Table Of ContentTHE EFFECT OF TAPER PINS
ON THE
TORSIONAL PROPERTIES OF CIRCULAR SHAFTING
THESIS
Suomitted in partial fulfilment
of the requirements for the
degree of
MASTER OF IÎRCHANICAL KNGIiEERING
at the
POLYTECHNIC INSTITUTE OF BROOKLYN
JACK PAULL
May 1950
Approved:
Theeii lAdviser
Head of De
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TABLE OF CONTENTS
Page
Illustrations ii
Acknowledgements iii
Dedication iv
Abstract V
I. INTRODUCTION 1
II. ANALYSIS OF SUBJECT 3
III. MATHEMATICAL ANALYSIS 7
IV. DESIGN AND CONSTRUCTION OF SPECIMENS AND APPARATUS 12
V. TEST PROCEDURE 22
VI. RESULTS OF TESTS 24
VII. DISCUSSION OF RESULTS 26
VIII. SUGGESTIONS FOR FUTURE INVESTIGATIONS 42
IX. BIBLIOGRAPHY 43
TEST DATA APPENDIX 45 - 57
ILLUSTRATIONS
Photographs and Drawings Page
PLATE A: TAPER PIN ENDS MOUNTED IN LÜCITE 14
PLATE J: FIVE SETS OF SPECIMENS WITH CHUCKS 14
PLATES B THROUGH I:
PHOTOMICROGRAPHS OF PIN MATERIAL . 15
PLATE K: ADAPTER CHUCKS l6
PLATE L: POINTER HALF OF EXTEN80METER 17
PLATE M: DIAL HALF OF EXTENSOMETER 18
PLATE N: SPECIMEN #2 IN EXTENSOMETER 20
PLATE 0: CONTROL SPECIMEN #13 IN EXTENSOMETER 20
PLATE P; SPECIMEN #26 IN EXTENSOMETER 20
PLATE Q: VIEW OF SPECIMEN #2 MOUNTED IN MACHINE 21
PLATE R: VIEW OF TORSION TEST MACHINE WITH
SPECIMEN #2 READY FOR TEST 21
PLATE S: VARIOUS SHAFT FAILURES 23
PLATE T; BROKEN HALVES OF SHAFT FAILURE HELD TOGETHER
TO SHOW ELONGATED HOLE f4ADE BY PIN 23
SPECIMEN DRAWINGS SP-1 THROUGH SP-3Û APPENDIX 58 - 87
ii
ACKNOWLEDGEMENTS
The author wishes to thank Èïr, E. Rudolph of the R, C, A, Victor
Division for his cooperative efforts in supplying the materials necessary
for the tests, and Mr. W. T. Engel, also of the R. C. A. Victor Division,
for his helpful advice in the interpretation of test results.
The photography was ably carried out by Mr. Seymour Lieberman, whose
suggestions helped make this thesis a success.
Florence Pauli, who edited and typed the first draft, was of great
assistance to the author in completing the thesis.
ill
DEDICATION
In loving appreciation for patience and indulgence for these many
years, I dedicate this paper to Florence, my wife.
iv
ABSTRACT
The author has shown, analytically and experimentally, that when a part
such as a gear or cam is taper pinned to a shaft, a ratio of average pin
diameter to shaft diameter of «395 makes for equal stress in pin and shaft
when the pin and shaft materials have equal shear strengths. When the pin
material is of different shear strength from that of the shaft material a
new ratio would be determined. When the pin used is of higher strength than
the shaft, the optimum ratio'of equal stress would be lower than .395; for a
pin of lower strength the optimum ratio would be hi^er than .395. It is now
possible for the designer, knowing the material and diameter of a shaft to
which a part is to be assembled, to select a pin of such a sise that it,
rather than the shaft, would fail and yet would transmit torsional loads
adequately.
The writer has found that a light press fit between shaft and hub
together with pinning will increase the total torque which an assembly will
transmit satisfactorily.
I. INTRODUCTION
The most frequently recurring problem of thé machine designer is the
attachment of links or "members" of a machine to drive shafting. The methods
of making such attachment are many, the most common being by screws, various
types of keys or pins and interference fits.
Locating a gear or lever by means of set screws most frequently requires
that a "flat" be machined on the shaft. This type of fastening is useful as
a temporary fastening under light loads. The key driven into ways machined
in both the shaft and hub is one of the best means of transmitting torque, but
is relatively poor in its resistance to end pressure. In addition, the keyway
cut into the fitted parts predetermines the position, radially, of hub and
shaft. This feature does not affect the attachment of gears, pulleys and
wheels but makes its use with cams ani coordinated levers less useful. The
interference fit is of use on small shafting but does not offer positive
assurance of retaining the positioning of the joined part; particularly under
impact or repeated loading. Moreover, frequent removal of the part from the
shaft tends to break down the interference especially in the force and drive
fits and leaves a heavily scored shaft.
The type of fastening which seems to be the best one frcwn an all-around
point of view for many links and cams is the pin. It is positive in trans
mitting torque and resisting end thrust, and permits the necessary machining
after the assembly of the parts. The taper pin has certain advantages over
the dowel or straight sided pin in that the taper pin will drive easier, it
will bring the holes in shaft and hub into alignment as it is driven, it can
be more easily removed and finally the tapered hole is easier to ream to size.
It is the practice in assembling cams at the company with which the writer
is employed to mount a set screw in the hub of the cam and to assemble it on
the shaft with a light press fit. The position of the cam radially on the shaft
is established by hand actuated trials of the linkage operated by the cam,
using the set screw for temporary positioning. When the position is fixed, the
hub and shaft are drilled and reamed for a taper pin.
II. ANALYSIS OF SUBJECT
When it is decided to use a taper pin to locate a part on a shaft,
thought must be given to the size of the pin needed, keeping in mind the
shaft diameter, the hub diameter, the kind of material of which the pin
is to be made and the magnitude and kind of loads being applied. In most
cases it is possible to increase the factor of safety of a designed assem
bly by increasing the size of a loaded part. In the case of a member being
pinned to a shaft, increasing the size of the pin would decrease the size
of the shaft at the point where the pin is located; increasing the size of
the shaft would not strengthen the pin. It would, therefore, be necessary
to increase the size of both shaft and pin to gain strength for the joint.
This, at the very least, would make for a cumbersome and more expensive
connection. It would seem, therefore, most desirable to design a connec
tion which would provide the greatest strength in both the shaft and pin
when it is known that the tear-out strength of the hub is adequate.
With the above points in mind, the writer investigated available
literature to determine raathenatical and test methods which would permit
relating pin and shaft diameters to give the most efficient connection.
Seely (1) showed the effect of circular holes on specimens under
tension by the use of elastic theory. When a tensile load is applied
through a pin which fills the hole, a high compressive stress is devel
oped directly underneath the hole. Further out along the line of action
of the pin but away from the edge of the hole the stress reduces to zero.
The concentration of tensile stress at the edge of the hole transverse to
the line of action is about the same as occurs when no pin fills the hole,
that is, about three times the tensile stress at the edge of the specimen.
