Gallery, Projects and General > How do I??

Math for machinist tapers...

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AdeV:

--- Quote from: RussellT on February 08, 2013, 05:25:34 AM ---This may confuse you - but that's OK because at the moment it's just me that's confused.

If the diameter tapers by 7 units in 24, then the radius must taper by 7 units in 48.  So if you're looking to set an angle on a top slide to cut a taper then surely the angle you need is arctan(7/48).  I think it's difficult to use trig on the 7/24 as there is a shortage of right angles and for the reasons given by Marv it's not the same as half arctan(7/24)

--- End quote ---

Russell - that's what I thought.... but the reason we're wrong is actually relatively easy to show using a diagram; see attached.

The first figure shows the full 7/24 taper. The included angle between b1 and c1 (from an imaginary point at the rear of the taper) is arctan(7/24), or 16.whatever degrees.

If we halve the taper angle, to 7/48; we get the 2nd figure. Now the included angle between b2 and c2 is 8.3 degrees. However, if we rotate the taper so it sits flat on baseline a; you can see it no longer forms a right-angle triangle; and thus, our trig rules go out of the window..

Indeed, it should be clear that if you halve the b1/c1 included angle, you end up with the actual angle of taper; that is the angle between a and b1, or a and c1.

HTH!

trevoratxtal:
Fascinating topic full of good info many thanks. :clap:
One small point
type "7/24".. well that is some ancient way of telling degrees or angle i guess.. 7 inch per foot.. right
this equals 7 inch to 2 feet, twelve  inches to the foot, some times quoted as 3 1/2 inch to the foot but I don,t think it works quite right that way as AdeV says.
Whatever a very interesting topic.  :beer: :beer:
Trev

NeoTech:
*sits stares into a wall, smoke coming out of ears...* deargod... they arent making it easy are they, those machinist/invetor standardisation guys.... :bang:

this is why im asking..

Dont think for 1sec, just coz you know cad, your gonna do it right.  :bang: :bang:

BillTodd:
You still don't need to know the angle in degrees ;) 

International taper #40
Gage line (diameter of large end) = 1.7500"
Pilot diameter (parallel at small end ) = 1.000" +/- 0.005
Length  (gage to end of pilot)  = 3 7/8" (3.875")
Taper 3.5" per foot

[edit] Helps if one keeps to fractions :)

andyf:
As Bill says, you don't need to know the angle. Not having a sine bar, I would arrange a plunger indicator lying flat and with the plunger at exactly 90° to the lathe bed, and the plunger touching the side of my top slide. I would then set the angle of the top slide so that, when the carriage is moved along by 24 units, the dial indicated a variation of 3.5 units. The greater the distance over which the measurement is taken, the better. My top slide is 120mm long, so I would  look for an indication of 14mm over a carriage movement of96mm. 14:96 is the same ratio as 3.5:24.

It is easier to measure distances precisely than to measure angles accurately, though the dial indicator stil has to be set horizontal and at 90°  to the bed.

Alternatively, you can set the toolholde up to run true on your lathe, and adjust the top slide angle until a DTI mounted on the top slide with its finger at centre height shows no movement as it is run along the taper. The top slide should then be at the right angle to bore the taper in your spindle, using a tool at centre height.

Andy

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