Using A Taper To Set The Compound On A Lathe, Version 3

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Using a Taper to set theCompound on a Lathe,Version 3By R. G. SparberCopyleft protects this document.1You are looking down on a lathe setup. On the left is my 3 jaw chuck. Heldin the chuck is a drill being used as amandrel. On the drill shank is a JacobsFlex collet. Contacting the Flex colletis my Dial Test Indicator (DTI) whichis clamped to a support that is fixed tomy Quick Change Tool Post.Only now can I explain what I'mdoing. I'm running my DTI back andforth along the centerline of this tapered surface while adjusting the angle of mycompound. My goal is to be able to move the DTI across this surface and have itsneedle not move. When this occurs, I have set my compound to the same angle asthe taper. It will then be possible to cut this taper on stock held in the chuck.I really hate doing tapers because it is so frustrating to repeat the "measure-adjustmeasure" cycle until finally the DTI reads zero-zero. There has to be a better way.Well, I think I found it. Most likely this technique can be found in some old ShopTricks book, but I've never seen it.1You are free to copy and distribute this document but not change it.R. G. SparberJune 11, 2011Page 1 of 8

My goal is to be able to read how many degrees I must rotate my compound inorder to get the right taper. I will use my DTI as a means of reading a consistenttouchdown point. This is really the best way to use a DTI anyway. It is only trulyaccurate when telling you that0,0you are back to a preset point.taper's surfacecompound's movementcross slide's movementI start by aligning the compound to thetaper by eye. This should get me within a fewdegrees. Record the angle shown on the collar of thecompound.Then I feed in on the compound and the cross slide until I read 0 on the DTI at the0,0 point shown above. All subsequent readings of the dials are done by feeding inso as to avoid backlash error on the lead screws.The cross slide is now backed out enough that the DTI does not hit the taper at thefar end. I then feed in the compound and record the distance from 0.Then plug these values into this nasty looking formula: Note that there is an arcsine (sin-1) and a cosine (cos) operator in there. Somecalculators give you a choice of angles in degrees or radians. Choose degrees.R. G. SparberJune 11, 2011Page 2 of 8

Let’s try this out.First I set my DTI, cross slide dial, and compound dial to zero at my 0,0 point. Iback out my cross slide to prevent the taper from hitting the DTI finger.I then move my compound 0.400".I note that my compound angle is around 69 .Next I feed in the cross slide until the DTI again reads zero. The cross feed dialtells me I am 0.010" in front of my zero point.I calculated the correction angle using my nasty looking equation.1. Subtract the compound angle from 90 .[90 - 69 21 ]2. Take the cosine of this value being careful to have my calculator set todegrees and not radians.[cosine of 21 0.934]3. Multiply the result by the cross slide distance.[0.934 x 10 9.34]4. Divide by the compound’s distance.[9.34/400 0.0234]5. Take the arcsine of the result.[1.3 ]6. I now have the correction angle.This tells me that my compound is 1.3º from the desired taper.I back the DTI away from the taper, note the angle on the compound's collar, andunclamp the compound. Then I move the compound such that the DTI's fingermoves closer to the taper. I stop turning when I have moved the number of degreescalculated. In my case I moved from around 69 to around 70 . Note that this is thecompound angle and not the taper angle.If the compound fed in past the zero point, then I would have needed to rotate thecompound in the opposite direction.I run the taper check again and find my cross slide moved 0.001" when thecompound was fed in 0.400". This is an error of 0.15º. That is close enough for meto use the old measure-adjust-measure procedure.I feed in the cross slide so the DTI showed the 0.001" rise. Then I unclamped thecompound and gently tap the compound to rotate it until the DTI read zero.R. G. SparberJune 11, 2011Page 3 of 8

