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
ABSTRACT .................................................................................................................... vii
1. BACKGROUND ......................................................................................................... 1
1.1
PROBLEM DESCRIPTION .............................................................................. 3
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
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.
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
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
ABSTRACT
This study analyzed the worst-case scenario loading of the bolt lugs in a M1903
Springfield 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 stressed of the bolt lugs
were calculated.
vii
1. BACKGROUND
At its simplest, a firearm can be thought of as a tube 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. In order to
do that, some low pressure firearms will use the inertia of the bolt, but most will require
the bolt to interlock with the main structural component of a rifle, the receiver. The
locking methods, and 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
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
1
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
A single design of rifle may be chambered in a number of calibers (which may be
changed by replacing or recutting the barrel). 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
Arisaka, have been known to regularly withstand pressure well above the design
cartridge values. 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 and manufacturing techniques have
resulted in much more 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
2
Internationale Permanente pour l'Epreuve des Armes à Feu Portatives (Permanent
International Commission for Firearms Testing, or CIP) in Europe. By using the
maximum cartridge pressure and knowing the size of the base of the cartridge (called,
somewhat counter intuitively, the "head") the "bolt thrust" value can be calculated. This
is the maximum thrust with the bolt may be expected to withstand during firing. Any
given firearm action has a maximum bolt thrust value; as long as each caliber 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 two
rounds at 130% of the rated pressure of a cartridge, though the exact overpressure will
vary by cartridge. The firearm is then disassembled and examined for any sign of
cracking or plastic deformation Particular attention must be paid to the locking
mechanism, such as the bolt lugs described above.
In older firearms, with less advanced manufacturing techniques, this testing
procedure was particularly important. 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 rifles
owner. To solve this problem, better heat treat procedures were implemented. During the
build-up to the Second World War, the raw materials and heat treat process were
changed once again, to nickel-bearing steel known as WD 2340.
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,
3
careless handling, and potentially inconsistent ammunition. This has been done
historically 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 taken as least material values, 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 was considered for the FEA, 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 simliar 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 WD2340
(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
material. As yield and terminal strengths will rise with the increase in strain rate, the
static analysis 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). During normal firing, this 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 75,000psi was applied to the
area of the cartridge base, as shown by the area highlighted blue in Figure 5.
Figure 5: Boundary Load
Figure 6: Fixed Constraint
Loaded surface is highlighted in blue.
Constrained surface is highlighted in blue
This is considered the worst case loading condition. The leading face of the receiver ring
was fixed in position, as shown by Figure 6, to simulate the forces due to the rest of the
un-modeled material. This method of modeling allows the receiver to flex under load.
Without some flexibility, the peak stresses calculated on the bolt lugs are both higher
and more concentrated than would occur under real-world conditions.
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, as localized portions of the model are likely to
enter into plastic deformation in areas of high stress concentration (such as the root
fillets of the locking lugs). As strain hardening data was not available for WD2340 steel,
the strain hardening curve for SAE 4340 was used, as the material properties of SAE
4340 are very similar to WD2340, and SAE 4340 is a common material for modern bolt
8
heads. Meshing was done with the "Physics Controlled Mesh" option in COMSOL, with
the sizing set to "Fine." The resulting mesh was acceptable, 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 mesh is shown in Figure 7, with just
under 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 with 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,
but not to the extent often shown by the model. To demonstrate this effect, a two
dimensional slice 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 down. 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 also becomes
important when looking at overall stretching of the bolt and receiver, as higher rigidity is
often correlated to a more accurate firearm.
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
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 10: Surface Stress Values (Von Mises)
12
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, this
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 receiver, the areas in red
14
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 hardeneing
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 isosurfaces. 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 unity.
15
Figure 14: Percentage of Yield
16
4. CONCLUSION
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