Screwcutting in the Lathe for Home Machinists E-Book

Martin Cleeve

• Herausgeber: Fox Chapel Publishing
• Kategorie: Lebensstil
• Sprache: Englisch
• Veröffentlichungsjahr: 2021

Seitenzahl: 341

Beschreibung

Screwcutting in the Lathe for Home Machinists is a complete guide detailing the uses of a lathe for all forms of screwcutting in all thread forms, pitches, and diameters. Working in both imperial and metric standards, this comprehensive and invaluable resource will inform you on everything you need to know about lathe screwcutting. Also included are calculations, gear trains, conversions, and other helpful reference tables. Author Martin Cleeve was a well-respected contributor to Model Engineer magazine for more than 30 years. A known perfectionist to high-quality and accurate work, he designed and described many original lathe accessories, which have been made and regularly used in hundreds of amateur and professional workshops.

Leseprobe

SCREWCUTTING IN THE LATHE

Martin Cleeve

Copyright © 2021 by Martin Cleeve and Fox Chapel Publishing Company, Inc., Mount Joy, PA.

Copyright © Special Interest Model Books Ltd 2006

First published by Argus Books Ltd. 1984

Second edition published by Special Interest Model Books Ltd. 2002

First published in North America in 2021 by Fox Chapel Publishing, 903 Square Street, Mount Joy, PA 17552.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright holder.

Print ISBN: 978-1-4971-0173-9eISBN: 978-1-63741-040-0

To learn more about the other great books from Fox Chapel Publishing, or to find a retailer near you, call toll-free 800-457-9112 or visit us at www.FoxChapelPublishing.com.

We are always looking for talented authors. To submit an idea, please send a brief inquiry to [email protected].

CONTENTS

Acknowledgment

SECTION 1

INTRODUCTION

Introductory notes – Conversion notes – Quick reference thread sizing formulas

SECTION 2

PRINCIPLES OF LATHE SCREWCUTTING

Altering the pitch – Calculations – Simple and compound gear trains – Schematic gear train presentation – Calculations for mixed number TPI – Equal ratio setting – Threads designated by lead – Proving gear trains – Self-act feeds from leadscrews – Diametral pitch worms – Formula for worms by DP – The DP formula – how evolved – Proving worm thread gearing.

SECTION 3

GEARING AN ENGLISH LEADSCREW FOR METRIC THREADS

50-127 translation ratio explained – Basic conversion formula – Checking metric gear trains – Modified gearing systems for metric pitches with an English leadscrew – Reduced pitch translators – Alternative translation gearing – The 2-21 (63-160) method – Checking the 2-21 gearing – 13-33 translation gearing and 15-38 – Worms sized by module – Gearing an English leadscrew, practical examples.

SECTION 4

LATHES WITH METRIC LEADSCREWS

Probable standard pitches for metric leadscrews – Screwcutting calculations – Gearing for English threads with a metric leadscrew – Disadvantages of 127-50 step up – Disadvantages overcome by alternative translation ratios – Very small pitch errors – Proving metric – English gear trains – Finding exact pitch given – Quick checking for nominal pitch – Worms for gears sized by module: gearing with metric leadscrew – Worms sized by DP: gearing with metric leadscrew – Change gear calculations by approximation.

SECTION 5

PROBLEMS AND ANALYSIS OF REPEAT PICK-UP

Meaning of pick-up – Examples – The thread dial indicator or leadscrew indicator – Action of English indicator – Metric threads: pick-up – Geared leadscrew indicators – Special application of leadscrew indicator: How to pick-up for short metric threads being cut from an English leadscrew – Leadscrew indicator for metric leadscrews – Pick-up when gearing is approximate – Repeat pick-up from chalk marks – Repeat pick-up: electrical indication – Pick-up with dog-clutch control – Advantages and theory – A little-known method for obtaining even faster screwcutting with dog-clutch control – Calculating metric pick-up.

SECTION 6

MULTIPLE-START THREADS

Automatic start indexing (by dog-clutch control) – Designation of multiple start threads – Feasibility test (to ascertain whether or not any given leadscrew is suitable for indexing a required number of starts automatically) – Pick-up for automatic multiple start indexing – Metric multiple start threads from an English leadscrew – Automatic start indexing possibilities by dog-clutch control explained – Automatic start indexing of metric multiple-start threads from metric leadscrews – Special leadscrews for auto-start indexing – Special leadscrew design formula: For metric working, for English working – Example of lathe with dog-clutch control to the leadscrew drive.

