Main Report

Evaluation of Roller profile for Specific Requirements

1.0 INTRODUCTION

Fuel Injection plays a very important role in a Diesel Engine. The timing and pressure of

injection influences the performance parameters of the engine. Injection pressure was previously

attained by having a pump for every cylinder of the engine. The drawback of this type of

injection mechanism is that the flow of fuel into the cylinder couldn’t be monitored and varied

during the operation of the engine. To overcome this problem and to promote the cleaner burning

of diesel, the concept of Common Rail Direct Injection was developed around 1950. The concept

was way ahead of its time and couldn’t be physically realised.

Due to the advances in the Electronic industry, the complicated concept was realised with the

help of sensors, programmable circuitry etc. Till the recent past Common Rail technology was

highly advantageous in medium sized vehicles, i.e. vehicles with 4 or more cylinders. As the

emission norms are becoming more stringent, the Common Rail technology is being introduced

in small sized vehicles.

Common rail direct fuel injection is a modern variant of direct fuel injection system for petrol

and diesel engines.

On diesel engines, it features a high-pressure (over 1,000 bar/15,000 psi) fuel rail feeding

individual solenoid valves, as opposed to low-pressure fuel pump feeding unit injectors (Pumpe

Düse or pump nozzles). Third-generation common rail diesels now feature piezoelectric injectors

for increased precision, with fuel pressures up to 1,800 bar/26,000 psi.

In gasoline engines, it is utilised in gasoline direct injection engine technology.

1.0.1 History:

The common rail system prototype was developed in the late 1960s by Robert Huber of

Switzerland and the technology further developed by Dr. Marco Ganser at the Swiss Federal

Institute of Technology in Zurich later of Ganser-Hydromag AG (est.1995) in Oberägeri.

The first successful usage in production vehicle began in Japan by the mid-1990s. Dr. Shohei

Itoh and Masahiko Miyaki of the Denso Corporation, a Japanese automotive parts manufacturer,

Manipal Institute of Technology 1


developed the common rail fuel system for heavy duty vehicles and turned it into practical use on

their ECD-U2 common-rail system mounted on the Hino Rising Ranger truck and sold for

general use in 1995. Denso claims the first commercial high pressure common rail system in

1995

Fig 1.1: Common rail fuel system close up

Modern common rail systems, whilst working on the same principle, are governed by an engine

control unit (ECU) which opens each injector electronically rather than mechanically. This was

extensively prototyped in the 1990s with collaboration between Magneti Marelli, Centro

Ricerche Fiat and Elasis. After research and development by the Fiat Group, the design was

acquired by the German company Robert Bosch GmbH for completion of development and

refinement for mass-production. In hindsight the sale appeared to be a tactical error for Fiat as

the new technology proved to be highly profitable. The company had little choice but to sell,

however, as it was in a poor financial state at the time and lacked the resources to complete

development on its own. In 1997 they extended its use for passenger cars. The first passenger car

that used the common rail system was the 1997 model Alfa Romeo 156 1.9 JTD, and later on

that same year Mercedes-Benz C 220 CDI.

Common rail engines have been used in marine and locomotive applications for some time. The

Cooper-Bessemer GN-8 (circa 1942) is an example of a hydraulically operated common rail

diesel engine, also known as a modified common rail.

Vickers used common rail systems in submarine engines circa 1916. Doxford Engines Ltd.

(opposed piston heavy marine engines) used a common rail system (from 1921 to 1980) whereby

a multi-cylinder reciprocating fuel pump generated a pressure of approximately 600bar with the

fuel being stored in accumulator bottles. Pressure control was achieved by means of an


http://en.wikipedia.org/wiki/Locomotive

http://en.wikipedia.org/wiki/Mercedes-Benz_W202

http://en.wikipedia.org/wiki/JTD_engine

http://en.wikipedia.org/wiki/Alfa_Romeo_156

http://en.wikipedia.org/wiki/Mass-production

http://en.wikipedia.org/wiki/Robert_Bosch_GmbH

http://en.wikipedia.org/wiki/Fiat

http://en.wikipedia.org/wiki/Research_and_development

http://en.wikipedia.org/w/index.php?title=Elasis_S.C.p.A.&action=edit&redlink=1

http://en.wikipedia.org/w/index.php?title=Centro_Ricerche_Fiat&action=edit&redlink=1

http://en.wikipedia.org/w/index.php?title=Centro_Ricerche_Fiat&action=edit&redlink=1

http://en.wikipedia.org/wiki/Magneti_Marelli

http://en.wikipedia.org/wiki/Engine_control_unit

http://en.wikipedia.org/wiki/Engine_control_unit


adjustable pump discharge stroke and a "spill valve". Camshaft operated mechanical timing

valves were used to supply the spring loaded Brice/CAV/Lucas injectors which injected through

the side of the cylinder into the chamber formed between the pistons. Early engines had a pair of

timing cams, one for ahead running and one for astern. Later engines had two injectors per

cylinder and the final series of constant pressure turbocharged engines were fitted with four

injectors per cylinder. This system was used for the injection of both diesel oil and heavy fuel oil

(600cSt heated to a temperature of approximately 130°C).

1.0.2 Principles:

Solenoid or piezoelectric valves make possible fine electronic control over the fuel injection time

and quantity, and the higher pressure that the common rail technology makes available provides

better fuel atomisation. In order to lower engine noise the engine's electronic control unit can

inject a small amount of diesel just before the main injection event ("pilot" injection), thus

reducing its explosiveness and vibration, as well as optimising injection timing and quantity for

variations in fuel quality, cold starting, and so on. Some advanced common rail fuel systems

perform as many as five injections per stroke.

Fig 1.2: Flow Diagram of a Common rail system


http://en.wikipedia.org/wiki/Electronic_control_unit

http://en.wikipedia.org/wiki/Noise_(environmental)

http://en.wikipedia.org/wiki/Atomisation

http://en.wikipedia.org/wiki/Electronic_control_unit

http://en.wikipedia.org/wiki/Piezoelectric


Common rail engines require no heating up time and produce lower engine noise and emissions

than older systems.

Diesel engines have historically used various forms of fuel injection. Two common types include

the unit injection system and the distributor/inline pump systems. While these older systems

provided accurate fuel quantity and injection timing control they were limited by several factors:

They were cam driven and injection pressure was proportional to engine speed. This

typically meant that the highest injection pressure could only be achieved at the highest

engine speed and the maximum achievable injection pressure decreased as engine speed

decreased. This relationship is true with all pumps, even those used on common rail

systems; with the unit or distributor systems, however, the injection pressure is tied to the

instantaneous pressure of a single pumping event with no accumulator and thus the

relationship is more prominent and troublesome.

They were limited on the number of and timing of injection events that could be

commanded during a single combustion event. While multiple injection events are

possible with these older systems, it is much more difficult and costly to achieve.

