Automatic Transmission Gear Material Selection

ByDominick Carluccio

William HoldenTahjee Seymour

Date: 4/28/15 Instructor: Professor Samardzic

ME438-102 : METALLURGYSPRING 2015

Table of Contents

Abstract

Introduction

Theory

Proposed Materials

Material Analysis

Material Selection

Conclusion

Nomenclature

References

Appendix

1

2

5

10

17

28

29

31

32

33

Abstract

Helical gears are used in automatic transmissions to allow the gear teeth to engage more

gradually then spur gear teeth causing them to run smoother and quieter. When selecting the material

for helical gears, it is very important to take the correct mechanical properties into account. Some of the

most important mechanical properties to consider are, yield strength, hardness, cost, modulus of

elasticity and density. The main objective of this report is to investigate possible candidates and perform

a material selection analysis to choose an appropriate material and procedure for a helical gear inside a

BMW M4 sports car powered by a six cylinder 3.0 liter turbocharged engine coupled to a Getrag

7DCI700 Powershift 7-Speed Dual-Clutch Transmission.

Introduction

The first attempt at an Automatic Transmission (using hydraulic fluid) was introduced by the

company General Motors in 1937. The transmission was semi-automatic and promoted as the

Automatic Safety Transmission (AST). It was implemented in hopes of becoming the new standard for

vehicles, boasting high increases in fuel economy, greater efficiency, and the new feature of clutch-less

driving. Unfortunately the AST was quickly dubbed a failure due to unreliability, high installation costs,

and low consumer demand. In two years time the AST ceased manufacture. However in 1940 GM

designed a new version of the transmission called the Hydra-Matic, the first fully automatic transmission

ever created. With a noticeable drop in installation cost among other features, the Hydra-Matic became

the first mass produced and commercially used auto transmission. In 1948 the first auto transmission

using a torque converter was introduced by Buick (called the Dynaflow). Soon after, companies such as

Packard and Chevrolet quickly followed suite. At this time vehicle transmissions were only two speed.

Not until the early 1950’s did the first three speed auto transmission appear (equipped with torque

converter) created by Borg Warner, an American automotive industry and parts supplier. Three speed

auto transmissions with torque converters remained the top seller for 30 years until the automatic

transmission with overdrive was introduced to the market, providing four or more gears, improved fuel

economy, and increased efficiency. Since the inception of the overdrive the most notable improvements

on the automatic transmission have been the increased number of forward gears and the cross over to

electronically controlled transmission from mechanically controlled operations.

The major components of the automatic transmission are the compound planetary gear set,

torque converter, bands, clutches, hydraulic system, valves, modulators, and the Electronic Control

Module. Not all components will be discussed. The primary function of the automatic transmission is to

transmit engine power to the drive wheels (rear, front, or all wheels). Power is transmitted in the

transmission through the use of gears connected at various ratios. Without a transmission cars would be

limited to one gear ratio which ultimately results in the sacrifice of either acceleration or top speed.

While a manual transmission does indeed complete the same task, the automatic transmission differs by

using the same set of gears to produce multiple ratios rather than locking and unlocking different gears

to the output shaft via a manual clutch. The numerous gears used to accomplish power transmission is

called a compound planetary gear set. For a four speed automatic transmission the compound planetary

gear set includes two sun gears, two planet carriers, and an outer ring that is responsible for the output

of the transmission. Generally in a transmission the 3rd speed (gear) is set at a 1:1 (read one to one) ratio

with the outer ring, gear ratios smaller than 1:1 put the transmission into overdrive. Overdrive is any

ratio that leads to the ring gear (output) rotating faster than the driven input gear (example being a .8:1

gear ratio).

All automatic transmissions come with the shifting positions Park, Reverse, Neutral, and Drive,

with some vehicles coming with additional options such as manually locking at 3rd, 2nd, and 1st gear. The

shift into Park positions a Parking Pawl (a steel pin) into the rotation path of the output gear, effectively

impeding the shaft from rotating. The Parking Pawl’s primary purpose is to keep the engines power from

reaching the drive wheels. Moving the shifter to the Reverse position triggers a solenoid that causes an

additional gear to engage, thus reversing the rotation of the output shaft. Neutral disengages all gears

disconnecting the transmission from the driven wheels. Drive allows the automatic transmission to

engage all gear ratios as needed. Ratios are controlled by an on board computer called the Engine

Control Unit (ECU). The ECU monitors a large network of sensors within the car to ensure conditions are

in normal operating ranges. If available, shifting into the 3rd, 2nd, or 1st position locks the transmission in

said gear, disallowing upshifts while enabling any lower gear ratios to engage if needed.

