Measurement of Tilt of a spindle shaft

[Haristhota]

Hi, 

I am trying to find out tilt of a spindle shaft using precision lapped double ball target which is attached to the spindle using two capacitive sensors at two balls in one direction (either X or Y). As shown in the figure.

I am able to fit the data (30 rotations data)  after eccentricity removal as least square circle and obtaining two centre points (x1, y1) and (x2, y2). The actual distance between the two ball centres are given.

How to calculate the spindle shaft tilt using this information.?

[Henrik_Volkers]

Your drawing is missing the tilt information, maybe that would have reminded you to basic school trigonometric

Since the distance between the two ball can be assumed constant, the displacement d=sqrt((x1-x2)²+(y1-y2)²) = l_b*sin(a)

with l_b the length between the balls and  a the tilt angle. (Tilt orientation is now up to you ;))

I assume you checked the influence of the sensor displacement and change of ball diameter.. 😉

For small angles I learned at school a~sin(a)~tan(a), but what is a small angle? 😄

Do you know what a sine bar is, and how to handle it?

[Haristhota]

"I assume you checked the influence of the sensor displacement and change of ball diameter.. "

 I didn't get this.

I found eccentricity sine wave corresponding to the RPM and i am removing it and fitting the data as LSC to find the centre coordinates.

This is how i am trying to calculate the tilt in micrometers and angle in microradians (expected) but i could get the proper results

[Henrik_Volkers]

It depends on how you measure the ball distance 😉

I was assuming case I

a capacitive sensor migth measure case II

a laser triangulation sensor measure case III (and the ball radius migth came into play 😉 )

for small values the difference migth be negitible (and a~sin(a)~tan(a))