-Wire Technology
6.5 Six-Wire Circuit
6.6 Dual-Channel Principle
6.7 Connection of Half and Quarter Bridges
6.8 Protection Against Disturbing Influences
References
Chapter 7: Signal Processing
7.1 Introductory Viewing
7.2 Analogue Instrumentation Amplifier
7.3 Digital Amplifier Concepts
7.4 Compensation Method
7.5 Multipoint Measurement
References
Chapter 8: Calibration of Devices for Measuring with Strain Gages
8.1 Introduction
8.2 Measurement Chain
8.3 Characteristic and Sensitivity
8.4 Calibration of the Entire Measurement Chain as a Measuring Device
8.5 Compensators
8.6 Transducers
8.7 Calibration Measures
8.8 Calibration of Measuring Arrangements with Self-Installed Strain Gages
References
Chapter 9: Determination of mechanical stresses from strains measured with strain gages
9.1 Introduction
9.2 Terms of Stress and Strain
9.3 Elastic Deformation and Stress of a Tensile Rod Under Uniaxial Tensile Loading
9.4 The Biaxial Stress State
9.5 Mohr's Circle
9.6 Deformation Circle
9.7 Types of Rosettes and Grid Notation
9.8 Evaluation Formulas for 0/45/90° Strain Gage Rosettes
9.9 Evaluation Formulas for 0/60/120° Strain Gage Rosettes
References
Chapter 10: Application examples of elastic deformation
10.1 Initial Considerations
10.2 Principal Directions are Known
10.3 Stress Analysis for Unknown Principal Directions
10.4 Simultaneous Measurement of Multiple Load Components
10.5 Diaphragm Rosettes
References
Chapter 11: Determination of Thermal Stresses
11.1 Emergence of Thermal Stresses
11.2 Sensing the Prevented Thermal Expansion at Identical Temperature at the Compensation Gage and the Active Strain Gage
11.3 Determination of the Restricted Thermal Expansion by Computational Correction of the Measured Values with Previously Measured Thermal Outputs on Dummies
11.4 Determination of the Restricted Thermal Expansion by Mathematical Correction with the Thermal Outputs Determined at the Original Measurement Object
11.5 The ‘Reversible’ Strain Gage
11.6 Separation of the Mechanical Strain from the Thermal Strain
11.7 Compensated Half-Bridge Strain Gage with Compensation Resistor
References
Chapter 12: Strain Gages as a Means for Experimental Determination of Residual Stresses
12.1 Preliminary Observation
12.2 Cutting-Down Method
12.3 Layer Removal Method
12.4 Ring-Core Method
12.5 Hole-Drilling Method
Bibliography
Chapter 13: Stress Analysis Using Strain Gages in the Elastoplastic Deformation Range
13.1 Introduction
13.2 Equivalent State with Elastic Deformation
13.3 Elastoplastic Deformation
13.4 Stress Analysis
13.5 Practical Example of Application
13.6 Tensorial Representation of the Elastoplastic Deformation
References
Chapter 14: Strength Theories
14.1 Preview
14.2 Concept of Effective Stress
14.3 Experimental Results
14.4 Maximum Stress Theory
14.5 Maximum Shear Theory
14.6 Extended Shear Theory
14.7 Plastic Potential Theory
14.8 Distortion Energy (Shape Changing) Theory
14.9 Octahedral Plane Shear Stress Theory
References
Index
End User License Agreement
List of Tables
Table 2.1
Table 2.2
Table 2.3
Table 2.4
Table 3.1
Table 3.2
Table 5.1
Table 9.1
Table 10.1
Table 14.1
Table 14.2
List of Illustrations
Fig. 1.1
Fig. 1.2
Fig. 1.3
Fig. 1.4
Fig. 1.5
Fig. 1.6
Fig. 1.7
Fig. 1.8
Fig. 1.9
Fig. 1.10
Fig. 1.11
Fig. 1.12
Fig. 1.13
Fig. 1.14
Fig. 1.15
Fig. 2.1
Fig. 2.2
Fig. 2.3
Fig. 2.4
Fig. 2.5
Fig. 2.6
Fig. 2.7
Fig. 2.8
Fig. 2.9
Fig. 2.10
Fig. 2.11
Fig. 2.12
Fig. 2.13
Fig. 2.14
Fig. 2.15
Fig. 2.16
Fig. 2.17
Fig. 2.18
Fig. 2.19
Fig. 2.20
Fig. 2.21
Fig. 2.22
Fig. 2.23
Fig. 2.24
Fig. 2.25
Fig. 2.26
Fig. 2.27
Fig. 2.28
Fig. 2.29
Fig. 2.30
Fig. 2.31
Fig. 2.32
Fig. 2.33
Fig. 2.34
Fig. 2.35
Fig. 2.36
Fig. 2.37
Fig. 2.38
Fig. 2.39
Fig. 2.40
Fig. 2.41
Fig. 2.42
Fig. 2.43
Fig. 2.44
Fig. 2.45
Fig. 2.46
Fig. 2.47
Fig. 2.48
Fig. 2.49
Fig. 2.50
Fig. 2.51
Fig. 2.52
Fig. 2.53
Fig. 2.54
Fig. 2.55
Fig. 2.56
Fig. 2.57
Fig. 2.58
Fig. 2.59
Fig. 2.60
Fig. 2.61
Fig. 2.62
Fig. 2.63
Fig. 2.64
Fig. 2.65
Fig. 2.66
Fig. 2.67
Fig. 2.68
Fig. 2.69
Fig. 3.1
Fig. 3.2
Fig. 3.3
Fig. 3.4
Fig. 3.5
Fig. 3.6