SECTION 7

SINGLE POINT LATHE THREADING TOOLS

Various single point threading tools discussed – High speed steel – Stellite – Blackalloy – Tungsten Carbide – Carbon steel – Cutting angles – Internal threading tools – Inserted bit tools – Internal thread tool bit fitted by brazing, a tested design – Thread tool sharpening and grinding – A simple jig for the production of accurate angles and a new design retractable, adjustable height, swing-clear, general purpose and threading toolholder – The thread tool grinding jig described – Sharpening external and internal threading tools of various types: solid-with-shank and inserted bit.

SECTION 8

PRACTICAL ASPECTS OF LATHE SCREWCUTTING

Four ways of depthing a screw thread – Five ways of depthing a nut thread – Square thread cutting – Acme thread cutting – Nut threads: notes on bore sizing – The percentage approach to bore sizing for nuts – Tap finishing – Special tap making – Multiple-start threads – How cut in lathe without dog-clutch control – Multiple-start nut threading – How cut in lathe without dog-clutch control – Multiple start thread indexing by use of leadscrew indicator – Multiple-start worm thread notes – General observations: Thread crest radii – Taper threads – Improvised cutting method – Screwcutting speeds – Lubrication – Effect of coolant on light cuts – Screwcutting troubles, possible causes.

SECTION 9

PRACTICAL THREAD SIZING MEASUREMENT

Definitions of screw thread terms – The 3-Wire method of thread checking – Wire diameters and thread depth – Three wire formula for 55 deg. screws – Checking Whit, thread by metric measure – One-wire checking – Pitch diameter calculations – Acme thread checking – Summary of formula for 1-wire checking – Helix angle of screw threads – Formula – Gauging nut threads – Thread classes – Threads designated by class.

APPENDIX 1

LIST OF TABLES

ACKNOWLEDGMENT

I am greatly indebted to the Editor of MACHINERY’S SCREW THREAD BOOK (Ed 20) for his kind permission to make use of information contained therein. Indeed without such guidance it would have been impossible to make any sound pronouncements on thread depths, basic sizes, and thread gauging methods. However, apart from space considerations, it would obviously be unfair to reproduce large verbatim extracts from the SCREW THREAD BOOK, so for those requiring more detailed information on threads, as distinct from producing them, I can but recommend the SCREW THREAD BOOK itself.

Martin Cleeve

Publisher’s Note

The publishers regret to record the death of the author, after submitting his manuscript but before it had been typeset.

‘Martin Cleeve’ was a pen-name used by Kenneth C. Hart, a respected contributor for some 30 years to the Model Engineer. His painstaking, perfectionist approach to high-quality, accurate work, which so clearly comes through in this book as in all his other writing, led him to design and describe many original lathe accessories which have been made and are regularly used in hundreds of amateur and professional workshops alike, perpetuating the memory of an engineer for whom only the highest standards would suffice.

SECTION 1

Introduction

It has been said that lathe screwcutting cannot be taught from books, which seems to imply that students must learn this particular skill from trial and error after gathering a few basic facts from an instructor. However, this outlook may arise partly from the fact that few general engineering books can spare the necessary space, and partly because writers seldom take the trouble to make any specialized study of lathe screwcutting, with the result that the same few scraps of information are handed down from generation to generation without any attempt at sorting the wheat from the chaff; perhaps to disguise this deficiency it is sometimes remarked that too much emphasis can be placed upon the ability to cut threads in lathes. However, in this respect, while ordinary turning calls for the use of little more than common sense, efficient and time-saving lathe screwcutting cannot be undertaken on the same basis, and if a lathe operator is not in possession of all the relevant facts he may not be able to avoid wasting time: time which on small batch production can sometimes amount to whole working weeks, not just the odd 30 minutes. For example, it is not always necessary to follow the time-wasting instruction: ‘For all other threads, reverse the lathe’ (an instruction referring to tool repositioning between threading passes). Moreover, the adverse conditions for which lathe reversal is supposed always to be necessary can sometimes be turned to advantage for indexing the starts of multiple-start threads by a method whereby, after an initial setting, indexing takes place between every single threading pass without additional attention from the operator, and having the advantage that all starts (individual helices) are machined to identical proportions to close limits.

