Selection of Material for
Driver Insert
To: Professor Robert Heard
CEO
All Sorts of Sports Company
Team Members:
David Birsen
Brooke Gladstone
Huan Kiat Koh
Date:
Executive Summary
Table of Contents
1. Problem Definition
2. Literature Review of the Problem
3. Methodology of Approach to Problem
4. Details of Design, Selection Method
4.1 Deriving Material Indices and Initial Selection
4.2 Further Selection Criteria
4.3 Final Selection
5. Recommendations for Design
6. References
7. Appendices
Appendix A: Table of Shortlisted Materials
Appendix B: Titanium Alloys
Appendix C: Depth and Mass Calculations
Appendix D: Material Processing Charts
1. Problem Definition
The goal of the project is to design a material for the driver insert that is
competitive in the market both in terms of performance (COR = 0.83) and cost (less than
$5), is easily produced in bulk (500,000 parts per year), and is recyclable. The
constraints and objectives are listed below.
Constraints:







Cross-sectional area is approximately oval, with length of 90mm and height of 55mm.
Cost needs to be less than $5.00 per part.
Recyclable
High Young’s Modulus
Yield Stress needs to be greater than stress at impact
Coefficient of Restitution (COR) must be equal to or less than 0.83
Processability: needs to be made in bulk
Objective:
Minimize the mass (and thus depth) since lighter clubs can be swung faster to get a
farther distance. This should minimize the amount of material used and hence also the
production cost.
Free Variables:


Mass, Choice of Material, Processing Method
Manufacturing Process
2. Literature Review
Something…
3. Methodology of Approach to Problem
A systematic approach was adopted to solving this problem and selecting the best
material for the driver insert. Using the constraints and objectives listed above, material
indices were derived and a coupling line was plotted in the Ashby selection software CES
(Level 2) to determine a group of candidate materials, as shown in Fig.4.1. The group
was then reduced by taking into account factors such as processability and recyclability.
The properties of the remaining materials were listed and compared, and the general
material (e.g. titanium alloys) with the best combination of cost, carbon dioxide footprint
and mechanical properties was chosen. Finally, the software was expanded to Level 3 and
the specific alloy with the best properties was selected.
4. Details of Design, Selection Method
4.1 Deriving Material Indices and Initial Selection
The objective to minimize the depth of the driver insert can be written in equation
form by rearranging the equation for mass such that the depth is expressed in terms of
mass, area and density:
𝑚 = 𝐴𝑑𝜌 ⇒ 𝑑 =
𝑚
𝐴𝜌
(1)
The problem is constrained by the area of the face, a price that must be less than
$5.00, a Coefficient of Restitution (COR) not more than 0.83, and a material that is
recyclable. The following equation for the COR was obtained from Johnson:
−1⁄8
𝜎𝑦 1⁄2 0.5𝑚𝑉 2
𝑒 = 3.8 ( ) (
)
𝐸
𝜎𝑦 𝑅 3
(2)
Where 𝑒 is the COR, 𝜎𝑦 is the yield strength of the material, 𝐸 is the Young’s
Modulus, 𝑚 is the mass of the driver insert, 𝑉 is the tangential velocity of the golf club
head just before impact, and 𝑅 is the radius of the indenter, which in this case is the golf
ball. Rearranging such that 𝑚 is the subject of the equation obtains:
1⁄ −8
2
𝑒
𝐸
𝑚 = 2 [( ) ( )
3.8 𝜎𝑦
]
𝜎𝑦 𝑅 3
( 2 )
𝑉
(3)
Substituting Equation (1) into (3) and solving for 𝑑:
2𝑅 3 3.8 8 𝜎𝑦5
𝑑= 2 ( ) ( 4 )
𝑉 𝐴 𝑒
𝐸 𝜌
(4)
𝜎5
Hence, the first material index, 𝑀1 = 𝐸4𝑦𝜌. The second constraint, which fixes the cost,
determines the second material index, 𝑀2 . The equation for cost is determined by
multiplying the mass by the cost per mass:
𝐶 = 𝑚𝐶𝑚 ⇒ 𝑚 =
Inserting (1) into (5):
𝐶
𝐶𝑚
(5)
𝑑=
𝐶 1
𝐴 𝐶𝑚 𝜌
⇒ 𝑀2 =
(6)
1
𝐶𝑚 𝜌
The two equations (4) and (6) provide a range of values where 𝑑 needs to fall into in
other to satisfy the constraints, as expressed below:
2𝑅 3 3.8 8 𝜎𝑦5
𝐶 1
( ) ( 4 )≤𝑑≤
2
𝑉 𝐴 𝑒
𝐸 𝜌
𝐴 𝐶𝑚 𝜌
It should be noted that the closer the value of 𝑑 to the lower bound, the closer the
coefficient of restitution is to 0.83, and also cheaper (less material). As 𝑑 increases, the
coefficient of restitution decreases, and the cost increases. When the thickness is at the
upper bound, the cost is $5 per part, as required during the derivation of 𝑀2 . While a
thinner driver face insert means a lower cost for the material, processing costs may go up,
especially when the ideal thickness is on the order of a few tens of microns.