For the typical distributor/inline system the start of injection occurred at a pre-determined

pressure (often referred to as: pop pressure) and ended at a pre-determined pressure. This

characteristic results from "dummy" injectors in the cylinder head which opened and

closed at pressures determined by the spring preload applied to the plunger in the

injector. Once the pressure in the injector reached a pre-determined level, the plunger

would lift and injection would start.

In common rail systems a high pressure pump stores a reservoir of fuel at high pressure up to and

above 2,000 bars (29,000 psi). The term "common rail" refers to the fact that all of the fuel

injectors are supplied by a common fuel rail which is nothing more than a pressure accumulator

where the fuel is stored at high pressure. This accumulator supplies multiple fuel injectors with

high pressure fuel. This simplifies the purpose of the high pressure pump in that it only has to

maintain a commanded pressure at a target (either mechanically or electronically controlled).

The fuel injectors are typically ECU-controlled. When the fuel injectors are electrically activated



a hydraulic valve (consisting of a nozzle and plunger) is mechanically or hydraulically opened

and fuel is sprayed into the cylinders at the desired pressure. Since the fuel pressure energy is

stored remotely and the injectors are electrically actuated the injection pressure at the start and

end of injection is very near the pressure in the accumulator (rail), thus producing a square

injection rate. If the accumulator, pump, and plumbing are sized properly, the injection pressure

and rate will be the same for each of the multiple injection events.

In medium and large duty engines the fuel is being pumped using Rotary Piston pumps. These

pumps if miniaturized would result in higher costs which would render the implementation of

Common Rail Technology in Small sized vehicles as economically unfeasible. The concept of

single reciprocating pumps was developed keeping the small sized as the target.

The reciprocating pump is driven by a cam which is mounted on the cam shaft of the engine. The

mechanism used is the cam and roller mechanism. The reciprocating plunger is connected to the

roller through a tappet which is enclosed by a guide. The load on the roller is very high which

leads to contact loading in the elements. The rolling of the elements effects a variable load on the

component, which leads to fatigue in the elements.

1.0.3 Delphi Unit Pump Diesel Common Rail System:

Delphi Unit Pump Diesel Common Rail (UPCR) System is an innovative engine management

concept that leverages advanced common rail technology a proven "green" strategy for very

small diesel engine programs. The system offers manufacturers a cost-effective, robust solution

to help them achieve optimal fuel efficiency and meet stringent emissions standards, such as

Euro 4.

The Delphi Unit Pump Diesel Common Rail System is specifically designed for 1-, 2-, and 3-

cylinder engine applications. It is ideal for small engine vehicles destined for emerging markets

and for entry-level vehicles that will be marketed in developed regions. It is also well-suited for

other nonautomotive diesel engine products such as small agricultural and industrial equipment.

Key features of the Delphi Diesel UPCR System include fast solenoid diesel injectors and a

common rail, a program-tailored engine control module (ECM), robust unit fuel pump with an

inlet metering valve, as well as an efficient, low cost fuel filter.



Fig 1.3: Delphi Diesel Unit Pump Common Rail System

The Components of the UPCR are:

1. Pump assembly

2. Tappet assembly

3. Engine Control Unit

4. Nozzle assembly

5. Rail



Benefits:

Low cost engine management system designed to provide the necessary high value

essential to the market success of low-end products and economy segment vehicle

programs.

Light weight, compact package size enables relative ease of application in very small

engine programs.

High system pressure (up to 1,600 bar) achieves high efficiency and excellent engine

performance.

Proven, compact fast response solenoid diesel fuel injectors are capable of up to five

injections per cycle. The multi-injection capability enables precise tuning of combustion

to help meet emissions, fuel economy and noise targets.

Simple, robust unit pump provides reliable performance and contributes to an overall

economical system cost.

The UPCR System is able to drive devices such as an exhaust gas recirculation (EGR)

valve and intake throttle control. Air management capability helps meet emissions

standards, such as Euro 4.

1.1 Statement of the problem:

Long fatigue life is one of the most important concerns while designing cylindrical rolling

elements. The stress induced in the bearing components mainly influences the life of the element.

It therefore becomes necessary to exactly determine stresses developed in rolling elements and

raceways. Roller bearings with rollers having flat contour surfaces suffer from edge

concentration. It was suggested as a remedy to use a contour profile also known as crown.

At Delphi-TVS the development of UPCR was hindered by frequent failure of the cam and roller

follower. Initially when the roller was indigenously developed the interface was failing

aggressively with the cam profile being completely worn out. The roller was outsourced to a

leading bearing manufacturer and prototypes were used in the pump. The life of the rolling



element has been drastically improved but the elements still fail before 1e7 revolutions. The

standards specify that the elements must maintain its integrity up to 1000 hours of operation.

The recent failures in the rolling elements have been in the form of pitting on the rollers and on

the lobe of the cam. The pitting pattern when observed has been spread over the roller and its

distribution has been uneven around the circumference of the roller. The distribution of pitting

on the roller can be described as progressively increasing and then diminishing back to the initial

point. The failure in the cam is observed over the lobe of the cam, where the load is the highest

and the radius of curvature is the least. Hence the failure can be ascertained to be load induced.

1.2 Objectives of the Study:

As stated previously, the failure in the present cam roller assembly is load induced. The common

cause for failure in contact mechanics is contact fatigue. This failure is visible to the eye by the

presence of pitting marks on the rolling elements. The driving cause of contact fatigue is the

shear stress present in the interface due to contact loading. The shear stress is below the surface

of the contact elements.

This project aims to evaluate the stresses, for the present dimensions of the cam-roller assembly.

Then various profiles are to be evaluated both theoretically and analytically keeping the

dimensions of the elements constant. This would help in narrowing down to the best profile

under the present scenario.

Redesigning the cam roller assembly, if necessary, to bring the dimensions well within the

strengths of the material. Testing of the prototypes will be undertaken to confirm the compliance

of the design to real time situation

1.3 Scope of the Study:

There are 4 basic types of roller profiles that are used in rolling elements. These profiles have

their own benefits and drawbacks. This project would compare all the profiles and their

variations to shortlist the best profile for this application.



The first step would be to calculate the stresses theoretically in the present combination of the

cam-roller assembly and then evaluate the same, using an analysis software. The next step would

involve calculating the stresses for various profiles under the same load conditions.

The material properties such as Tensile strength, Compressive strength, Fatigue Strength are to

be evaluated along with other associated properties. A comparison of stresses in the elements and

strength of the material would help in narrowing down to the cause of failure.

Once the failure causing stress has been identified, the cam-roller assembly will be redesigned to

get the stresses well within the limit. Then the elements will be undertaken for prototyping and

real time experimentation.



