Finite Element Stress Analysis of a 1903 Springfield Rifle Bolt
by
Daniel J. Flavin
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master of Engineering
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December, 2014
© Copyright 2014
by
Daniel Flavin
All Rights Reserved
ii
CONTENTS
CONTENTS ..................................................................................................................... iii
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
GLOSSARY ..................................................................................................................... vi
KEY WORDS .................................................................................................................. vii
ABSTRACT ................................................................................................................... viii
1. BACKGROUND ......................................................................................................... 1
1.1
PROBLEM DESCRIPTION .............................................................................. 4
2. METHODOLOGY ...................................................................................................... 5
2.1
GEOMETRY ..................................................................................................... 5
2.2
MATERIALS ..................................................................................................... 6
2.3
FEA .................................................................................................................... 7
3. RESULTS AND DISCUSSION ................................................................................ 10
3.1
TWO DIMENSIONAL EXAMPLE ................................................................ 10
3.2
THREE DIMENSIONAL RESULTS .............................................................. 11
3.2.1
Displacement ........................................................................................ 12
3.2.2
Peak Stress ........................................................................................... 12
3.2.3
Plastic Deformation .............................................................................. 14
4. CONCLUSION.......................................................................................................... 17
REFERENCES ................................................................................................................ 18
Appendix A: Material Properties, SAE 2340 Steel ......................................................... 19
Appendix B: COMSOL Report ....................................................................................... 20
iii
LIST OF TABLES
Table 1: Material Properties of Heat Treated SAE 2340 ................................................... 6
iv
LIST OF FIGURES
Figure 1: Bolt Action Rifle Nomenclature and Cross Section (Brophy 67) ...................... 1
Figure 2: Bare Rifle Bolt ................................................................................................... 2
Figure 3: Bolt Model in CAD (exploded view) ................................................................. 5
Figure 4: FEA Geometry ................................................................................................... 7
Figure 5: Boundary Load ................................................................................................... 8
Figure 6: Fixed Constraint ................................................................................................. 8
Figure 7: Model Mesh ....................................................................................................... 9
Figure 8: Two Dimensional FEA Sample (Von Mises Stress) ........................................ 10
Figure 9: Calculated Values of Displacement ................................................................. 11
Figure 10: Surface Stress Values (Von Mises) ................................................................ 12
Figure 11: Surface Stress Values (Von Mises), Peak ...................................................... 13
Figure 12: Calculated Areas of Failure ............................................................................ 14
Figure 13: Calculated Areas of Failure (Cross Section) .................................................. 15
Figure 14: Percentage of Yield ........................................................................................ 16
Figure 15: Barrel Rupture due to 125 ksi Test Cartridge ................................................ 17
v
GLOSSARY
Action: the mechanical parts of a firearm, which manipulate the cartridge and seal the
breech.
Barrel: a metal tube, through which the projectile is propelled by a controlled explosion
and the resulting rapid expansion of gas.
Bolt: the part of the firearm action which blocks the rear of the chamber (sealing the
breach) during firing, but is moved to allow a new cartridge to be loaded.
Bolt action: a specific form of firearm action in which the bolt is manipulated by hand
between each round fired.
Bolt thrust: the amount of rearward force exerted by the cartridge during firing. The
force is transmitted into the bolt, which must be strong enough to contain it.
Breech: the end of the barrel closest to the operator, where the chamber is found.
Cartridge: a unit of ammunition consisting of a bullet, gunpowder, casing, and primer
assembled into a single piece.
Chamber: The portion of the barrel in which the cartridge is inserted prior to firing. The
shape of the chamber will closely match the shape of the cartridge.
Firearm: a portable weapon which launches projectiles through an explosive force
Lug: a projecting portion of the assembly for the purpose of transferring forces between
two parts
Muzzle: the end of the barrel from which the projectile exits
Proof Load: a cartridge loaded to a higher than standard pressure, used for safety testing
of newly manufactured firearms
Receiver: a portion of the firearm action which houses the operating pieces and connects
to the stock and barrel assemblies.
