Machinist

[Lawrence London <lfljvenaura@gmail.com>]

http://www.practicalmachinist.com/vb/general/turning-accurate-tapers-my-take-old-task-278663/

Thread: Turning Accurate Tapers - my take on an old task.

• View First Unread

• LinkBack

• Thread Tools

• Search Thread

• Rate This Thread

• Display

01-18-2014, 11:06 AM #1

Forrest Addy

Diamond

Join Date

Dec 2000

Location

Bremerton WA USA

Posts

8,947

Turning Accurate Tapers - my take on an old task.

Let’s say you need to cut a male taper on your lathe like maybe a #4 Morse. A #4 Morse has 0.62326” total taper per ft according to Machinery’s handbook. You have no taper attachment. You have a good sleeve to use for a gage. You want the first trial of the taper to be as accurate as possible.

First order of business is to determine if the taper is to have a driving tang or is cropped like the shank end of a dead center. If you need a tang, center drill both ends 5/16” in the lathe and then mill the tang detail according to #4 Morse manufacturing data.

Let’s assume the #4 Morse taper shank tool you have to make is 14” long over-all. You need an accurate length to calculate the correct tailstock offset. The center penetrates some distance into the center drilled hole so the question is what is the effective depth of the center and how much deduction do you take from the overall length. A good assumption is midpoint on the conical land of the center drilled prep.

Another consideration: the taper axis is inclined with respect to the spindle axis and the offset tailstock axis by a amount to generate the half angle of the taper. The tension on the center and the cutting forces make the conical centers “waller out” the center drilled conical lands until it resembles an annular section of a torus. An inclined plane intersecting a cone generates a type of ellipse. A torus by definition is round. Thus a torus inclined on a cone makes contact at two points – in our example in the horizontal plane. There will be some uncertainty in the vertical plane but one safe to ignore because forces affecting the taper turned in a lathe lie in the horizontal plane.

Given the above, it would appear that some metal deformation could be expected as work progresses requiring occasional center take-up to minimize lost motion along the taper’s axis. In effect the over-all length will be reduced by what I have come to call an “important trifle”. These are small details but significant when cutting accurate tapers from the get-go. Looking at our original problem: a #4 Morse taper has 0.0519 taper per inch. If the overall part length is 14.000 inches, the tailstock offset is (0.0519” / 2) x 14.000” or 0.3636”.

The effect on the taper is proportionate to over-all length / effective length. In our example where the effective length is 13.955 (or some such figure) the proportionate error factor is 1.0032. Since the #4 Morse taper is roughly 4” long the taper error calculated by our example is 0.0129” on the radius – larger on the big end. Total taper error on the big end is 0.0256. These small trifles have a way of stacking up. You may have a rough idea of how to determine the effective length between centers (don’t neglect the cosine of the half angle in your calculations) but rough is not precise. The effective length has to be precisely determined otherwise whatever tailstock offset you may use will be a stab in the dark.

The question is how to eliminate these uncertainties so they don’t plague us with accreting trifles?

Consider: a ball resting in a conical recess (like a center-drilled hole) makes circular contact at the plane of intersection. The ball can be spun in any direction but its circular intersection with the cone remains unchanged.

This may exploited for our purposes. Anneal some 3/8” dia balls salvaged from a defunct bearing. Grip them one by one in a collet and center-drill 5/16” full depth and with a dinky little boring bar tool out the conical recess to clean up. Make plenty because you will lose them in the chips. Re-harden and draw to Rc58 or so. Make some of larger and smaller sizes. I call these little aids “olive balls” because they resemble pitted olives to my overheated imagination. .

A 3/8 ball contacts a 60 degree cone on a 0.328 dia. Make your center-drilled center preps accordingly. Apply a small blob of sticky grease in the center-drilled holes, stick in the balls and mike over them. Deduct one ball diameter from the mike size to obtain the effective part length between ball centers. Use this length to calculate tailstock offset. Using the olive balls in the center-drilled holes place the part to be taper turned between centers and go to town. The balls will accommodate the nutating part axis as it rotates between offset centers. They will burnish a little land in the center prep that in no way interferes with later operations where a center has to be employed.

If your offset is accurate and your tool on center you should be able to cut an accurate taper from scratch. Chances are you will need to make a few offset corrections because that is how it goes in the machinist’s trade

BTW. Machine tapers have to be accurate as hell if they are to seat properly. If I was to make the taper tolerance call, I’d hold taper sockets nominal to -.0002 per inch of diameter and the male taper nominal to +0.0002 per inch of dia. Axial tol on the gage line is widely available and is usually +/- 1/64.” In the absence of proper gages most shops use new or nearly new sockets and shanks for gaging. While this expedient has its hazards I’ve seen good tooling made this way. Few lathe hands bother tooling the last little refinement to a machine taper. They get it a thou or two oversize and stone or polish to final fit. A good lathe hand can with care fine tune tapers rivaling work generated on a cylindrical grinder in about the same time for the first few parts.

Comment? Analysis?