EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines 89 Dynamic Calibration of Axial Fatigue Testing Machines. Why is it important and how is it accomplished? G. Dahlberg, MTS Systems Corporation, Eden Prairie, USA There can be negative direct effects on material quality, safety, and testing productivity due to errors associated with fatigue testing of materials and components. Significant errors may be present in the cyclic force amplitude measurement accuracy of fatigue testing machines. As with all material testing, materials and or components will either be under tested or over tested. There is simply no way to perform a materials test that contains zero error or has a zero value for the measurement uncertainty. Under testing a material or component may lead to safety, warranty, and liability problems due to premature failure or damage. This is of particular concern for the transportation and medical industries. Under testing conditions exist when the testing machine endlevel forces are not achieved and or the test speed, frequency, or cycle count is less than required to meet testing criteria. Over testing a material or component may lead to waste of time and material for design, fabrication, and test. Over testing is expensive and can potentially reduce competitive advantage. An over testing condition typically occurs when forces exceed the testing criteria. When errors due to acceleration or mass loading errors are present, both over testing and under testing conditions can occur within the duration of the test. Performing a dynamic calibration of the testing machine is the only effective method of quantifying measurement errors that effect dynamic system performance. National, International, and Commercial Accreditation programs will require the estimate of measurement uncertainty related to fatigue testing results. This paper examines processes specific to the calibration of Constant Amplitude Fatigue Testing Machines. The paper presents a list of contributing error sources associated with dynamic forces in constant amplitude fatigue testing machines. Methods for determining the magnitude of the errors in dynamically operated fatigue testing machines are examined. Examples of actual calibration/verification data are included. Referenced calibration/verification procedures include, ISO 4965: 1979(E) Axial load fatigue testing machines Dynamic force calibration Strain gauge technique, ASTM E467-98a Standard Practice for Verification of Constant Amplitude Dynamic Forces in an Axial Fatigue Testing System, MIL-STD-1312B Military Standard Fastener Test Methods, Boeing D2-2860 Procedures for Mechanical Testing of Aircraft Structural Fasteners. Calibration - The set of operations which establish, under specified conditions, the relationship between values indicated by a measuring instrument or measuring system, or values represented by a material measure or a reference material, and the corresponding values of a quantity realized by a reference standard. (1)(2) The term Calibration has often been associated with the act of making adjustments. When in fact the calibration process provides information so that adequate adjustments can be made if required. Performing a calibration does not always require an adjustment. It is relatively easy to determine measurement uncertainty related to the static operation of a fatigue testing machine. Determining measurement uncertainty and or evaluating testing machine performance under dynamic conditions is more complex. Calibrating or verifying the performance specific to one testing criteria may not necessarily provide evidence that the system is capable of performing under dif- (1) ISO 10012-1: 1992(E) (2) ANSI/NCSL Z540-1, 1997. Calibration The set of operations, which establish, under specified conditions, the relationship between values indicated by a measuring instrument or measuring system, and the corresponding standard or known values derived from the standard.
90 EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines (3) Recommended Practice for the Analysis of the Dynamic Behaviour of Servo-Hydraulic Fatigue Testing Machines, ENC Nuclear Energy, 005/95-001, January 1995 (4) ISO 376: 1999(E), Metallic material Calibration of force-proving instruments used for the verification of uniaxial testing machines. (5) ASTM E74-00a, Standard Practice of Calibration of Force- Measuring Instruments for Verifying the Force Indication of Testing Machines. ferent conditions. It is my opinion that there will always be some amount of error present when performing cyclic testing with material testing machines. Acceleration errors occur due to deflection of the system force indicating device and the amount of mass between the moving portion of the force indication device and the specimen. This mass is normally comprised of a specimen gripping apparatus, a stud, and preloading washers. These errors may be insignificant depending on frequency, cyclic force endlevels, and machine configurations. On the other hand, dynamically induced acceleration errors can be quite large. For some tests requiring high frequency and relatively large forces, significant errors can be anticipated. Testing machines designed to run these types of tests may incorporate a mass compensation technique. This might consist of an accelerometer mounted on the moving mass, usually the grip assembly. The signal from the accelerometer is feed through conditioning electronics back into the system s control circuitry to compensate for mass loading effects. If mass compensation