Thread-forming fastener having dual lobulation and dies for making the same

A thread-forming screw has a work-entering section for forming a thread in a workpiece and a work-holding section adjacent thereto. Both sections are of an arcuate, polygonal lobular configuration in cross-section. The amount of lobulation on the holding section is considerably less than the lobulation on the work-entering section, which is of such magnitude as to insure effective thread-forming at low torque. The lobulation on the holding section is preferably just sufficient to effect a locking action with the thread of the workpiece and also to improve the stripping torque of the screw from the workpiece. The work-entering end of the fastener also has a pilot thread of about one turn and with a uniform width over 360.degree. and sized approximately the same as the pilot hole in the workpiece to prevent cocking of the fastener as it is initially inserted into the pilot hole. Thread-rolling dies for forming the fastener have a die section with grooves of equal depth to roll the pilot thread.

BACKGROUND OF THE INVENTION 
This invention relates to improvements in thread-forming fasteners and to 
thread-rolling dies used for making the same. 
One type of thread-forming screw which has been commercially successful in 
many parts of the world is that of the type shown in the U.S. Pat. No. 
3,195,196 to Phipard that issued July 20, 1965. The screw shown in that 
patent is of a type having a lobular pitch surface cross section in the 
form of a generally arcuate polygon with an odd number of arcuate sides 
merging gradually with intermediate thread-swaging lobes. The 
work-entering end of the screw is tapered toward the work-entering point 
of the screw for insertion into the workpiece pilot hole. Preferably the 
screw has three lobes. A screw of the foregoing type has a generally 
uniform lobulation throughout its threaded length. Since the work-entering 
end forms the thread and the holding or shank section subsequently mates 
with the thread in the workpiece, the thread must have a lobulation that 
provides a low driving torque for thread formation and yet a high locking 
ability for engagement with the workpiece. Consequently, the amount of 
lobulation in the screw is necessarily a compromise to effect the best 
possible combination of low-driving torque and good locking ability. 
Generally, the screws are designed to favor thread forming. 
It has also been proposed to produce thread-forming fasteners with a 
lobular work-entering portion and a circular holding section. Typical of 
such screws are those shown in U.S. Pat. Nos. 3,246,556 to Phipard that 
issued Apr. 19, 1966 and to Muenchinger 3,681,963 that issued Aug. 8, 
1972. However, where the holding section is of circular cross section 
there is a reduction of stripping torque and a reduction in the effective 
locking action with the workpiece as compared to the lobular form. Because 
the holding section is of circular cross section there are no lobes or 
like areas that tend to bite into the workpiece to effect a locking action 
and an increase in both strip torque and locking action. 
Another problem in self-tapping fasteners resides in the difficulty in 
aligning the fastener with the hole in the workpiece, particularly in 
workpieces of substantial thickness. When a self-tapping fastener is 
introduced into the pilot hole of a workpiece, the fastener tends to have 
its central axis lie at an angle to the central axis of the hole of the 
workpiece. The reason for this lies in the fact that the tapering lead 
thread of the screw tends to trace a spiral path with the result that in 
any cross section there is substantially no more than one point from the 
thread whose distance from the axis is one half the pilot hole diameter. 
Thus, in theory the screw axis at the starting may have an angularity as 
much as the angle of the taper of the thread. Such angularity or "cocking" 
of the screw is objectionable in that there is difficulty in starting the 
screw in a threading operation without undue end pressure. Also the screw 
may end up "cocked" when fully threaded into the workpiece. 
OBJECTS AND SUMMARY OF THE INVENTION 
An object of this invention is to provide a thread-forming fastening device 
in which the tapered work-entering section is of a substantial lobulation 
to insure ease of thread formation whereas the holding section of the 
screw is of a considerably lesser lobulation, namely only a very moderate 
out of round to the extent necessary to insure an adequate prevailing 
torque and locking ability of the screw. This is in contrast to present 
day lobular thread-forming screws wherein the lobulation tends to favor 
thread-formation rather than holding power. 