Under consideration is the 7 speed transmission for the BMW M4 for the purpose of creating a

component of its gearbox. The M4 uses an automatic transmission type called a Dual Clutch

Transmission or DCT. The layout of a DCT is essentially the combination of two manual gearboxes in one,

however all gear shifts are conducted automatically with electronic and hydraulics controls. Instead of

using a compound planetary gear set, the DCT uses all external gears and two shafts connected to each

of the clutches. Made possible with a hollow outer shaft and a solid inner one, the DCT can hold a

relatively large number of gears by placing said gears on different shafts. To clarify, on a 6 speed

transmission the first of two clutches is responsible for the odd gears (1, 3, 5 in addition to reverse) laid

on the inner shaft and the second clutch controls the even gears (2,4, and 6) laid on the outer shaft.

With two clutches operating alternating gears the shift time drops to a mere eight milliseconds while the

best automatic transmission shift times hover around 100 milliseconds. A decrease in shift time

significantly increases fuel economy due to the shortened time the engine power is disconnected from

the gears. Also, a short shift time decreases the severity of a phenomenon known as “Shift Shock” which

is the jerking motion one is susceptible to when the transmission changes gears. Shift Shock is more

prevalent in manual transmission vehicles especially with an unskilled driver. The component being

analyzed in the DCT is the connection between the driving pinion and one of its corresponding gears. For

the creation of the gears, five chosen materials will be thoroughly analyzed in order to find the best

combination of density, strength, cost, and hardness.

Theory

The transmission under consideration is the Power Shift 7DCI700 7-Speed M Double Clutch with

Drive Logic and Launch Control manufactured by Getrag and found in BMW’s M4, but also available in

the M3 and M5. BMW has played a large part in the development of recent automatic transmissions and

was the first company to release a fully automated manual gearbox in a production car in 1996. Since

then they have worked with Getrag to develop even more efficient automatic transmissions that are

now able to even outperform manual transmissions. Like most automotive technology, the double

clutch automatic transmissions were a

derivative of 80’s and 90’s Formula 1

sequential gearboxes and BMW played their

part in past years of Formula 1 so they had

access to this technology when it was most

valuable.

Dual clutch transmissions are the forefront of future automatic transmissions and are growing in

popularity amongst automotive manufacturers every year. A dual clutch transmission is comparable to

two manual transmissions; it utilizes two wet clutches with gears 1, 3, 5, and 7 on the first clutch and

gears 2, 4, and 6 on the second clutch. Like most transmissions though, the dual clutch transmissions

utilize helical gears to minimize vibrations. Their use of wet clutches eliminates the need of a torque

converter; it uses a series of wet pads to reduce friction in a pressurized cylinder to transfer power, the

clutch is disengaged by reducing the pressure of the cylinder. Dual clutch transmissions will typically

outperform manual transmissions because it utilizes the two clutches to minimize the time in between

Figure 1: The 2015 BMW M4

gear shifts and maximizing the quality of the mesh increasing the comfort level as well. While one clutch

is engaged on one shaft the next gear can be set up for the second clutch, the second clutch then

engages while the first disengages reduces the time between shifts to milliseconds. The manner of

upshifting and downshifting are almost

identical and are controlled by the

electronic control module (ECM); hard

acceleration will tell the transmission to

shift up, and hard braking will tell the

transmission to shift down. Modern day

dual clutch transmissions have been put

to the test and the world fastest drag racers with manual transmissions can’t shift as fast as these dual

clutch transmissions.

BMW has developed Drivelogic which is their software that controls the transmissions and

ultimately tells it how to act. The smooth gear changes that this transmission is possible of achieving are

largely a result of Drivelogic telling the transmissions exactly when to mesh gears and engage clutches.