A coupling line can also be written in terms of 𝑀1 and 𝑀2 by equating (4) and (6).
2𝑅 3 3.8 8
𝐶
2𝑅 3 3.8 8
( ) 𝑀1 = 𝑀2 ⇒ 𝑀2 = 2 ( ) 𝑀1
𝑉2𝐴 𝑒
𝐴
𝑉 𝐶 𝑒
(7)
Using values from the literature as well as given in the problem, 𝑉 = 40𝑚𝑠 −1 , 𝑅 =
21.3𝑚𝑚, 𝑒 = 0.83, 𝐶 = $5.00, equation (7) becomes:
𝑀2 = 4.66 × 10−4 𝑀1
(8)
Equation (8) allows us to determine the position of the coupling line on the CES
software. With the two material indices as the axes, the coupling line is plotted in
Fig.4.1.1 to identify material candidates, which should lie in the bottom left of the plot
since the indices are to be minimized in order to minimize depth.
Fig.4.1.1: Material selection using Level 2 of CES software. The coupling line along with the selection box
shows materials that are suitable for selection.
The selection box narrows down the choices to tin, nickel alloys, nickelchromium alloys, tungsten alloys, nickel-based superalloys, and titanium alloys, as well
as ceramics such as tungsten carbides, aluminium nitride, boron carbide, etc. However,
there are processing limitations in order to produce the driver inserts in bulk, and
furthermore the material must be recyclable. Applying a minimum of 3 to castability and
weldability in the Limiting Stage, the list of materials is further reduced to only nickel,
nickel-based superalloys, nickel-chromium alloys, tin, and titanium alloys.
4.2 Further Selection Criteria
In addition to the two material indices, a third factor must be considered: the yield
strength of the material must be greater than the stress generated on impact to prevent
plastic deformation and hence failure. a typical impact force is approximately 9000N
(Glenn Elert). Using the impact radius of 21.3mm, this gives a stress of 6.3MPa. There
also have been reports of the force being as large as 18000N, corresponding to a stress of
12.6MPa. Hence, only materials with a minimum yield strength greater than 12.6MPa are
suitable.
Moreover, one final criteria that should be taken into account is that the driver
insert must not fracture on impact with the golf ball. Hence the ideal material should have
a sufficiently large critical crack length.
The material properties of the five shortlisted materials listed above were
tabulated and can be found in Appendix A. The results after comparison are as follows:
Tin is rejected due to its low yield strength. Nickel superalloys have the smallest critical
crack length for fracture and hence are also rejected. Nickel-chromium alloys have a
minimum thickness of less than a micron which is not realistic to manufacture in bulk.
Nickel is a good candidates due to the low cost of material and low CO2 footprint.
However, its thickness needs to be kept close to its lower bound in order to maintain the
coefficient of restitution to be near 0.83. Titanium alloys have a small range of thickness
between 2.32mm and 4.64mm, which is easily controlled and processed in bulk.
4.3 Final Selection
With this information, we were able to make the final material
selection. Materials that lie along the selection line optimize the combination of the
material properties while minimizing the material indices, and titanium alloys are closest
to the coupling line. Therefore, we have selected a titanium alloy for use as a driver
insert.