2.0 LITERATURE SURVEY

Zaretsky (1992) developed a method for estimating components design survivability by

incorporating the finite element analysis. Horng et al. (2000) developed a deformation equation

for the circular crowned roller compressed between two plates. (Poplawski et al. 2000) analyzed

four roller profiles using both a closed form solution and finite element analysis (FEA) for stress

and life. Kania (2005) calculated the deformation of the bearing by the FE models, in which

rolling elements are replaced by the truss elements. Brandlein et al. (2000) explained how one

can reduce the peak stresses to increase the bearing life by giving logarithmic profile and also

discussed to reduce ill effect of misalignment with logarithmic profile. Harris (1991) discussed

the influence of different surface profiles in minimizing edge stresses and use of roller full

length. He also explained the drawbacks of different profiles under heavy loads and how

logarithmic profile is a remedy to overcome those drawbacks (Steven M. Peters et al 2000).

The various types of profiles that are used in a roller bearing are:

1. Flat Profile

2. Spherical Profile

3. Logarithmic Profile

4. Partially Crowned Profile

Flat Profile:

Fig 2.1: Flat Profile



This is the simplest type of profile. This profile is preferred when the length of the roller and the

corresponding element is the same. The flat profile of the roller results in an edge stress

concentration at roller ends. It is shown in the figure, where the contact stress is very high at

edges. In flat-profiled cylindrical bearings as the load increases the contact stress increases

linearly. For the present case the maximum contact stresses obtained at the corner of the roller at

the inner raceway. The horn shape shows the edge stress concentration. As the load increases the

edge stress also increases. Contact stresses at the middle part of the roller are constant and

relatively low. (P.V.V.N. Prasad, et al 2004)

Spherical Profile:

To prevent high stresses at edges, the roller surface incorporated with a circular crowning. This

eliminates the edge stress concentration at the low and moderate loads. With increase in the

crowning radius, the maximum contact stress decreases up to a certain limit. On further increase

in the crowning radius, the contact stress increases with increase in the crowning. The maximum

contact stress is at the middle of the roller surface. With the increase in the load, the contact

length also increases. At high loads the edge concentration takes place. This profile is good for

low and moderate loads. (P.V.V.N. Prasad, et al 2004)

Fig 2.2: Spherical Profile

Logarithmic Profile:

A logarithmic profile is generated using a mathematical logarithmic function. Under all loading

conditions, the logarithmic profile (LP) uses more contact length of the roller than either the fully



crowned or partially crowned roller profiles. Edge loading tends to be avoided in LP especially at

heavy loads. (P.V.V.N. Prasad, et al 2004)

Fig 2.3a: A cylindrical roller with logarithmic profile Fig 2.3b: Logarithmic profile zoomed in h(x) direction

There are various types of logarithmic profiles, which are differentiated by the formula used to

generate the profile. The first formulation for the profile was generated by Lundberg, according

to which the deviation from the straight profile is given as

Where

Where

hhl

is the multiplier of a Lundberg’s profile deviation, h

is the deviation of the roller

generator from the straight profile,

hl

is the maximum value of the deviation of the profile

according to Lundberg, ε is the corrective exponent. p is the radial load on the roller, Σρ is the

curvature sum, E is the Young’s modulus of elasticity, l is the length of the roller and is the

distance from the centre of the roller.


h( x )= 4 p2

E2 Σρ ( hhl ) ln l1+e−g−(2x / l)2 ε

g=0.5−ln4 p

lE Σρ

hl=4 p2

E2 Σρ (0 .5−ln4 plE Σρ )


The roller profile, which is generated for higher load than the applied load, gives the lower

contact stress than the profile generated at the applied (operating) load. After certain limit the

contact stress increases even though the profile generated at higher than the applied load. As

multiplying factor increases the contact length of the roller decreases and the contact stresses

increases with increase in the correction factor. At lower loads than the profile designed load the

contact length is small. As the load increases the contact length increased. For loads above the

designed load, the contact length increases but the contact stress is not uniform and slight edge

stress concentration occurs. The LP of roller results no edge stress concentration at the low,

medium and high loads and contact stresses are distributed uniformly along the length of the

roller.

Lundberg’s Profile is very difficult to manufacture. (Fujiwara, et al, 2007) Hence Johan’s Gohar

profile which is derived from Lundberg’s profile is preferred when it comes to ease of

manufacturing.

Where

a- Half effective length of contact

b- Half width of contact

E’- Effective Young’s Modulus,

E- Young’s Modulus

υ- Poisson’s Ratio

l- Effective Contact length

Q- Load

x- position in axial direction

z(x)- deviation from straight profile


z ( x )= 2QπlE '

ln1

1−(1−. 3033b/a )(2 x /l )2

E '= E

1−ϑ2


However, when this equation is applied, carrying out the calculation using the technique to be

described later results in edge stress occasionally. This trend becomes more remarkable under the

presence of misalignment. Providing a cylindrical roller or conical roller with a straight section

may be desirable for machining or functional reasons; however, using this equation does not

allow a straight section to be set up.

To solve this problem, three design parameters, K1, Km, and zm, are introduced into equation.

K1- Multiple of Q

K2- Ratio of crowning length to a

zm- Drop at the end of effective contact length

Fig 2.4: Partially crowned Logarithmic profile parameters

This profile is a partially crowned profile where the crowning is logarithmic in nature. Other type

of partially crowned profile can have spherical or tapered profiles.

In the flat profile of a cylindrical roller as the applied load increases the maximum stress also

increases linearly. Whereas in the circular and logarithmic profiles, the variation of the contact

stresses with the load is not linear. As the radius of the crown of roller surface increases the


z ( x )=2 K1Q

π lE 'ln

1

1−(1−e

− zm π lE '

2K1Q )( y−aK2a

+1)2


maximum stress decreases for the same applied load. In the trend is same in logarithmic profile

also i.e. the maximum stress decreases with the increases design load for the profile up to a

particular limit, afterwards it increases. In the circular crowned profile as the load increases the

uniformity of the stress along the length of the roller vanishes rapidly. In logarithmic profiled

roller as the load increases the length of the contact increases. In the flat profile as the load

increases the edge loading increases.

The logarithmic profile is the remedy for the edge loading at high-applied loads. The circular

crown also eliminated the edge loading but the contact length remains very less. Logarithmic

profile generated at the correction factor of 1 and multiplying factor of 3 gives uniform

distribution of contact stresses along the length of the roller. For increase in the multiplying

factor the contact length increases and with increase in the correction factor the contact stress

increases. Even in logarithmic profile bearings for very heavy loads the small edge stress

induces. It remains to be seen how LP behaves for combined loadings in the bearings i.e. with

non-uniform distribution of the applied load on bearing rings.

