Time Constants

What they are, and Why Nanomechanics cares about them

At Nanomechanics, Inc. we are quite proud of what the time constant is for our Nanoindenters, but it is not a common specification for other manufactures to list. Because of this, we think it is helpful to demonstrate what effect a time constant has on your data.

The definition of a time constant, according to the Oxford English dictionary, is a time which represents the speed with which a particular system can respond to change, typically equal to the time taken for a specified parameter to vary by a factor of 1− 1/e. A time constant is also the time for a system to decrease 1/e of its final value. This definition is mirrored by general textbooks on the subject such as "General Physics" by Douglas Giancoli(1984, p. 524). In summary, A time constant is a physics limitation for any electrical system.

Volts Graph
Source:Wikicommons, Ktims

1-1/e is roughly 63.2%. This means if your system was step loaded by 1, the time the system took to get to .632(63.2% of 1) would be the time constant. For a displacement sensor, the time constant reflects the time for a change in displacement to be electrically measured. A system can take data at a much higher rate then a time constant, but the fastest rate at which the data can reflect a change in the sensor is indicated by the time constant.

Nanomechanics proudly has a 20 μs time constant for making a displacement measurement. To illustrate what a difference that high speed time constant can make the following graph demonstrates a sine wave with a fast time constant(light green Your browser does not support the HTML5 canvas tag.), and one which takes a measurement 10 times slower(dark green Your browser does not support the HTML5 canvas tag.), and a system measuring the sine wave 1000 times slower(teal Your browser does not support the HTML5 canvas tag.).

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For comparison, there are other companies who sell nanoindenters that measure displacement ten thousand times slower then Nanomechanics. Nanomechanics is driven to offer the highest speed data acquisition on the market, and this has pushed us towards the lowest time constant on the market. For example, if a nanoindenter takes a displacement sensor has a 1 second time constant and takes data at .1 seconds, then the indenter will only add new information every 10 data points. Therefore, when Nanomechanics designed an indenter with exceptionally fast data acquisition, we had to design a nanoindenter with the smallest time constant on the market.

Where this might be important to your indentation experiment, is if you are trying to measure anything that happens quickly. To try this out, Experiment with a system where you can you can disturb the system and see what three different time constants measure.

The Fast Time Constant

10 Times Slower

50 Times Slower

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As you can see, the speed of the time constant makes a huge difference in how much information you get about what happens to the system in a test. A slow time constant makes it difficult to identify when a disturbance happened. A slow time constant might hide a peak value if the system recovers quickly, and a slow time constant might hide how the system reacts after it is disturbed.

To really illustrate what a difference a time constant can make, try adjusting the time constant yourself. With a data set of random noise, graphed in dark green( Your browser does not support the HTML5 canvas tag.), you can see how if you have a smaller time constant the data appears far less noisy. This is a common trick companies who advertise low displacement noise use to get very clean data. When you move the slider bar, it will change the time constant for the graph.

Adjust the Time Constant

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Current Microseconds/measurement: 50

You can see that when the time constant is very slow what is actually just a noisy signal starts to look like a smooth signal. Conversely, the faster the time constant the easier it is to see the signal. It is possible to see how a longer time constant can create ultra-low noise floors for instrumentation, but how a longer time constant will also hide the underlying process.

For any one preforming impact testing, high strain rate, failure testing, or looking at dynamic behaviour a low time constant is a necessity. These types of test are only possible on a machine that is capable of measuring rapid changes in the material, and the only way to do that is for your nanoindenter to have a low time constant. For any other type of experiment, a low time constant allows for a researcher to get as much information as possible. The information gained gives the researcher an opportunity to decide what to examine in an experiment instead of the analysis being limited by the physical limitation of the instruments sensors.

Hopefully this demonstrates why Nanomechanics is proud to be the industry leader for time constants. For more information, please contact us at +1-877-386-6262 or