There are three types of titanium alloys: alpha, alpha-beta, and beta, as described
in Table 4.3.1. Alpha alloys are not an option because they too ductile and not often
commercially produced. This table shows that the alloy with the best performance is the
beta alloy. An important part of the selection process is choosing a material, such as a
beta alloy, that can easily be formed into the desired shape to simplify production and
lower costs. Also, the beta alloys offer high strength and fracture toughness so the insert
will not fail during use.
Alpha
Alpha-Beta
Beta
 HCP crystal structure
 Good toughness
 Good ductility
 Moderate strength
 Highest corrosion resistance of the alloys
 Good creep resistance
 Formable
 Weldable
 Lower density
* Ti-5Al-2.5Sn is the only true alpha alloy that is commercially produced
(it is ductile, so would not be a good choice for the driver insert)
 Medium to high strength
 May creep at high temperatures
 Cold forming limited
* Typically used in aerospace
 BCC crystal structure
 Heat treatable
 High strength
 Good creep resistance
 Increased fracture toughness
 Weldable
 Excellent formability
 Easier room temperature forming and shaping than alpha-beta alloys
* Best choice for the driver insert due to its availability and processability
Table 4.3.1: Differences between the three types of titanium alloys
Since the part is to be mass-produced, the cost must be as small as
possible. Estimating the upper limit of the weight as 0.1 kg and a price per part of $5
(including material and manufacturing costs), the price should be close to $50/kg. The
actual cost of manufacturing is not known, so this conservative estimate accounts for
that. Using this restriction on cost and limiting the selection to only recyclable titanium
alloys, the following Level 3 selection plot was obtained (Fig.4.3.1).
Fig.4.3.1: Specific titanium alloy selection using Level 3 of the CES software.
Eleven materials pass all stages (full list in Appendix B), but as shown in the
Table 4.3.1 above, we wish to select a beta alloy for optimal performance and
processability. Therefore, the only beta alloy available to select with these limitations is
Titanium, beta alloy, Ti-5Al-2Sn-4Mo-2Zn-4Cr (Ti-17).
Given the relevant material properties in the Table 4.3.2 below, and by assuming
the area of the face is approximately oval, the depth and mass of the Ti-17 alloy driver
insert was calculated to be 1.556𝑚𝑚 and 28.1𝑔 respectively (see the Appendix C for full
calculations).
Material Property
Density
Price
Young’s Modulus
Yield Strength
Value
4.64 × 103 𝑘𝑔/𝑚3
$52.2/𝑘𝑔
1.1 × 1011 𝑃𝑎
1.12 × 109 𝑃𝑎
4.4 × 107 𝑃𝑎 ∙ 𝑚1⁄2
38.6𝑘𝑔/𝑘𝑔
Yes
Fracture Toughness
CO2 Footprint
Recyclable
Table 4.3.2: Properties of selected material
4.4 Processing Methods for Titanium Beta Alloy
Using processing charts from Ashby (Appendix D), a summary of processing
means for titanium beta alloy is shown below:
Processes that
are compatible
with Ti alloys
(metals)
Sand casting
Die casting
Investment
casting
Low-pressure
casting
Forging
Extrusion
Sheet forming
Powder
methods
Electromachining
Conventional
machining
Processes
capable of
forming flat
sheets
Processes that
are economical
at a batch size
of 500,000
parts per year
Fails
Fails
Fails
Processes
meeting the
section
thickness
constraint of
approximately 1
mm
n/a
n/a
n/a
Fails
n/a
n/a
Fails
Fails
Sheet forming
Fails
n/a
n/a
Sheet forming
n/a
n/a
n/a
Sheet forming
n/a
Electromachining
Conventional
machining
Electromachining
Conventional
machining
Fails
n/a
n/a
n/a
Fails
Table 4.4.1: Summary of available processing methods.
Based on these findings, the titanium alloy for the driver insert can only be
processed by sheet forming. Sheet forming will be performed to create thinner parts at a
small cost. There will be some additional costs to manufacturing since we are stretching
the limit, but the only other viable options would be electro-machining or conventional
machining, however both of these are uneconomical to use at the specified batch size.