Stock: the portion of the firearm used by the operator for support and aiming by holding
against the shoulder
Trigger: the mechanical lever used to actuate the firing mechanism
vi
KEY WORDS
Rifle
Bolt action
Locking lug
Receiver
Stress
Finite Element Analysis
FEA
M1903 Springfield
vii
ABSTRACT
This study analyzed the worst-case scenario loading and resulting stressed of the bolt
lugs in a M1903 Springfield bolt action rifle. The load-carrying portion of the bolt head
and the corresponding portion of the receiver were modeled in Solidworks, using legacy
drawings and surviving examples of spare bolts. The model was then loaded into
COMSOL finite element analysis software using material properties of the now obsolete
steel. Using the static solid mechanics module with plasticity, the loading and internal
stresses of the bolt lugs were calculated. Results showed that the stresses in the bolt lugs
approached, but did not exceed, the yield strength of the material.
viii
1. BACKGROUND
At its simplest, a firearm can be thought of as a tube strong enough to resist the forces of
an explosion, which is plugged at one end and open at the other. In modern cartridge
firearms, the plug must be mobile in order to allow loading and removal of cartridges.
This mobile plug is called the bolt, and must be capable of withstanding many thousands
of pounds of pressure during firing. To do so, some low pressure firearms will use the
inertia of the bolt, but most will require the bolt to interlock with the receiver, the main
structural component of a rifle. Locking methods, and the methods of operating them,
vary widely amongst different types of firearms. One common method is the manually
operated bolt, or bolt action, rifle. First developed in the mid-1800s, and used by both
military and civilians, it is still a popular method of achieving power and accuracy in
sporting and hunting applications.
Figure 1: Bolt Action Rifle Nomenclature and Cross Section (Brophy 67)
Red: Bolt Body
Orange: Receiver
Blue: Barrel
1
Yellow: Cartridge
Many modern bolt action rifles are "Mauser-style" rifles, based off a design developed
for the German military in 1898. This action uses two large locking lugs at the front of
the bolt to engage with the receiver. The operational portions of a rifle of this style are
shown in Figure 1, with important portions of the assembly color-coded. A bare bolt of
this style is shown in Figure 2. The chamber, with the loaded cartridge, would be to the
right of the bolt face
Figure 2: Bare Rifle Bolt
1: Bolt face 2: Locking lugs 3: Extractor grooves 4: Bolt body 5: Backup lug 6: Bolt handle
While any individual rifle is capable of firing a specific cartridge, a family of
rifles may share identical receivers and bolts with only minor modifications required to
fire a variety of different cartridges. Each unique caliber of cartridge has a specified peak
pressure, which until recently was a "best guess" due to the difficulty in measuring
pressures upwards of 50 ksi in a matter of milliseconds. In order to ensure strength,
designs were often very conservative. Some designs, such as the Japanese Type 99
Arisaka, have been known to regularly withstand pressure well above the design
cartridge values (Hatcher 210). Less conservative designs, particularly for military arms
which saw high firing counts, would occasionally have to be recalled and rebuilt in order
to ensure the safety of the user. Modern measuring methods have resulted in much more
2
accurate measurements of peak pressure, and these values are regulated and published by
two organizations, the Sporting Arms and Ammunition Manufacturers' Institute
(SAAMI) in the United States, and the Commission Internationale Permanente pour
l'Epreuve des Armes à Feu Portatives (Permanent International Commission for
Firearms Testing, or CIP) in Europe. By knowing the maximum cartridge pressure and
the size of the base of the cartridge, the force imparted by the cartridge on the bolt face
can be calculated. Called the “bolt thrust”, this value is the maximum loading which the
bolt may be expected to withstand during firing. Any given firearm action has a
maximum bolt thrust value; as long as each cartridge chosen for use remains below the
calculated bolt thrust, the action is safe to operate.
