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Morse Taper Error

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  • Morse Taper Error

    Let me preface my question by thanking Frank Ford for his wonderful site,, which has provided me (a novice) a wealth of inspiration and a lot of great accessories and devices.

    Frank has posted a project he made or using a sine bar to quickly set the compound to cut tapers:

    In making the simple device, there is always cumulative error installed, which leads to the question, what is maximum allowable error (in degrees) in producing an acceptable morse taper??

  • #2
    The female taper should be 0.0005" to 0.0003 large on the should be +/- 0.0002 on the big end regardless of size. At least that's the way I make them when the occasion arises. I don't know what the commercial tolerance are nor do I have a reference.

    What that works out to in angular error depends on the taper length. A #1 Morse would have more taper error than a #5 following my rule of thumb.

    Go ahead and set the taper attachment from the sine bar. You will change it slightly to correct the inescapable error anyway. Lathes seldom follow their taper attachments perfectly. I usually stoned the fit under power to refine it after I got pretty close. Blue a new ground sleeve for a female gage. For a male gage use a like new lathe center. When a light coat of blue hits full length you're good enough.
    Last edited by Forrest Addy; 06-30-2008, 12:16 AM.


    • #3

      I seem to recall the JTiers had some figures on that.

      I tried "Google" but in terms of figures for tolerance/allowances it seems that reference to the ANSI (or the UK or DIN/ISO) standards might be best.


      • #4
        Morse Tapers

        Actually it was nothing simpler than 1/4" in 10"- and then some fool couldn't measure- and the error became a standard

        Mystified Me


        • #5
          Actually, Morse tapers are 5/8" per foot nominal taper not 1/4"" per foot - which is the standard for taper pins and machine tool gibs.

          Steven Morse who designed the taper system and produced the first gages in 1864. He did a hell of a job striving for 5/8" per foot considering the lack of measuring equipment and standards of his day. The tapers today duplicate the features of the original gages. The orginal gages were amazingly round and conical and fit each other precicely even after 150 years. The original Morse taper gages are one oif the few international standards dependent on the original artifacts as a master reference.

          It helped that Morse also invented the present form of the twist drill (furnished with Morse taper shanks) and made them so well and in such numbers that his taper series replaced all other taper systems for general machine spindle use. The Morse taper series became popular so rapidly they eclipsed every other taper system including ones that were technically superior to the Morse such as the Jarno. Morse tapers were the M/S DOS of the day: a defacto standard even before it came into wide use.

          If you look at a list of Morse tapers you'll see that his tapers varried as much as .030 per foot. But bear in mind that this was before micrometer dials on machine leadscrews and the micrometer while invented long before that time was not popular until Brown and Sharpe came along later. Fits were made via transferring from inside to outside calipers and referencing scales.

          Put yourself in the place of Steven Morse and using the equipment and materials he had available. Then make a set of ring and plug taper gages as accurate as the originals striving for 5/8' per inch actual total taper. Aint easy, is it. Wouldn't hurt to walk a mile in the other fello'ws moccasins before you call him a fool.
          Last edited by Forrest Addy; 06-30-2008, 11:31 AM.


          • #6
            Thanks, Forrest for the history of the MT tapers. I have wondered why each taper is slightly different but have not seen an explanation before.



            • #7
              Morse Tapers

              Actually, I stated 10" not 12" .
              10" is the Classic length for doing the sine.

              You know the Square on the whatsit is equal to some of the snares on the other two dangles.

              Euclid or Pythagoras and we go back to the solution of the squares using the easily divisible 100 rather than 144 using the projection of squares and the solution of them by Euclid's geometry on right angled triangles.

              Did it when I was 15 and Euclid was in his prime- numbers of course.

              err, yes????

              Norm- tripping over his 'guessing stick' to do Naperian logarithims.
              You know the logarithim of a number to a given base in the index of the power to which the base must be raised in order to produce the number?


              • #8
                Morse Taper Error

                Thank you for taking the time to respond, Forrest. Your answer is much appreciated.