Therefore, the cost incurred from sheet forming is insignificant compared to the cost that
would be incurred from the other machining methods. Titanium has a naturally occurring
surface oxide layer that serves as protection such that the sheets do not require any
special surface finishing. After sheet forming, the individual inserts will be stamped out
and then polished to achieve the desired aesthetic appearance.
5. Recommendation for Design
Based on our detailed analysis, the optimal selection to meet the objective and
constraints is a Titanium, beta alloy, Ti-5Al-2Sn-4Mo-2Zn-4Cr (Ti-17) driver insert with
a depth of 1.556𝑚𝑚 and mass of 28.1𝑔 . This insert will be processed by sheet
forming. The individual inserts will be stamped out and then polished to achieve the
desired aesthetic appearance.
References
Ashby, Michael F. Materials Selection in Mechanical Design, Second Edition. Oxford:
Reed Educational and Professional Publishing Ltd, 1999. Print.
Elerf, Glenn. Force of a Golf Club on a Golf Ball. The Physics Factbook. 2001. Web.
12th April 2012.
Johnson, K. L. Contact Mechanics, Chapter 11. Cambridge [Cambridgeshire]:
Cambridge University Press, 1985. Print. (Page 363, 364)
Titanium and Titanium Alloys. Everything Material, ASM International. 2012. Web. 7th
April 2012.
Titanium Alloys – Characteristics of Alpha, Alpha Beta and Beta Titanium Alloys. A to Z
of Materials. 2004. Web. 9th April 2012.
Appendix A: Table of Shortlisted Materials
Material: Nickel
Density (kg/m3)
Price $/kg
Value
8.83 × 103
42.4
Young’s Modulus (Pa)
1.9 × 1011
Yield Strength (Pa)
7 × 107 −
9 × 108
Fracture Toughness (Pa.m1/2)
CO2 Footprint (kg/kg)
8 × 107
8.82
Thickness 𝑑1 (m)
3.08 × 10−5
Thickness 𝑑2 (m)
3.44 × 10−3
Critical Crack Length (m)
2.52 × 10−3
Total CO2 Footprint of
Material (kg)
Material: Nickel-based
Superalloys
Density (kg/m3)
Price $/kg
1.04
Value
Justification/Remarks
7.75 × 103
Lower bound. Would help give
upper bound of cost and thickness.
Upper bound. Gives upper bound of
overall price.
Lower bound. Gives upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not yield.
Upper bound, to give upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not fracture.
Upper bound, to give the maximum
33.7
Young’s Modulus (Pa)
1.5 × 1011
Yield Strength (Pa)
3 × 108 −
1.9 × 109
Fracture Toughness (Pa.m1/2)
6.5 × 107
CO2 Footprint (kg/kg)
Justification/Remarks
Lower bound. Would help give
upper bound of cost and thickness.
Upper bound. Gives upper bound of
overall price.
Lower bound. Gives upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not yield.
Upper bound, to give upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not fracture.
Upper bound, to give the maximum
potential CO2 production.
Obtained from 𝑀1
2𝑅 3 3.8 8 𝜎 5
𝑑1 = 2 ( ) 4
𝑉 𝐴 𝑒
𝐸 𝜌
𝜎5
= 0.59979 4
𝐸 𝜌
Obtained from 𝑀2
𝐶 1
1
𝑑2 =
= 1286.1
𝐴 𝐶𝑚 𝜌
𝐶𝑚 𝜌
Use 𝐾1𝐶 formula as it is the lowest
𝐾1𝐶 ≈ 𝜎𝑦 √𝜋𝑐
Maximum per part from larger of
𝑑1 and 𝑑2 .
9.2
Thickness 𝑑1 (m)
3.79 × 10
−3
potential CO2 production.