The maximum Hertz stress-life exponents were determined for the individual roller profiles and

the resultant individual lives were compared. The following results were obtained (Brian L.

Vlcek, et al, 2000):

1. With the closed form solution and not considering edge or stress concentrations, the flat roller

profile has the longest predicted life followed by the end-tapered profile, the aerospace profile

and the crowned profile, respectively. The full crowned profile produces the lowest lives. While

there are life differences between the end tapered profile and the aerospace profile, these

differences may not be significant. For the FEA solution which considered stress concentrations

the end tapered profile produced the highest lives but not significantly different from that of the

aerospace profile followed by the crowned profile and the flat roller profile, respectively.

2. The effect of edge loading on the flat roller profile is to reduce life at the higher load by as

much as 98 and 82 percent at the lower load. The actual percentage calculated depends on the

analysis used.



3. The resultant predicted life at each stress condition not only depends on the life equation used

but also on the Weibull slope assumed. The least variation in predicted life with Weibull slope

comes with the Zaretsky equation. At all conditions calculated for a Weibull slope of 1.11, the

ANSI/ABMA/ISO standard result in the lowest lives. Except for the Weibull slope of 1.11 at

which the Weibull equation predicts the highest lives, the highest lives are predicted by the

Zaretsky equation. For Weibull slopes of 1.5 and 2, both the Lundberg-Palmgren and Ioannides-

Harris (where τu equal 0) equations predict lower lives than the ANSI/ ABMA/ISO standard.

4. Based upon the Hertz stresses for line contact, the load-life exponent p of 10/3, results in a

maximum Hertz stress-life exponent n equal to 6.6. This value is inconsistent that experienced in

the field. Lundberg and Palmgren’s justification for a p of 10/3 was that a roller bearing can

experience “mixed contact,” that is, one raceway can experience “line contact” and the other

raceway “point contact.” This is certainly not consistent with the vast majority of cylindrical

roller and tapered roller bearings designed and used today.

Coating on surfaces:

There is a wide range of coating techniques and careful selection of the appropriate coating

material and method is a pre-requisite for an effective coating. Prior to selecting the coating

material and method the first question to be asked is whether wear or friction is of greater

concern. If the prime objective is to reduce friction then a solid lubricant coating should be

selected and the coating method will, in most cases, be either sputtering or a combination of

painting and baking (Gwidon W. Stachowiak).

To suppress wear by the application of coatings, it is first necessary to determine the mechanism

of wear occurring, e.g. whether abrasive wear or some other form of wear is present. Although

most coatings can suppress several forms of wear, each type of coating is most effective at

preventing a few specific wear mechanisms. Therefore during the selection process of the most

effective coating to suppress wear in a particular situation, i.e. coating optimization, the

prevailing wear mechanism must first be recognized and assessed. The basic characteristics of

the coatings which can be achieved by the methods described in the previous section in terms of

wear control are summarized in the figure.



It can be seen from figure that while the optimization of a coating to resist abrasive wear is

relatively simple, i.e. it is sufficient to produce a thick hard surface layer with toughness high

enough to prevent coating fracture, other wear mechanisms require much greater care in coating

optimization.

Fig 2.5: Basic characteristics of coatings in terms of wear control.

Characteristics of Wear Resistant Coatings:

Studies of wear resistant coatings reveal that hard coatings are most effective in suppressing

abrasive wear. An example of this finding is illustrated in figure which shows the wear rate of a

pump rotor as a function of the hardness of the coating applied to the surface. It can be seen from

figure that the abrasive wear rate declines to a negligible value once a PVD coating of titanium

nitride, which is characterized by extremely high hardness, is employed.

In this example abrasive wear was caused by very fine contaminants present in the pumped fluid

and the size of the abrasives was sufficiently small for a thin PVD coating to be effective. In

other applications where the abrasive particles are much larger, thicker coatings are more

appropriate.

It was also found that thin films of ceramics such as titanium nitride are quite effective in

suppressing adhesive wear in poorly lubricated and high stress contacts. For example, when a

cutting tool is coated with titanium nitride, adhesion and seizure between the tool and metal chip

does not occur even when cutting is performed in a vacuum. Titanium nitride coatings were also



applied to gears and the scuffing tests on coated and uncoated gears revealed that the critical load

and scuffing resistance for coated gears is much higher.

Fig 2.6: Example of the resistance of a hard coating, TiN, to abrasion

This coating also reduces the coefficient of friction in unlubricated sliding as well as wear rates,

e.g. coefficients of friction close to 0.1 between titanium nitride and zirconium nitride coatings

on hardened bearing steel have been observed. Unfortunately titanium nitride coatings do not

provide corrosion resistance. Since zirconium and hafnium belong to the same IVB group of the

periodic table of chemical elements as titanium, some similarity in wear properties of their

compounds can be expected. In fact, hafnium nitride was found to give the best wear resistance

performance in tests on cutting tools. Zirconium nitride is also extremely useful as a coating. It

should also be mentioned that for hard coatings to be effective, adequate substrate hardness is

essential. Therefore hardened steels and materials such as stellite are generally used as a

substrate for this type of coating.

Fretting wear can be mitigated by the use of hard coatings, e.g. carbides, especially at small

amplitudes of fretting movement. However, at higher fretting amplitudes, spalling of the carbide

coatings renders them ineffective.



Coatings produced by ion implantation, in certain applications, can also provide large reductions

in wear. Since the coatings produced by this technique are very thin they are only effective in

reducing wear at low load levels as illustrated.

Fig 2.7: Effect of nitrogen ion implantation on wear rates of stainless steel in unlubricated sliding

The performance of non-metallic coatings such as tungsten carbide used for rolling elements is

related to the operating conditions. For example, it was found that 100-200 [μm] thick plasma-

sprayed coatings on steel and ceramic balls fail by surface wear when lubrication is poor or by

sub-surface delamination when lubrication is effective.

Wear-resistant coatings can be as vulnerable to oxidative wear as monolithic metal substrates.

For example, copper causes rapid wear of cutting tools coated with titanium nitride, titanium

carbide or a combination of both compounds. It was found that the primary cause of rapid wear

of the titanium nitride and carbide coatings is a catalytic effect of copper on the oxidation of the

nitride and carbide to titanium oxide which is then rapidly worn away. In contrast, the oxidation

of chromium nitride in air is much slower than titanium nitride, thus permitting the chromium

nitride to effectively protect machining tools from wear by copper.



3.0 Methodology

The load on the roller is the force required to pressurize the fuel to 1600 bar. During pumping, in

a reciprocating pump, the forces that need to be overcome are the frictional force, spring force,

and the fluid force.