A further object of this invention is to provide a thread-forming fastener 
with dual lobulation of the type and for the purpose stated in which the 
relative lobulation of the work-entering section and the work holding 
section is defined within certain empirical limits which will result in a 
screw that is more effective for both threading and holding than has been 
possible with screws of the types referred to previously herein. 
Another object of this invention is to provide a self-threading fastener of 
the type stated in which there is a pilot thread of about one turn which 
is used to prevent cocking of the fastener as it is introduced into the 
pilot hole of the workpiece and also to reduce the amount of end pressure 
needed to start the screw. This pilot thread has a crest cross section of 
substantially uniform width throughout 360.degree. and has a maximum 
crest diameter that is less than the maximum crest diameter of thread in 
the work-holding section. The uniform width of the pilot thread is 
slightly less than the diameter of the pilot hole in the workpiece. 
A still further object of this invention is to provide a die pair for 
forming the fastener of the present invention, each die of the pair having 
thread-forming ridges for rolling a thread on the holding section and the 
tapered thread formation on the work-entering section, and a further 
section having ridges and grooves of equal depth to form the pilot thread. 
In accordance with the foregoing objects the fastening device has a 
continuous rolled thread on both its work-entering section and its 
work-holding section and with the thread formation on the work-entering 
section being tapered and having a pitch surface cross section in the form 
of a generally arcuate polygon with an odd number of arcuate sides merging 
gradually with intermediate thread-swaging lobes. The thread formation on 
the work holding section likewise has a pitch surface cross section in the 
form of a generally arcuate polygon with an odd number of arcuate sides 
merging gradually with intermediate lobes. The number of sides and lobes 
in the holding section are respectively the same as the number of sides 
and lobes in the work-entering section, and with the radius of curvature 
of the arcuate sides in each section being substantially greater than the 
radius and curvature of the lobe in that section. The lobulation in the 
holding section is substantially less than the lobulation in the 
work-entering section, the lobulation being defined as the maximum 
distance from the crest of the thread at an arcuate side to the circle 
that inscribes the crest of the thread at the adjacent lobes. The 
lobulation in the work-entering end is sufficient to provide a low-torque 
thread-forming action while the lobulation in the holding section is a 
sufficient departure from a circular configuration to enhance the locking 
effect in the holding section and also to increase the stripping torque 
when the holding section is threaded into the workpiece. These improved 
results are due to the limited amount of elastic deflection of the lobular 
regions of the holding section when the screw is tightened in the 
workpiece thread. 
The maximum and minimum lobulation of each section is defined within limits 
which are hereinafter specified.

DETAILED DESCRIPTION 
Referring now in more detail to the drawings there is shown in FIGS. 1-3 a 
screw blank 2 having at one end thereof a hexagonal driving head 4 and 
adjacent flange washer 6. The blank also comprises a shank section 8 of 
lobular, arcuate triangular cross section and an intermediate tapered 
transitional portion 10 also of lobular, arcuate triangular cross section. 
However, the extent of lobulation, namely the amount of out of round, of 
the tapered transitional portion 10 is greater than the extent of 
lobulation in the section 8, as may best be seen from FIG. 2. Forwardly of 
the tapered transitional portion the blank has a lead section 12 also of 
lobular arcuate triangular cross section and preferably the same as that 
in the portion 10. As will be seen hereafter, when the blank 2 is passed 
between the thread rolling dies of FIGS. 9 and 10, the thread formation on 
the holding section B (FIG. 4) will be rolled out of the metal of the 
section 8 whereas the thread formation on the work-entering section A 
(FIG. 4) will be rolled on the metal on the tapered transitional portion 
10 and lead section 12. 
The lobular cross section of the blank section 8 is defined by the lobes 
14,14,14 which merge with arcuate sides 16,16,16 having longer radii of 
curvature than that of the lobes 14,14,14. Likewise, the transitional 
portion 10 has lobes 18,18,18 and intermediate sides 20,20,20, the latter 
having longer radii of curvature than do the arcuate sides 16. The 
respective arcuate sides and lobes are all symmetrically arranged about 
the longitudinal axis 22 of the blank 2. The lobes 18 form respective 
axial continuations of the lobes 14, although the lobes 18 are more 
sharply defined than are the lobes 14. The transverse width of the blank 
taken through the axis 22 is uniform throughout 360.degree.. An important 
aspect of this invention, however, lies in the fact that the 
cross-sectional configuration of the section 8 is not circular but is 
lobular, but with a lesser amount of lobulation than that which is in the 
transitional portion 10 or the lead sections 12. The preferred 
relationship between the lobulation in the section 8 and that in the 
portion 10 and section 12 will depend upon the desired relative lobulation 
in the finished screw between the work-entering section and the holding 
section. These preferred relative amounts of lobulation have been 
analytically determined, and will be hereinafter more fully described. 