Obtained from 𝑀1
2𝑅 3 3.8 8 𝜎 5
𝑑1 = 2 ( ) 4
𝑉 𝐴 𝑒
𝐸 𝜌
= 0.59979
Thickness 𝑑2 (m)
4.92 × 10−3
Critical Crack Length (m)
3.73 × 10−4
Total CO2 Footprint of
Material (kg)
Material: NickelChromium Alloys
Density (kg/m3)
Price $/kg
Young’s Modulus (Pa)
Yield Strength (Pa)
Fracture Toughness (Pa.m1/2)
CO2 Footprint (kg/kg)
1.36
Justification/Remarks
8.3 × 103
Lower bound. Would help give
upper bound of cost and thickness.
Upper bound. Gives upper bound of
overall price.
Lower bound, to ensure even the
weakest material will not yield.
Upper bound, to give upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not yield.
Lower bound, to ensure even the
weakest material will not fracture.
Upper bound, to give the maximum
potential CO2 production.
Obtained from 𝑀1
2𝑅 3 3.8 8 𝜎 5
𝑑1 = 2 ( ) 4
𝑉 𝐴 𝑒
𝐸 𝜌
𝜎5
= 0.59979 4
𝐸 𝜌
Obtained from 𝑀2
𝐶 1
1
𝑑2 =
= 1286.1
𝐴 𝐶𝑚 𝜌
𝐶𝑚 𝜌
Use 𝐾1𝐶 formula as it is the lowest
𝐾1𝐶 ≈ 𝜎𝑦 √𝜋𝑐
Maximum per part from larger of
𝑑1 and 𝑑2 .
36.4
2 × 1011
3.65 × 108 −
4.6 × 108
8 × 107
8.82
9.3 × 10−7
Thickness 𝑑2 (m)
4.26 × 10−3
Critical Crack Length (m)
9.63 × 10−3
Material: Tin
Obtained from 𝑀2
𝐶 1
1
𝑑2 =
= 1286.1
𝐴 𝐶𝑚 𝜌
𝐶𝑚 𝜌
Use 𝐾1𝐶 formula as it is the lowest
𝐾1𝐶 ≈ 𝜎𝑦 √𝜋𝑐
Maximum per part from larger of
𝑑1 and 𝑑2 .
Value
Thickness 𝑑1 (m)
Total CO2 Footprint of
Material (kg)
𝜎5
𝐸4𝜌
1.21
Value
Justification/Remarks
Density (kg/m3)
Price $/kg
Young’s Modulus (Pa)
Yield Strength (Pa)
Fracture Toughness (Pa.m1/2)
CO2 Footprint (kg/kg)
7.26 × 103
19.9
4.1 × 1010
7 × 106 − 15
× 106
1.5 × 107
2
Thickness 𝑑1 (m)
2.22 × 10−11
Thickness 𝑑2 (m)
8.9 × 10−3
Critical Crack Length (m)
3.18 × 10−1
Total CO2 Footprint of
Material (kg)
Material: Titanium Alloys
Density (kg/m3)
Price $/kg
0.50
Value
4.4 × 103
63
Young’s Modulus (Pa)
1.1 × 1011
Yield Strength (Pa)
7.5 × 108 −
1.2 × 109
Fracture Toughness (Pa.m1/2)
CO2 Footprint (kg/kg)
Thickness 𝑑1 (m)
5.5 × 107
44
2.32 × 10−3
Lower bound. Would help give
upper bound of cost and thickness.
Upper bound. Gives upper bound of
overall price.
Lower bound. Gives upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not yield.
Upper bound, to give upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not fracture.
Upper bound, to give the maximum
potential CO2 production.
Obtained from 𝑀1
2𝑅 3 3.8 8 𝜎 5
𝑑1 = 2 ( ) 4
𝑉 𝐴 𝑒
𝐸 𝜌
𝜎5
= 0.59979 4
𝐸 𝜌
Obtained from 𝑀2
𝐶 1
1
𝑑2 =
= 1286.1
𝐴 𝐶𝑚 𝜌
𝐶𝑚 𝜌
Use 𝐾1𝐶 formula as it is the lowest
𝐾1𝐶 ≈ 𝜎𝑦 √𝜋𝑐
Maximum per part from larger of
𝑑1 and 𝑑2 .
Justification/Remarks
Lower bound. Would help give
upper bound of cost and thickness.
Upper bound. Gives upper bound of
overall price.
Lower bound. Gives upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not yield.
Upper bound, to give upper bound
of thickness.
