# Accurately measure a bolt hole circle?

I need to accurately measure (+/-0.25mm) the bolt hole circle drilled into a heavy metal plate. There are three holes on one plate and nine holes on a second plate. The plates are approximately 300mm diameter. The holes are approximately 18mm diameter tapped M20 and the bolt hole circle is about 200mm diameter.

When known, I will create a mating part on the CNC mill and lathe. The finished part rotates at around 2000 RPM, so the accuracy of the machining and fitment will determine the vibration of the finished system.

How can I measure the hole circle? Tools? Technique? Calculations?

• A bore gauge may work. For example: this one – atom44 Nov 10 '16 at 18:09

The bolt pattern should be a standard; if there are three bolt holes then there should be 120 degrees between each hole. If there are nine bolt holes then there should be (360/9) = 40 degrees between each hole.

Let's talk for a second about vibration. Vibration will exist if the centerline of your flange does not coincide with the centerline of the existing flange. While your bolt pattern does matter, it doesn't matter that much. If you are relying on your bolt pattern to perfectly align two pieces of rotation machinery you are doing it wrong. The machinist that attaches the two flanges together should have a means to shim one piece of equipment, or the other, or both.

You need to rely on the shims to bring the two centerlines together, both coincident and parallel. Again, if you're relying on the bolt pattern to do this for you, then that implies that the flange needs to be perfectly attached to the shaft, that the bearings have to be perfectly sized with no room for dimensional tolerance, the body has to be perfect, the mounting feet have to be perfect, and the sub-structure to which both pieces of equipment attach has to be perfect. You need to have room for adjustment where the machinery bolts down. You will never attain the degree of perfection required to count on a bolt pattern to mate two pieces of rotation equipment.

So, that said, where vibration does matter with regards to your bolt pattern is that your bolt pattern should be EVEN. If you have three bolts that are supposed to be 120 degrees apart, but two are 110 degrees apart and the others are 125 each, then you'll get vibration because the bolt pattern isn't rotationally symmetric.

So, my advice to you would be to get the bolt pattern dimensions from the existing flange, then ignore minor variations and make your new pattern as symmetric as you can achieve. If the existing flanges are threaded, then your holes are through holes. There needs to be some tolerance there for the bolt to be able to pass through, and the tolerance should also allow for the minor variations in hole placement in both parts.

The clamping force of the bolts holds the flanges together. The shims under the mounting feet of the machinery brings the centerlines together. The location of the holes matters for vibration only if they're not rotationally symmetric. The fit of the the flange doesn't have anything to do with vibration provided you have adequately clamped the two flanges together and you aligned the shaft centerlines to be coincident, and again, that's done by moving the equipment, not by adjusting the flange bolt holes.

I'm harping on this to try to impress on you that a flange with through holes is not, and should not be, a piece of high precision equipment. You might need the face to be very flat if you're using a gasket, and it should definitely be perpendicular to the shaft centerline, but the through holes are just through holes. If one flange is able to rotate relative to the other flange then you haven't torqued it well enough and/or you haven't used enough fasteners. If the flanges were able to have relative motion then you're "riding the clutch" so to speak and can expect (very) premature joint failure.

So, all that said, here's how to calculate what the parameters should be for your circular bolt pattern.

1. Find the angular distance between bolts, $\theta$, by dividing 360 degrees by the number of bolts. A 3-bolt pattern is 120 degrees between fasteners, 4-bolt is 90, 9-bolt is 40, etc.
2. For a threaded hole, thread a bolt into each of two adjacent holes. Not necessary if you can get the measurement tips of a pair of calipers into the holes, but it does make it easier.
3. Measure the largest outside-outside distance between the two bolts. Measure the smallest inside-inside distance between the two bolts. Average those numbers (add together and divide by two) and you get the center-center distance.
4. The bolting pattern's radius is given by:

$$r = \frac{\mbox{average distance}/2}{\sin{(\theta /2)}} \\$$

Now you can put your blank flange on a lathe, find the center, measure out a radius $r$, mark that circle, and locate your through hole centers at the appropriate angular positions on that circle. If you're doing it by hand you could open a compass to the $\mbox{average distance}$ between bolt holes that you found, put the pointy end anywhere on the circle and sweep it, then move the pointy end to any sweep-circle intersection and sweep again.

Here's a graphic if that'll make it any clearer:

• I'll comment on a point that maybe I didn't reiterate enough that there needs to be a tolerance in the through hole. When you clamp any connection together with a bolt, you shouldn't be relying on the bolt to hold any shear force. The faces should be clamped together enough that they generate enough static friction to prevent relative motion. Relying on the bolt to carry a shear load implies that you're willing to let one flange rotate (relative) to the point that the bolt "picks up" the load, and then continue to rotate as the threads deform, and then you've got mangled threads- it's bad. – Chuck Nov 10 '16 at 19:17
• Thank you Chuck, that was a very comprehensive answer and the math works. To align the two plates, there is a raised rim just inside the bolt circle which I will use to achieve concentricity with the bore. I am reasonably convinced that it is truly concentric with the baseplate bolt hole circle. – Donald Gibson Nov 10 '16 at 21:01
• With the two parts assembled, the final operation will be to machine the rims to final diameter on the lathe and hopefully remove most of the balance offset. The baseplate is a precision component, so I have confidence that the machinist that created it know what (s)he was doing, however your observations about the position of the bolts affecting balance are accurate. I will take some careful measurements before cutting a \$x,000 piece of machinery! – Donald Gibson Nov 10 '16 at 21:21
• @DonaldGibson - The comments you made make me uneasy. As I stressed repeatedly above, you should not be relying on dowels, countersunk holes, or any other handicap to get two pieces of rotating machinery aligned. The flange that has through holes should have enough tolerance to allow a precision alignment to be performed. The flange itself does not constitute a precision alignment. I would strongly urge you to watch an alignment procedure before you continue. There's a playlist by that channel, too, if you want to see more videos. – Chuck Nov 11 '16 at 18:56
• There are too many other places in the machine for dimensional tolerancing issues. The net result is that your axis of rotation is not going to be exactly parallel to the machinery feet. – Chuck Nov 11 '16 at 18:59

One approach is to use a transfer punch to transfer the hole centres onto another plate. This is complicated a bit by the fact that the holes are threaded so you may need to machine one to the correct diameter.

This will certainly make it easier to measure the centre distances. A similar method would be to make up some short studs, centre drill them and measure the distances with dividers.

With either method you should be able to construct the centre point of the pitch circle diameter using dividers http://www.mathopenref.com/constcirclecenter.html

You can also get centre squares althoug hthis does depend on the outside edge of the plate being round and concentric with the PCD.

It may also be that the CNC mill has the capability to be used as a coordinate measuring machine. This would certainly be the most straightforward way to get accurate measurements as you can just input the data to your CAD software and construct whatever dimensions you need.

It is also worth considering that you can improve the fit of bolted connections by using dowel pins to provide alignment while still allowing adequate clearance holes for the bolts.

Similarly it may be worth making your component slightly oversized then bolting them together and machining both to the finished size at the same time .

• Thanks for the help Chris. The mill has a tram and center finder so the machine setup will be very accurate. Alignment and vibration are the primary concerns. I was also considering chamfered holes and custom studs to fit the parts with some very small tolerances for alignment. The chamfered fit should achieve the same alignment as dowels would, without the need to align and drill the baseplate which is part of some extremely expensive equipment. – Donald Gibson Nov 10 '16 at 21:14