is normally applied during testing, calibration must be performed with the compensation applied. Testing machine elements that affect dynamic performance of fatigue testing machines: Frame stiffness Specimen stiffness Moving mass Deflection of moving mass Machine resonance Actuator friction Test parameters that affect dynamic performance of fatigue testing machines: Cyclic force endlevels Frequency Waveform shape An excellent body of work is available from the ECN, titled Recommended Practice For the Analysis of the Dynamic Behavior of Servo-Hydraulic Fatigue Testing Machines. (3) This study goes into great detail related to all elements of a testing machine used for fatigue work. Although all elements related to items listed above can contribute to measurement uncertainty, examining each element is beyond the scope of this paper. Measurement Uncertainty and Error sources related to dynamic calibration of fatigue testing machines: Uncertainty Source Static Calibration of the testing machine Static Calibration of the dynamometer and instrumentation Data Acquisition instrumentation (testing machine) Data Acquisition instrumentation (dynamometer) Temperature Operator influence Depending on the type of fatigue tests being evaluated, the error source related to the static calibration of the dynamometer and dynamometer instrumentation can vary greatly. For Tension-Tension or Compression- Compression testing where relatively low forces are required, the resolution and noise of the system may introduce errors of at least 0.5%. For testing that does full Tension-Compression cyclic tests, as long as the lowest endlevel forces are not below 10% of the system s force indicating capacity, corrections can be made to make the dynamometer indication equal to the system force indication. This will produce data relative to the static testing machine calibration and not relative to true force. One method that can reduce the uncertainty and make the calibration more closely related to true force would be to calibrate the dynamometer and instrumentation against force proving references per ISO 376 (4) or ASTM E74. (5) This is only feasible if a generic dynamometer can be used for the
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines 91 This calibration procedure would be difficult to use for calibrating systems used for many fastener testing applications. Many fastener tests are Tension-Tension cyclic tests and have recommended turndown ratios of 0.1. (7)(8) This means that if the maximum desired peak force for the test is to be 10 kn, the minimum test force would be 1 kn. Performing dynamic calibration below 20% of the capacity of the dynamometer is not permitted. Accuracy, stability, and repeatability of modern data signal conditesting system calibration. Fixturing would normally not be readily available to suit strain gauged specimens for force-proving calibration. It would be cost prohibitive to produce adequate fixtures for the calibration of a large number of dynamometers in this manner. The best way to assess the errors related to dynamic forces applied to a specimen during test is to perform a two channel method of dynamic system calibration. The equipment used in performing a two channel calibration process consists of a strain gauged specimen commonly referred to as a dynamometer, dynamometer conditioning electronics, and a two channel data acquisition instrument for acquiring dynamic force data from the dynamometer and the testing system s conditioned force indicating device. A typical system used to measure the output of the dynamometer and achieve high resolution and accuracy is an automated data acquisition system utilizing a digital computer combined with an analog to digital (A to D) converter and associated input conditioning. The per channel sampling rate of the digital computer system must be sufficiently fast to collect the peak dynamometer signal within 0.2% of the true peak. If the dynamometer signal is free of noise and is a sine wave function, this would require 50 data points per sine wave cycle to ensure that the peak dynamometer signal values are within 0.2% of the acquired data. (6) It is strongly recommended that dynamic calibration be performed for each combination of specimen material type, stiffness, geometry and system configuration. Where is it not practical to test all expected configurations, it is recommended that tests be performed for configuration(s) with the largest expected acceleration errors. In all cases it is recommended that actual specimens be gauged for use as dynamometers. If a wide variety of specimens are usually tested with the fatigue testing machine, it may be sufficient to calibrate the machine with the softest and then the stiffest specimen. Calibration of the testing system during use can provide confidence that fatigue tests are being run with in expectations. When the dynamic calibration of a fatigue testing machine results in an out of tolerance condition, it is then important to be able to identify the sources of error contributing to the machine s performance. A major assumption is made when calibrating dynamic fatigue testing machines. It is assumed that there is precise correlation between force data acquired with a strain gauged device when static and dynamic forces are applied. I believe this assumption to be true. We have performed interchangeability tests with various dynamic specimens and force-proving devices demonstrating repeatability under static and dynamic conditions. This provides traceability for the dynamometer through transfer calibration against the testing machine s statically calibrated force-proving device. This however is not true for the dynamometer instrumentation. Electronic instrumentation must be calibrated with adequate waveform reference standards to ensure traceability. Methods of calibrating fatigue testing machines under dynamic operation: ISO 4965, Axial load fatigue testing machines Dynamic force calibration Strain gauge technique (6) ASTM E467-98a, Section A2.2.2. (7) MIL-STD-1312B, Military Standard, Fastener Test Methods. (8) D2-2860, Boeing Company, Procedures for Mechanical Testing of Aircraft Structural Fasteners
