Tapers

[Les Jones 1Participant @lesjones1]

Hi Chris,
I have an angle gauge similar to the one in your link and also "Wixey" type angle gauges. They only have a resolution of 0.1 Deg. which in most cases for tapers would not be good enough. Although the OP has not given any details as to what the taper is for and the angle of the taper.

Les.

[Jack Foreman 1Participant @jackforeman1]

Posted by Les Jones 1 on 12/08/2014 08:14:23:

……… Although the OP has not given any details as to what the taper is for and the angle of the taper.

Les.

It was a generalised question Les. In the respect of tapers being on of the present subjects of my learning and development. There was certainly nothing specific about it. And the replies and conversations have been very helpful.

[John CParticipant @johnc47954]

I think that this is a case where everyone can be right about the effect of measurement height on the taper – it depends on the accuracy you require.

To put it into perspective here are some numbers and the justification:

R is the radius of the taper at the chosen section.

h is the vertical error in positioning the measuring device.

d is the horizontal error caused by h.

A is the angle between sides R and R-d.

h will remain constant for all measurements.

What we want is d, the difference caused by h

R sin A = h

Sin A = h/R

A = Inv Sin h/R

R cos A = R-d

(R cos A) – R = R-d-R

d = R – (R cos A)

So to put some numbers in, for a sharp taper and large height error:

R = 10mm

h = 5 mm

A = inv sin 0.5 = 30 deg

d = 10 – (10 cos 30)

d = 1.339 mm

Now at the larger end of the taper

R = 20 mm

h still = 5 mm

A = 14.47 deg

d now = 0.635mm

So there is a radius difference of 0.704 mm, or 1.4 mm on the diameter.

This is just to show that an error will occur.

Now for MT2.

Small dia = 15.3 mm R = 7.65mm

Say h = 1mm

A = inv sin 1/7.65 = 7.51 deg

d= 0.065mm

Large dia = 17.7mm R = 8.85mm

A = 6.488 deg

d = 0.0566mm

Difference = 0.0083 mm on radius, or 0.016mm on diameter

That’s 6 tenths of a thou!

So measurement height does make a difference – whether it is significant depends on what you are doing!

[Keith LongParticipant @keithlong89920]

John – that's a pretty EXTREME case – 5mm tool height error on a 20mm diameter shaft!

The figures that Geo Thomas was using were a tool height setting error of between 10 and 30 thou inch, on a 2MT shank. The 10 thou error causes an end to end diameter error of 6 hundredths of a thou on and a hollow on the shank of 1.3 millionths of an inch. The 30 thou tool height error causes about half a thou end to end and 12 millionths of an inch hollow – pretty negligable and probably within tolerance anyway – if you can measure it in the home shop.

The point being made was that RELATIVELY SMALL errors in tool height or measuring height on a taper don't have very much effect at all – at the level of millionths of an inch, surface finish is probably as significant.

[Roderick JenkinsParticipant @roderickjenkins93242]

John,

Thanks for taking the time to do the trig. All the information is out there now.

Cheers,

Rod

[I.M. OUTAHEREParticipant @i-m-outahere]

Now what if we take into account that the device used to measure along that taper has a small radius like the nib on a dial indicator ?

Ian.

[John CParticipant @johnc47954]

Keith – yes, it is an extreme case – but it was to show that there is an error. Your results may differ….

John

[John CParticipant @johnc47954]

My pleasure Rod – it exercised the old grey matter a bit!

John

[Chris DentonParticipant @chrisdenton53037]

Posted by Les Jones 1 on 12/08/2014 08:14:23:

Hi Chris,
I have an angle gauge similar to the one in your link and also "Wixey" type angle gauges. They only have a resolution of 0.1 Deg. which in most cases for tapers would not be good enough. Although the OP has not given any details as to what the taper is for and the angle of the taper.

Les.

Ok, fair enough. It's what I use for anything that needs a taper and it's always been good enough for me

[John HinkleyParticipant @johnhinkley26699]

Back to the original topic…..

I've been working on a simple tool for setting my top slide to a specific angle, for threading etc. It's still in the experimental phase – i.e. it ain't finished, but drawings and a couple of poor quality photos are in an album, should you care to look. Should be self-explanatory. If not, ask. I think it may not be accurate enough for shallow tapers however. Time will tell.

John.

[Author]

Posts