# Would a cross correlation between vibrations in the X and Y directions help determine vibrations in the Z direction?

I have a 2D vibration sensor that can only measure in the X and Y directions, and it is mounted on top of a motor that is fixed into place, as shown in a rough sketch below.

Would I be able to work out the vibrations in the Z direction based on a cross-correlation of just the vibration in the X and Y directions?

• No -- X, Y, and Z are completely independent so long as they are all orthogonal. Unless you are dealing with a system where 'cumulative' properties apply. For instance, the cumulative mass participation(s) of an object fundamental modes in three axes. It seems we need more information. Jul 16 '19 at 1:23

Think it through.

Put a penny on a table. Slide it away from you and back -- that's x. Now slide it left and right -- that's y. Now pick it up, without moving it forward, back, right or left -- that's z.

If you're sensing x and y, will those change if you move the penny straight up?

If your sensor senses x and y, will it see z in any way shape or form?

• No, the sensor should not be able to work out the z-axis based on x and y-axes alone. Thanks for the confirmation.
– plu
Jul 13 '19 at 2:26

What vibrations are you interested in?

Are the vibrations somehow interlinked - what else beyond the question you placed to us do you know?

If you can constrain the question more, the situation may change. If you cannot, then @timwescott's answer is obviously the correct one.

• I'm doing some verification on some previous paper publications, where one party claims that a cross-correlation of the X and Y-axis determines the rotor shaft speed, while another claims that simply the Z axis is enough. In that specific case, either the X or Z-axis would work; @TimWescott 's answer is enough to confirm that in principle, any cross-correlation of X and Y should have nothing to do with Z.
– plu
Jul 15 '19 at 19:27
• Sounds like your comment would be well placed in the question itself. Jul 16 '19 at 8:26