Cutting a shallow taper

JimSchroeder

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Most of the lathes that we have access to do not have taper attachments and without such fixtures cutting tapers that are accurate can be a challenge. I have on numerous occasions had to cut tapers for collet adapters and for these to function properly they must be accurate. Fortunately the length of the taper is short and thus the compound slide can be used to provide the correct tool angle. The trick is to get the slide adjusted at or very close to the desire angle. One of the more common collets is the R8 which requires a taper of 8.425 degrees over a distance of 0.872”. An earlier post showed how to use a miter square in conjunction with 1-2-3 blocks to align the compound slide at the desired angle. I use a different method and I present that as an alternative, take your pick.

Measuring taper.jpg

















































Photo 1 – An ER-40 collet adapter aligned for turning. Note the dial indicator used to measure the slope of the compound slide.

With some simple trig tables it is very easy to compute the slope measured in decimal fractions per inch of carriage travel. Table 1 below shows the slope measured to ten thousands per angles between zero and twenty degrees and the tenths in between. To use this information place a dial indicator on “Y” axis and either using your DRO or another dial indicator move the carriage one inch and measure the slope of the compound slide. The slope of the ER-40 collet is 8.0 degrees for a depth of 1.377” From Table 1 this shows a slope of 0.1405 inches per inch of carriage travel. Dial indicators with 1 or 2 inches of travel will not measure in tenths but you should be able to extrapolate fairly closely.


Slope per inch of travel
Tenths of degree
Degrees00.10.20.30.40.50.60.70.80.9
10.01750.01920.02090.02270.02440.02620.02790.02970.03140.0332
20.03490.03670.03840.04020.04190.04370.04540.04720.04890.0507
30.05240.05420.05590.05770.05940.06120.06290.06470.06640.0682
40.06990.07170.07340.07520.07690.07870.08050.08220.08400.0857
50.08750.08920.09100.09280.09450.09630.09810.09980.10160.1033
60.10510.10690.10860.11040.11220.11390.11570.11750.11920.1210
70.12280.12460.12630.12810.12990.13170.13340.13520.13700.1388
80.14050.14230.14410.14590.14770.14950.15120.15300.15480.1566
90.15840.16020.16200.16380.16550.16730.16910.17090.17270.1745
100.17630.17810.17990.18170.18350.18530.18710.18900.19080.1926
110.19440.19620.19800.19980.20160.20350.20530.20710.20890.2107
120.21260.21440.21620.21800.21990.22170.22350.22540.22720.2290
130.23090.23270.23450.23640.23820.24010.24190.24380.24560.2475
140.24930.25120.25300.25490.25680.25860.26050.26230.26420.2661
150.26790.26980.27170.27360.27540.27730.27920.28110.28300.2849
160.28670.28860.29050.29240.29430.29620.29810.30000.30190.3038
170.30570.30760.30960.31150.31340.31530.31720.31910.32110.3230
180.32490.32690.32880.33070.33270.33460.33650.33850.34040.3424
190.34430.34630.34820.35020.35220.35410.35610.35810.36000.3620
200.36400.36590.36790.36990.37190.37390.37590.37790.37990.3819

Table 1 – To determine the slope per inch of carriage travel select the degrees and tenths of a degree the value is in the intersecting box. Example, 8.0 degrees is 0.1405” per inch of travel. I keep a copy of this on the wall over my lathe.

After you have removed enough material from the sloped surface so that the width of the cut is half way or more to the final dimension use some high spot blue to confirm you taper adjustment. In this business you need to make some assumptions from time to time and in this case I assume that the collet is of the correct size and has the correct taper. If some adjustment is needed reattach the dial indicator to help guide your adjustment. Photo 2 shows this on an ER-32 collet and adapter.

Hi spot blue.jpg


















































Photo 2 – High spot blue used to confirm the angle of the collet adapter, this is a ER-32 collet.

Being able to construct collet adapters for your equipment is a handy skill. I find more and more uses for collets as venture into new areas. I am particularly happy with the double-cut ER style of collets. As show I have an ER-40 adapter on my 10x22 lathe and use it extensively. Photo 3 shows a R8 adapter that is part of the tool head for a cutter grinder I built.

Tool head mounted on table.jpg


















































Photo 3 – Tool head for a cutter grinder that uses R8 collets.

These collets holders are not ground or hardened but for the average hobbyist they should give many years of service. My oldest and most used is the R8 holder on a cutter grinder that has been service for three years. As always if you have any questions or comments feel free to contact me either on this post of via private message.

Jim

Measuring taper.jpg Hi spot blue.jpg Tool head mounted on table.jpg
 
:man: Bookmarked this one.
*********Thanks**************Gator******
 
Thanks for the well thought ans well put tutorial Jim. That is a great article and since I am considering doing some collet type of work I will definately be refering to it often. Being a nobb machinist is tough, but I have learned some really creative ways to make parts and tools from projects just like yours. Again thanks for the info.

Bob
 
Jim,

Excellent work as usual and a great documentation. Thank you!

Steve
 
Very accurate method. I would only add that if you're tracing an existing taper to copy your contact tip on your indicator must be on center. If not, it will introduce error in the travel you read. One trick to get it there, if you are using a dti mounted on a QCTP is to eyeball it 0.050 below center and take a reading, then insert a 0.100 gage block under the stop nut and read again from the same start position. If the sweep readings don't agree, then adjust the nut. When you get them to agree, substitute a 0.050 block and you will be very, very close to center. It will practically eliminate error from being off centerline.

Also, the method described assumes that the side of the compound is actually parallel to the ways of it, and although usually they are close, no guarantees. But you can use the same basic method to check your taper after you cut it, and adjust as needed.
 
All good points Tony. The number of variables that can affect a setup such as this is long and sometimes almost impossible to take them all into account. That is the purpose of using the collet as the "master" and high point blue as the witness.

Jim
 
Totally agree, Jim. The final say is how the intended mating part fits. I've worked with seal tapers that required a blue wipe from a master certified plug, and it wasn't always easy to hit it first time no matter what was done.
 
Great idea! Have you ever tried making the ER collet nuts? I'd like to make an ER chuck but all the collet nuts are in metric threads.
 
Very nice suggestion, JimShroeder!

One question though, these numbers are obviously obtained from the sine of the angle. Every number in your table is slightly bigger than the sine of the angle. Example: sin(6.5 degrees)= 0.1132032 your table=0.1139 Why is this?
 
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