Potential errors in dynamic mechanical analysis testing and possible solutions.

Potential errors in dynamic mechanical analysis testing and possible solutions Dynamic testing of elastomeric materials has long posed a challenge to the testing community. A number of factors can lead to errors in the process of testing a material or component. These errors include fixture induced errors, machine induced errors and modeling errors. Machine induced errors include amplitude roll-off with frequency, amplitude scaling and phase delay errors in the transducer conditioners and data acquisition devices and servo-loop non-linearities. Fixture induced errors include changes in data due to specimen end effects, and acceleration errors due to large masses in fixturing. This article will discuss a number of machine and fixture induced errors and means of reducing or eliminating the magnitude of the error. It should be noted that a servo-hydraulic test system is evaluated in this article. However, a similar analysis should be made for any dynamic test system to determine the effect of errors on test data.

Elastomer test system

To understand how an error is caused and corrected in a servohydraulic test machine, a basic understanding of the function of an elastomer test machine is essential. Figure 1 presents a functional diagram of the system controls. The system illustrated is an MTS Model 831.50 Dynamic Elastomer Test System. This test system was configured to perform dynamic elastomer tests over a frequency range of 0.01 to 1000 hz. The system provides the capability to perform tests at either a constant mean load or displacement with a dynamic load displacement or acceleration amplitude. Material properties that can be measured by the test system include specimen stiffness, modulus, absorbed energy (phase angle) and transmissibility. The system utilizes a conventional analog servo-controller with four transducers and transducer conditioners for control of the applied forces, displacements and accelerations. Each transducer conditioner provides four amplication ranges for the transducer output signal. The transducers utilized in the system are a load cell, a piezo-electric load washer, an LVDT for actuator position, and an accelerometer to measure displacement at high frequencies. In addition, an accelerometer is attached to the load cell for compensation of specimen and fixturing mass.

A DEC PDP-11 computer and MTS computer interface provide test supervision, data acquisition, data analysis, amplitude control and function generation for the test system. Test function generation is controlled by a micro segment generator located in the computer interface. This command consists of a sinewave of a given dynamic amplitude centered about a given mean level. An auto-ranging feature is controlled by the computer to operate the transducer providing dynamic amplitude feedback measurement in the smallest range possible to obtain the highest resolution. A zero offset command is used to center the dynamic amplitude range about the mean level required to perform the test. During test execution, actuator displacement, force and command are simultaneously sampled by a high speed data acquisition device and stored in an array. An FFT routine is then used to analyze the data at the primary frequency. In addition, the computer is used for operator interface tasks including test preparation, test scheduling, data analysis, data presentation and system calibration.

Test system calibration

A utility program allows system calibration to remove the effect of frequency on the transducer conditioners. The transducer conditioners introduce a phase and amplitude error in amplifying and conditioning transducer output signals. The relative magnitude of the error is a function of the test frequency, and applied corrections must reflect this frequency effect. Prior to test system calibration, each transducer is calibrated to an NBS tracible source and appropriate ranging adjustments are made to provide the best linear fit over the transducer range. The A/D and D/A converters are also scaled to a reference voltage to insure that the appropriate command or feedback signals are being sent and received by the computer interface. To measure and correct for the phase and amplitude errors caused by the transducer conditioners, a reference sinewave is input to each of the transducer conditioners. Both the reference signal and the transducer conditioner output are stored as simultaneously sampled data pairs. The reference signal frequency is swept and the magnitude of phase and amplitude error as a function of frequency measured in the frequency domain and stored. This procedure is repeated for each transducer range for each transducer conditioner. A second order polynomial is used to curve fit the accumulated data for correction of the actual transducer data. The curve fit polynomial is of the form:

C = C3*Frequency [and]2 + C2*Frequency + C1 (1)

To correct data for a phase error, the correction, C, is subtracted from the measured phase. To correct for an amplitude error, the measured amplitude is multiplied by the corection factor. The error versus frequency data and corrections are calculated in the frequency domain rather than in the time domain. The curve fir relations are stored in memory and used to correct transducer data during test execution. Figure 2 illustrates typical phase and amplitude curves and the curve fit to the data. Note the volume of data required to correct for these errors. These errors exist for any system utilizing similar transducers.