Not only does Drivelogic coupled to this transmission result in a more comfortable ride than a typical

automatic transmission, but it also results in a better performing ride. Drivelogic is programed to only

shift radically when the car is going straight to prevent a larger change in force to the real wheels which

would result in a loss of traction, which is very dangerous around turns. Drive logic is also responsible for

synchronizing downshifts and engaging the clutch in a smoother fashion during down shifts so that same

large change in force doesn’t result in to large of a change in force to the rear wheels which could cause

a sudden loss of traction. Drivelogic also recognizes the driver’s unique driving manner and preferences

and tries to accommodate and adapt to those preferences.

The dual clutch transmission has 3 different driving modes Drive mode, Sport mode, and

Sequential Manual mode. Drive mode is fully automatic and designed to provide the most comfortable

and efficient characteristics of the transmissions and is similar to the drive selection in typical automatic

transmissions. Sport mode is also fully automatic but its programming is slightly different. Since

turbocharged engines perform best when the turbo is already spooled up, Sport mode keeps the engine

at the most optimal high revving range where the turbo can stay spooled up which will provide the user

instant torque similar to a naturally aspirated engine. Sequential Manual mode provides the user the

ability to manually select gear like in a clutch less sequential gear box.

This gearbox also provides the unique ability of launch control. Since a spooled up turbo

performs better than one that still has to be spooled up, this transmission allows the user to rev the

motor at a complete stop and spool up the turbo while the brake is held. Then the clutch is engaged

while the engine is revving allowing a launch from a stop with the maximum amount of torque possible.

BMW has developed a unique cooling system for this transmission that incorporates the cooling

cycle of the engine into the cooling system of the transmission. This not only keeps the oil at a perfectly

maintained temperature range, but it also heats up

the oil to within this range faster providing quicker

warm ups which reduce the amount of time that

the transmission has to overcome larger than

normal frictional forces from the oil in the

transmission. This will provide better efficiency

during startups and better performance under

heavy use when the transmission will produce a

large amount of heat from friction. Figure 3: BMW’s 3.0 liter six cylinder turbocharged engine

BMW has coupled a 3.0 liter turbocharged 6 cylinder (S55B30) coupled to their dual clutch

transmission. The S55B30 utilizes two twin mono-scroll turbochargers and produces 425 horsepower at

5500 RPM and 406 lb·ft of torque. The transmission transmits power to the rear wheel and is mounted

to the car with the engine longitudinally. In the seven speed gear box, the two gears with the highest

stress would be the meshing of the pinion to first gear which has a gear ratio of 4.81:1. The other gears

would experience lower stress values so stress analysis of the first gear mesh with the given materials

will suffice for the data needed for material selection.

When choosing a material for use in a transmission there are certain characteristics and

attributes of the material that are necessary. Gears

are very sensitive to geometric tolerance

differences so any change in the geometry of the

gear may result in chatter, vibrations, or even

ultimate failure of the gear as seen in figure (). The

causes of gear failure come in the form of bending

fatigue of the teeth, wear or contact fatigue on the surfaces, and scuffing which transfers material from

one gear onto the other. A high yield stress is the first and most important characteristic. When coupled

to most modern day automotive engines, gear teeth in the transmission will experience large forces and

resulting stress that the material must be strong enough to withstand. A high yield stress will prevent

the gear from failing due to bending fatigue. A high hardness is the second most important

characteristic, it is necessary to prevent any changes in the geometry of the gear so that the

transmission remains as smooth as possible. Any scuffing, wear, or contact fatigue on the surfaces will

result in chatter or vibrations and will ultimately weaken the gear and create stress concentrations.

Figure 4: Failure of helical gears due to high contact stresses

The third characteristic to take into consideration is cost. Like most engineering applications

choosing a material with a low cost is usually a limiting factor. Cost of the raw material should be

investigated as well as the machining and treatment costs. Sometimes shipping costs will be an issue as

well because some materials are exclusive to certain locations of the world. The fourth property to

consider for material selection is a low Young’s Modulus, or high vibration absorption ability. If a very

hard and stiff material was chosen for the whole gear the mesh would result in high vibrations. To

prevent this typically a more ductile material is chosen for the inner portion of the gear and then it is

case hardened to increase the hardness just on the outer surfaces. By choosing a material with a low

Young’s Modulus, but also with the ability to withstand wear and contact surface abrasion, this will

result in a very “smooth” transmission. The fifth most important property is a low density. The weight of

the car, and even more importantly, the weight of the drive train play a large role on fuel economy and

performance. By decreasing the weight of the drive train, the moment of inertia is also decreased; this

allows the motor to transmit power to the wheels quicker or with less force.