Having said that, it would only be fair to add that on deciding it might be a good idea to commit to paper the results of my researches, I had no idea that the describing of what is basically a simple process would call for such a plethora of writing, (and I have not used two words where one will serve) or indeed that the project would lead to two Patent Applications, one for an independently retractable and swing lathe toolholder (No. 1335978 – now lapsed), and one for a simple thread tool sharpening jig (No. 1417351 – not ‘Sealed’ although printed by the Patent Office), or that I would be devising formulas for the design of leadscrews of special lead for the automatic indexing of the starts of multiple-start threads when these cannot be auto-indexed from standard English or metric leadscrews.

In general, despite the rapid advancement in fully automatic machine control, the ordinary center lathe is likely to remain with us for a long time for the reason that it does not pay to set an automatic machine for only one or a few threaded components such as those required for jig and tool-making, or for experimental and prototype work. And in many instances, even when the quantity of components reaches the 50 to 150 total, a center lathe can offer a saving when compared with the cost of a more specialized machine and the time taken to set it.

On the other hand, automatic and semi-automatic threading attachments can now be obtained for use with standard center lathes, and such attachments can be fairly quickly set. However, the initial cost can be high, and this has to be weighed against the quantity of threading likely to be called for.

In contrast to the foregoing, I have heard it remarked that screwcutting facilities are not really necessary on center lathes these days, as all threads can be cut with taps and dies. Now although modern taps and die-heads are capable of cutting clean bright threads to close limits, their use sometimes calls for very high torques, whereas a center lathe always forms threads in easy stages, admirably suited to those components which by nature of their design could not be gripped with sufficient security to withstand the high torques imposed when tap or die running. Moreover a lathe will cut a thread of any pitch on any diameter: for example it is as easy to cut 16 tpi on a diameter of 4 in. as on a diameter of ½ in. or less, whereas the use of taps and dies limits one to standard sizes, and when only a few special threads are called for one obviously would not wish either to pay the high cost of special taps or dies, or to await delivery when such threads can be lathe screwcut for the trifling cost of a single-point threading tool and a few minutes of a lathe operator’s time. Similar remarks of course apply if a standard size tap or die is not in stock.

There is also the point that bores to be threaded are sometimes very short or shallow, a total depth being limited to say 3/16 in. or so (4.8 mm) with an abrupt shoulder or completely closed base. These threads are impossible to cut with a tap simply because the tap would ‘bottom’ before the necessary tapered lead had fully entered, whereas such threads are easily lathe screwcut with a single-point tool. I have also encountered external threads that were required to continue inside a recess – where of course no die could operate, and these had to be cut by the use of a special cranked threading tool. Another point in favor of lathe screwcutting is that threads so produced are concentric and symmetrically disposed about a component axis to close limits – i.e. are ‘square’ to axis.

METRICATION

Those brought up entirely with metric units will have no difficulty in following the recommendation that, with metrication, designers and engineers should work entirely from metric concepts. However, those of us long accustomed to working to English imperial measure tend to feel uncomfortable until we have converted metric figures into English units having a satisfactory meaning to us. For example, for a time we will not have a clear idea of the implication of a thread pitch error of, say, minus 0.003 mm until we have converted to inch measure and found that 0.003 mm equals 0.000118 in, or just 10 over 1/10 thou/inch. In this respect, too, many center lathes will probably remain in use with English feed dials graduated in thousandths of an inch, and metric thread sizing will have to be carried out to inch standards. The object here therefore is to deal with these problems of change in such a way that the reader may choose a line of action best suited to his particular need, and simple formulas are given to facilitate working to either metric or English units. As a matter of fact, partial metrication has led to the writer often having to lathe screwcut batches of 50 or 100 components with an English thread at one end, and a metric thread at the other end.

CONVERSIONS

Fortunately these days it is possible to buy a good basic electronic calculator for a very modest sum, so it is no longer necessary to occupy valuable space with conversion tables. Indeed, with a basic formula and a calculator, any necessary figures can be obtained far more pleasantly, quickly and accurately than by thumbing through fully tabulated data.