                I had a mentor (neighbor) who was a long time machinist and former "chair" of a college occupational (machinist) program, but recently his age and health issues have severely limited his ability to provide information. It's awfully nice to come have a place to ask questions you are unable to locate answers for in traditional sources.

                Again, thank you.


                • #9
                  For what it is worth, I looked it up, and the error stated in the "Machinery's Handbook" for the "American Standard Self Holding taper" that is identical in gage line dims to a Morse is that the taper must be within 0.002 per foot of the standard.

                  I didn't see one specifically for Morse in the reference I checked, but I am under the impression that I saw the same tolerance for Morse elsewhere.

                  I believe I also have seen that the tolerance is such that the fat end must be larger, or the small end smaller, so that it always is tight at the fat end.

                  Either way, I don't recommend that you rely on that. If you go to the limit, it might work for a mere drill. A drill is wedged in by the drilling force, and shouldn't be relied on for much precision anyhow.

                  But for a center, or anything else with pretensions of precision, you had better be within a few tenths, or the thing will wiggle like a pen in a pickle barrel.

                  Keep eye on ball.
                  Hashim Khan


                  • #10
                    MT fits

                    Forrest Addy and JTiers are probably and evenly certainly quite correct.

                    If real accuracy is required - as on a cylindrical grinder, the male and female tapers are "made to fit" (either individually or by "selective fit" from a batch). The concentricity of the "point" to or with the taper is not really such an issue as the tail-stock centre was "dead" (ie not moving). The head-stock taper was either "fixed" as well (with the drive/"dogs" rotating about the fixed centre) or else if the head-stock was "live" (ie the HS taper rotated with the spindle) the HS centre "point" (60 arc degree usually) was (re)ground after mounting and before mounting the work-piece on it.

                    Many HS centres that I used on lathes were "soft" so that they could be re-turned and "trued-up".

                    On some centres I have used the middle 2/3 or 3/4 of the "male" ("plug") was "relieved" so that the taper only contacted on the ends. This was quite OK as there was no need for the taper to "lock and drive" as it was the "location" that was important.

                    Any other "errors" can be "tuned out" by adjusting the tail-stock.

                    Most items that I've seen regarding taper-turning seem to assume that the top/compound slide or the taper turning attachment is not worn and will cut a perfectly straight cone. I would want to do some fairly accurate "proving" before I made that statement or assumption.

                    "Live" centres are a mixed blessing as it is quite difficult to actually determine where any "run-out" (as detected by a precision dial indicator) really is as there are components of the taper along and across the lathe (bed) longitudinal axis. "Trueing-up" a live centre is not as easy as it might seem either.

                    The situation may well be worse if using "adaptors" (ie MT4-MT3).

                    The "0.002" per foot" suggested is 0.002/12 = tan theta = 0.0001666

                    theta = 0.0095 arc degree = 0.5738 arc minutes = 34.38 arc seconds

                    "2 thou per foot" is only 1 thou per 6" which is hard enough in itself, but if there are any irregularities in the taper in terms of "straightness" or surface finish, there may well be even more problems.

                    As usual, Forrest's solution addresses all of these issues ie.
                    "blue it in" and "paper" it for the required and fit and finish by making one part to suit another.

                    The "self-locking" feature of a female morse taper in the tail-stock is used on its own without a "tang" for drills and is expected to "hold". If the TS MT is a "precision taper" then it soon will not be if we keep poking those rough drill tapers into the TS MT and especially if we keep "spinning" the drill (or drill chuck, reamer etc.) in the TS MT.

                    Few would abuse a mill quill taper the way a TS MT is abused but they still expect similar accuracy from both in terms of the quality of the MT (or other) taper/s and of the quills in the bodies of the mill head and tail-stock body. Its one hell of a "Big ask"


                    • #11
                      Originally posted by oldtiffie

                      As usual, Forrest's solution addresses all of these issues ie.
                      "blue it in" and "paper" it for the required and fit and finish by making one part to suit another.

                      Actually, the correct way is to blue it in to a standard taper gage, and check it with ring gages. The gage should be made closely to the standard.

