I need to measure a torque on an 8mm shaft of an electrical motor on a prototypical device. The expected torque is ~15 Nm and for the data processing I intend to use an Arduino. One requirement which excludes commercially available torque sensors, is the available installation space in the device as well as weight limits and the price. Due to the small diameter, I am afraid that the curvature of the shaft could be too high for the strain gauges - is there any recommendation or best practice how to handle that?
Many off the shelf torque meters are basically just a socket extension bar with a strain sensor (or several) wrapped around the outside.
Can you quanitfy how much space you have available, with pictures?
15 Nm is a fairly small amount of torque to measure through the deformation of a metal shaft. One way to solve this and also to increase the diameter (that your strain sensor has to fit around) would be as follows...
Add a hard-rubber coupling between your motor and the shaft it needs to drive. The rubber will deform a lot more than the metal would do, thus increasing the sensor's effectiveness. If you make the rubber a larger diameter (25mm perhaps if available space allows) then that should be less problematic for the strain sensor to wrap around.
A rubber shock absorbing engine mount (from just about any car) could probably be modified rather easily to this purpose.
One downside of this is that it would introduce some backlash into your motor drive. This can be reduced by using a harder rubber compound).
Without photos of your device it's rather hard to imagine what would work for you.