Proposed Materials

The following five materials were chosen by the design team to be analyzed for selection as the

material for a single internal gear for the automatic gear transmission:

SAE 950X SAE 4340H SAE 4720H XM023 CFRP (Carbon Fiber Reinforced Polymer)

SAE 950XSAE 950X is categorized as a High-Strength Low-Alloy Steel (HSLA) this means that the carbon

content of the steel is usually less than 0.3 percent. SAE 950X contains trace amounts of alloying metals

to enhance desired mechanical properties and sometimes resistance to atmospheric corrosion. The

HSLA steels typically achieve these properties without additional heat treatment.

SAE 950X Chemical Composition

C Fe Mn P Si S

<= 0.23% 97.43 – 100% <=1.35% <=0.04% <=0.90% <=0.05%

Table 1: Chemical Composition of SAE 950X Steel

Figure 5: Stress Strain Diagram for Plain Carbon Steel and SAE 950XTable 1 shows that the chemical composition of SAE 950X can range between 100% pure iron to

97.43% iron with mixed alloys. Figure 1 shows a comparison between plain carbon steel SAE 1010 with

SAE 950X. It is clearly seen that the area under the SAE 950X curve, in figure 5, is much larger than the

area under the SAE 1010 curve which means that the increased toughness is clearly seen. SAE 950X is

typically used where a good strength-to-weight ratio is required as HSLA steel cross sections are usually

20 to 30% lighter than carbon steel with the same strength.

SAE 950X Mechanical Properties

Ultimate Tensile Strength

Yield Tensile Strength Brinell Hardness Modulus of Elasticity

63,500 psi 49,200 psi 120-124 29,900 ksi

Table 2: SAE 950X Mechanical Properties

Table 2 shows a summary of the mechanical properties for SAE 950X. SAE 950X is available from

suppliers in China and Japan as well as limited quantity in the United States.

SAE 4340HSAE 4340H is a series of steel with main alloys of nickel, molybdenum and chromium. Each three

of these alloys has an effect of increase in hardenability. SAE 4340H has a favorable response to heat

treatment when quenched in oil followed by tempering. When tempered SAE 4340H displays a good

arrangement of strength and ductility and has a wide variety of uses in bearings, piston pins, ordinance,

gears, dies, and pressure vessels. 4340H can be machined by all conventional methods and can be bent

or formed by spinning or pressing in the annealed state. Heat treatment for strengthening is done at

approximately 1525 degrees F then followed by an oil quench.

SAE 4340H Chemical Composition

C Cr Fe Mn Mo Ni P Si S

0.37-0.44%

0.65-0.95%

95.04 – 96.53%

0.55-0.90%

0.2-0.3%

1.55-2.0%

<0.04% 0.15-0.30%

<=0.04%

Table 3: Chemical Composition of SAE 4340H Steel

Figure 6: Microstructure of SAE 4340H

SAE 4340H Mechanical Properties

Ultimate Tensile Strength

Yield Tensile Strength Brinell Hardness Modulus of Elasticity

186,000 psi 125,000 psi 363 29,000 ksi

Table 4: SAE 4340H Mechanical Properties

Figure 6 shows the microstructure of SAE 4340H at 25 micrometers. The black particles are

Bainite and the white or light grey particles are Martensite. SAE 4340H is available from 78 distributors

in North America and produced by 41 large mills.

SAE 4720HSAE 4720H is classified in the same series as SAE 4340H and is composed of the alloys

molybdenum, chromium and nickel and designed for good strength, wear resistance and toughness

properties. SAE 4720H is considered a moderately low carbon steel with approximately 0.17 -0.20%

carbon. The H variant of SAE 4720 is a special composition that has a good case hardening ability. SAE

4720H is rarely annealed as it impedes machinability but is usually normalized prior to case hardening.