GENERAL FORMULAS

The following formulas will be useful for general reference:

1 To convert inches to millimeters, multiply inches by 25.4.

2 To convert millimeters to inches, multiply by 0.03937, or divide by 25.4.

3 Given the pitch of a thread in millimeters, find the threads/inch:

4 Given the threads/inch, find the pitch in mm:

5 Given the inch pitch, find the metric pitch in mm:

6 Given the pitch in millimeters, find the inch pitch:

or

7 Given the threads/inch, find the pitch in inches:

8 Given the pitch by inch measure, find the threads/inch:

9 Given the metric pitch (mm), find the threads per centimeter:

10 Given the threads/inch, find the threads/cm:

NOTE: The notation ‘threads/centimeter’ is not ordinarily used or recognized, but is sometimes useful for explanatory purposes associated with lathe leadscrew gearing.

Unified & American screw thread form. 60 deg. included thread angle.

Thread crest may be flat, or given a radius of 0.108253 x Pitch.

Root radius =0.144338 × Pitch. (Also optional)

QUICK REFERENCE THREAD INFORMATION SUMMARY

DEPTH OF THREAD. (SCREW). BASIC DESIGN DEPTH

ISO Metric 60 deg.

By mm

By inch measure:

* This figure is a close approximation.

WHITWORTH & BSF 55 DEG.

By inch measure:

UNIFIED 60 deg.

By inch measure

By mm:

WHITWORTH & BSF 55 DEG.

By mm:

NUT BORE (MINOR DIAMETER) SIZING. RECOMMENDED MINIMUM

ISO Metric. 60 deg. By inch measure.

ISO Metric. 60 deg. By millimeters.

UNIFIED 60 deg. By inch measure.

UNIFIED 60 deg. By millimeters.

WHITWORTH AND BRITISH STANDARD FINE 55 deg.

By millimeters.

WHITWORTH AND BRITISH STANDARD FINE 55 deg.

By inch measure.

NUT BORE SIZING BY PERCENTAGE OF FULL THREAD

NUT THREAD DEPTHS

(Nut thread depths are taken from the surface of bores slightly larger than would be given by major screw diameter minus twice the depth of thread of the corresponding screw, hence basic nut thread depths are less than corresponding screw thread depths, and are really only useful as a guide. Actual nut thread depths may be greater or less than calculated).

ISO Metric. 60 deg. Depth of NUT thread by mm:

Depth of NUT thread by inch measure:

UNIFIED. Depth of NUT thread by inch measure:

Depth of NUT thread by millimeters:

WHITWORTH AND BRITISH STANDARD FINE

Depth of NUT thread by inch measure:

Depth of NUT thread by millimeters:

The Acme screw thread form. 29 deg. included thread angle.

THE ACME FORM THREAD 29 deg.

DEPTH OF THREAD – SCREW

By inch measure:

By millimetres:

NUT BORE (MINOR DIAMETER) SIZING

BASIC DESIGN DEPTH

plus 0.010

plus 0.254

NOTE: For the Acme thread (and for the trapezoidal form) the standard clearances between screw and nut appear to be extraordinarily liberal. Taking as an example a thread of 5/8 in. dia. x 8 threads/inch. the screw-thread depth is 0.0725 in. leaving a root diameter of 0.480 in., yet the recommended nut bore is 0.500 in., showing that a screw thread depth of about 0.064 in. (1.63 mm) would be sufficient, unless, of course, contrary instructions are received. Similarly, the major diameter of a 5/8 in. dia x 8 threads/inch ground thread tap is 0.654 in., i.e. 0.029 in. in excess of major screw diameter, thus offering an ‘annular’ thread clearance of 14.5 thou./inch (0.37 mm) which, to say the least, appears to offer a somewhat excessive space ‘for lubrication’, especially when compared with the much smaller clearances recommended for plain shafts and bearings.

THE TRAPEZOIDAL METRIC THREAD 30 deg. (Similar to the Acme form)

NUT BORE (MINOR DIAMETER) SIZING

For nut bores the most practical approach appears to lie in use of the percentage-of-full-thread formula, unless instructed otherwise.

THE SQUARE THREAD FORM.

Thread flank angle: 90 deg.

DEPTH OF THREAD: SCREW – By English or metric measure:

WIDTH OF THREAD SPACE – (Screw) W =0.5 x Pitch.

NUT BORE SIZING (Minor diameter) By English or metric measure:

(Without a “clearance allowance” the crests of a nut thread would contact or interfere with the root of a correspondingly basic sized square thread screw)

NUT THREAD DEPTH

As sized from the inner surface of (a slightly enlarged) minor nut diameter, nut thread depth will be the same as the screw thread depth.