Fig. 3.7
Fig. 3.8
Fig. 3.9
Fig. 3.10
Fig. 3.11
Fig. 3.12
Fig. 3.13
Fig. 3.14
Fig. 3.15
Fig. 3.16
Fig. 4.1
Fig. 4.2
Fig. 4.3
Fig. 4.4
Fig. 4.5
Fig. 4.6
Fig. 4.7
Fig. 5.1
Fig. 5.2
Fig. 5.3
Fig. 5.4
Fig. 5.5
Fig. 5.6
Fig. 5.7
Fig. 5.8
Fig. 5.9
Fig. 5.10
Fig. 5.11
Fig. 5.12
Fig. 5.13
Fig. 5.14
Fig. 5.15
Fig. 6.1
Fig. 6.2
Fig. 6.3
Fig. 6.4
Fig. 6.5
Fig. 6.6
Fig. 6.7
Fig. 6.8
Fig. 6.9
Fig. 6.10
Fig. 6.11
Fig. 6.12
Fig. 6.13
Fig. 6.14
Fig. 6.15
Fig. 6.16
Fig. 6.17
Fig. 6.18
Fig. 6.19
Fig. 6.20
Fig. 7.1
Fig. 7.2
Fig. 7.3
Fig. 7.4
Fig. 7.5
Fig. 7.6
Fig. 7.7
Fig. 7.8
Fig. 7.9
Fig. 7.10
Fig. 7.11
Fig. 7.12
Fig. 7.13
Fig. 7.14
Fig. 7.15
Fig. 7.16
Fig. 7.17
Fig. 7.18
Fig. 7.19
Fig. 7.20
Fig. 8.1
Fig. 8.2
Fig. 8.3
Fig. 8.4
Fig. 8.5
Fig. 8.6
Fig. 8.7
Fig. 8.8
Fig. 8.9
Fig. 9.1
Fig. 9.2
Fig. 9.3
Fig. 9.4
Fig. 9.5
Fig. 9.6
Fig. 9.7
Fig. 9.8
Fig. 9.9
Fig. 9.10
Fig. 9.11
Fig. 9.12
Fig. 9.13
Fig. 9.14
Fig. 9.15
Fig. 9.16
Fig. 9.17
Fig. 9.18
Fig. 9.19
Fig. 9.20
Fig. 9.21
Fig. 9.22
Fig. 9.23
Fig. 9.24
Fig. 9.25
Fig. 9.26
Fig. 9.27
Fig. 10.1
Fig. 10.2
Fig. 10.3
Fig. 10.4
Fig. 10.5
Fig. 10.6
Fig. 10.7
Fig. 10.8
Fig. 10.9
Fig. 10.10
Fig. 10.11
Fig. 10.12
Fig. 10.13
Fig. 10.14
Fig. 10.15
Fig. 10.16
Fig. 10.17
Fig. 10.18
Fig. 10.19
Fig. 10.20
Fig. 10.21
Fig. 10.22
Fig. 10.23
Fig. 10.24
Fig. 10.25
Fig. 10.26
Fig. 10.27
Fig. 10.28
Fig. 10.29
Fig. 10.30
Fig. 10.31
Fig. 10.32
Fig. 10.33
Fig. 10.34
Fig. 10.35
Fig. 10.36
Fig. 10.37
Fig. 10.38
Fig. 10.39
Fig. 10.40
Fig. 10.41
Fig. 10.42
Fig. 10.43
Fig. 10.44
Fig. 10.45
Fig. 10.46
Fig. 11.1
Fig. 11.2
Fig. 11.3
Fig. 11.4
Fig. 11.5
Fig. 11.6
Fig. 11.7
Fig. 11.8
Fig. 11.9
Fig. 12.1
Fig. 12.2
Fig. 12.3
Fig. 12.4
Fig. 12.5
Fig. 12.6
Fig. 12.7
Fig. 12.8
Fig. 12.9
Fig. 12.10
Fig. 12.11
Fig. 12.12
Fig. 12.13
Fig. 12.14
Fig. 12.15
Fig. 12.16
Fig. 12.17
Fig. 12.18
Fig. 12.19
Fig. 12.20
Fig. 12.21
Fig. 12.22
Fig. 12.23
Fig. 12.24
Fig. 12.25
Fig. 12.26
Fig. 12.27
Fig. 12.28
Fig. 12.29
Fig. 12.30
Fig. 12.31
Fig. 12.32
Fig. 12.33
Fig. 12.34
Fig. 12.35
Fig. 12.36
Fig. 12.37
Fig. 12.38
Fig. 12.39
Fig. 12.40
Fig. 12.41
Fig. 12.42
Fig. 12.43
Fig. 12.44
Fig. 12.45
Fig. 12.46
Fig. 12.47
Fig. 12.48
Fig. 12.49
Fig. 12.50
Fig. 12.51
Fig. 12.52
Fig. 12.53
Fig. 13.1
Fig. 13.2
Fig. 13.3
Fig. 13.4
Fig. 13.5
Fig. 14.1
Fig. 14.2
Fig. 14.3
Fig. 14.4
Fig. 14.5
Fig. 14.6
Fig. 14.7
Fig. 14.8
Fig. 14.9
Fig. 14.10
Fig. 14.11
Fig. 14.12
Fig. 14.13
Guide
Cover
Table of Contents
Begin Reading
Chapter 1
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Stefan Keil
Technology and Practical Use of Strain Gages
With Particular Consideration of Stress Analysis Using Strain Gages
Professor Dr.-Ing. Stefan Keil
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2017 Wilhelm Ernst & Sohn, Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Rotherstraße 21, 10245 Berlin, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978-3-433-03138-4ePDF ISBN: 978-3-433-60665-0ePub ISBN: 978-3-433-60664-3eMobi ISBN: 978-3-433-60782-4oBook ISBN: 978-3-433-60666-7
Preface
In 1995, when the first edition of this book was published in German language it soon became very popular, not only in German speaking countries, but also abroad. This first edition has been out of stock for a while. The demand from specialists around the world shows, however, that this book remains to be of interest, because strain gages find application in various fields and in large numbers. They are also often used by beginners in this specialist area. Fast and without much effort these sensor elements can be attached to building components in order to transmit vital information about their strength and operational safety. Comprehensive knowledge of the necessary basics on this topic is a prerequisite to carry-out correct measurements by means of strain gages, and for a proper analysis and evaluation of the measured strain. This is what this book covers. In practice, the measurement procedure and the processing of the readings can be a source of errors. This book points out what can go wrong and how it can be prevented.