Lower bound, to ensure even the
weakest material will not fracture.
Upper bound, to give the maximum
potential CO2 production.
Obtained from 𝑀1
2𝑅 3 3.8 8 𝜎 5
𝑑1 = 2 ( ) 4
𝑉 𝐴 𝑒
𝐸 𝜌
𝜎5
= 0.59979 4
𝐸 𝜌
Thickness 𝑑2 (m)
4.64 × 10−3
Critical Crack Length (m)
6.69 × 10−4
Total CO2 Footprint of
Material (kg)
3.49
Obtained from 𝑀2
𝐶 1
1
𝑑2 =
= 1286.1
𝐴 𝐶𝑚 𝜌
𝐶𝑚 𝜌
Use 𝐾1𝐶 formula as it is the lowest
𝐾1𝐶 ≈ 𝜎𝑦 √𝜋𝑐
Maximum per part from larger of
𝑑1 and 𝑑2 .
Fig.A.1: Table of properties of shortlisted materials.
Appendix B: Titanium Alloys
Titanium alloys that meet the restrictions on price and recyclability:
Titanium, alpha alloy, Ti-5Al-2.5Sn-0.5Fe, annealed
Titanium, alpha alloy, Ti-8Al-1Mo-1V, duplex annealed
Titanium, alpha alloy, Ti-8Al-1Mo-1V, single annealed
Titanium, alpha alloy, Ti-8Al-1Mo-1V, solution treated & stabilized
Titanium, alpha-beta alloy, Ti-6Al-2Sn-2Zr-2Mo, annealed
Titanium, alpha-beta alloy, Ti-6Al-2Sn-2Zr-2Mo, solution treated & aged
Titanium, alpha-beta alloy, Ti-6Al-2Sn-2Zr-2Mo, triplex aged
Titanium, alpha-beta alloy, Ti-6Al-4V, aged
Titanium, alpha-beta alloy, Ti-6Al-4V, solution treated & aged
Titanium, beta alloy, Ti-5Al-2Sn-4Mo-2Zn-4Cr (Ti-17)
Titanium, commercial purity, Grade 2
Appendix C: Depth and Mass Calculations
Calculation of the depth and mass of the selected Ti alloy driver insert:
90𝑚𝑚 55𝑚𝑚
𝐴 = 𝜋𝑎𝑏 = 𝜋 (
)(
) = 3887.72𝑚𝑚2 = 3.888 × 10−3 𝑚2
2
2
First constraint:
𝑑1 =
2𝑅 3 3.8 8 𝜎𝑦5
( ) ( 4 )
𝑉2𝐴 𝑒
𝐸 𝜌
(1.12 × 109 𝑃𝑎)5
2(0.0213𝑚)3
3.8 8
=
(
)
(40𝑚𝑠 −1 )2 (3.888 × 10−3 𝑚2 ) 0.83 (1.1 × 1011 𝑃𝑎)4 (4.64 × 103 𝑘𝑔 𝑚−3 )
= 1.556𝑚𝑚
Second constraint:
𝑑2 =
𝐶 1
$5
1
=
= 5.31𝑚𝑚
−3
2
−1
𝐴 𝐶𝑚 𝜌 3.888 × 10 𝑚 ($52.2 𝑘𝑔 )(4.64 × 103 𝑘𝑔 𝑚−3 )
The closer the value of 𝑑 is to the lower bound, the closer the coefficient of restitution is
to 0.83, hence the minimum thickness will be used, i.e. 𝑑 = 𝑑1 = 1.556𝑚𝑚.
Using this depth, the mass of Ti alloy used is then:
𝑚 = 𝐴𝑑𝜌 = (3.888 × 10−3 𝑚2 )(0.001556𝑚)(4.64 × 103 𝑘𝑔 𝑚−3 ) = 0.0281𝑘𝑔
Appendix D: Material Processing Charts
Fig.D.1: Process-material matrix to find processes that are compatible with metals.
Fig.D.2: Process-shape matrix to find processes that are capable of forming flat sheet metal.
Fig.D.3: Process-section thickness range chart to narrow down processes to those that are capable of
forming a part with thickness close to 1mm.