3.0.1 Force Calculation:

Load due to Pressure,

F = P x A

Cross-sectional Area of the Plunger,

A =

πbd2

4

= 4.419x10-5

F =160x106 x 4.419x10-5

=7068.59 N

15% frictional losses assumed,

F =

7068 .59. 85

= 8316 N

Total deflection, d =Lift+ initial compression

=6+5= 11mm



Spring Force,

Fs = K x d

= 11 x 29.85

= 328.35 N

Acceleration in m/s2,

acc = .01164 x

36×N2

1000

= 6704.64 m/s2

Inertia Forces,

FI = m x acc

= 6704.64 x 0.1635

= 1096 N

The Total Load acting on the roller,

L = F + Fs + FI

= 8.316 + 0.328 + 1.096

= 9.74 kN

The Load on the roller is transferred indirectly and is in the form of a distributed load on the pin

over the length of contact with the tappet. The loading is offset and cannot be used directly in the

equations stated in the references. The first step would be to convert the offset load into a point


BUSH

Roller

PIN

Load Load


load on to the centre of the roller. A 2-dimensional image is shown in figure3.1, and the steps

involved in the conversion are shown.

Fig 3.1: Schematic diagram of load transfer

3.0.2 Load Transformation:

The load distribution over the pin is shown in figure3.2. The load from the tappet is in the form

of a UDL of 1132.56 N/mm and the length of contact between the pin and the tappet is 4.3mm.

The pin is supported by the bush whose length is 13.35mm. But during loading, pin acts as an

overhanging beam and due to the deformation of the pin the support from the bush is converted

into a 2 point support at the ends of the bush.

Fig 3.2: Load Distribution over the pin



The UDL is converted into a point load, at the centre of distribution. The Reaction R 2 is the

reaction force on from the bush and is the main point where the load is transferred to the bush

and then to the roller. R1 is the Reaction that is generated, when the pin is constrained at its

midpoint. The reaction R1 is the load that would act at the centre of the roller under the present

loading conditions.

Fig 3.3: Free body diagram over half the length of the pin

On solving the force distribution diagram

4870+R1=R2

Taking moment about R1

4870×9 .85-R2×6 .675=0⇒R2=7186 . 44 N

Hence,

R1=2316 .44N

The overall force considering the whole length of the roller is

L=2 R1

L=4632. 88N



3.0.3 Contact Stresses in a flat profile[6]:

The Contact Pressure on the roller is

σ con=0 .564 (√ F (1/R1+1 /R2)lΔ )

Where

Δ=1−ν

12

E1

+1−ν

22

E2

=1−. 292

202e 9+ 1−.32

205e 9

= 8.97 x 10-12 Pa-1

Therefore Contact Pressure

σ con=0 .564 (√4632 .88 (1 /. 01+1/ . 016 )l×8 .97 e-12 )

=

167 .822×106

√l

The Stresses at the region of contact are

σx = σz = - σcon

σy = - 2υ x σcon

=

−100.693×106

√ l



The length of the roller is calculated for the Maximum normal stress and is

l=(167 . 822×106

2000×106 )2

l = 7.04 mm

The present roller at the length of 14.35 mm suffices the requirement of minimum roller length

of 7.04mm. This is just under the consideration of normal stresses and not any other form of

stresses.

At the present length of 14.35 mm,

The Normal stresses are quantified as

σx = σz = - 1395.925 MPa

σy = 837.55 MPa

The maximum shear stress is calculated as

τxz = 0.304 σcon

= 424.36 Mpa

The Principal Stresses in the material for pure rolling is the normal X,Y,Z axis stresses, due to

the absence of applied shear.

The roller is then evaluated under the Von Mises Stress Criteria

σmax = √σ x2+σ y

2+σ z2−σ xσ y−σ y σ z−σ zσ x

= 558.375 MPa.



3.0.4 Dynamic Loading Condition[6]:

In real time contact problems, lubrication is in the form of Elasto-Hydrodynamic lubrication.

This type of lubrication and operating conditions causes the roller to slide and roll over the cam,

hence introducing the effect of friction. In contact mechanics, the phenomenon where rolling and

sliding takes place simultaneously is known as dynamic loading. This is the real time condition

in rolling contact mechanics.

B=12 ( 1

R1

+1R2

)=171 . 48

m1+m2=Δ

Half contact width,

a=√2π×m1+m2

B×Fl

a=2 .616×10−5

√ la=0 .0001037m

σ con=2×Fπ×a×l



Since the elements undergo complete contact with each other, the co-efficient of friction is

μ=0.33.

f max=μ×σcon

= 465.261 MPa

The Principal Stresses will be maximum on the surface, at

xa=0. 3

The normal stresses are

σ x n=−σ con¿ √1− x2

a2

= -1331.63 MPa

σ xt=−2× f max ¿

xa

= -279.156 MPa

σ zn=−σcon ¿√1− x2

a2

= -1331.63MPa



σ z t=0

τ xzn=0

τ xzt=−f max¿√1−x2

a2

= -443.83 Mpa

The total Normal stresses are

σ x=σ xn+σ xt

=−1775 . 46 MPa

σ z=σ zn+σ zt

=−1331 .63 MPa

τ xz=−443 .83 MPa

σ y=ϑ×(σ x+σz )=−932 .127 MPa

In a flat profile roller, end stresses are generated as the cam width is larger than the roller width.

The end stresses are quite larger than the maximum contact stresses. End stresses can be reduced

by changing the profile of the roller surface. A crowned surface reduces the end stress effect to

an extent. The limiting factor the profile is the load. As the load on the roller, contact length

increases. When the contact length equals the length of the roller, end stress is caused in the

roller.

3.0.5 Crowned Profile calculation[6]:

In spherical crowning the profile is crowned at a particular radius, to negate the effect of edge

stresses. This type of evaluation is an iterative process as there is no particular formulation to

provide the best possible crowning radius for the element dimensions. For a crowned profile,

initially the dimensions are generated for a flat profile and then keeping the dimensions constant

the profile is varied to investigate on the effect of variation in profile parameters.



The contact region with a spherical profile is in the form of an ellipse, unlike a rectangle in a flat

profile. The contact dimensions are vastly influenced by the radius of curvature of the elements.

The geometric co-efficient such as A and B are used to find an parameter ϕ which will help in

generating the contact patch dimensions.

These applied stresses are also the Principal Stresses that occur at the point of contact.


3 21

3 21

1

'22

'11

2

'22

2

'11

'22

' `11

4

)(3

4)(3

c o s

2c o s1111

21111

21

111121

23

A

mmFkb

AmmF

ka

A

B

RRRRRRRRB

RRRRA

a bF

b

a

co n

224

3

1

)21(2

)21(2

baa

k

a

bk

baa

ba

b

co nz

co ny

co nx


At the end of the major axis of the contact ellipse the shear stress at the surface is

τ xz=(1−2ν )k3

k42 ( 1

k4

tanh−1k 4−1)σ con

At the ends of the minor axis of the contact ellipse the shear stress at the surface is

τ xz=(1−2ν )k3

k42 [1− k3

k4

tan−1( k 4

k3)]σcon

These stresses are static stresses and are principal stresses. During the calculation of the stresses

the effect of friction has not been taken into consideration. During analysis of dynamic stresses

in the crowned profile the stress calculation tends to be more complex and is best done using any

analytic software. Hence the theoretical stress evaluation is limited to static stresses.