FIGS. 4-7 show the screw 13 that is formed by rolling the blank of FIGS. 
1-3 in the dies of FIGS. 9-10. More particularly, the screw 13 comprises a 
work-holding zone or section B and a work-entering zone or section A as 
shown in FIG. 4. It will be seen that the section A runs from the 
beginning of the thread, namely at or near the work-entering tip 26 to the 
maximum diameter part 15 of the tapered thread formed in the work-entering 
section A. The work-holding section B extends from the maximum diameter 
part 15 of the work-entering section A for a predetermined length, usually 
the balance of the thread. This generally runs substantially to the washer 
6. The juncture of the zones A and B is not abrupt but preferably the 
zones A and B gradually and smoothly merge with one another. 
The thread formation in the work-entering section A is of the usual profile 
having a root 28, a pitch 30 and a crest 32. The pitch line is indicated 
by broken line 30. Furthermore, the root, pitch, and crest cross sections 
are each in the form of a generally arcuate polygon with an odd number of 
arcuate sides merging gradually with intermediate arcuate lobes. More 
specifically, and as is preferred, the arcuate polygon is a triangular 
one. Furthermore, the tapering of the thread formation on the 
work-entering section A results from the fact that the crest cross section 
progressively diminishes in width, the taper being toward the tip 26. 
Consequently, and as best seen in FIG. 6, the work-entering section A may 
be said to have thread-swaging lobes 34,34,34 joined by arcuate sides 
36,36,36 gradually merging with the lobes 34,34,34. The crest 
cross-section, the root cross section, or the pitch cross section, as the 
case may be, will each be a lobular, arcuate, triangular shape similar to 
that shown in FIG. 6. 
The thread formation in the work-entering section A continues into the 
work-holding section B wherein the pitch 30 of the thread as well as the 
root 28 are the same as in the section A. The crest 38 is not tapered but 
is of uniform width throughout 360.degree.. By uniform width it is meant 
that the distance between any two parallel planes tangent to the crest 
will be uniform or constant regardless of the orientation of those planes. 
Preferably also, this uniform width throughout 360.degree. is also true of 
the pitch and root. In any event and as best seen in FIGS. 6 and 7, the 
holding section B has a crest cross section with lobes 40,40,40 that merge 
with intermediate sides 42,42,42. 
As will best be seen by a comparison of FIGS. 6 and 7, the amount or extent 
of lobulation of the holding section B is considerably less than that of 
the work-entering section A. The moderate amount of lobulation in the 
holding section B will result in some elastic deflection of the lobular 
portions 40 due to stress concentrations therein. Consequently, an 
improved locking action of the holding section B thread with the thread 
formed in the workpiece P will be provided. 
Also on the work-entering section A intermediate the tapered thread 
formation and the tip 26 is a pilot thread 44 which may be a thread 
formation of one or more turns, as desired. The pilot thread 44 merges 
with the tapered thread formation of the zone A; however, the pilot thread 
44 is not tapered but is of uniform width throughout 360.degree.. This is 
best shown in FIG. 5, which illustrates the pilot thread as having a crest 
diameter approximately the same as the diameter of the hole 46 in the 
workpiece. The one or two turns of pilot thread 44 result in the alignment 
of the screw axis 22 approximately with the longitudinal axis or center 
line of the workpiece hold 46, thereby to prevent cocking of the screw 
during beginning of the threading operation. The pilot thread 44 also 
reduces the amount of end pressure required to start the threading 
operation. The crest diameter of the pilot thread 44 is preferably the 
same as or slightly less than the pitch diameter 30 for most general 
applications. 
