# Do digital linear scales stretch?

1. Jul 11, 2015

### Ranger Mike

Hello friends, i hope this is correct forum.
If digital linear scale with a resolution of 0.1 micron is attached to a very flat piece of aluminum, at 68 degrees F, and is calibrated with a laser interferometer, and is then exposed to a slow increase of temperature to 100 degrees F, then permitted to cool to the 68 degrees F temperature, will the scale itself be damaged?
If this process was repeated with a piece of hand lapped granite , what would be the result?
what long term effects will the heat process have done?

2. Jul 11, 2015

### Dr. Courtney

The way to solve the problem is to compute whether the compressive force that results from the heating compresses the material beyond its elastic limit.

3. Jul 11, 2015

### Ranger Mike

i was thinking thermal expansion would effect the scale mounting. aluminum vs. granite thermal expansion.

4. Jul 11, 2015

### Dr. Courtney

You need to define what is really rigid in the experiment and what is allowed to thermally expand.

In thermal expansion "damage" problems it's the difference in expansion between things that are rigidly connected that is important.

You cannot damage anything that is only connected at one end (as your problem defines it). You need the scale to be squeezed or pulled between two plates. What is connecting the two plates and are the connections subject to thermal expansion also.

5. Jul 13, 2015

### Ranger Mike

If we have a 100 mm long aluminum sample and change the temperature 5 °C (9 °F), it is observed to grow 25 micron in length. Can it be assumed if we had a 1000 mm long sample it would grow 250 micron or is this a dangerous false assumption?

6. Jul 14, 2015

### Baluncore

You can assume things are linear as a first approximation. Some aluminium alloys change crystal structure and hence dimensions when thermally cycled.

The problem is that many metals need to be age cycled over the operating temperature range before they will give consistent results. Study the annealing and work hardening characteristics of the alloy. It is also important to look at a phase diagram for the alloy and determine if you are in the vicinity of, or crossing a transition.

7. Jul 14, 2015

### MRFMengineer

What kind of scale is it? glass? PCB? Metal tape? How is it mounted to the aluminum or granite?

8. Jul 15, 2015

### Ranger Mike

renishaw metal tape scale mounted directly on granite. in next case , renishaw metal tape scales on renishaw fast track stainless steel mounts then bolted to aluminum

9. Jul 15, 2015

### Baluncore

When you bolt stainless steel to aluminium, what coefficient of expansion do you expect would apply ?

10. Jul 15, 2015

### Ranger Mike

baluncore..that is my concern..stainless steel has a low expansion rate and the scale is anchored at one location only so it can expand and the aluminum machine is referenced to these scales for positioning...i think it is a poor engineering idea. two dissimilar thermal expansion materials and growths

11. Jul 15, 2015

### MRFMengineer

As long as you follow the mounting instructions for mounting from Renishaw, you should be fine. It sounds like you are using them for your intended purpose.

The scale is your length reference, it should only expand about one point, that is your zero point. The stainless scale helps compensate for growth of the aluminum frame. The scale should not expand with the machine, it should be allowed to float relative to its zero point. Then you can calculate temperature based position error based on the stainless CTE alone.

What is your main concern?