Table 3.1: Stress calculation for various crown radii

Table 3.2: Factors Ka and Kb against Φ

Φ 0 10 20 30 35 40 45 50 55 60 65 70 75 80 85 90

Ka ∞ 6.612 3.778 2.731 2.397 2.136 1.926 1.757 1.611 1.486 1.378 1.284 1.202 1.128 1.061 1

Kb 0 0.319 0.408 0.493 0.53 0.567 0.604 0.641 0.678 0.717 0.759 0.802 0.846 0.893 0.944 1



As the radius of crowning is increased, the contact width and the contact length for a

particular load increases. The length of contact is limited to the length of the roller and the

width to the width of contact for a flat profile. The roller length is limited to the present

length l = .01435m, as the any change in length would require changes in the manufacturing

process parameters.

Hence for a given maximum length, the crowning radius at which minimum contact stresses

occurs is to be evaluated. It has been observed that the contact pressure reduces with the

increase in crowning radius up to a limiting crown radius. After the limiting crown radius, the

contact stress increases with the increase in crown radius.

3.0.6 Logarithmic Profile evaluation:

Theoretical evaluation of spherical profile under static load has generated stresses to be above

the design limit of 2000 MPa. This calls in for evaluation of other possible profile such as the

logarithmic profile. The stress calculation for a logarithmic profile cannot be done

theoretically; hence analytic software is used to evaluate the stresses generated during

loading.

For the purpose of this project, two types of profiles have been evaluated and their stress

results have been compared with the profile used in the failed roller. The profiles have been

generated for a design load of 9740N. The two profiles are John’s-Gohar profile and

modified John’s-Gohar profile. These profiles have been selected for their ease of

manufacturing.

For John’s-Gohar profile:

The parameters a, b, l are the results of flat profile calculation.

Modified John’s-Gohar profile:


z ( x )= 2QπlE '

ln1

1−(1−. 3033b/a )(2 x /l )2

z ( x )=2 K1Q

π lE 'ln

1

1−(1−e

− zm π lE '

2K1Q )( y−aK2a

+1)2


The parameters taken for design in the modified John’s-Gohar profile is zm=0.025, K1=1,

K2=0.696.

Calculation of the deviation is for one side from the midpoint of the axis and the other is the

mirror image.

Table3.3a: John’s Gohar Profile

Table 3.3b: Modified John’s Gohar Profile (Partially Crowned)

For modified John’s-Gohar profile, deviation of the profile from the flat profile starts 5mm

away from the midpoint of the axis, on either side.



3.1 Analysis & Results:

3.1.1 Steps involved in analysis:

Analysis was carried out using ANSYS v 11.

Modelling: All the four components i.e. pin, bush, roller and cam were modelled as separate

volumes. Pin, bush and roller was partially modelled (2 quadrants) where as the cam was

modelled as a cylinder whose outer radius is the lobe radius and only one quadrant is

modelled.

Meshing: The model was meshed with two different materials. The material properties for

the pin, bush and roller was the same, where as the second material was applied to the cam.

The element type was 10-noded tetrahedron with three degrees of freedom. Due to the

complexity and time consumption, element size was restricted to .7 mm.

Boundary Conditions: Symmetric boundary conditions were placed on the surface where

ever required. The cam was constrained at the inner diameter in all directions.

Contact Elements: The various volumes were stand alone and there was no surface or node

relation between them. Contact elements were introduced at the following interfaces:

1. Pin-Bush interface

2. Bush-Roller interface

3. Roller-Cam interface

The first volume corresponds to the contact element whereas the second volume corresponds

to the target element. The target and contact elements were surface to surface.

Since there are three interfaces of contact elements, use of friction is compulsory, which

makes evaluation of static loading difficult. Contact algorithm was set to penalty method due

to its simplicity. Due to the restriction in mesh size, the elements were placed apart by a

particular distance. Hence changes were made with initial adjustment. Changes can be

established with initial penetration or initial contact closure, though the latter is more

appropriate. Sometimes, even though initial penetration has been specified, the contact used

to report open status. Here closing the contact would generate the result. If either of the two is



not employed or the status of contact was open then the software would generate an error of

rigid body motion. Element time increment was maintained to be reasonable.

Loading:

Initially, the load was applied as surface pressure over the nodes. Pressure was applied on

either sides of the pin over the length of contact with the tappet. On analysis it was found that

the stresses generated were much less than the theoretically calculated stresses.

The load application was changed from uniform pressure to uniformly distributed loading.

The load distribution was calculated as follows:

Q- total load

Nn- number of selected nodes

On application of UDL on the nodes, the stresses generated were comparable to the

theoretical stresses. The only drawback in this type of load application is there will be stress

singularity around the point of load, due to the intensity of loading in that particular region.

Analysis Controls:

Analysis is of static type without any variation of loading properties. Since the analysis is

complex and is iterative in nature loading steps need to be specified. The controls varied in

the analysis are listed below

Automatic time stepping: ON

Number of substeps: 10

Maximum number of substeps: 100

Minimum number of substeps: 5

Equation solver: Program chosen (normally Sparse- Direct)


UDL= QNn


1

1000

10011002

1003

X

Y

Z

JUN 19 201016:20:41

ELEMENTS

UF

Fig 3.4: Isometric view of the meshed component with Boundary Conditions

1

100010011002

1003

X

Y

Z

JUN 19 201016:21:37

ELEMENTS

UF

Fig 3.5: Side View of the meshed component with Boundary Conditions



3.1.2 Results:

1

MN

-1692

-1486-1279

-1072-865.307

-658.53-451.752

-244.975-38.198

168.58

DEC 3 200909:52:17

NODAL SOLUTION

STEP=1SUB =7TIME=50SY (AVG)RSYS=0DMX =.025445SMN =-1692SMX =168.58

Fig 3.6: Stress distribution Flat profile with the presence of edge loading

1

MN MX X

Y

Z

-1751

-1535-1320

-1104-888.453

-672.889-457.326

-241.763-26.199

189.364

DEC 3 200910:12:12

NODAL SOLUTION


Fig 3.7: Stress distribution in Spherical profile



1

MN MX

10001002

X

Y

Z

-1959

-1727-1495

-1263-1031

-798.982-567.044

-335.106-103.168

128.77

DEC 3 200910:48:07

NODAL SOLUTION


Fig 3.8: Stress distribution in John’s- Gohar profile

1

MNMX X

Y

Z

-1888

-1655-1423

-1190-957.744

-725.224-492.705

-260.186-27.667

204.852

DEC 3 200910:26:53

NODAL SOLUTION


Fig 3.9: Stress distribution in partial logarithmic profile (modified John’s-Gohar)



Table 3.4: Comparison of Stresses for Various Profiles

Profile σcon(Mpa) σx (Mpa) σy (Mpa) σz(Mpa) τyz(Mpa)

Flat 1336 -684.74 -1240 -1692 377.77

1900 radius 1384 -835.75 -1267 -1751 377.038

Johns-Gohar's 1723 -1005 -1341 -1959 332.56

Partial Log 1566 -1061 -1359 -1888 429.979

ANSYS results proved the previously discussed problem of Edge Loading in Flat profile.