To test the level of safety, manufacturers are required to proof test their firearms,
under both SAAMI and CIP regulations. Proof testing usually consists of firing “proof
rounds,” cartridges loaded at approximately 130% of the standard peak pressure of the
firearm being tested. The firearm is then disassembled and examined for any sign of
fracture or plastic deformation. Particular attention must be paid to the locking
mechanism, such as the bolt lugs described previously.
In older firearms, with less advanced manufacturing techniques, this testing
procedure was particularly important to ensure safety. Despite the testing, issues would
occasionally arise. For example, in the period leading up to the First World War, the
United States army used the M1903 Springfield rifle, a bolt action built on the Mauser
pattern (so closely, in fact, that the Mauser company later sued the US government and
won royalties for patent infringement (Brophy 323)). Inconsistent heat treatment of the
rifle receivers, built of high-carbon steel, resulted in some rifles in the field suffering
catastrophic failures of the receiver during firing, at times severely injuring the
individual holding the rifle. To solve this problem, better heat treat procedures were
implemented. During the build-up to the Second World War, the raw materials were
changes to a nickel-bearing steel known as WD 2340, with the heat treatment altered to
reflect the requirements of the new steel.
3
1.1 PROBLEM DESCRIPTION
The most dangerous failure of a bolt action rile is the failure of the locking lugs, as this
will both release the high pressures normally contained with the chamber, and propel the
bolt rearwards, into the face of the firer. The sensible engineering approach, then, is to
design the bolt-to-receiver interface with a large factor of safety, particularly in military
firearms which are expected to have a long service life despite harsh environments,
careless handling, and potentially inconsistent ammunition. Historically, these design
calculations have been done with pencil and paper, but modern technology allows a
more advanced and accurate approach. Utilizing computer aided design (CAD) and
finite element analysis (FEA), a design can be analyzed electronically to determine
failure points and modes. In this report, the M1903 Springfield rifle bolt was measured,
modeled, and analyzed for stress loads under firing conditions.
4
2. METHODOLOGY
2.1 GEOMETRY
The model was built in SolidWorks computer aided design (CAD) software. Dimensions
were pulled from a government drawing of a field guage (Brophy 596), used to establish
safe headspace in a rifle. This was compared to a vintage M1903 bolt, to ensure that all
critial dimensions on the field guage matched the critcal dimension of the “live” bolt. All
dimensions were modeled as least material tolerance limits, in order to take the most
conservative case.
Figure 3: Bolt Model in CAD (exploded view)
1: Cartridge Base
2: Bolt Head
5
3: Receiver Ring
Only the head of the bolt, the bolt face to the rear of the locking lugs, was considered for
the FEA. This was done in order to reduce calculation time, as the remaining portions of
the bolt are not stressed to any significant factor. Portions of the bolt forward of the front
bolt face were not modeled for similar reasons. All units were done in US customary
units (inch/pounds/seconds), rather than metric, to match source material.
Models were also created for the base of the cartridge, using the SAAMI
standard sizing, and a receiver ring. By modeling the base of the cartridge, known load
pressures could be directly input into the model, reducing the likelihood of a calculation
error. The receiver ring is a stand in for the main body of the receiver. Clearance hole
sizing on the reaction ring was taken from the machining plan for the receiver (Brophy
549), but other dimensional values may be approximate due to the difficulty in locating
an accurate dimensional drawing of the finished receiver.
2.2 MATERIALS
Both the bolt and the reciever are made from a now-obsolete steel known as WD 2340
(Hatcher 224). This is the War Department’s designation for Society of Automotive
Engineering (SAE) 2340 steel (Hatcher 231), which was taken off the SAE standards in
the early 1950s. The bolt material was hardened to a Rockwell Hardness C of 33-44
HRC (Hatcher 226), equal to approximately 280 – 400 on the Brinell scale of hardness.
Using the lower end of the hardness scale, aproximately 300 Brinell, results in the
material properties shown in Table 1, taken from the material available in Appendix A.