A significant number of the first-edition books were purchased by experts from abroad. Repeatedly the question arose as to whether the book would be available in English, since English is world-wide the language most commonly used by engineers. The English version of the book at hand meets this request. The book deals with the technology of strain gages as an independent specialist field. It covers the relevant questions on electrical engineering and elaborates on the required fundamental principles of the strength of materials. Questions on digital signal processing are reviewed comprehensively. Paramount to this book is an application-orientated presentation of the contents.
The measurement by means of strain gages includes a number of individual stages which are elaborately described in this book: preparation of the measuring points, attachment of strain gages, connection and arrangement of cables, selection and settings of devices, and particularly for the strengths analyses: calculation of the mechanical stresses on the basis of the measured strains. The technology of strain gages is also dealt with in detail, since this knowledge will add to the understanding of the limits to what is feasible by the application of strain gages, and what is not. The application of strain gages can lead to amazing results. It is however also limited by the laws of physics.
The book includes a number of genuine examples which can be seen as role models for the solution of similar tasks.
Professor Dr.-Ing. Stefan Keil Lippstadt, May 2017
1Historical Review
It is an irrefutable fact that the strain gage was invented by two different people at almost the same time. They were situated at widely separated places in the USA and they did not, at that time, have any contact with each another [1.1]. Professor Arthur C. Ruge of the Massachusetts Institute of Technology (MIT) was one of these inventors; the other was Edward E. Simmons. At the California Institute of Technology (Caltech) in 1936, Simmons was investigating the stress–strain behaviour of metals under shock loads. He was at the time a student and worked as a research assistant at the Institute.
To measure the force introduced in the specimens by impact, he used a dynamometer equipped with fine resistance wires made from constantan. The tests carried out by Simmons were part of a research project of Dätwyler and Clark that started in 1936 [1.2]. Although details of the tests and the measurement method used were not published until 1938 [1.3], the start date of the project (1936) shows that it was Simmons who invented the strain gage principle. Publication about the tests and the used measurement method was divulged not before 1938 [1.3]. In 1940, Simmons's invention was patented at the United States Patent Office. Figure 1.1 shows the test equipment that Simmons used for the measurement of shock loads on metal specimens. The dynamometer is equipped with measuring wires made from constantan. The drawing is taken from the Patent [1.4]. This shows that a strain gage based transducer was patented before the strain gage itself.
Fig. 1.1 E.E. Simmons's dynamometer equipped with measuring wires for the measuring of shock loads on metal specimens [1.4]
In 1938 the other inventor, Professor Arthur C. Ruge, with the support of his assistant J. Hanns Maier investigated in the field of engineering seismology the influence of earthquakes on mechanical structures. His test object was a small scale model of an elevated water tank, mounted on a vibration table. However, because the stress was low and the model's skin extremely thin they failed to measure the strain in the tank wall using normal mechanical or optical strain instrumentation available at that time. One day the saving idea came to him, and he attached the thin wire from a potentiometer with Duo household cement to the water tank and was immediately rewarded with excellent and reproducible measurement values.
The resistance change in metallic wires caused by strain due to tensile loading changed the voltage drop in the wire and could be measured with a simple bridge circuit [1.5, 1.6]. The strain gage was now born also on the east coast of the USA.
Figure 1.2 shows a photograph taken by J. Hanns Maier of Professor Ruge carrying out experiments on the model of a water tank using the first strain gages invented by him and his assistant Maier. Strain gage rosettes are cemented to the model's base. Also visible in the photograph is an acceleration transducer made by Ruge using resistance wires.
Fig. 1.2 A.C. Ruge carrying out experiments on a small scale model of a water tank fitted with the first strain gages mounted on a vibration table in 1938
For easier handling Ruge cemented the measuring wire to a carrier paper that had been stiffened by cementing the paper to two Plexiglas end pieces with a brass spacer bar serving as a handling frame and lead wire holder. The brass spacer bar was removed after cementing. Figure 1.3 shows one of the first strain gages made by Ruge with and without brass bar and with the felt protection layer removed. The strain gage seen in Figure 1.3 was patented in 1944 [1.7].