92 EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines (9) ISO 4965, Section 11.2 Accuracy. (10) ASTM E467, Section 5.2. (11) ASTM E467, Section 9. Accuracy. tioning and data acquisition systems allow for tests with endlevels much below 20%. Stated in section 10.2.2.3 Apply the mean force and the various dynamic force ranges, and at each dynamic condition check the operating frequency and record the maximum and minimum values of the fluctuating electrical strain output from the calibration bar. The section requires the frequency to be checked but does not specify how or with what accuracy this check should be performed. Also, the section requires that the maximum and minimum values from the calibration bar be obtained but there is no mention of obtaining values from the testing machine. This would imply a single channel method but Section 11.2 states, The results obtained from the procedure derived in 10.2 shall be compared with the force readings (corrected as necessary, see 4.2) indicated by the machine. This might mean that a second data acquisition channel is connected to the testing system s conditioned force indicating device for simultaneous acquisition of the dynamometer and system force indicating signals. Or it may be referring to a chart recorder or a peak/valley recording device. The text is not clear. The document goes on to require the preparation of basic calibration curves comparing the machine indication of force versus the dynamometer indication of force. This is required in Section 13. The errors in the maximum and minimum forces under consideration shall not exceed 2% of the maximum tensile or compressive force of the machine scale in use. This requirement for accuracy is not absolute as the error in the calibration equipment is not taken into account. (9) ATSM E467, Standard Practice for Verification of Constant Amplitude Dynamic Forces in an Axial Fatigue Testing System The Standard Practice is not titled a calibration so I will use the term verification while describing the process even though the process qualifies as a calibration by definition. A full dynamic verification per ASTM E467 currently requires a dynamometer, dynamometer conditioning electronics, a two channel data acquisition system, and a conditioned force indicating output connection from the testing system. The overall accuracy of the dynamometer and the associated instrumentation shall contribute less than 25% of the total error of the dynamic measurement being made. (10) As fatigue testing manufacturers change designs in an attempt to reduce system costs, it is very likely that fatigue testing systems in the future will not come configured with a standard analog conditioned output from the system force indicating device. The E467 procedure consists of programming the fatigue testing machine for combinations of cyclic force endlevels and frequencies relative to actual specimen testing. With the dynamometer fixtured in the testing machine the machine is started and simultaneous data from the dynamometer s conditioning electronics and the testing systems force indicating device is acquired. A software routine then examines paired data for each cycle and computes amplitude and force indication errors. The maximum errors are then provided in the verification report. This practice recommends the following error tolerance, expressed as the percentage of the span for that cycle: (11) Maximum Dynamic Endlevel Error (Peak or Valley) = ± 1.0%
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines 93 Example 1, shows the results of a dynamic verification performed in compliance with ASTM E467. I have not included a copy of the client, system configuration, and dynamometer configuration page. Example 1 Dynamic Verification Report per ASTM E467 Dynamic Verification Results Dynamometer Static Verification Applied Load (Lbs. Force) Indicated Force (Lbs.) Dynamometer Force (Lbs.) Error (Lbs.) Error (% of Indicated Force) Max. Ind. Endlevel -5% of Ind. Span 18715.9 18698.9-17.0-0.091 Max Ind. Endlevel 19580.0 19579.2-18.8-0.096 Max. Ind. Endlevel +5% of Ind. Span 20480.7 20461.9-18.8-0.092 Min. Ind. Endlevel +5% of Ind. Span 2842.9 2862.2 19.2 0.676 Min. Ind. Endlevel 1957.9 1976.4 18.5 0.943 Min. Ind. Endlevel -5% of Ind. Span 1077.9 1099.4 21.5 1.996 Dynamic Verification Data Freq. Max. Ind. Span Peak Error Peak Error Min. Ind. Span Valley Error Valley Error Average Span Repeatability Pass/Fail (Hz) (Lbs.) (Lbs.) (% of Span) (Lbs.) (Lbs.) (% of Span) (Lbs.) (% of Avg. Span) 10 17628.36 58.85 0.334 17652.63 28.07 0.159 17634.55 0.230 Pass 20 17638.98 59.82 0.339 17664.76 28.37 0.161 17641.41 0.205 Pass 25 17631.40 54.05 0.306 17669.31 41.86 0.237 17647.38 0.150 Pass 30 17642.01 67.11 0.380 17648.08 57.61 0.326 17633.91 0.223 Pass 40 17729.96 75.32 0.425 17729.96 147.86 0.834 17641.80 0.264 Pass 50 17766.36 36.44 0.205 17704.19 104.52 0.590 17662.45 0.368 Pass 60 17645.05 23.49 0.133 17667.73 175.62 0.994 17660.82 0.412 Pass 70 17632.91 29.77 0.169 17678.41 194.56 1.101 17648.84 0.823 Fail Test Setup and Data Acquisition Sampling Information Test Frequency Samples/second Samples/Cycle Test Duration Sec Wave Shape Mean Force (LBS) 10 1000 100 5.000 Sine 10780 20 2000 100 2.500 Sine 10780 25 2500 100 2.000 Sine 10780 30 3000 100 1.667 Sine 10780 40 4000 100 1.250 Sine 10780 50 5000 100 1.000 Sine 10780 60 6000 100 0.833 Sine 10780 70 7000 100 0.714 Sine 10780