The clearance allowance may be any amount felt desirable for lubrication, unless of course, precise instructions are given.

The Square thread screw form.

For side (flank) clearance, the thickness of the body of a nut thread will also be slightly less than the 0.5 x P. space dimension of the corresponding screw thread.

SECTION 2

The Principles of Lathe Screwcutting

The drawing, Fig. 1, shows in an elementary way the principles of thread cutting by means of a master screw: a leadscrew (pronounced ‘leed’, by the way). Points to note are that the spindle, which is revolving with the chuck and component to be threaded, drives the leadscrew through gearing: in this example by two gears each having 45 teeth and therefore giving a ratio of 1:1. By this means the leadscrew will revolve at exactly the same speed as the piece to be screwed, and at the same time will cause the nut (which is prevented from rotating) to move from right to left by a certain distance for each revolution of the leadscrew. If the leadscrew has 8 threads to the inch, or a pitch of 1/8 inch, each exact revolution of the leadscrew will cause the nut to advance 1/8 inch. If the nut is made to carry a suitable holder provided with a pointed tool, and this is brought into contact with the truly cylindrical workpiece, then a helix will be circumscribed thereon, and the distance between any two adjacent helices will be 1/8 in., quite regardless of the actual diameter of the workpiece and regardless of the actual speed of rotation, because if the work speed is altered, so is the leadscrew speed in the same proportion.

Fig. 1 Illustrating the basic principles of lathe screwcutting.

Fig. 2. Inside view of the carriage apron of a small lathe. The pinion at the left engages with a rack fixed to the lathe bed. The half-nuts may be seen at the right, and leadscrew indicator is fitted at the left.

(The plummer-block type bearer held a non-standard anti leadscrew deflection bush. This became unnecessary with a change to the square thread form leadscrew.)

In practice the nut is split into two pieces or “halves” each provided with a slideway backing, mounted in corresponding guideways so that by means of a hand-lever and cam-type mechanism each half can be moved radially outwards, thus disengaging the leadscrew. The leadscrew nut thus becomes known as “the half-nuts”, “the clasp nut”, or the “split nut”.

The photograph Fig. 2 is an inside view of the apron of a small lathe and will give an idea of the arrangement. The half-nuts are shown in the disengaged position. The small pinion at the left engages with a rack for hand traversing the lathe carriage when required.

A pair of half-nuts suitable for the apron shown may be seen in the photograph, Fig. 3.

Referring again to our basic diagram, Fig. 1, the initial helix circumscribed on the workpiece may be regarded as the first of a series of “cuts” or “threading passes” as may be seen again at the foot of Fig. 4 which, if read upwards, shows how a screw thread is formed by a succession of passes each a little deeper than the previous one, until the thread is complete. The diagram, of course, indicates only a few of the greater number of passes required before a full depthing and sizing is reached.

Fig. 3. A pair of half-nuts for use in a small lathe.

Fig. 4. Showing how a screw thread is formed by a succession of cutting passes of progressively increasing depth.

ALTERING THE PITCH.

CALCULATIONS

From what has already been said it follows that if the leadscrew (Fig. 1) can be caused to revolve at exactly one half the speed of the component, and the leadscrew has 8 threads to the inch, then for each half revolution of the leadscrew the component will make one complete turn and one complete helix will be circumscribed. One complete helix for each half revolution of the leadscrew equals 16 complete helices for 8 revolutions of the leadscrew. For each 8 revolutions of the leadscrew the tool will move through a distance of one inch: accordingly 16 helices or threads to the inch would be formed on the component.

In our basic example (Fig. 1) the leadscrew could be made to rotate at half the speed of the component by removing the two 45 teeth gears, A and B, and fitting a driver of 30 teeth at A, and a driven of 60 teeth at B, on the leadscrew.

Actually, of course, it is not possible to so relate the distance between the lathe spindle and the leadscrew that no more than two gears of equal or different size may be arranged to meet all ratio needs, so what is known as a “quadrant” or “change gear arm” is provided, upon which intermediate gearing may be assembled and adjusted not only for desired ratios, but to bridge the gap between the lathe spindle or tumbler reverse and the leadscrew gear.