The austenitizing temperature for SAE 4720 before quenching is 1500-1550 degrees F followed by

quenching in water or oil. SAE 4720H is manufactured mainly in China and India

SAE 4720H Chemical Composition

C Cr Fe Mn Mo Ni P Si S

0.17-0.23%

0.30-0.60%

96.55 – 97.93%

0.45-0.75%

0.15-0.25%

0.85-1.25%

<0.035% 0.15-0.30%

<=0.04%

Table 5: Chemical Composition of SAE 4720H

SAE 4720H Mechanical Properties

Ultimate Tensile Strength

Yield Tensile Strength Brinell Hardness Modulus of Elasticity

95,000-128,000 psi 50,100-80,000 psi 187-229 29,700 ksi

Table 6: SAE 4720H Mechanical Properties

Figure 7: SAE 4720H Alloy Steel Round Bar

Table 5 shows the chemical composition for SAE 4720H steel. The alloying composition of 4720H

is fairly similar to 4340H but with minor differences in quantity for each alloying element. Table 6 shows

the summary of mechanical properties

Figure 7 shows an example of SAE 4720H round bar stock from the manufacturer. For gear

manufacturing, the gear material would typically be cut from an end of the round bar stock then further

machined on a lathe and tooth cutting machine.

XM023XM023 is a steel alloy designed and manufactured by XTRAC. XTRAC is a worldwide leader in the

design and manufacture of transmission systems covering motorsports, defense and marine. XM023

steel alloy was developed specifically for the use in Formula One race transmissions and was used to

secure the championships for 2005 and 2006. XM023 was developed to improve upon the bending

fatigue and bearing properties. The tempering temperature for XM023 is approximately 390-480

degrees F. XM023 is used as a variety of gearbox internals including gears, mainshaft, layshaft, hubs and

selector forks. Unfortunately XM023 steel alloy is a proprietary material and no mechanical properties

are available to the public.

Carbon Fiber Reinforced Polymer (CFRP)Carbon fiber reinforced plastic or CFRP is a composite of strong carbon fibers bound within a

matrix polymer. The specific composite chosen for this project is Quantum Composites Lytex 4149.

Often the polymer is a thermoset resin such as epoxy but vinyl, polyester and nylon are sometimes used.

CFRP exhibits a very large strength to weight ratio and is commonly used where strength, rigidity and

weight are the most important factors. The composite is made up of two major parts, a matrix and

reinforcement. For this project the reinforcement is the carbon fiber that provides the high tensile

strength and the matrix is epoxy resin. The Mechanical properties depend on the characteristics of the

two components of the composite as well as the orientation of the fibers within the matrix. Typically the

reinforcement gives the composite its strength and rigidity. Although CFRP has a high strength to weight

ratio, a major design limitation is the lack of a definable fatigue endurance limit. This is extremely

important for gear material selection as the gear will constantly be experiencing cyclic loading and will

result in fatigue. It is extremely difficult to document the mechanical properties for carbon fiber

composites as the manufacturing process, matrix materials, fiber orientation and atmospheric

environment all have an effect on the mechanical properties.

Lytex 4149 is composed of 55% carbon fibers and 45% resin epoxy matrix.

Lytex 4149 CFRP Mechanical Properties

Ultimate Tensile Strength

Yield Tensile Strength Brinell Hardness Modulus of Elasticity

Not defined 41,900 psi 32-54 65,000 ksi

Table 7: Lytex 4149 CFRP Mechanical Properties

Table 7 shows the mechanical properties for the CFRP. Notice that the ultimate tensile strength

is not defined as it depends on the orientation of the carbon fibers. The hardness is determined from

the properties of the matrix. In this case the hardness is fairly low compared to the other researched

materials because it is a function of the resin epoxy.

Figures 8 and 9 : Microstructure of Carbon Fiber Reinforced Polymer

Figures 8 and 9 above shows the microstructure of CFRP in side view (LEFT) and end view

(RIGHT). The individual carbon fibers can easily be seen.

Summary

Mechanical PropertiesMaterial Ultimate

Tensile Strength

Yield Tensile Strength

Brinell Hardness

Modulus of Elasticity

Comments

SAE 950X 63,500 psi 49,200 psi 120-124 29,900 ksiSAE 4340H 186,000 psi 125,000 psi 363 29,000 ksi Excellent HardenabilitySAE 4720H 95,000-

128,000 psi50,100-

80,000 psi187-229 29,700 ksi Good Hardenability

XM023 N/A N/A N/A N/A Proprietary MaterialCFRP Not defined 42,000 psi 32-54 65,000 ksi Unknown Yield,

Undefined Fatigue Endurance

Table 8: Comparison of characteristics between materials

Material Analysis

Heat TreatmentHeat treatment for gears is usually favorable as it allows the ability to improve strength and

hardness to the surfaces of the gear teeth to prevent wear and failure over time. The two basic steps in

hardening steel is to heat the steel to some temperature above its transformation point so that it

becomes entirely austenitic in structure, then to quench the steel at some rate faster than the critical

rate to produce a martensitic structure. Although not all of the materials considered in this report are

able to be heat treated, two of the materials benefit from an additional heat treatment. Carburization is

also not taken into account as none of the proposed materials undergo treatment.