Comparing the stresses generated, Flat Profile with edge loading and Spherical profile

developed the same amount of maximum stress. Compressive Stresses in John’s-Gohar

Profile is higher than the all the profiles. Compressive Stresses in all the profiles is under the

design limit of 2000MPa.

The Shear stress in John’s-Gohar profile is the least and is comparatively lesser than flat and

spherical profile. Both Flat and Spherical profiles have almost the same shear stress generated

through them. The stress limit for shear stress is not defined. Hence, material tests are

required to be carried out, to confirm the values of shear stress limit.



4.0 MATERIAL TESTING

All the details on material properties like Young’s Modulus, Tensile strength, Ultimate

strength, Compressive strength, Endurance limit is either unknown or undocumented. Hence

to provide a comprehensive study on the best possible profile and also suitable dimensional

changes to the Cam-Roller interface it is important to conduct the required material tests.

4.0.1 Tensile Test:

Fig. 4.1: Tensile test specimen

Four specimens were submitted to the materials lab at Delphi-TVS for conducting material

test. Test report for two specimens was provided by them which are provided in fig 4.2a and

4.2b. Tensile test is just a basis for starting fatigue testing of the material. Using the tensile

strength report, the range for loading the fatigue specimen can be narrowed down to.

4.0.2 Compressive Strength:

Compressive tests were not carried out for the material, as there was a documented report

available with the Design Dept. The document was from a leading bearing manufacturer

which stated that the compressive stresses in the roller should not exceed 2000 MPa.



Fig. 4.2a: Tensile Test results for Specimen 1

Fig. 4.2b: Tensile Test

results for Specimen 2

4.0.3 Fatigue Testing:



The most important cause of failure in contact fatigue is the shear stress which causes the

material to shear off from the surface of the material. Shear endurance limit cannot be

directly generated using any existing tests. Hence, tensile endurance limit is evaluated from

R.R. Moore’s rotating bending test. From the Tensile Endurance strength, Shear endurance

strength can be derived using suitable formula. Total 16 specimens were prepared. For the

load of 9 kg 4 specimens were tested according to the standards.

Fig. 4.3: Fatigue Test Specimen

Table 4.1: Fatigue Test Results

Load (Kg)

Stress induced (Mpa)

Average life (revolutions)

Shear Stress (Mpa)

16 575.97 485 345.5812 450.00 10255 270.0011 418.51 26630 251.1110 387.02 157100 232.21

9 355.535220000 (Stopped) 213.32

8.655 344.67

3600000 (Stopped) 206.80

8 324.041000000 (Stopped) 194.42

5.0 REDESIGN



The endurance tests revealed that the shear stress generated in the contact elements was

greater than the endurance shear strength. Considering all the profiles analysed, even John’s-

Gohar profile generated shear stress larger than the strength. This can be one of the main

causes for failure. Since, varying the type of profile didn’t solve the cause of reducing the

stresses; hence a change in dimension is required to get the stresses.

Since the compressive stresses are within the limit, any increase in dimension is intended to

reduce the shear stresses. The roller reciprocates at a high speed; hence varying the

dimensions would cause higher vibrations to be generated due to the larger reciprocating

mass. Hence it is important to know that the limiting factor for increasing dimension will be

vibration.

Volume is directly proportional to the length and to the square of radius. Hence increasing the

radius would increase the volume rapidly than what is caused by increasing the length of the

roller. When comparing the variation in contact stresses, stresses reduce at a faster rate with

the increase in length against the same increase in radius.

The other choice for dimension change will be the increase in the minimum radius of the

cam. The radius of the cam is the least at the lobe of the cam. Hence to attain a higher lobe

radius the mass of the cam has to be increased. In other words the minimum cam radius needs

to be increased.

5.0.1 Flat Profile:

To start off with the redesign, the three variables are roller length, roller radius and the cam

lobe radius. Here it is preferred to keep the roller radius constant due to the problems

associated with reciprocating vibrations.

Having just one equation and two unknowns it is quite confusing to play with dimensions.

Hence an excel sheet was developed with all the influencing parameters, where in any change

in a dimension would generate the subsequent results. This table is made flexible to

incorporate material changes. Due to the usage of this table, the stress reduction due to

variation in any particular dimension or properties, hence giving a clear interpretation to the

solution. As discussed in the previous chapters we initially start the design for a flat profile,

the dimensions are further incorporated to other profiles. The various parts of the table are

listed below.



Table 5.1: Material Properties and loading parameters

Pumping Pressure, P 160.00Bore Dia, bd 7.00Cam base circle Diameter, Dc 40.00Minimum Cam Dia, Dm 36.00Roller Dia, Dr 20.00Spring Stiffness, K 29.85Compressive Stress Limit, after FOS considerations 2000.00Total mass of the reciprocating assembly 0.16Maximum Acceleration of the roller (reciprocating), acc (mm/deg2) 0.0116Maximum Cam rpm, N 4000.00Length of contact 18.00Coefficient of Friction 0.33Pin Length 29.20Bush length 17.00Tensile Endurance Strength 352.20Shear endurance strength 211.32 Material Properties Poissons ratio for Roller 0.30Poissons ratio for Cam 0.29

Youngs Modulus of Roller2.05E+0

5

Youngs Modulus of Cam2.03E+0

5Material Constant for Roller 4.44E-06Material Constant for Cam 4.51E-06

Table 5.2: Load Calculation

Plunger Area 38.48

Force6157.5

2

After 15% frictional losses7244.1

4 Total Spring Deflection 11.00Spring Force 328.35

Total Maximum force7572.4

9FOS 1.25

Max Force after FOS9465.6

2



Table 5.3: Load Transformation

Load ConditionsLoad contact length 4.60half length 8.50distance of load midpoint from bush end

3.30

R1 6570.25R2 1837.44

Table 5.4: Contact Conditions

Due to the loading conditions, the load acting at the centre of the roller

3674.89

Geometry Co-efficient 0.0778width of contact 0.1223

Contact Pressure1062.7

3Frictional Pressure 350.70

Table 5.5: Contact Stresses generated in the interface

Stressesaxes X Z Y Shearnormal -1013.78 -1013.78 0.00transverse -210.42 0.00 -334.55total -1224.20 -1013.78 -671.39 -334.55

Table 5.6: Legend

Dimensions in mmStress and Pressure in M PaMass in kgCalculated quantities Variables Final Results



5.0.2 Spherical Profile:

Previously the crowning radius having the least contact pressure was wrongly predicted due

to the usage of linear interpolation. During analysis, the best crowning radius was narrowed

down and results were tabulated.