Property
Value
Young’s Modulus, elastic (typical to steels)
29,700 ksi
Young’s Modulus, plastic (estimated)
300 ksi
Poisson’s Ration (typical to steels)
0.29
Density
0.284 lb/in3
Yield Stress
128 ksi
Terminal Stress
150 ksi
Table 1: Material Properties of Heat Treated SAE 2340
6
2.3 FEA
The CAD model was imported into COMSOL Finite Element Analysis (FEA) software,
using the stationary (static) solid mechanics module. This was chosen in lieu of a
dynamic analysis to reduce the effect of the high strain rate on the strength of the
materials. As the strain rate increases, the values for yield and terminal strenegth will
also rise. By utilizing a static analysis, the results are more conservative than the values
given by the dynamic module.
The orientation of the model is show in Figure 4. The material properties
described in section 2.2 were input for the receiver ring and bolt. Material properties for
C26000 annealed cartridge brass were used for the base of the receiver (MatWeb, LLC).
Figure 4: FEA Geometry
Model loading was determined through examination of worst-case scenarios of
bolt thrust loading. The cartridge fired by the M1903 rifle is the .30-06, with a maximum
SAAMI pressure rating of 60,000psi (SAAMI) . Proof testing of the rifle occurred at
7
75,000psi (Hatcher 198). Under normal firing conditions, full pressure would be
contained with the case, and friction between the case sides and the rifle chamber would
decrease the bolt thrust. However, abnormal conditions, including excess lubricant in the
chamber or the structural failure of the cartridge, can result in the full thrust being
transmitted to the bolt. Therefore, the maximum proof loading pressure of 75,000 psi
was applied to the area of the cartridge base, as shown by the area highlighted blue in
Figure 5. This is considered the worst case loading condition.
The leading face of the receiver ring was fixed in position, as shown by Figure 6.
By modeling the receiver ring in this way instead of having the bolt anchored against an
unmoving ring, reactive forces of the receiver are more closely approximated. Failing to
allow some displacement of the receiver locking surfaces would result in artificially high
stress loads at the points of contact between the bolt and the receiver.
Figure 5: Boundary Load
Figure 6: Fixed Constraint
Loaded surface is highlighted in blue.
Constrained surface is highlighted in blue
In order to insure that the flexibility of the lugs would be properly simulated,
plasticity with strain hardening was added to the model. While increasing calculation
time, it ensures a more accurate result due to localized portions of the model undergoing
plastic deformation in areas of high stress (such as the root fillets of the locking lugs). As
strain hardening data was not available for WD2340 steel, the strain hardening curve for
8
SAE 4340 was used. The material properties of SAE 4340 are very similar to WD2340,
and SAE 4340 is a material commonly used for modern rifle bolt actions.
Meshing was done with the "Physics Controlled Mesh" option in COMSOL, with
the sizing set to "Fine." The resulting mesh was reviewed, with very fine elements in the
areas of most concern. Finer meshes were attempted, but very quickly reached the limits
of the computer hardware available. The final acceptable mesh is shown in Figure 7,
with just fewer than 117,000 tetrahedral elements ranging from 0.015 to 0.12 inches.
More information on the meshing values can be found in Appendix B.
Figure 7: Model Mesh
9
3. RESULTS AND DISCUSSION
3.1 TWO DIMENSIONAL EXAMPLE
Some difficulty was had in attaining clean results from the FEA analysis, due to the
inherent complexity of the geometry. This was particularly true at points of
discontinuous loading where some increase in loading would be expected due to shear
effects, but not to the extent often shown by the model. To demonstrate this effect, a two
dimensional cross section of the bolt was modeled and analyzed.
Figure 8: Two Dimensional FEA Sample (Von Mises Stress)
10
The results are shown in Figure 8. The topmost picture shows the bolt head, with the bolt
thrust loading being applied from the top. The central image shows the extreme ends of
the contact area between the bolt and receiver have "hot spots," or areas of stress notably
higher than the surrounding areas. The bottom image illustrates how the hot spots are the
result of a single node, at the edge of the contact point. The extreme peak values are
representative of the limits of the FEA software to handle edge conditions.