The photograph Fig. 5 shows a typical arrangement for a small lathe of the instrument type. Each of the slotted quadrant arms carries a movable “stud” for the intermediate gearing, and the whole quadrant may be pivoted about the leadscrew axis by releasing the locking handlever. This illustration also shows a tumbler reverse mechanism which may be seen in its three positions in the diagram Fig. 6.

Fig. 5. Showing the tumbler-reverse and change-gear quadrant on a small lathe. This all-steel quadrant with a single front locking lever is the author’s own design.

Some earlier lathes of this kind were sold without a tumbler reverse mechanism, but when one is fitted, suitable driving wheels for the quadrant gearing are mounted on an extension spigot S which is integral with the final driven gear G of the tumbler reverse. For later explanations it will be convenient to refer to gears fitted to this spigot as “first gear drivers” and to call the spigot itself “the tumbler reverse output spigot”.

Fig. 6. A tumbler-reverse mechanism shown in three positions: neutral above, forward and reverse below.

Normally on lathes of this kind, the first gear driver will rotate at exactly the same speed as the lathe spindle. The tumbler reverse is used either to cause the leadscrew to revolve “backward” for cutting left-hand threads, or to correct the direction of rotation of the leadscrew in the event of a gear train being of a nature that makes a correction necessary.

For a simple lathe of the type illustrated, a set of gears is provided, and with them it is possible to assemble a great variety of ratios between the lathe spindle and the leadscrew. These gears are known as “change gears”. Special mention is made of these because of certain differences in the way in which sets are sometimes made up. For this particular lathe it is customary to provide a set of gears as follows: Two having 20 teeth, and one each of 25, 30, 35 and so on up to 75 teeth together with one of 38 teeth for reasons which will be explained later. However, in future such a set will be referred to as “20-75 by fives” or merely as a “set rising by fives”. Change gears rising in size by four teeth at a time, say 24, 28, 32 and so on are not unknown and, of course, such a set would be referred to as “rising by fours”. But what should be noted is that for example, a gear of 32 teeth would be “special” to a set rising by fives while a 55 teeth gear would be “special” to a set rising by fours and a gear of 33 teeth would be “special” to both sets.

Before giving a general formula for change gear calculations it will be helpful to consider the basic requirements for cutting a thread of 24 to the inch with a leadscrew of 8 threads to the inch.

If we wish to cut, over a given length, three times as many helices on a component as are contained in the same length of leadscrew, the leadscrew must rotate at one third the speed of the component. This can be arranged by using a 20 teeth gear as a first gear driver and a 60 teeth gear on the leadscrew, but as these two gears will be positioned too far apart for direct meshing, the gap is bridged with spare change gears, which for this purpose become temporarily known as “idle gears”, or “idlers”. Any number of idle gears may be interposed without affecting the ratio between the first driver and the last given gear although design limitations usually restrict the possible number of idlers to two. The diagrams, Fig. 7, will give an idea of the necessary 1:3 ratio, the left hand drawing showing the gearing “straightened out” for clarity, and the right hand drawing showing the gearing as it would be assembled on the lathe.

The idlers A and B, Fig. 7, are shown as a 65 and 40, but their actual size is of no importance provided they are capable of bridging the space between the first 20 driver and the last 60 driven.

Some find it difficult to understand that the interposition of one or more idle gears cannot affect the ratio between the first driver and the last driven gear. One way of looking at the question is to consider that the teeth velocities of the intermediate idlers must be exactly the same as the teeth velocity of the first driver, therefore the effect of meshing the leadscrew gear with the idler gear cannot differ from the effect of meshing the leadscrew gear directly with the first gear driver. Again, idle gears can no more affect the ratio between the first driver and the last driven than could a chain, or the number of links in a chain that may be needed to couple the first and last gear. What does happen is that small idlers will revolve more quickly and large idlers more slowly relative to the first driver, but as a drive is not being taken from the hub of the idle gear, or gears, their speed of rotation can be of no consequence. It is worth noting, however that in a manner similar to that of the tumbler reverse, with the interposition of one idle gear the direction of rotation of the last driven gear will be the same as that of the driver, and the interposition of two idle gears will reverse the direction of rotation of the final driven gear relative to the first driver.

Fig. 7. An example of a simple gear train. Gearing shown is for 24 tpi with an 8 tpi leadscrew.

At the left the gear train has been ‘straightened out’ for clarity. At the right the same gearing is shown as assembled on a quadrant. The tumbler-reverse (TR) although shown, plays no part in the ratio.

