Component required to detect change of length

Question

I am looking for a means to measure the length of a ca. 1 m long metal bar. Due to temperature changes it will expand and contract, and I want to be able to compensate for that electronically, say once per second or thereabouts.

So I don't need an actual measurement of length, I just need to know if it is over or under length, ideally with a precision of ca. 0.1 mm. Obviously, I need care in how to mount such a sensor, but that is a separate issue, and rather dependant on how the measuring tool works!

Answer 1

You can get inexpensive glass linear scales with adequate 5um resolution (1um for a bit more). They have an incremental quadrature TTL output, so easily read with an MCU, Arduino etc. If incremental output is okay for you this is one way to get there. Note that you would reset the count at power up and it will detect changes from that initial position, not an absolute measurement of length.

Although you can get long scales, over 1m, the scales themselves, even very expensive ones, tend to have CTE similar to most metals, of the order of \$10^{-5}\$/°C. So you could buy a short scale, mount it on (readout centered between mounting points) on a 19mm diameter Invar bar and take that out of the equation.

Here is a typical short scale (150mm). No idea of the reliability of this particular supplier, do your due diligence.

Answer 2

Calculating Δlength instead of measuring it directly seems easier and cheaper.

If size and material of the bar are known (or at least constant across a production run) and the bar's temperature can be measured (in one or more places), you should be able to calculate the bar's change in length accurately and easily.

The sensors will be relatively cheap, no length reference or extra mechanical mounting is needed, and a-linearities can be taken care of in software.

Answer 3

I am looking for a means to measure the length of a ca. 1 m long metal bar.

The good old fashioned way of detecting movement changes was using a dial-test-indicator (DTI). Nowadays you can get them with a data output: -

I believe some of them use Bluetooth for data transmission.

ideally with a precision of ca. 0.1 mm

The one above has a resolution of 0.01 mm.

Answer 4

Measure or "cutting" ...

just need to know if it is over or under length, ideally with a precision of c. 0.1mm .

I would use primary a fixed "microscope" if I could place the bar against a stop on one side.
When done, I would use an LVDT sensor device with calibration (if the bar is well "terminated"). Obviously, you need however a "reference".

Or something as this

Answer 5

In principle I would use a sheet of glass as a reference plane and mount one end of the bar securely to the glass. At the other end I would mount transmission gratings, one on the bar and the other on the glass, and count Moire fringes as the bar changes length.

Answer 6

For pendulum applications where temperature-induced length changes are of concern, you need to be measuring atmospheric pressure and temperature anyway to do corrections related to air damping. If the environment is a confined space where significant changes to air composition are possible, you'll need a gas analyzer too.

So, you already should have a solid ambient air temperature measurement. From that you derive the length of the rod. You can also instrument the rod with a 4-wire Pt-100 temperature sensor. I've seen it done using 4 rods in parallel, each used as a conductor, with the Pt-100 sensor mounted on one of them, with tiny wires connecting it to the other rods.

But in any case, the temperature is an excellent proxy for thermal expansion. You can characterize the pendulum beam for thermal mass and thermal resistance to ambient air, to compensate for dT/dt at least to the first order.

If the rod is long and significantly loaded by the pendulum weight, then you'll also be making non-linear corrections due to dynamic stretching of the rod (centripetal force it exerts on the weight).

So, I'd say - if you have to worry about temperature, then you have to worry about all that other stuff too, since it all falls within an order of magnitude of each other, design-dependent of course.

It will be a pendulum.

Is this for a museum display or an educational demo? I'm at a bit of a loss as to what one would use a pendulum for in a professional capacity otherwise...

But in any case: all this seems like a problem for a metrologist. The electrical engineering end of things is the simplest. A proper metrological error analysis will inform what you must measure, and how to best measure it using measurement devices available.

The question to be off-topic here, since without a metrological analysis to substantiate that you absolutely must measure physical length and nothing else will do... it's a classic XY problem. I would go as far as saying that a proper analysis will tell you that you do not need to measure the actual length of the rod.

Answer 7

Use an optical distance measurement sensor in the axis of the bar.

Option 1, if the end of the bar is in the open:

===================   <|
bar                   sensor pointed towards end of bar

Option 2, if you can't have anything in the axis of the bar:

                   |  <|  sensor pointed towards sheet at end of bar
===================|=============== 
bar                ^  
                   |
              metal sheet at the end of the bar

In option 2, you could also measure from the start of the bar, but usually the shorter the distance the better the accuracy.

Many sensors have specs suggesting very poor accuracy, but some users seem to have obtained sub-mm accuracy. There are a few more suggestions in that page.

Answer 8

It might be possible to determine the length of the bar by striking it and measuring the dominant resonant frequency, which should decrease with an increase in length. It may also be possible to apply sound waves by means of a loudspeaker or other audio device, and determine the frequency of resonance. Along the same lines of thought, perhaps a form of time domain reflectometry could be used, where a pulse could be applied to one end of the bar and the time to receive a reflected pulse from the other end could determine its length.

However, from what I have read, the frequency of a tuning fork's change with temperature is more dependent upon changes in Young's modulus, and that varies greatly with type of material. But even if the change in pitch (or time of reflected pulse) is determined by temperature, it should still be possible to further correlate that to length if the coefficient of expansion is known.

Some information:

https://cpb-ap-se2.wpmucdn.com/learn.stleonards.vic.edu.au/dist/5/110/files/2012/08/temperature-tuning-fork-annotated.pdf

http://www.isjos.org/JoP/vol5iss1/Papers/JoPv5i1-3TuningFork.pdf

https://physics.stackexchange.com/questions/60339/frequency-of-a-tuning-fork

https://web.cecs.pdx.edu/~tymerski/ece331/Lab2_TDR_331.pdf

Answer 9

A change of length of 0.1mm over 1000mm means a strain of 1e-4. That is well within the capabilities of a strain gauge. The large advantage of a strain gauge is that you do not need a separate stable mounting location.

The principal disadvantage is that you are doing a relative measurement, so you will need some information about the beam beforehand. Furthermore, if used incorrectly, the strain gauge temperature will affect the measurement. To get accurate readings, consider three- or four wire strain gauges in some bridge configuration. Beam bending can be cancelled in the measurement by using strain gauges on opposing sides of the beam.

Accuracy is limited by the electronic circuit driving and reading the gauges, but off-the-shelf equipment is readily available that should work well enough for your application.

Answer 10

I know this is not what you asked. But in order to measure the length of a 1 meter rod, you will probably need to use a 1 meter rod made out of a material that has a low or zero coefficient of thermal expansion (CTE). If you have a 1 meter rod made from a material with a low or zero CTE, then the easier thing is to just use it as the pendulum in the first place and skip the measurements.

Possible materials are invar and graphite fiber reinforced plastic. The CTE of invar over the range 0 to 100 C is about 1.2 ppm / K. You are trying to achieve a measurement accuracy of 0.1mm. That is about 100 ppm in a 1 meter bar. So this seems feasible. The 1 meter invar rod will increase in length by about 0.1 mm as it is heated from 0 C to 80 C.

If you don't use something like this, you will find, upon analysis, that you are at the mercy of some other CTE, such as the CTE of the material to which you mount your laser or other apparatus. The entire room housing your pendulum will have a CTE, so mounting a remote sensor introduces a leg between the remote sensor and pendulum that is subject to thermal expansion.