                      Only if you merely need two fitting pieces does the "blue it in to the socket" work, unless you "know" the socket is correct. of course, I don't HAVE a standard taper gage, although I expect I could make one. The ring gage might be a bit more tricky....... The taper gages I have seen are open 'fish-tail" gages where you sight the contact on the taper, similar to sighting a square.

                      Keep eye on ball.
                      Hashim Khan


                      • #12
                        Orders of accuracy

                        I'd agree JT if we were in an ideal world and had the machines, controlled conditions and metrology to make - and regularly check - the guages you suggest. These guages by definition require to be at least one order of accuracy better than the parts that will be measured against them. The tools in the metrology part of the equation require to be at least one and preferably at least two orders of accuracy better than the guages they are checking.

                        But in the average HSM world that most of us live in, we have to make the best of what we have. That usually means making one part to suit another which for practical purposes can approach the accuracy of the ideal mentioned above. This after all is only a variation of the three plates system of making surface plates - and "Camel-back" straight edges.

                        (As an aside, every time I see the mention of camel back, I visualise camels "humping it". Is a guage with two humps a Dromedary and if a Camel and a Dromedary were humping it - what would you have?

                        Yeh - I know - too many years with the Navy and too much time on my hands).

                        Never the less, I expect that Forrest's advice to make one part to fit another is very sound and practical as it will work very effectively and can be done with basic tools and a modicum of skill, patience and perseverance which are hall-marks of the HSM-er and are in plentiful supply - and its free.


                        • #13
                          perhaps you missed the fact that I don't have a gage either?

                          The "right" way and the way we actually do it are often two different things............

                          But, anyone with access to some basic measuring stuff, like gage blocks and sine bar, plus a cheap granite flat, can make a very credible gage for any morse taper.

                          With adequate gage block sets under $100, and a sine bar at $30 or so, (chinese of course) anyone can get into precision lengths and angles for a relatively low cost.

                          I tend to reject the idea that a home shop must be crude and totally oriented at "git 'r dun". Please reference Mcgyver's recent post, or Rich Carlstedt's monitor engine post for details................. Lane has some goodies as well, and there are many others.

                          Keep eye on ball.
                          Hashim Khan


                          • #14
                            Originally posted by J Tiers
                            perhaps you missed the fact that I don't have a gage either?
                            I don't recall your saying that.
                            So you did JT - so you did - I checked - my apologies
                            [End edit]

                            The "right" way and the way we actually do it are often two different things............
                            Depending on the resources available and the performance criteria - they are often the same.

                            But, anyone with access to some basic measuring stuff, like gage blocks and sine bar, plus a cheap granite flat, can make a very credible gage for any morse taper.
                            On the face of it, that makes it all seem all too simple and a "lay-down misere'".

                            The absolute basic and possibly quite difficult thing is getting the "guage" and the sine-bar into the same axial alignment or else we are into the very difficult area of "compound angles" - which are not for the cautious or faint-hearted. Making the guage is one thing, but using it may well be another. If the guage is a "wedge" to be placed on the work, there are two possible problems: the guage and the work must be in full contact and in perfect axial alignment else we are back to compound angles; secondly, any error on the "wedge" even if applied perfectly to the job will result in a doubling of that error on the job.

                            If the guage is a tapered cylinder/frustum of a cone, it will need to be mounted on centres that are set pretty well very precisely to be equally above the table/plate. It will need to be a very good tails-stock quill with a very close fit in the TS plus any movement of the quill for checking of the job will need to be re-set with a very accurate test dial indicator (TDI) as the TS quill clamp is applied. Any error will be doubled at the TS end of the taper. My Tool & Cutter grinder centres are precision fits - one is "fixed" and the other spring-loaded and not clamped - so if I were grinding the taper on my T&C grinder I would not only have the angular/location accuracy required but could also be sure that the "edge" of the cone was straight and a far superior ground finish as is required of a MT which is very difficult to duplicate without "papering'' as Forrest Addy suggested. I'd be surprised if the majority of members have a T&C or cylindrical grinder, so I guess they have to use their lathes.

