Pythagoras theorem - Shaft alignment TIR

[earth_physics]

Homework Statement

I am going the do some alignment of a shaft.I use a dial indicator for measurement, and use rim-face techniques. Then I need do calculate the total TIR (Total Indicated Runout).

Here is my result of my measurement (Dial indicator).

Top: 0
Right: +0,08
Bottom: -0,27
Left: -0,35

Homework Equations

Then I was being told if I want to calculate the total TIR then I have to use Pythagoras theorem.
Why do I need to use that?
What has Pythagoras theorem to do with this?
Is it posible to draw it to get better understanding?

The Attempt at a Solution

 

[jbsteele]

Pythagoras theorem is used here to calculate the total TIR by computing the square root of the sum of the squares of the individual measurements. The total TIR = √((0.08)² + (0.27)² + (0.35)²) = 0.42mmYes, it is possible to draw it to get better understanding. Here is a diagram: * Top - 0 | * | Right + 0.08 | | | * | Bottom - 0.27 | \ | | \ | | * | Left - 0.35 -------------------------In this diagram, the four points represent the measurements taken with the dial indicator for each of the four sides. The total TIR is then calculated using Pythagoras theorem, which gives the length of the diagonal line between the four points.

 

[kerimek]

Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the context of shaft alignment TIR, this theorem is used to calculate the total TIR by taking into account the different measurements obtained from the dial indicator on each side of the shaft.

In your case, the top and bottom measurements are perpendicular to each other, and the left and right measurements are also perpendicular to each other. By using Pythagoras theorem, we can calculate the total TIR by finding the square root of the sum of the squares of the four measurements. This will give us the overall deviation of the shaft from its ideal alignment.

To better understand this concept, you can draw a right triangle with sides representing your measurements and use the Pythagorean theorem to calculate the hypotenuse, which will be the total TIR. This will help visualize how the different measurements are combined to give the overall TIR.

In conclusion, Pythagoras theorem is a useful tool in calculating the total TIR in shaft alignment, as it takes into account all the different measurements obtained from the dial indicator and gives a comprehensive understanding of the shaft's alignment.