94 EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines Dynamic Verification Error Convergence Graph
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines 95 ASTM E467 Annex (12) A1. Estimate of system inertial Errors A1.1 Conditions of Use A1.1.1 The body of Practice E467 describes in detail the testing necessary to do a full verification of a test machine s dynamic force measurement capability. Due to its relative complexity, and the need to do a dynamic verification each time specimen stiffness/grip weight/crosshead height and frequency are changed, this annex was created. This annex provides a method for estimating the force measurement errors resulting from acceleration of any mass between the specimen gage section and the force transducer sensing element. As long as inertial errors are the dominant source of dynamic error this method provides a reasonable verification of dynamic accuracy. The annex goes on to state in section A1.2 that, If the estimated force error is greater than 0.5% of the loading span, then the error must be quantified by experimental verification as described in the main part of Practices E467. The annex describes two methods for computing this error. Method (A1.1) Accelerometer method: An accelerometer is attached to the fixturing at the position of maximum displacement between the force transducer and the specimen. Using the maximum acceleration indicated, along with the fixturing weight, calculate the force error as: Fi = W/g a where: Fi = the inertial force, W = the weight of the inertial mass, g = gravitational acceleration, and a = the inertial mass acceleration. Method (A1.2) Displacement Method A1.5.1 For purely sinusoidal motion of the force transducer and alternative method is to measure the displacement of the force trans- ducer and calculate an error. This may be calculated by: Fi = Ma = -M(2. π. f) 2. X where: M = the inertial mass, F = the operating frequency, Hz, X = the inertial mass displacement, and a = the inertial mass acceleration. I am not aware of any one currently using either of the methods described in the annex. I had hoped to have had time to perform these methods prior to preparing this paper and was unable to line up an adequate machine for the evaluation. The methods are based on solid theory and should prove correct. Selecting an accelerometer with the appropriate sensitivity may prove difficult. There may however be additional methods utilizing modeling software that could be substituted under certain conditions. ASTM E467 specifically states that the fatigue testing system s control accuracy is not verified with the practice. This is an important point because some test require that endlevels are constant with in stated specifications. (13) Evidence of control accuracy can be obtained from the dynamometer data acquired during an E467 verification but it is not required at this time. When excessive acceleration induced errors are present it may be possible to select an alternate frequency or endlevel force for testing. The fastener testing industry in the US is required to test fasteners used in commercial and military aircraft. Currently two standards are being adhered to, Boeing Company s D2-2860 specification and MIL-STD 1312B. Fastener manufacturers and testing laboratories often want to test at the highest forces and frequencies possible to reduce the time necessary to perform tests for qualification of material. This allows material to move through the manufacturing and acceptance process (12) Italicized text taken directly from ASTM E 467. (13) ASTM E466-96, Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials, Section 7.3.
96 EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines faster. In these cases, testing laboratories can adjust their testing protocol so testing machines will operate over force endlevels and frequencies that minimize the level of dynamic induced errors. Example 2, shows the results of a single channel verification method performed incompliance with MIL-STD 1312B, Appendix C, Alignment and Load Verification of Axial- Load Fatigue Testing Machines. I have not included copies of pages that show the client, system configuration, dynamometer configuration, or the static calibration of the dynamometer. Example 2 Dynamic Verification (Range 1) Dynamometer ID#: 13393 Range: 50000 Lbf. Frequency: 4 Hz Dynamometer Indication (Range 1) Static (Lbf.) Dynamic (Lbf.) Errors (%) Minimum Maximum Minimum Maximum Amplitude(p-v) Max. Load 1014.5 9996.0 1112.5 10050.0-0.490 0.540 2089.0 19935.5 2084.5 20100.0 0.266 0.216 3082.5 29970.0 3074.5 30150.0 0.102 0.065 4069.5 40001.0 4100.0 40200.0-0.029 0.050 5046.0 49998.5 5122.5 50100.0-0.170 0.002 (DynMax DynMin) (StaticDynMax StaticDynMin) X 100 Dynamometer Indication Amplitude Error = (StaticDynMax StaticDynMin) Maximum Load Error(%) = (DynMax StaticDynMax) X 100 StaticDynMax The remainder of this example is not required for compliance with the calibration standard but provides valuable additional information related to the dynamic performance of the system.