Reapplying the compound clamps did move me a little but the error was less than0.0005".Be careful when tapping the compound because there is backlash in the cross slide.You want the tapping to rotate the compound and not move the apron.My educated guess is that the true taper angle is 20 (which equals 90 minus thecompound angle of 70 ).EvaluationSo how good is this process? The best way I know to test it is by making a sampletaper and fitting it to a known female taper with Hi-Spot ink.Here is the female taper that will receive the taper I willmake. The inside surface has been lightly coated with HiSpot ink and will remain wet for a long time.I then took a piece of scrap aluminum andturned a taper. I then pressed it into thefemale taper and Hi-Spot ink transferred. Becareful to just press it in and not turn it asthat can smear the ink.The goal is to have the taper evenly coated with ink. In my case, thesurface finish was not that good so I had to run a file over it.EdwinB suggests the following if you must file on a lathe:“The recommended technique is to pass the file under the work withthe tang of the file passing between two fingers on the right hand. Fingers on theleft hand press up on the bottom of the file (the left thumb does not touch the file).If the file catches on the chuck, it will be forced away from your body, your righthand will be pushed away from the chuck, and your left hand should be pusheddown (away from the chuck) and since you aren't grabbing the file, the left handshould not be drawn toward the chuck.R. G. SparberJune 11, 2011Page 4 of 8

This technique does require that the operator reach over the work with his/her righthand, so he/she should ensure they have no jewelry or loose-fitting clothing (whichis SOP when working around a lathe anyway).”Before closing, I will explain the equation.R. G. SparberJune 11, 2011Page 5 of 8

For the Math GeeksOur goal is to adjust the compound’s angle to match the taper angle. I have a fairlygood idea what the taper’s angle, B, is because I have adjusted the compound byeye to get close. The estimated taper angle equals 90 minus the compound angle.For now, assume that I know the angle exactly. I also know how far I moved mycompound and my cross slide. The compound’s movement is the hypotenuse of aright triangle. But the cross slide’s movement is not exactly the rise of this righttriangle. What I really need is distance “h” shown in red. But note that the righttriangle formed by h and the cross slide distance is similar to the triangle formedby our taper. This means that the angle of our little triangle equals our taper angle.I can then write:!# % &"Where:h is the rise of our right triangleS is the cross slide’s distanceB is the taper angleR. G. SparberJune 11, 2011Page 6 of 8

Solving for h to get!" ' # % &With h in hand, I can find my correction angle by noting that(%)* !,Substituting in my equation for h gives(%)* -which can be written as(Where:" ' # % &.,"%)* - # % &.,A is the amount you must move the compound to match the taperS is the distance moved on the cross SlideR. G. SparberJune 11, 2011Page 7 of 8

C is the distance moved on the CompoundB is the estimated taper angle which equals 90 minus the compound angle.The reason for this odd correction in angle is due to how compounds are marked.They are showing what is called the compliment of the angle I define as my taperangle. This is a right triangle so one angle is 90 and the sum of all three angles inany triangle must equal 180 . So we end up with180 90 the compound angle the taper anglewhich can be rearranged to saythe taper angle 90 - the compound angleI did pull a fast one on you here. I assumed I knew the taper angle when in fact Ionly know it approximately.It turns out that is OK because even moderate error in the taper angle estimate hasa small effect on our answers. If I assume that I can know the taper angle within 5 , my correction angle varies by no more than 0.1 independent of the taperangle.AcknowledgementsThanks to the following: Malcolm of the gingery machines yahoo group forfinding an algebra error; Pierre of this same group for finding a serious typo;toolmaker48 of the atlas craftsman yahoo group for various insights; and toEdwinB also of the atlas craftsman yahoo group for his advice on using a file on alathe.I welcome your comments and questions. All of us are smarter than any one of us.Rick SparberRgsparber@aol.comR. G. SparberJune 11, 2011Page 8 of 8

Using a Taper to set the Compound on a Lathe, Version 3 By R. G. Sparber . moves closer to the taper. I stop turning when I have moved the number of degrees calculated. In my case I moved from around 69 to around 70 . Note that this is the compound angle and not the taper angle. If the compound fed in past the zero point, then I would have needed to rotate the compound in the opposite .

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