Fig. 1.3 Ruge's strain gage from 1938 a) with brass bar as an installation aid b) without brass bar and without grid protection layer
In 1938 in accordance with custom, Ruge duly submitted the bonded wire ‘resistant strain gage’ idea to the MIT patent committee. The committee's answer deserves quoting. The reply of the MIT reads: ‘…this development is interesting; the Committee does not feel that the commercial use is likely to be of major importance...any rights which the Institute may have in this invention should be waived in your favour…’ [1.8]. This meant that Ruge was free to exploit the invention as his own.
In 1939, Ruge and his colleague Professor Alfred V. deForest, with support of the heavy machine construction firm Baldwin-Southwark Corp. started the manufacture and sale of strain gages. The first answer by Baldwin-Southwark to Ruge's licence offer is also worthy of note: ‘We are in the locomotive business and not going to make postage stamps’ [1.6]. But after a convincing demonstration of strain gage performance in 1939, a profitable cooperation started between Ruge-deForest and Baldwin-Southwark. The beginning was marked by the registration of the strain gage. The invention was patented by the United States Patent Office on June 6 in 1944. When, in 1955, Ruge-deForest sold out to Baldwin-Lima-Hamilton, at that stage they employed more than 200 people.
Before the patent registration of Ruge's invention, Baldwin-Southwark arranged an agreement between Simmons and Ruge-deForest that recognized Simmons as well as Ruge as inventor of the strain gage [1.6]. At the end of the discussion which led to the agreement, Tatnall suggested in a spirit of fun that the new product be named SR-4; S and R for Simmons and Ruge, and the numeral 4 representing the four people who took part in the final discussion (Tatnall as instigator of the discussion, Clark as colleague of Simmons from Caltech, deForest as Ruge's colleague from MIT and Hathaway as patent attorney from Baldwin). This designation was registered as a trademark.
Figure 1.4 shows an SR-4 strain gage with paper carrier as it was when it became world-famous. It can be seen from Figure 1.4 that the SR-4 strain gage bears the number 2 292 549 of Simmon's patent. After the SR-4 agreement a legal battle ensued between Simmons and Caltech for whom Simmons was working when he made the invention. Caltech claimed they sponsored the development and asked a 60/40 split on royalties. Caltech lost the case, because, at the time the invention was made, Simmons was a student and not on the Caltech payroll.
Fig. 1.4 SR-4 strain gage with paper carrier from 1941 the protective felt layer is half removed
In 1939, Ruge and deForest started their partnership with Baldwin-Southwark for development engineering and manufacture of strain gages and strain gage devices for sale. In 1941, they got the first solid sizeable order from Baldwin for stock gages – 50 000 in one order for all types. These were intended to last a year, but actually lasted two month. Figure 1.5 shows one of the first strain gage packages as sold in that time.
Fig. 1.5 One of the first strain gage packages as sold by Baldwin in 1941
Simmons and Ruge were not the first scientists to recognize the resistance change in metallic wires caused by tensile loading and the possibility of using this phenomenon to measure mechanical quantities [1.9].
In 1908, the privy councillor Dr S. Lindeck was working on the development of precision resistors at the National Technical Institute (Physikalisch-Technische Reichsanstalt) in Berlin. He wound thin Manganin wire, embedded in shellac, onto brass tube coil formers. He was amazed when he found that the resistance of these elements was dependent on the weather. He found that rising humidity caused the shellac to swell, straining the manganese wire, whose resistance increased.
To investigate this phenomenon in more detail, he closed off both ends of the tube wound with the Manganin wire and placed it under an internal pressure of about 60 bar. As a result, the resistance changed proportionally with the pressure – and therefore with the strain – and suggested that this effect could be used in pressure measurement [1.10]. Unfortunately no-one at that time took up Lindeck's idea which only received its technical verification in a patent from Simmons for a bonded strain gage pressure transducer about 35 years later [1.11]. Because no figure of Lindeck's equipment is available, a sketch from Simmon's patent is all we can give here, in order to explain Lindeck's suggestion. Figure 1.6 gives the sketch from this patent.
Fig. 1.6 ‘Bonded strain gage pressure transducer’, resistance wire wound on a thin-walled tube with closed ends [1.11]
The first technical application of the change in resistance of wires in dependence on their strain for the measurement of pressure was made by Nernst [1.12]. The photograph in Figure 1.7a, which was first published in 1928, shows the pressure indicator designed by Nernst. He used freely tensioned resistance wires of 0.5–1.0 mm diameter and a few centimetres in length which were strained in proportion to pressure. The cylindrical transducer body contains a piston which is pushed by the pressure against the tensioned wires.
Fig. 1.7 First technical application of the change of resistance due to strain for pressure measurement a) pressure transducer developed by Nernst in 1917 b) pressure curve in an internal combustion engine measured with the transducer shown in a)
The Figure 1.7b shows the pressure characteristic in the cylinder of a combustion engine as measured by Nernst with this device. With the aid of this pressure transducer Nernst could measure the point of ignition in a four-stroke engine. The change in resistance is very small, but it is sufficient to feed an oscilloscope. This pressure transducer was first used by Nernst in 1917, who was at that time with Siemens and Halske in Berlin [1.13].
Another device, which was used in civil engineering for strain measurements in concrete and which had freely tensioned resistance wires, was described by Eaton in 1931 under the designation ‘electric resistance strain gage’ [1.14]. The device, shown schematically in Figure 1.8 [1.15], contains a Wheatstone half bridge circuit consisting of prestressed wire sections. One bridge arm has two sections which are strained when the device is pulled, whereas another section in the other arm of the bridge is relieved.