SAE 4340H can be heat treated by heating the material to approximately 1525 degrees F then

quenching in oil. It is important to quench SAE 4340H in only oil as it would lead to corrosion if it were to

be quenched in water.

SAE 4720H can also benefit from heat treatment. SAE 4720H can be case hardened or carburized

but is rarely annealed as it impedes machinability. The austenizing temperature for SAE 4720H is 1500-

1550 degrees F then quenched using water or oil.

CostCost Per Cubic Inch

SAE 950X * SAE 4340H SAE 4720H * XM023 CFRP *

$0.17* $0.65 $0.18* N/A $1.71*

Cost is a major consideration when selecting a material for large scale manufacturing. To

estimate the cost to have the helical gear made it is important to take the raw material cost into

account. The cost per unit volume for the raw material was calculated, the results can be seen below in

Table 9.

Table 9: Cost Per Cubic Inch By Material

It is important to note that the cost per cubic inch marked with (*) are rough estimations based

on varying geometry and do not include shipping from origin of manufacture. The cost estimation for

SAE 4340H is based off of a quote for 5” diameter round bar by 12 feet long from a distributor located

in North America. Both SAE 950X and 4720H could not be sourced within North America and would need

to be imported from China. BMW GmbH does own their own carbon fiber manufacturing plants so the

cost analysis on CFRP was based on an average assuming that BMW doesn't pay more than the average

price for their carbon fiber production. The CFRP cost estimation only includes the raw materials and

does not include any cost pertaining to casts, molds or instruments required to cure the matrix.

Stress and Pitting AnalysisFor the dual clutch transmission under

investigation, the mesh of the pinion to first gear

has the highest stress loads and also the location

of the minimum factor of safety; so a bending

stress and pitting analysis on the mesh of the

pinion and first gear will be sufficient to determine

the maximum stresses in the transmission. This

mesh results in a gear ratio of 4.81:1. The equation

used to determine bending stress and pitting is

from the AGMA design equations from AGMA Standard 2001-C95. The bending stress equation is similar

to the one used for spur gears but with a slight modification for helical gears. The mode of stress

application for pitting failure is contact stress and the contact stress equation is also similar to the one

for spur gears but with a slight modification as well.

A factor of safety of 2 was used for the design of the gears and pinions. All the gears and pinions

had the same geometrical design except for their face width. The shafts were designed using the max

shear stress formula and the geometrical preferences were researched and borrowed from previous

designers but also modified to accommodate the five proposed materials. The motor that was applied to

the transmission produced 425 hp at 5500 RPM and 406 lb-ft of torque. This translates to 232 lbs of

force on the gear teeth with a pitch line velocity of 2522. The overload factor for the transmission was

assumed to be 1.3 (light shock) considering the quality of modern bearings and vibration absorption

material used in design today.

After the analysis was investigated, the contact stress ended up being the more sensitive portion

of the stresses on the gears. The teeth particularly took the highest amount of stress as seen in figures

11 and 12. The pinion took the highest load and the original geometric design had to be modified for use

Figure 10: Pinion and 1st Gear Mesh for Analysis

with the two materials SAE 950x and CFRP because the factor of safety was not high enough. Their width

had to be increased from 2 inches to 3 inches.

SAE 950X Steel

Figure 12: X Y plane view of stress locations: Isometric view of stress locations

Figure 13: Bending Analysis of SAE 950X

Figure 14: Pitting Analysis of SAE 950X

SAE 4340H Steel

Figure 15: Bending Analysis of 4340H

Figure 16: Pitting Analysis of 4340H

SAE 4720H Steel

Figure 17: Bending Analysis of 4720H

Figure 18: Pitting Analysis of 4720H

CFRP (Carbon Fiber Reinforced Plastic)