Servohydraulic non-linearities

A servohydraulic system acts in a linear fashion over a relatively small frequency band. For a high performance elastomer test system this frequency band extends out to approximately 100 hz. Linear behavior is defined as maintaining a constant dynamic output given a constant amplitude command. Figure 3 shows a plot of the ratio of servo-loop command to feedback transducer output versus frequency over the range of 0 to 1000 hz. This plot is the reciprocal of the open loop transfer function of the servo-control loop. At low frequencies the ratio of input command to feedback transducer output is unity or the commanded amplitude is actually delivered by the servo-system. As the frequency of the sinewave input is increased, the command required to achieve the desired amplitude increases. This is due to a number of factors including servovalve non-linearities, inertial effects of oil flow in the system, oil compressibility and controller non-linearities. As the frequency approaches 800 hz, oil column effects reduce the command required to deliver the desired dynamic amplitude. Once past the oil column resonance, additional servo-loop response roll-off occurs. A given desired dynamic amplitude requires a larger magnitude of command signal due to the servo-loop roll-off except in the vicinity of the oil column resonance point. No exact curve fit can be used to correct for this amplitude change with frequency.

Amplitude correction coefficients are stored for each range based on the curve plotted when the amplitude control algorithm is active. The amplitude corection coefficient is the ratio of the servo-loop command to the transducer output. These amplitude correction coefficients are used to seed the amplitude control algorithm used on the system. The use of an amplitude control algorithm is important for comparison of test data at different frequencies. Specimen stiffness values are typically different at reduced dynamic amplitudes. If amplitude corrections were not applied, a comparison of specimen stiffness values would not be relevant. At higher frequencies, specimen stiffness would be inaccurate because of lower dynamic amplitude caused by roll-off in performance in the servo control loop.

It is important for the amplitude control algorithm to act in as few cycles as possible to limit the amount of specimen heating that occurs. Heating of the specimen due to hysteresis losses causes errors in specimen value measurement. To quickly and efficiently obtain the desired dynamic amplitude for a test, the correction coefficients defined above are used in a proportional amplitude control algorithm of the form:

Command (actual) = (command/feedback) * desired amplitude. (2)

This algorithm acts quickly to achieve the desired dynamic amplitude. In addition, an operator selectable tolerance band is set during test procedure definition. Data acquisition for the actual values to be measured occurs once the dynamic amplitude is within the defined tolerance band. Fewer cycles are required to achieve the desired amplitude tolerance level as the tolerance band width is increased. The actual command to feedback ratio values used during a specimen test to reach the desired level of dynamic amplitude accuracy are stored with the test procedure file. A succeeding test would then start at the command level used in the prior test. Therefore, fewer cycles are needed to meet the amplitude control accuracy in succeeding tests.

Mass acceleration compensation

One of the errors that occurs at high frequencies and high dynamic loads is the superposition of mass acceleration forces on the force transmitted through the specimen. This superimposed load is caused by acceleration of the test specimen and test fixturing that are attached to the load cell. This additional "load" results in an inaccurate measurement of specimen stiffness. Specimen stiffness appears to increase with increasing test frequency as the magnitude of the superimposed load increases. The magnitude of this source of error is reduced by using an accelerometer attached to the active or moving part of the load cell to measure the amplitude of the movement of the fixture and specimen mass. This signal is scaled by an appropriate value corresponding to the fixture and specimen mass and summed into the load transducer conditioner to eliminate this error. This method does have one drawback, however. The amount of mass actually attached to the load cell can be frequency dependent. For example, the mass of the actuator rod may appear to be decoupled from the load cell at low frequencies, but add a large amount of accelerated mass at higher frequencies. In general, this method reduces the magnitude of this error to an acceptable level for specimen and fixturing with relatively low masses.

Speciman end effects

A form factor is often used to correct for specimen end effects and to normalize the data. While the form factor is often derived empirically, specimen handling and fixture condition may result in errors in data. Figure 4 shows the plot of stiffness versus frequency for a single specimen run with different end conditions. The higher stiffness curve was generated by running the specimen on a dry smooth aluminum platen. The lower stiffness curve was run after the same specimen was lubricated with hydraulic oil and again immediately run. Lubricating the specimen ends resulted in an apparent difference of stiffness by a factor of two. Figure 5 is plot of tan delta versus frequency for the two specimen tests described above. Note that the use of the hydraulic oil more than doubled the damping value measured for this material. Care must be exercised when comparing data values when form factors are applied to verify that the same effect is being corrected. Differences in fixture roughness, the presence of foreign substances on the specimen and fixture, differences in fixturing and bonding and differences in humidity can all affect test results.

Summary

This article discussed a number of errors that can occur in high frequency testing of elastomeric materials. These errors induced by the measuring device must be corrected to provide a relevant comparison between test samples. These errors are introduced by both the test machine and specimen fixturing. Machine induced errors include servo-loop non-linearities, transducer conditioner phase and amplitude errors, and A/D and D/A scale off-sets. Fixturing induced errors include changes in data due to specimen end effects, and superimposed loads due to fixture and specimen mass. A number of approaches were presented to reduce or eliminate these errors from test data. An understanding of test measurement device induced errors allows relevant comparison of data.

This article is based on a paper given at the ACS Rubber Division Fall 1989 meeting.