3.2 THREE DIMENSIONAL RESULTS
The three dimensional model took approximately ten minutes to calculate on an
3.30GHz Intel Core I5 machine with 8 gigabyte of RAM. The results were then plotted
for several different values: displacement, areas of peak stress, and areas of plastic
deformation.
Figure 9: Calculated Values of Displacement
11
3.2.1
Displacement
The displacement values are shown in Figure 9, where the bolt face is show as moving
0.00002 inches under firing load. While these values do not directly affect the factor of
safety inherent in bolt design, they are important to help determine areas which will be
expected to undergo greater values of strain hardening. The displacement is also of
interest when considering the overall stretching of the bolt and receiver, as higher
rigidity is often correlated to a more accurate firearm.
Figure 10: Surface Stress Values (Von Mises)
3.2.2
Peak Stress
The peak calculated stress for the model was 4.2x105 psi, which is significantly higher
than the terminal strength of the material, shown in Table 1 as 1.5x105 psi. However,
examining Figure 10 will show that the bulk of the model is well below the peak value,
with higher stresses at the contact points and several points on the bolt lugs. The peak
values are in fact nearly invisible on the model, unless careful use of the zoom function
12
is used, as shown in Figure 11. These peak loads appear to be a function of the
discontinuous nature of the mesh at those points, as demonstrated in section 3.1.
Figure 11: Surface Stress Values (Von Mises), Peak
In order to determine the exact location of the peak loading, the Von Mises stress was
compared to the terminal strength of the material. This highlighted every node or
element where the calculated stress would result in a material failure during firing. These
results are shown in Figure 12. The black coloration in this figure highlights areas which
exceed the terminal strength of the material. As expected from previous results, the areas
are all edge discontinuities in the mesh. While it is possible that some of the high
stresses at the root of the bolt lugs would be concerning to a designer, the relatively low
stresses of the surrounding area suggest that the bolt would not undergo failure during
firing, which real world testing has borne out.
13
Figure 12: Calculated Areas of Failure
Black areas exceed the terminal strength of the material
3.2.3
Plastic Deformation
As entering the plastic range is generally considered a failure for a static structure, the
examination of plastic deformation was the most important result of the analysis. Due to
the tight tolerance requirements of firearms actions, plastic deformation of the bolt might
easily result in an unsafe or unusable firearm. As shown in Figure 10, the stress values
appear to approach and possibly exceed the yield strength of 1.28x105 shown in Table 1.
However, that value can be expected to rise with the inclusion of strain hardening.
Figure 13 demonstrates that difference between the yield calculation with and without
strain hardening. In the left-hand imagine of the figure, a cross section of the bolt and
14
receiver, the areas in red are where the calculated Von Mises stress exceeds the initial
yield strength of the material. This image would suggest that the bolt lugs are too small,
as large portions of them enter the plastic range of the material. However, the right-hand
picture shows the same cross section with the inclusion of strain hardening effects. In
this image, several isolated and disjoint nodes appear to have entered the plastic range,
suggesting the material is on the cusp of deformation, but most portions of the bolt lugs
are not yet ready to yield.
Figure 13: Calculated Areas of Failure (Cross Section)
Left: Without strain hardening
Right: With strain hardening
Having determined that the bolt lugs are nearing the yield point, but not yet entering
it when the effects of strain hardening are accounted for, Figure 14 shows the results of
dividing the Von Mises stress by the yield stress, and plotting is surfaces. In this
diagram, each surface identifies a ten percent increase in stress ratio. The maximum
stress is 95.05% of the yield stress. This suggests that the bolt lugs will not undergo
plastic deformation in the worst-case conditions modeled here. However, any higher
loading will probably result in a factor of safety less than one, indicating the imminent
failure of the bolt.