Figure 19: Bending Analysis of CFRP

Merit Analysis

Series Alternatives Yield Stress (ksi) Hardness (BNH) Youngs Modulus (ksi x 1000) Density (lb/in^3) Cost (lb/in^3)1 950X 49.2 120 29.9 0.284 ≈ 0.172 4340H 125 363 29 0.284 0.653 4720H 50.1 187 29.7 0.284 ≈ 0.1754 CFRP 42 32 65 0.066 ≈ 1.71

Attribute Ranking Points Nomalized Ij

Density 1 0.066666667Youngs Modulus 2 0.13

Cost 3 0.20 Hardness 4 0.27

Yield Stress 5 0.333333333

Material Yield Stress (ksi) Hardness (BNH) Youngs Modulus (ksi x 1000) Density (lb/in^3) Cost (lb/in^3)1 0.086 0.266 0.025 0 12 1 1 0 0 0.6883 0.097 0.468 0.019 0 0.9964 0 0 1 1 0

Material Mi Merit Percents950X 0.3029 30.29

4340H 0.7376 73.764720H 0.3589 35.89CFRP 0.2000 20.00

Table 10: Merit Analysis

Material Selection

With the exception of the steel alloy XM023, the materials have been ranked based on a five

attribute merit analysis. The attributes consist of Density, Cost, Elasticity, Yield Stress, and Hardness. The

attribute of Machinability, though important, is an aspect of a material’s production which can be

factored into the Cost attribute. Other attributes such as Wear Resistance and Ductility are also

important however, similarly to Machinability, Wear Resistance is a byproduct of Hardness while

Ductility is generally determined with a material’s Modulus of Elasticity. Important attributes that could

not make the list such as Fatigue life are simply too difficult to ascertain. Each of the five attributes

chosen for the merit analysis were given a rank ranging from the most important (5) to the least

important (1). The ranking from most to least important is as follows, Yield Stress, Hardness, Cost,

Elasticity, and Density. This information can be found in table 10. The analysis yielded the highest value

for the steel alloy 4340H at 73.76 percent, trailed by 4720H at 35.89 percent. The pure steel alloy 950X

came third with a merit percent at 30.76 with CFRP following at a low 20 percent. Steel alloy 4340H is

the clear material selection with its prevailing Brinell Hardness reaching 363, a magnitude difference of

176 over its nearest contender, 4720H. With the highest yield strength at 125 ksi, the 4340H material is

inferior only in the Elasticity and Cost which due to their rankings didn’t affect 4340H’s outcome of being

the best material for the gear set. It should be noted however that this outcome may have changed if

the attributes of the steel alloy XM023 had been made available.

Conclusion

This report demonstrates an understanding of mechanical properties required to adequately

select an appropriate material for the BMW M4 sports car powered by a Getrag 7DCI700 Powershift 7-

Speed Dual-Clutch Transmission. Using Theory from machine design, the design limits for hardness and

yield strength were defined by the equations for tooth bending and pitting in helical gears. The results

from the merit analysis concluded that SAE 4340H has the correct combination of properties required to

prevent the gear from failing. Overall this design report was successful in selecting an appropriate

material for a helical gear and allowed the students an opportunity to use the course material in a real-

world scenario.

NomenclatureTorque [ft·lbs] THorsepower hpRotations per Minute RPM, NRotational Velocity [rad/s] ωInner Diameter [in] di

Outer Diameter [in] do

Inner Radius [in] ri

Outer Radius [in] ro

Pressure Angle [degrees] φHelix Angle [degrees] ψDiametral Pitch [teeth/in] Pd

Face Width [in] FTransmitted Load [lbs] Wt

Pitch Line Velocity [ft/min] vl

Factor of Safety Sf

Overload Factor Ko

Quality Class of Gear Set Qv

Size Factor Ks

Rim Thickness Factor KB

Stress Cycle Factor YN

Temperature factor KT

Reliability Factor KR

Allowable Stress [psi] Sal

Geometry Factor J, IPitch Diameter [in] dDynamic Factor Kv

Load Distribution Factor Km

Stress [psi] σPoisons Ratio υ, μYoung’s Modulus [psi] EElastic Coefficient [(lb/in2)0.5] Cp

Hardness Ratio Factor CH

Axial Contact Ratio mF

Carbon CIron FeManganese MnPhosphorus PSilicone SiSulfur SChromium CrMolybdenum MbNickel NiCarbon Fiber Reinforced Plastic CFRP

References

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