FIGS. 8 and 8a show the manner in which the preferred amounts of lobulation 
in the sections A and B can be determined. FIG. 8a shows a value K, which 
is a measure of out of roundness or lobulation. Thus, the value of K or 
lobulation may be defined as the maximum distance from the crests of the 
thread at an arcuate side 36 or 42, as the case may be, to the circle 48 
that inscribes the crest of the thread as shown in FIG. 8a. This value of 
K is plotted as a function of the diameter of the stress area, abbreviated 
as DSA. For a screw of circular cross section (crest, root and pitch) the 
stress area is the area of the circle whose diameter is the arithmetic 
mean of the pitch diameter and the root diameter of the thread. For a 
thread of lobular cross section the definition is the same except that the 
root diameter is measured at the point of maximum root diameter at a lobe 
in the holding section B. 
The straight or substantially straight lines 50 and 52 of FIG. 8 (not to 
scale) were determined by computation of the stress area (and hence its 
diameter) for various known lobular arcuate triangular screws, such as 
U.S. National Fine and National Coarse screw series in addition to various 
standard metric sizes. A scattering of points (not shown) based on out of 
round produced the lines 50, 52 which were approximately at the boundary 
of the spread of points plotted. In each instance the lobulation was 
uniform throughout. Consequently, for each DSA value the ordinate 
extending between plots 50 and 52 represents the range of maximum and 
minimum lobulation for the work-entering section A. That same ordinate 
line extended downwardly to cut across the plots 54, 56 will produce the 
maximum and minimum lobulation for the holding section B for that 
particular screw. Like lines 50,52, it is assumed that plots 54 and 56 are 
also substantially straight lines. 
It has been found that the slope of the line 50 is substantially 0.042 and 
the line 50 intersects the zero line for DSA at a point 50a which is 0.05 
millimeters. The line 52 intersects the zero point for DSA at 52a, which 
is 0.04 millimeters and the slope of the line 52 is approximately 0.020. 
Line 54 representing the maximum holding section lobulation has a slope of 
substantially 0.0176 and intersects the 0 line for DSA at 54a which is 
also 0.04 millimeters. Finally, line 56 has a slope of 0.0025 and 
intersects the origin 56a of the graph of FIG. 8. 
Thus, the work-entering section, the maximum and minimum lobulations K 
(expressed in millimeters) are as follows: 
Maximum K = 0.042 DSA + 0.05 
Minimum K = 0.020 DSA + 0.04 
The maximum and minimum lobulations K (expressed in millimeters) for the 
holding section are as follows: 
Maximum K = 0.0176 DSA + 0.04 
Minimum K = 0.0025 DSA 
The range of lobulation in the work-entering section may vary depending 
upon the material of the workpiece. In any event, the lobulation can be 
designed to favor low torque threading. On the other hand, the lobulation 
in the holding section need only be sufficient such that the lobes therein 
are deflected so as to provide a locking action with the workpiece. For 
thin metals only a slight amount of lobulation may be needed. 
With further regard to the minimum lobulation of the holding section B, the 
value K = 0.0025 DSA is a practical minimum lobulation that can be 
fabricated and measured. The suitability of this K value may be verified 
by analogy with the contact stress between cylinders of different 
diameter, one rolling within the other, and having a load applied radially 
outwardly through the center of the smaller circle. By this analogy it is 
believed that the radial force on the rolling cylinders is analogous to 
the radial component of force of the thread engaging its mating thread 
where elastic materials are involved. Referring to FIG. 8b, the larger and 
smaller circles C1, C2 have radii R and r respectively. The value of K 
represents the out of round of the lobular form and the load through the 
centers of the circles represented by P. The elastic deflection of the 
cylinders represented by circles C1 and C2 is assumed as the value K. If K 
= 0.0025 DSA, then K = 0.005R. The relationship of r and R is known for a 
given K. Thus, for K = 0.005R, the value r = 0.98134R. Also it may be 
readily derived from the known equation a.sup.2 = K (2r -K) that the 
contact zone a = 0.099R where a is the half chord of the circle C2 shown 
in FIG. 8b. 