15
Figure 14: Percentage of Yield
16
4. CONCLUSION
During the modeling and FEA portions of this analysis, every effort was taken to be
conservative in calculations. To analyze the bolt under worst possible firing conditions,
three areas were considered. First, the dimensions of the model were taken in least
material condition, resulting in the weakest bolt allowed by drawing tolerances. Second,
the maximum possible bolt loading was utilized, which greatly exceeds anything likely
to be seen during the service life of the rifle. Finally, despite conditions which would
result in high strain rates, the effect of strain rate on yield strength was ignored. Despite
these handicaps, the bolt stress was limited to around 95% of the yield stress of the
material, though only due to the effects of strain hardening. This suggests that the bolt is
at the very limits of its ability to withstand the force of firing, and that minor changes to
material properties or calculation methods may show failure of the bolt lugs.
More accurate calculation of bolt stress would require a more thorough
understanding of the material properties. While this analysis used the best available data,
a modern testing of WD 2340 steel to understand the effects of heat treatment and strain
hardening would result in more accurate FEA inputs. Efforts to refine the FEA meshing
and analysis to help remove the mesh discontinuities would also reduce spurious data.
The model methods used here may also be extended to other parts of the rifle.
Modeling the chamber and barrel, including the friction coefficient between the cartridge
and chamber walls, would result in a more accurate measure of the bolt thrust. Including
the barrel in the analysis could also demonstrate which would fail first, the hoop strength
of the barrel or the shear strength of the bolt locking lugs. An extreme case of historical
testing is shown in Figure 15, where a test cartridge rated for 125,000 psi ruptured the
chamber of an M1903 Springfield, while the bolt and receiver maintained integrity.
Figure 15: Barrel Rupture due to 125 ksi Test Cartridge
17
REFERENCES
Al, Varmint. Stolle Panda Bolt Stress and Deflection Analysis. 8 February 2013.
Website. 9 September 2014. <http://www.varmintal.com/abolt.htm>.
Brophy, William S. The Springfield 1903 Rifles (The Illustrated, Documented Story of
the Design, Development, and Production of all the Models of Appendages, and
Accessories). Mechanicsburg, PA: Stackpool Books, 1985. Book.
Hatcher, Julian S. Hatcher's Notebook : A Standard Reference Book For Shooters,
Gunsmiths, Ballisticians, Historians, Hunters, And Collectors. Harrisburg, PA:
Stackpole Co., 1957. Book.
Iron and Steel Division Report. "Iron and Steel Specifications." The Journal of the
Society of Automotive Engineers IX.6 (1921): 392-422. Journal Article.
Lilja, Dan. A Look at Bolt Lug Strenght. 2002. Website. 8 September 2014.
<http://www.riflebarrels.com/articles/custom_actions/bolt_lug_strength.htm>.
MatWeb, LLC. Cartridge Brass, UNS C26000 (260 Brass), OS025 Temper tubing. 2014.
Web Site. 02 10 2014.
Ozmen, Dogan, et al. "Static, dynamic and fatigue analysis of a semi-automatic gun
locking block." Engineering Failure Analysis 16.7 (2009): 2235-2244.
SAAMI. "Maximum Cartridge / Minimum Chamber, 30-06 Springfield." Technical
Paper.
2012.
PDF
Document.
24
September
2014.
<http://www.saami.org/pubresources/cc_drawings/Rifle/3006%20Springfield.pdf>.
—. "Velocity and Piezoelectric Transducer Pressure: Centerfire Rifle." Industry
Standard.
2013.
Digital
Docutment.
<http://www.saami.org/specifications_and_information/specifications/Velocity_
Pressure_CfR.pdf>.
Yu, V.Y., et al. "Failure Analysis of the M-16 Rifle Bolt." Engineering Failure Analysis
12.5 (2005): 746-754. Web.
18
Appendix A: Material Properties, SAE 2340 Steel
The following information is taken from the Journal of the Society of Automotive
Engineers, Volume 9, 1921.
Material Composition, in Percentage:
Carbon
0.35-0.45
Manganese
0.50-0.80
Phosphorus
0.04 max
Sulfur
0.045 max
Nickel
3.27-3.75
Material Properties, taken from tensile tests:
19
Appendix B: COMSOL Report
The following pages contain the COMSOL output report, including all major inputs and
values used in the analysis.
20