Help solve complex math problem... reward if found.

[Asm109]

You can't know this since the other diameters are not given. It could touch at the .705 dimension .

I can. See post #9. 1.41 dia ball is tangent at .705. Its a 2:1 ratio. because sin of 30 degrees is 0.5.

 

[Ischgl99]

Not fair. You guys are using advanced knowledge of chambers. The .0500 dimension was not given. It was not specified that this was a gauge ball. still good work on solving it! Does this help the OP?

I assumed it was a gauge ball since that is how these things get measured. It has nothing to do with chambers in particular, any angled surface that needs to be measured is frequently done with a ball or round pin. Exactly the way thread gauges work. With gauge balls or gauge pins, you can use some high school trig to solve it. Every machinist will need trig at some point, if you didn’t have that in high school, or forgot it, it would be helpful to spend some time and learn it.

The key to this type of problem is checking to see if the 1” ball hits at the gauge dimensions of the drawing. Once you see that the 1” ball will intersect at 0.5” instead of 0.705”, you can figure out what the new lengths are. That becomes your new gauge dimension for your calculations since that will be where the ball will contact the cone. Something you need to remember when doing these, for balls or gauge pins, the tangent point is always perpendicular to a line from the center of the circle to the OD where the ball touches the cone. That is important to remember since it is how you figure out what angle to use in your calculations. Since the cone is a 30 degree taper, that would make the angle between the center line and the radius intersecting the tangent point also 30 degrees. Those two angles will always be identical.

 

[xr650rRider]

Normally using the tool below to measure an existing barrel in order to duplicate it. Not necessarily the best tool for blueprinting a tenon. You don't really care what the tangent point is. Glued-in actions can't be used for fitting while the barrel is in the lathe.
https://www.pmatool.com/pma-barrel-micrometer/

 

[LVLAaron]

I hadn't put much thought into the fact that the ball will be "resting" on the chamber, and not on the cone itself. That poses a challenge to my usual process. I guess I'd have to do the cone last and adjust the math for a .5377 opening.




On the topic... other manufacturers just give you the dimension and or process to cut the cone:

Custom Rifle Actions | The F-Class Panda Action

Our F-Class Panda Custom Aluminum action is specially designed for long range shooting. Learn how we created the perfect action for those far shots!

www.kelbly.com

https://americanrifle.odoo.com/web/content/145679

 

[xr650rRider]

Also realize that some well meaning gun plumbers put a chamfer on the cone/chamber junction. This further f's up the measurement unless you put an identical chamfer. But any chamfer there results in an unsupported chamber.

You'll see some additional pieces for measuring the cone is just a flat disc that has the cone angle cut onto it. Some have a stub that projects down into the chamber. But a disc, cut at same angle as cone your measuring, will rest on the cone and allow a more accurate measurement with the ball. Your copying, so you just duplicate that measurement on new barrel.

 

[LVLAaron]

Also realize that some well meaning gun plumbers put a chamfer on the cone/chamber junction. This further f's up the measurement unless you put an identical chamfer. But any chamfer there results in an unsupported chamber.

You'll see some additional pieces for measuring the cone is just a flat disc that has the cone angle cut onto it. Some have a stub that projects down into the chamber. But a disc, cut at same angle as cone your measuring, will rest on the cone and allow a more accurate measurement with the ball. Your copying, so you just duplicate that measurement on new barrel.

Yeah, I've seen the "intake valve" style gauges. I think I'll make some up.

 

[xr650rRider]

Yeah, I've seen the "intake valve" style gauges. I think I'll make some up.

That stem is more of a handy feature to hold the part after cutting taper, parting off and turning around. Grab the stem in a collet and face it off.

 

[pontiac428]

Why can't you measure off of a headspace gauge? Have you finished the chamber yet, or are you doing the cone first?

 

[xr650rRider]

I know where the .705" is from. That's the outside diameter of the bolt nose. If you had the action in hand, that is where you would check the bolt nose clearance with plastigauge or a piece, small diameter solder or lead squirt.

 

[xr650rRider]

Why can't you measure off of a headspace gauge? Have you finished the chamber yet, or are you doing the cone first?

I cut the chamber and establish proper headspace with same tool and headspace gauge. Then the cone starts at chamber wall and you measure with other tool until you establish the proper cone depth, so you have around .005"-.008" bolt nose clearance.