The average unit compressive stress, denoted as T, may be derived by using 
the so-called Hertz equations and related material which are known and 
may, for example, be found in M. F. Spotts, Mechanical Design Analysis, 
pp. 166-171, published in 1964 by Prentice Hall, Englewood, New Jersey, 
U.S.A., especially the formulae at Figure 9.6 on p, 171. Assume that the 
cylinders C1, C2 are of steel (modulus of elasticity E1 = E2 = 3 .times. 
10.sup.7 psi) and that the load P = T(2a). Using the known Hertz formula: 
##EQU1## 
It can be determined that T = 8936 psi or 61614 Kilo Pascals. 
For a determination of maximum compressive stress the known Hertz equation 
below may be used: 
##EQU2## 
Using the same values as above, it can be derived that the maximum stress 
is about 13,276 psi (91538 Kilo Pascals). In a thread the stress would 
actually be distributed over a smaller area per unit length of the screw 
which would tend to raise the maximum stress. Nevertheless, even doubling 
this maximum stress is well within the elastic limits of the materials. 
The following represent test data (Metric and English) on the screw of the 
present invention compared with (1) standard tri-lobular screws having 
uniform lobulation in the holding and thread-forming sections (designated 
Type I), and (2) screws having a lobular thread-forming section and 
circular holding sections (designated Type II). Specimen screws were 
tested in weld nuts of Rockwell B hardness of 82-84 having a 0.280 inch 
(7.11 mm) pilot hole diameter. Screws were nominally size 5/16 - 18 (M 7.9 
.times. 1.41). The value X in each case represents the arithmetic average 
of the data. For the Type I, screw K = 0.30 mm. For the type II screw, K = 
0.46 mm. maximum in the lead section. For the screw of the invention, K = 
0.152 mm in the holding section B and K = 0.356 mm in the thread-forming 
section A. The DSA in each instance is approximately 6.56 mm. 
DATA I 
______________________________________ 
STARTING END PRESSURE: 
______________________________________ 
INVENTION TYPE II 
______________________________________ 
Pounds Newtons Pounds Newtons 
______________________________________ 
7 31.1 7 31.1 
61/2 28.9 12 53.4 
6 26.7 93/4 43.4 
8 35.6 7 31.1 
51/2 24.5 111/2 51.2 
51/2 24.5 10 44.5 
X = 6.42 X = 28.5 X = 9.54 X = 42.5 
______________________________________ 
DATA II 
______________________________________ 
Maximum angularity (cocking) at start of driving operation: 
______________________________________ 
INVENTION TYPE II 
______________________________________ 
2.degree. 1.degree.40' 
11/2.degree. 
3.degree.10' 
1.degree. 2.degree. 5.degree.5' 33/4.degree. 
2.degree. 2.degree.15' 
21/2.degree. 
1.degree.50' 
11/2.degree. 
21/2.degree. 
21/2.degree. 
31/2.degree. 
______________________________________ 
DATA III 
______________________________________ 
Maximum drive torque to fully thread test nut: 
______________________________________ 
INVENTION TYPE I TYPE II 
______________________________________ 
LB- NEWTON- LB- NEWTON- LB- NEWTON 
INS. METRES INS. METRES INS. METRES 
______________________________________ 
74 8.36 80 9.04 78 8.8 
86 9.72 80 9.04 81 9.15 
75 8.47 70 7.91 76 8.6 
80 9.04 95 10.73 68 7.68 
80 9.04 85 9.60 86 9.72 
85 9.60 80 9.04 73 8.75 
91 10.78 80 9.04 79 8.93 
83 9.38 80 9.04 79 8.93 
83 9.38 80 9.04 75 8.47 
82 9.26 80 9.04 80 9.04 
X = X = X = 
81.9 X = 9.25 81 X = 9.15 
77.5 X = 8.75 
______________________________________ 
DATA IV 
______________________________________ 
Prevailing (locking) torque: 
______________________________________ 
INVENTION TYPE I TYPE II 
______________________________________ 
LB- NEWTON- LB- NEWTON- LB- NEWTON- 
INS. METRES INS. METRES INS. METRES 
______________________________________ 
42 4.75 20 2.26 
45 5.08 30 3.39 Ten (10) specimens 
47 5.31 20 2.26 showed zero pre- 
62 7.00 20 2.26 vailing torque after 
50 5.65 20 2.26 forming internal 
60 6.78 20 2.26 thread in test nut - 
50 5.65 15 1.69 virtually finger free 
60 6.78 25 2.82 engagement. 