That the leadscrews of some of the smaller lathes have left hand threads may be explained by the fact that a handwheel, which can be fitted to the leadscrew at the right-hand end, may be turned clockwise to feed the carriage toward the chuck.

Before continuing with details of a general formula, it will be convenient to mention that although a leadscrew of 8 threads to the inch appears to be the standard today for the range of smaller lathes, an earlier machine may be found to have a leadscrew of 10 threads/inch. With larger industrial lathes having leadscrews of 4 or even 2 threads/inch we are not really concerned at this stage because they will be fitted with selective gearboxes and calculations will not normally be required. Accordingly, to keep explanations within reasonable bounds it was felt best to deal chiefly with calculations for leadscrews of 8 threads/inch. Metric leadscrews will be dealt with later.

The simple examples already given for 8,16 and 24 tpi with a leadscrew of 8 tpi showed that gearing was required in the ratios 1:1, 1:2 and 1:3, or, in terms of the number of threads to the inch of the leadscrew to the number of threads to the inch for which the lathe was to be geared, 8:8, 8:16, and 8:24, and finally in terms of the number of teeth in the driving and driven gears: 45:45 (or any two of equal size), 30:60, and 20:60.

Accordingly, the number of teeth in the driving gear divided by the number of teeth in the driven gear, or leadscrew gear, is equal to the number of threads to the inch of the leadscrew divided by the number of threads to the inch for which the lathe is to be geared, a statement which may be condensed to the convenient form:

The abbreviated form Drivers/Driven will be used in all subsequent examples. The reason for the plural in Drivers arises from the fact that there may be more than one driver and more than one driven gear in a “compound train”, as will be explained shortly. But when there are more than one of each, the expression Drivers/Driven should be read as “The multiple of the number of teeth in individual driving gears divided by the multiple of the number of teeth in individual driven gears.”

USE OF FORMULA

Suppose we wish to gear a lathe for a thread of 9 to the inch, and the leadscrew is of 8 to the inch, substituting the known figures we have:

accordingly a first driver of 8 teeth driving a leadscrew wheel of 9 teeth would give the desired ratio, but as gears of only 8 and 9 teeth would be impracticable we have to multiply both numerator (8) and denominator (9) by some number that will increase the number of teeth to a convenient figure. If it is known that the change gears rise in sizes by five teeth increments, then there is no point in multiplying both numerator and denominator by any number except 5, or multiples of 5:

Had the gears risen by increments of four teeth, the gearing, with an 8 t.p.i. leadscrew would become:

In either instance, of course, it would be necessary to interpose one or two idle gears of any convenient size to bridge the gap between the first driver and the leadscrew gear. One is often sufficient, although it suited the writer’s purpose to keep two gears spare to the set (a 65 and 40) more generally in place on the intermediate quadrant studs. But this means a larger range of screw gearing can be set by changing only the one leadscrew gear and moving the idlers to suit the new diameter.

Further examples similar to the foregoing are easily calculated mentally. Nevertheless it will be revealing to set out the gearing for all threads of from 6 to 15 tpi. A leadscrew of 8 tpi will be assumed:

What should be noted in the list is that the driver remains at 40 throughout the range, and if this is replaced by a 20, then the threads/inch for which the lathe will be geared will be exactly double in each case. For example, the 9 tpi will increase to 18 tpi and the 13 to 26 tpi.

COMPOUND GEAR TRAINS

With a range of change wheels of from 20 to 75 teeth, the limit for simple reduction gearing consisting of one driver and one driven, (or leadscrew gear) is reached at the 20:75 ratio, which, with a leadscrew of 8 tpi sets the lathe for cutting 30 tpi. Gearing for a greater number of threads/inch therefore calls for the use of “compound gearing”.

One example of compound gearing is to be found in the wheels required for a thread of 40 to the inch. The same basic formula is used:

and substituting the known figures for a leadscrew of 8 tpi we have:

but if we now multiply 8 and 40 by 5, we get 40/200, and although this halves to 20/100, the 100 gear is outside our range. We therefore resolve 8/40 into factors:

the factors are then raised to available change gear sizes by multiplying both 2 and 5 by 10; and 4 and 8 by 5:

The next question is, having found the gears, how are they set on the lathe?