Fig. 1.8 Schematic sketch of the ‘electrical resistance strain gage’ made by Carlson in1931 which had freely tensioned resistance wires for strain measurement in concrete [1.15]
In 1935, Carlson, upon whose idea the design is probably based, reported that about 1500 of these strain measuring devices in an encapsulated version were cast in concrete constructional elements. However, he also reported on the numerous problems that occurred during measurements, such as through temperature effects and corrosion [1.16].
All the historical examples described above are based on the change in resistance of wires stressed by mechanical strain. In all cases, a Wheatstone bridge circuit was used to measure the change in resistance. This bridge circuit was invented by two scientists in the UK, who independently of one another, were dealing with electrical circuits to measure the electrical resistance of metallic wires. Their names were Samuel Hunter-Christie and Charles Wheatstone. They used the knowledge gained by Simon Ohm [1.17] to develop a circuit, with which it was possible to measure the electrical resistance of wires in spite of the instability of the voltage sources that were then available. Although Hunter-Christie published information about his circuit in 1833 [1.18], and it was ten years before Wheatstone's publication in 1843, the circuit was called after Wheatstone. This circuit became the standard circuit for measurements using strain gages and is still widely used today.
Figure 1.9 shows the Wheatstone bridge circuit in its original form. This circuit enabled Wheatstone to measure the resistance of electrical connecting wires in spite of the instability of his voltage source. He wrote about the response of his galvanometer to changes in the strain of the copper wire that was used [1.19], and the date of these measurements (1843) was very early in the history of strain gages.
Fig. 1.9 The Wheatstone Bridge Circuit in its original form (1843) [1.19]
In Figure 1.9 we can see the historic measurement device as used by Wheatstone in 1843. It consists of a wooden board with screw clamps Z and C used for connecting the supply voltage, the resistance wires Za and Ca, and screw clamps c, d, e and f for connection the resistances to be measured. Wheatstone tapped the diagonal voltage between a and b, using a sensitive galvanometer. An adjustable short-circuiting arm mn served as a zero balance.
Wheatstone explicitly made reference to his circuit's suitability for the measurement of small changes in resistance, and even at this early stage he was able to perceive relative changes in resistance of about two parts per thousand.
The next step was made by Thomson. Also in England, he conducted the first objective investigations into the changes of resistance caused by the strain in wires in 1856. He used a bridge circuit as invented by Wheatstone, in which, as shown in Figure 1.10, thin copper or iron wires were stretched by weights [1.20]. He found proportionality between the strain and the change of resistance and determined several gage factors, as they would be called today, but without specification of exact data.
Fig. 1.10 Thomson's bridge circuit for the measurement of changes in the resistance of metal wires under tensile load (1856) [1.20]
Thomson used in his test device the bridge circuit as invented by Wheatstone, but without any knowledge of Wheatstone's invention. In this way the Wheatstone bridge circuit was invented again.
Both Wheatstone's and Thomson's paper had long footnotes about their appropriate priorities. For example, Thomson wrote that he found out one hour before his lecture that Wheatstone had already discovered a similar circuit. In those days, it was more a matter of personal honour to be the first with the invention than to protect the invention itself by means of a profitable industrial patent.
The first systematic investigation into resistance change of various wires during tensile loading took place in the 1930s. E. Cerlinsky, working at the German Research Institute for Aviation in Berlin-Adlershof, found that constantan wire was the most suitable material for measurement purposes, a fact which still applies today [1.21].
Figure 1.11 illustrates the research setup used by Cerlinsky. A 30 cm long measuring wire as part of a Wheatstone bridge circuit was strung between a fixed point and the tip of the pointer on a balance. The balance was loaded using a weight and tared using a counterweight. The modulus of elasticity of the wire material could also be determined by measuring the displacement of the tip of the pointer with a microscope.
Fig. 1.11 Research setup for measuring the gage factors of resistant wires as performed by Cerlinsky in 1938
After the invention of the strain gage in 1938 in the USA it was quickly recognized that one could measure more than just strain with strain gages. All mechanical quantities that cause strains in materials can then be detected indirectly by using strain gages. The first transducers equipped with strain gages were built. The major benefits of the new measurement principle led to the improvement of strain gages through systematic development work. They became smaller and less sensitive to temperature, creep behaviour, and fatigue strength was improved. With strain gages used for the construction of transducers the more favourable, less moisture-sensitive phenolic resin (Bakelite) was used as the carrier material.
Initially with strain gages mainly were built transducers for pressure and torque. Strain gages offered in the 1940s the only way to measure power in drive trains of engines under operating conditions without affecting their dynamic characteristics through effects on the measured object. Force transducers with strain gages firstly were used in 1938 at the MIT in wind tunnel measurements on model aircrafts [1.22]. The simple way by installing strain gages on a construction part making this to a force measuring element quickly became known and used. These measuring elements brought no additional measuring displacement into the system and did not change its stiffness. The new method did not need any moving parts such as levers or pointers. With appropriate cover of the measuring points quantities could be measured even under harsh environmental conditions. Probably the biggest advantage was in the electrical output signal that could be transmitted over long distances to a measuring station. One of the first spectacular applications was the centre of gravity determination of aircraft during the loading process with the help of strain gages installed on the landing gear. In 1942 this possibility was used by Cox and Stevens Aircraft Company with force transducers developed by Ruge-DeForest [1.22, 1.23].