55 6.21 30 3.39 
50 5.65 35 3.95 
X = X = X = X = 
52.1 5.89 21.50 2.65 
______________________________________ 
DATA V 
______________________________________ 
Fail (Strip) torque: 
______________________________________ 
380 42.93 320 36.16 342 38.64 
365 41.24 300 33.90 305 34.46 
380 42.93 295 33.33 346 39.09 
380 42.93 300 33.90 315 35.59 
375 42.37 320 36.16 303 34.23 
365 41.24 325 36.72 322 36.38 
370 41.80 315 35.6 297 33.56 
375 42.37 275 31.07 341 38.53 
380 42.93 310 35.02 332 37.51 
355 40.11 319 36.04 363 41.01 
X = X = X = X = X = X = 
372.5 42.08 307.9 34.79 326.6 36.90 
______________________________________ 
DATA VI 
______________________________________ 
Axial tensile pull-out load from test nut after tightening to 
275-285 pound-inches (31-32 Newton-Metres) 
______________________________________ 
INVENTION TYPE I TYPE II 
______________________________________ 
LBS. KN LBS. KN LBS. KN 
______________________________________ 
7375 32.80 7000 31.14 7500 33.36 
8125 36.14 7000 31.14 7585 33.74 
7500 33.36 6500 28.91 7750 34.47 
7187 31.97 6750 30.02 8000 35.58 
7625 33.92 6375 28.36 7875 34.81 
7125 31.69 6687 29.74 7915 35.21 
7750 34.47 7250 32.25 7500 33.36 
7937 35.30 6625 29.47 8000 35.58 
7625 33.92 6625 29.47 8165 36.32 
7500 33.36 6750 30.02 8165 36.32 
X = X = X = X = X = X = 
7574.9 33.69 6756 30.05 7840 34.87 
______________________________________ 
Turning now to FIGS. 9 and 10, the pair of dies shown comprises a 
stationary die 51 and a movable die 53, the latter movable in the 
direction indicated by the arrow 53a. The dies are of similar construction 
so far as their thread-rolling construction is concerned; therefore, like 
numbers will indicate parts in the two dies 51, 53. The dies 51, 53 at 
least in the direction extending along the length of the blank, (i.e. 
transversely along the dies) has a generally flat profile. Thus, the die 
51 has a flat section 55 along one side thereof. The die 51 also has 
alternating ridges and grooves 56, 58 for rolling the thread onto blanks. 
More particularly the die 51 comprises a first longitudinal section 60 
with thread-forming ridges and grooves for forming the thread in the 
holding section B. Adjacent the first section 60 is a second longitudinal 
section 62 for forming the thread-swaging thread on the work-entering 
section A. Additionally, there is a third die section 64 for rolling the 
pilot thread 44. The second section 62 has truncated ridges 66 plus 
grooves 68 of varying depth to form a taper on the thread in the section 
A. In the section 64 the ridges are likewise truncated but the grooves 70 
are of equal depth so as to form the pilot thread 44 of equal width 
throughout 360.degree.. 
The flat end portions 55 of each die lie in respective planes substantially 
coincident with the plane of the ridge 66 associated therewith. Such ridge 
66 also coincides with those truncated die ridges that are between the 
ridge 66 and the flat surface 55. 
The dies 51a, 53a of FIG. 11 are similar to the dies 51, 53 except that 
each includes a ridge and groove design resulting in a screw in which the 
width of the root, namely its transverse dimension, increases toward the 
tip 26. Thus, the ridges 66, 67, 69, etc. are progressively further away 
from the plane of the flat end portion 53. The result is that in the 
fastener of FIG. 12 the roots 29, 31, 33, etc. are progressively wider in 
the direction toward the tip 26.