What should be remembered here is that all gears in the numerator side are driving gears, and all gears in the denominator side are driven gears. It is generally necessary or more straightforward, however, to position the largest driven gear on the leadscrew, but provided the driven gears remain in a driven portion of the train the ratio will not be affected. Hence we may reverse or exchange the denominators to 20/40 x 20/50 and the gears would be set on the quadrant in the manner shown in the diagram, Fig. 8. Gear meshing limitations would prevent the direct engagement of the 20 first driver (No. 1) with the first driven 40 (No. 2), so the idle gear (A), here shown as a 65, is interposed. The 40 gear is coupled to the second 20 driver (No. 3) so that both revolve together, and the second 20 driver is then engaged with the 50 leadscrew wheel. (No. 4).

SCHEMATIC GEAR TRAIN PRESENTATION

The customary method for showing actual gear meshing sequences or arrangements in tabulated form calls for the use of fairly complicated headings to show not only the first driver and leadscrew gear, but whether or not the intermediate quadrant studs carry only an idler, or two wheels keyed together, as for compound trains. Thus the written layout of individual examples for explanatory purposes becomes sufficiently tedious as to discourage the presentation of more than an absolute minimum number, a circumstance which would interfere seriously with later discussions on gearing for metric pitches and allied matters.

Fig. 8. An example of a single-compound gear train. Gearing shown is for cutting 40 tpi with an 8 tpi leadscrew.

At the left the gear train has been ‘straightened out’ for clarity. At the right, although the tumbler-reverse (TR) is shown, it plays no part in the final ratio.

With the foregoing disadvantages in mind a need was felt for a more straightforward method for indicating the actual positions of the gears on the lathe: a method which once explained would not call for the repetition of headings referring to first drivers, studs and leadscrew gear, or for any special mention of gears which are keyed together on the same quadrant stud.

The schematic method requires headings only for explanatory purposes, and here are three examples:

In each case the lines connecting the gears show that the gears so joined are in direct mesh. Gears placed one above the other show that they are coupled or keyed together. Letter A is short for ‘ANY’, and refers to any spare gear of suitable size that may be used as an ‘idler’ to connect main train gears that are too small to mesh directly together.

The gear at the extreme left is always the first driver, and the gear at the extreme right always the leadscrew wheel. Hence, if only one idle wheel had been used in the simple train, the layout would read:

20 — A — 60

It was convenient to use letters instead of numbers in terms of gear teeth to illustrate the double compound train because, when resolving a fractional solution into a practical layout it is necessary to ascertain that the sum of the number of teeth held by gears D and E exceeds the sum of C plus F by a minimum of five teeth otherwise C and F will mesh and will either lock the train solid, or prevent the proper meshing of D and E.

Sometimes it is useful to show the idle gears actually used, in which case the layout for 24 tpi with an 8 tpi leadscrew might read:

20 — 65 — 40 — 60

In a single compound train the idle gear may be placed between the first or second pair of main gears, and provided that the driving gears remain in a driving position, the ratio will not be altered:

20 — 50

20 — A — 40

will give exactly the same ratio as

20— A — 40

   20 — 50

Please also notice (1) a simple train such as

20 — A —A — 40

would be written for arithmetical checking purposes as

Fig. 8A. An example of a double-compound gear train. Gearing shown is for a metric pitch of 1.75 mm. to be cut from a leadscrew of 8 tpi. (This particular ratio calls for use of a 21T gear).

(2) The single compound train

(3) The double compound train

B D F being drivers and C E G the driven gears. An example of a double compound train is given in Fig. 8A.

FURTHER CALCULATION NOTES

The calculation of change wheels for a thread of 19 to the inch is rather less obvious than the examples previously given. Assuming a leadscrew of 8 tpi we have:

If we multiply 8 and 19 by 5 we get 40/95, which would serve well enough had we a 95 change gear, but we assume that the set stops at 75 teeth. What should be noted now is that if no wheel is available that is an exact multiple of 19, then precision gearing is impossible. However, the change gear set will probably include a special wheel of 38 teeth, whereupon our initial formula will read:

where the multiplication by 2/1 is simply written in to hold the ratio. Proceeding from here, if the 8 and 1 are now multiplied by 5 we have

and finally, multiplying 2 and 5 by 10 gives:

which could be set on the lathe:

20 — A — 38

   40 — 50

In the example just given, 19 is, of course, a prime number, and the impossibility of exactly