In 1952, a further important step of strain gage development was taken by Peter Jackson in the UK, when he invented the etched foil strain gage [1.24–1.26]. He was working at Saunders-Roe on the Isle of Wight and was occupied with stress analysis of rotors of helicopters. He had difficulties with the then available wire strain gages because of fatigue failures, slip ring noise problems and lack of sensitivity. He had problems getting undisturbed signal transmission from the rotating parts, and with the poor dynamic strength of the wire strain gages which were then being used. Signal transmission from the rotating part using slip rings required high output signals because the big slip rings with their high rim speed generated high noise voltage. During his daily crossing by ferry from Southampton to Cowes, Jackson learned from talks with colleagues about circuits made by etching copper-clad Bakelite, which were being used in amplifiers. These first printed circuits were developed by Paul Eisler who was at that time working with the Technograph Company [1.27].
As a result the idea arose to try to make strain gages also by etching foils similar to the printed circuits with the aim of producing strain gages that could withstand higher supply voltages than wire gages. This idea was realized with the aid of the Technograph Company who had produced the first printed circuits in cooperation with P. Eisler. It was thought at the time that these new strain gages with a cost of only a few cents each would force the wire gage off the market. However, the first foil gages had large dimensions and poor fatigue characteristics due to the rough etched edges. It took a few years before foil strain gages reached a satisfactory quality. Figure 1.12 shows foil strain gages from the early Saunders-Roe production. Due to the fact that there are certain limits for the supply voltage of wire strain gages Jackson initiated the production of foil strain gages and used them for his task. The first foil strain gages made by Saunders-Roe were made from CuNi foil with 0.02 mm thickness and nominal resistance of 55 Ω.
Fig. 1.12 First foil strain gages produced by Saunders-Roe
Technograph produced the first foil strain gages for Saunders-Roe and Tinsley under a Saunders-Roe licence. Jackson did not show interest in applying for a patent for which Technograph had applied in the US. The story is given in more detail in [1.28]. There one can read that Peter Jackson attended the 1988 Fifty-Year Anniversary Celebrations of the strain gage in Portland, Oregon, where he was horrified and speechless that his invention was attributed to Paul Eisler, who was instrumental in commercializing Peter's invention, an application of the printed circuit, made by Technograph. Since Peter Jackson had left the UK in 1955, he did not even know about that part of strain gage history and how popular and widespread his invention had become [1.28]. In 2000, Peter Scott Jackson passed away at the age of 84 in Del Mar, California.
Fig. 1.13 Die-cut strain gages manufactured by Dentronics Inc. in the 1960s
A different method of foil gage production was developed by Denyssen in the USA. In 1963, a US patent was granted to Pete Denyssen of Dentronics Inc. concerning the manufacturing of foil strain gages by using a die-cut method, by contrast to the more common chemical etching process [1.29]. Figure 1.13 shows strain gages produced by using the die-cut method.
The main advantages of die-cut strain gages were that foil material could be used that could not be chemically etched by eliminating the etched ‘feather edges’ the fatigue life could be improved. Dentronics' biggest customer for these gages was Lockheed. Dynisco also used Dentronics' platinum–tungsten strain gages with strain sensitivity over twice that of the conventional constantan foil, which worked at lower stress levels and hence had higher overload capability.
In 1972 Dentronics Inc. was taken over by the Magnetic Head Company, and ten years later Magnetic Head Company ceased its production, and since then die-cut strain gages have been only of historic interest [1.30]. A remark should be made here about the invention by Denyssen: in 1948 in the USA a patent was granted to van Dyke and Dennis about manufacturing strain gages by punching [1.31].
The first strain gages to be produced in large quantities in Germany were manufactured by the former Hottinger Messtechnik GmbH. In the wake of a licence contract with Baldwin-Lima-Hamilton Corp. (USA), Karl Hottinger gained access to the expertise of the BLH Corporation with regard to the manufacture of strain gages and strain gage transducers [1.32]. In June 1955, Hottinger began preparations for his own production of strain gages in Germany. In December 1955 the first pilot production batch of German manufactured strain gages was offered.
Figure 1.14 shows samples from the first production batch, which were offered under the designation FB (F = flat grid; B = Bakelite). Hottinger started his strain gage production with the intention of using them as the basis for the production of transducers. In 1956, Hottinger Messtechnik GmbH began selling its first load cells, which were fitted with Hottinger Messtechnik strain gages.
Fig. 1.14 First strain gages manufactured by Hottinger Messtechnik GmbH in Darmstadt; they were flat-grid Bakelite gages
The design of the spring element for his transducer (Figure 1.15) has, despite the lack of experience in those days, stood the test of time, and it is still used with only slight modifications today [1.33].
Fig. 1.15 Spring body of the first load cell made by Hottinger Messtechnik GmbH in 1956 [1.32] (nominal load ±2 t, accuracy class 0.2%)
Another essential step for mass production of sensor and transducer elements was taken with the introduction of the lamination technique. The production technology of foil strain gages is based on photo-chemical etching. Using this method any shape of flat grid patterns can be translated into a greatly reduced real measurement grid. The method not only allows the etching of single strain gages from the foil, but in one operation you can etch complete full- or half-bridge circuits, including connecting elements and more or less complicated balancing and compensating structures [1.34]. Such a full bridge circuit being on a carrier foil can be laminated in a single operation on the spring body of a transducer [1.35]. The time-consuming gluing of individual strain gages and their interconnections with soldered wires is thus replaced by the lamination technique with a single production step.