                            With adequate gage block sets under $100, and a sine bar at $30 or so, (chinese of course) anyone can get into precision lengths and angles for a relatively low cost.
                            No need for that either. I can do a very passable job with any two good cylinders and a stock for spacing. Once I know the diameters of the end "rollers" and the angle I need, it is only a simple CAD or trigonometry exercise to determine the length of the spacer and then make it quite accurately on a lathe. No sine bar, guage blocks or surface plate needed. My mill table is quite flat and co-planar.

                            I tend to reject the idea that a home shop must be crude and totally oriented at "git 'r dun".
                            I neither said, inferred nor intended that.

                            The "right way" is the way that suits the person who wants or makes the taper and any tools. If it suits him it suits me - what-ever his standard (or perceived lack of them) are. It is his "call". The rest of us are just observers and/or advisers - nothing more.

                            Suffice to say that I don't lack for the "right" tools to do most jobs - in both the "making" and "measurement" aspects. I much prefer to reduce a job to the absolute basics or fundamentals as regards design and "making" as it is quite challenge to get it "right" under those circumstances. It might surprise how well they turn out when I use the "right/correct" way to measure or check them.

                            I don't make a lot of stuff for use outside the shop. It is either "something for making something (else)" or just to try out an idea or process - in that case, when I am satisfied with the process, I just "junk" the part/material. I am more interested in attaining and maintaining skills. "Product" is rarely an issue. But if I get both - so much the better.

                            If that is a definition of "getting 'er done" then I am pleased to say that I am as guilty as hell - but bloody pleased about it.

                            Please reference Mcgyver's recent post, or Rich Carlstedt's monitor engine post for details................. Lane has some goodies as well, and there are many others.
                            I am not too sure of the relevance or context of that.

                            I am a long-time admirer of the skill that all three have. I would not be surprised, if the occasion required or warranted it, if they had used means and processes that some might not regard as "right" or "good enough" or "get 'er done" in the eyes of purists. But it is not my place to surmise or make judgment in that regard. I suggest you ask them directly. I won't as it is none of my business.

                            I support Forrest Addy's advice as it sure does work for me.

                            I am in no position to make judgments on how others may deal with these issues.

                            You may be assured that in the absence of any compelling need to do otherwise, that I will continue to "get 'er done" in my own way.
                            Last edited by oldtiffie; 07-07-2008, 03:51 AM.


                            • #15

                              I see that you have yet again made a nearly clean sweep trashing of my every statement.......... Apparently your reference to wikipedia is intended to mean that everything I said was SO STUPID as to be totally and completely wrong, idiotic, and unbelieveably ridiculous.

                              Thank you very much....... We have a NEW winner in the IOWOLF competition.....

                              The "right way" is NOT "the way we do it out on the farm". There IS a right way, sorry to disabuse you of your notions (which i know you don't really adhere to).

                              They are NOT "often the same" in the home shop, which is usually not supplied with every possible convenience for metrology.......... the right way may NOT be possible. But there is no reason to abandon it as impossible...... and therefore unworthy of consideration.

                              Are there problems in getting a gage set right? sure.... but it IS indeed possible, and NOT so impossible as you say.

                              As far as the angle-off, one can check for the "nearest approach" when 'swinging thru" and see that there is one position where the taper occludes light uniformly. Since teh taper form was generated as a round cone form, there is exactly ONE line of maximum diameters. if the form swings thru, AND occludes in one position, it is as close to correct as that type gage can check.

                              This does not assure totally correct 3-D form, which I may have mentioned (ring gages etc) but it WILL assure taper form if checked in a couple places.

                              If you can generate a 90 deg angle, scrape or grind a surface flat, and can set a sine bar or use rolls (that might be more difficult for the average person), one can set a gage with movable bars to the correct angle. Refer to "Advanced Machine Work" by Smith. I think the gage form I mean is shown in that.

                              It might be easiest to generate a "setting dummy" (perhaps rolls or a wedge form) of the correct angle first, and set the gage to that. Such a system would allow using the gage tool for more than one taper type......

                              Am I going to have to MAKE one to show you?

                              Keep eye on ball.
                              Hashim Khan