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines 97 System Indication (Range 1) Static (Lbf.) Dynamic (Lbf.) Errors (%) Minimum Maximum Minimum Maximum Amplitude (p-v) Max. Load 1000 10000 1004.2 10002.4 0.016 0.005 2000 20000 2002.16 20003.8-0.003-0.002 3000 30000 3008.94 30000.6-0.001-0.001 4000 40000 4001.85 40003.5 0.000 0.000 5000 50000 5005.99 50009.2 0.002 0.000 Dynamic Waveform Analysis (Range 1) (All force values are Lbf.) Minimum Peaks Minimum Valleys Peak Cycles Valley Cycles 9909.0 1112.5 10 10 19952.5 2084.5 10 10 29959.0 3074.5 10 10 39996.5 4100.0 10 10 49859.5 5122.5 10 10 Average Peaks Average Valleys Max. Amplitude (p-v) Min. Amplitude (p-v) 9928.5 1119.5 8825.5 8796.5 19966.0 2090.0 17889.5 17859.0 29970.5 3084.5 26898 26864.5 40008.5 4109.5 38911.5 35878.0 49970.5 5130.5 44876 44725.0 Std. Deviation Peaks Standard Deviation Valleys Average Amplitude (p-v) Std. Dev. Amplitude 10.0 4.0 8809.5 8.0 7.5 6.0 17876.0 9.5 8.5 8.0 26886.5 9.5 7.5 7.0 35899.5 10.5 5.5 5.5 44840.0 5.4 System Indication readings are acquired from the testing machine using the peak /valley meter feature available through the testing system software. The Static minimum and maximum values are entered as the system programmed endlevels. The Dynamic minimum and maximum values are entered from the peak/valley meter running on the testing machine. This provides some level of confidence in the system s data acquisition accuracy.
98 EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines Many United States MIL-STD practices are being superseded by industry and or commercial standard practices. The ASTM committee that has the responsibility for revising E467 meets twice a year. I expect that with in the next year, E467 will include a single channel verification method for use with constant amplitude fatigue systems. Conclusions: 1.) Dynamic calibration of fatigue testing machines is a complex task. Automated calibration data is acquired, reduced, and reported. Software must be available to process and report the data. 2.) Dynamic calibration of fatigue testing machines is expensive and time consuming. 3.) Performing a dynamic calibration of a fatigue testing machine is the only way to adequately assess measurement uncertainty and errors associated with the performance of cyclic fatigue tests. 4.) Until recently, accreditation bodies have largely overlooked the need for testing laboratories to perform dynamic calibration of fatigue testing machines. It is my opinion that accreditation pressures will increase and adequate methods of determining measurement uncertainty for fatigue testing machines under dynamic operating conditions will be required. Bibliography [1] ISO 4965: 1979(E), Axial load fatigue testing machines Dynamic force calibration Strain gauge technique. [2] ASTM E467-98a, Standard Practice for Verification of Constant Amplitude Dynamic Forces in an Axial Fatigue Testing System. ASTM Volume 03.01. [3] MIL-STD-1312B, Military Standard Fastener Test Methods and Appendix C, Alignment and Load Verification of Axial-Load Fatigue Testing Machines, 1984 [4] Boeing Co. D2-2860, Procedures for Mechanical Testing of Aircraft Structural Fasteners, 1970 [5] ISO 10012-1: 1992(E), Quality assurance requirements for measuring equipment Part 1: Metrological confirmation system for measuring equipment. [6] ANSI/NCSL Z540-1-1994. Calibration Laboratories and Measuring and Test Equipment General Requirements. [7] ISO 376: 1999(E), Metallic materials Calibration of force-proving instruments used for the verification of uniaxial testing machines. [8] ASTM E74-00a, Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force indication of Testing Machines. ASTM Volume 03.01. [9] ASTM E466-96, Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Material. ASTM Volume 03.01. [10] Recommended Practice for the Analysis of the Dynamic Behaviour of Servo-Hydraulic Fatigue Testing Machines, edited by G.L. Tjoa, ECN Nuclear Energy, 005/95-001, January 1995. Netherlands Energy Research Foundation ECN.
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