Another possibility for installing strain gage circuits on measuring bodies of transducers is provided by the thin film technology that was introduced in the early 1970s. This technique involves successively depositing on the measuring body an insulating layer, a highly conductive contact and reverse zones, the metal resistor patterns and finally an inorganic insulating layer [1.36].
References
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[1.23] Stein, P.K. (1990) A brief history from conception to commercialization of bonded resistance strain gages and brittle coatings; Lf/MSE Newsletter No. 33, Jan. 1990, publ. by Stein Eng. Services, Inc., Phoenix, Arizona, USA.
[1.24] Jackson, P.G.S. (1952) Improvement in or relating to strain gauges. British Patent Specification 720,325. Application Date Aug. 21, 1952.
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[1.29] Denyssen, I.P. (1963) Strain Gage and Method of Manufacture, US-Patent 3,078,431. applied 8.7.1959, granted 1963.
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, pp. 2105–2113.
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, History of strain gages, brittle coatings and load cells, pp. 77–82.
[1.33] Manual of force transducer type U1 of Hottinger Baldwin Messtechnik GmbH (1956).
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2Fundamentals of Strain Gage Technology
2.1 Measurement Principle and Structure
2.1.1 Basic Principles
Strain gages are now employed in many technical fields. They are not used solely for the measurement of strains, being also very suitable for the construction of transducers for the measurement of mechanical quantities. In these transducers strain gages measure the strains arising in the measuring element of the transducer due to the mechanical quantity that the transducer is measuring. In this way it is possible to indirectly measure, for example, forces and torques using strain gages. Apart from transducer construction, experimental stress analysis is a popular field of application for strain gages. This entails the determination of the mechanical stresses from the measured strains obtained during measurement, providing information on the measurement object loading. The same principle is always involved, that is the strain gage detects the mechanical strain and changes its resistance accordingly.
With experimental stress analysis which is carried out to find the loading in the measurement object, the mechanical stress states have to be calculated from the measured strains. The interrelationship between deformation and stresses in a component is given by the material laws relevant to the component material and the state of loading. In the region of elastic deformation Hooke's Law is used, but it cannot be applied in the elastoplastic deformation region [2.1]. With deformation that extends beyond the yield point, material laws must be applied that take into account the degree of plastic deformation [2.2]. These material laws do not have any formal role in the construction of transducers, because they are calibrated directly in the units of the quantity that the transducer is designed to measure.
The clear advantages exhibited by strain gages are based on the conversion of the strain into an electrical signal. Strain, as the mechanical quantity to be measured, produces a change in resistance in the strain gage, resulting in a change of the output voltage from the Wheatstone bridge circuit into which the strain gage is connected. The quantity ‘strain’ is converted into an electrical quantity which is easy to process. The Wheatstone bridge circuit has excellent methods of compensating for unwanted effects on the strain gage, such as temperature changes. These compensation techniques have been developed to a very high degree, particularly in transducer design. Since transducers are calibrated directly in the unit of the mechanical quantity that is to be measured, the strain gages in these transducers are not used directly for the measurement of strains, but for the indirect measurement of the relevant mechanical quantity.
The basic operating principle of the strain gage is that the changes in the strain on the surface of the measurement object are transferred to an electrical conductor which is bonded to the surface and which changes its resistance accordingly. From these measured changes in resistance the changes in the strain occurring can be found very accurately. The first bondable strain gage, which was produced in the USA in about 1940, consisted of a meander-shaped metal wire glued to a paper carrier. Various manufacturing methods were employed, leading to different designs of strain gage.
As shown in Figure 2.1, one of the methods involved gluing a meander-shaped wire flat onto a carrier, so that the active parts of the resistance wire were parallel and aligned in the measurement direction. The flat-grid gage so produced has pronounced loop-shaped return points on the ends of the grid.
Fig. 2.1 Various designs of wire strain gages
Another manufacturing method utilizes a flat auxiliary carrier, around which the resistance wire is wrapped, as also illustrated in Figure 2.1. The auxiliary carrier, complete with the wire, is then glued to the carrier. With these wrap-around strain gages the active lengths of measuring wire are not parallel and have no pronounced return points at their ends.
Gustafsson in Sweden first introduced the flat-grid gage in the form of a cross-link gage in which the return points of the measuring wire are replaced by transverse links of thicker material as shown in Figure 2.1. These types of cross-link gages with their very low transverse sensitivity were marketed under the tradename ‘Tepic’ by the company Huggenberger in Zurich. Because of their high manufacturing costs they never succeeded, and production ceased in 1994.
A form of wire gage that is still used, particularly for measurements at high temperature, is the free-grid gage. These gages are basically flat-grid gages without any carrier and are bonded to the measurement object using insulating bonding agents, such as ceramic putty.
Figure 2.1 shows the structure of a free-grid gage, which has an auxiliary carrier. The auxiliary carrier is only used as a mounting aid and is removed during the bonding procedure.
The introduction of the foil strain gage in the 1950s represented an important development in strain gage technology which, particularly in recent years, has been dominated by the demands of experimental stress analysis and transducer construction. Numerous strain gages of this type, with characteristics matched to the relevant application, are now available. However, foil strain gages are all made in a very similar manner and only differ in the shape and size of the grid and in the materials that are used for the carrier and the measuring grid. The basic design of a foil strain gage, as used in huge quantities in many fields of application, is illustrated in Figure 2.2.
Fig. 2.2 Basic design of a standard foil strain gage with metal measuring grid, as used in large quantities
An approximately 5 µm thick metal measuring grid foil is supported on a plastic insulating carrier foil about 25 µm thick. The measuring grid shape is produced photo-chemically by an etching process. The measuring grid is protected by a covering layer about 12 µm thick.
