A couple of weeks ago we calculated cold alignment targets from field data. We ended up with angles and offsets but the class wanted to go through the math involved in calculating the foot values. It was an interesting math exercise so if you’re up for some brain stretching, follow along.
Here are our target values expressed as angles and offsets. So how do we get the values at the feet? If you think back to your algebra class, you might remember some of the math for working with lines.
The equation that drives our corrections at the feet is this equation for a line: y = mx + b.
- y = distance the movable shaft is from the x-axis, or the stationary shaft centerline of rotation—the value we’re looking for at the feet.
- m = measured slope of the shaft—the angularity. Mind the sign of the angularity.
- x = distance along the movable shaft we’re interested in—the distance from the coupling center to the feet we are interested in.
- b = initial starting location at the coupling center—the offset. Mind the sign of the offset.
This might look familiar if you have used dial indicators.
In the vertical situation we have been presented with, m = -0.212 mils/in and b = -1.801 mils (I’m taking the raw data from the alignment file to get the extra digits). To find the value at the front foot, we see the foot is located 5.4” + 11” or 16.4” from the coupling center.
Substituting these values in our equation, we have
y = -0.212 mils/in * 16.4” + (-1.801) mils
y = -3.48 mils – 1.801 mils
y = -5.23 mils for the front feet
For the back foot, we are looking for the total distance from the coupling center, 5.4” + 11” + 40”.
y = -0.212 mils/in * (16.4” + 40”) + (-1.801) mils
y = -0.212 mils/in * 56.4” – 1.801 mils
y = -11.98 mils – 1.801 mils
y = -13.78 mils for the back feet
We didn’t bother with horizontal offsets. With no angular change and only 1.0 mil of movement it just wasn’t necessary.