A strain gage measures the mechanical strain that occurs in the longitudinal direction of its measuring grid. This strain produces a change of resistance in the strain gage measuring grid that in turn produces a measurable imbalance in the electrical bridge circuit in which the strain gage is connected. Resistance changes in the strain gage can however be caused by effects other than the mechanical strain occurring in the measurement direction of the strain gage. As well as the actual measurement effect, that is the mechanical strain in the measurement direction, thermal effects and creep phenomena generally form the main causes of changes in resistance. If hydrostatic pressure is acting on a mounted strain gage, then a resistance change also occurs. The effect of transverse strain (the change of resistance due to strains acting transverse to the measurement direction) may be significant for precision measurements, but it is of no significance for transducer construction due to the calibration techniques employed. These disturbance variables, which produce unwanted changes of resistance superimposed on those due to the mechanical strain, are discussed in the following sections.
The strain gage must have at least two electrical contact points which enable it to be connected in the bridge circuit used for the measurement, for example by soldering. These connecting pads can be of various shapes; Figure 2.3 shows some typical examples.
Fig. 2.3 Examples of different designs of connecting pads
In principle, any configuration of measuring grid can be produced by the photochemical method, which means that strain gages can be ideally matched to special geometrical requirements, as required for example in transducer design.
The linear strain gages with metal measuring grids that are available today have an active length of measuring grid from about 0.5 mm to 150 mm. Irrespective of the length of the measuring grid, the nominal resistances are normally between 100 ohm and 1000 ohm. An almost unimaginable number of different grid configurations and grid combinations forming multi-grid strain gages are now available for both experimental stress analysis and for transducer construction. Figure 2.4 shows a few selected examples of different grid combinations.
Fig. 2.4 Examples of different grid shapes for foil strain gages
Strain gages detect the effective strain occurring in the surface of the measurement object at the point of installation, as defined in Eq. (2.1). If strain gradients occur in the measurement object along the axis of the strain gage measuring grid, then the strain gage behaves as an integrating measuring element and measures the mean of the strain arising in the region of the active length of the measuring grid, according to the law of averages in the integral calculation (Figure 2.5). In Eq. (2.1) is the strain magnitude detected by the strain gage and converted to a change in resistance, x1 and x2 are the longitudinal coordinates defining the active lengths of measuring grid in the measurement direction.
The strain gage is therefore a genuine strain transducer in contrast to many other devices used for strain measurement which just measure a change in length and refer it to an initial measurement length.
Fig. 2.5 Integrating measurement of the strain gradient over the active length of the strain gage measuring grid
It should be noted however, with regard to Eq. (2.1), that this type of integration takes place along each track of the strain gage and the expression ε(x)/(x2 − x1) applies under the assumption that no strain gradient is present transverse to the measurement direction. The result εSG is therefore the sum of the integration results along each of the strain gage tracks. This way of looking at the problem becomes more significant if the longitudinal strain to be measured has a gradient transverse to the measurement direction, which is the case, for example, at the edges of holes or grooves. Then different strains act on the separate strain gage tracks and the overall result εSG is the arithmetic mean from the integration results of all the strain gage tracks.
The integrating characteristic is a significant consideration in the selection of the length of measuring grid of a strain gage to be used for a certain measurement task. If noticeable strain gradients are to be expected in the surface of the measurement object, for example in notches or at changes of cross-section, then short measuring grids should be employed in order to obtain measurements as integrated results over short distances. In this manner, the changing strain that is measured will be as close as possible to the actual strain. Chains of strain gages are available that, for example, combine ten measuring grids, each with 0.6 mm length of measuring grid, over a length of 10 mm. The measurement supplied by each separate grid corresponds to the mean of the strain over a distance of 0.6 mm. Figure 2.6 shows a strain gage chain at the base of a tooth on a straight-toothed gearwheel for the measurement of the strain distribution when the tooth is loaded in a testing device. Figure 2.6 shows the arrangement of the chain in a diagram and also a photograph of the bonded, unwired chain that is still to be covered.
Fig. 2.6 a) The strain gradient occurring in the longitudinal direction of the strain gages; b) A strain gage chain fitted to the rounded base of a tooth on a gearwheel. The chain has extremely short lengths of measuring grid so that, as far as possible, the real strain gradient is measured
However, there are also applications in which the non-uniformity in the strain distribution caused by inhomogeneities in the measurement object material is regarded as a disturbance, and a representative mean is required as the result. This might, for example, be the case for measurements on concrete, where gravel inclusions produce strain gradients, or for metals with large crystal grains. In these cases strain gages with long measuring grid lengths tend to be preferred and, for example, lengths of up to 150 mm for measurements on concrete are used [2.3].
Measurement results found on concrete with a number of short strain gages and one long one are compared in Figure 2.7. The short gages indicate different strains depending on the position, whereas the long gage supplies a representative mean.
Fig. 2.7 Strain gage results on an inhomogeneous material (concrete) with a number of short strain gages and one long one
For cases in which the longitudinal strain to be measured has a significant gradient in the transverse direction, narrow strain gages are used, close together, to measure the strain with as little gap as possible. An example here is the use of a strain gage chain to measure the strain distribution in the vicinity of a hole in a tensile beam. It is known that the strain increases towards the edge of the hole due to the stress concentration caused by the hole. To measure this strain gradient a strain gage chain is used as shown in Figure 2.8