From the previous analysis, the best crowning radius was evaluated to be 1900 mm.

A=12 (1R1

+1R1

'+1R2

+1R2

' )¿0 .1630

B=12 √(1R1

−1

R1' )

2

+(1R2

−1

R2' )

2

+2×(1R1

−1

R1' )×(1R2

−1

R2' )

¿ . 1619

Cosφ=(BA )¿0 .9935

Using the above mentioned value of Cosϕ we generate an equation with three unknowns i.e.

R1

,

R1'

and

R2

. The equation generated will be having an unknown

R1'

. The other two values

were determined previously while designing a flat profile.

C×R×R1'2+2×(Cos2φ+1 )×R×R1

' +C=0whereC=(Cos2 φ−1 )

R=(1R1

+1R2

)

Solving the above equation for the values

R1=10,

R2=18, the value of

R1'

is obtained as

1984mm. The roller profile was crowned spherically for the radius specified.

5.0.3 Logarithmic Profile:



In the previous analysis it was noted that John’s Gohar profile, generated the least amount of

shear stress within the roller, even though the contact pressure was higher than the flat profile

and spherical profile. Hence it was decided to analyse the contact stresses for the present

roller dimensions for the logarithmic profile.

Table 5.7: Logarithmic profile for various design load

X 4.5kN Y(x) 5kN Y(x) 7.9kN Y(x) 12kN Y(X) 15kN Y(x)0.00 0 0 0 0 00.90 6.87E-06 7.63E-06 1.21E-05 1.83E-05 2.29E-052.25 4.41E-05 4.90E-05 7.74E-05 1.18E-04 1.47E-043.60 1.19E-04 1.32E-04 2.09E-04 3.17E-04 3.97E-045.40 3.04E-04 3.38E-04 5.34E-04 8.11E-04 1.01E-036.75 5.62E-04 6.25E-04 9.87E-04 1.50E-03 1.87E-039.00 3.24E-03 3.60E-03 5.69E-03 8.64E-03 1.08E-02

The table listed above displays the deviation from a flat profile for various loads. This study

is an extra addition to the process, to know the behaviour of the profiles under the same

loading.

5.1 Redesign Results:



1

MN

MX

X

Y

Z

-264.235

-222.408-180.581

-138.754-96.927

-55.1-13.273

28.55470.381

112.208

MAY 21 201015:59:47

NODAL SOLUTION

STEP=1SUB =7TIME=50SYZ (AVG)RSYS=0DMX =.022115SMN =-264.235SMX =112.208

Fig. 5.1: Shear stress distribution for roller with spherical profile with radius 4950mm

1

MN

MX

10011002

X

Y

Z

-333.132

-283.19-233.248

-183.306-133.364

-83.422-33.48

16.46266.404

116.346

MAY 24 201010:15:10

NODAL SOLUTION




Fig. 5.2: Shear stress distribution over the length of the roller for logarithmic profile designed for 4.5kN

1

MN

MX

10011002

X

Y

Z

-328.339

-278.88-229.422

-179.963-130.505

-81.046-31.588

17.8767.329

116.787

MAY 24 201010:14:06

NODAL SOLUTION


Fig. 5.3: Shear stress distribution over the length of the roller for logarithmic profile designed for 5kN



1

MN

MX

10011002

X

Y

Z

-300.751

-254.134-207.517

-160.9-114.283

-67.666-21.049

25.56872.185

118.802

MAY 24 201010:11:36

NODAL SOLUTION


Fig. 5.4: Shear stress distribution over the length of the roller for logarithmic profile designed for 7.9kN

1

MN

MX

10011002

X

Y

Z

-277.864

-234.547-191.23

-147.914-104.597

-61.281-17.964

25.35368.669

111.986

MAY 31 201006:16:43

NODAL SOLUTION





1

MN

MX

10011002

X

Y

Z

-268.617

-226.029-183.442

-140.854-98.266

-55.679-13.091

29.49772.084

114.672

JUN 29 201016:53:49

NODAL SOLUTION



On initial observation it is found that the shear stress in the roller with spherical profile is the

least. But it is higher than the shear endurance limit. It is important to remember that the

tested material is EN31 where as the material used in the roller is 100Cr6. Hence a

competitors profile was tested, and comparison was made. It was noted that the stresses

generated in the spherical profile is much lesser than the competitor’s profile.

Table 5.8: Comparison of stresses for various profiles


Profile σx (MPa) σy (MPa) σz (MPa) τxy(MPa)

Flat -1676 -927.83 -917.63 -354

Spherical -1174 -599.9 -584.79 -264

John's Gohar

4.5 kN -1503 -745.75 -678.01 -333.13

5 kN -1479 -731.59 -662.99 -328.34

7.9 kN -1333 -663.34 -576.31 -300.75

12 kN -1154 -579.13 -534.18 -277.86

15 kN -1466 -612 -591.62 -268.62


6.0 SCOPE FOR FUTURE WORK

The material used in the roller is 100Cr6 where as the material used for testing is EN31. This

is so because the 100Cr6 is not readily available in India. To validate the endurance limit and

make the design more realistic, the first step would be to test cleaner material 100Cr6.

For any fatigue test the surface finish plays a very important role. Due to the unavailability of

centreless grinding facility with the service providers around the establishment, the best

surface finish that was attained was using finishing emery. It is recommended to finish the

test specimen after heat treatment process using a centreless grinding machine.

The rollers nowadays are coated with a harder material to delay the advent of surface cracks.

The fatigue specimen is to be tested with and without surface coating to compare the benefits

of coating in the roller, when it comes to failures with surface cracks.

Whenever it comes to reciprocating components, the mass of the components is kept bare

minimum. As this design advocates increase in dimensions, it throws the components into a

region of higher vibration. It is therefore recommended to conduct vibration analysis and also

to optimize the mass of the elements. Mass away from the surface can be reduced, as the high

intensity stresses occur at the surface and not within the material.

This project fell short in validation of the obtained results due to the paucity of time and

unavailability of the test rigs. Thus, the most important recommendation would be to validate

the redesigned components to provide a better understanding of the results.



7.0 RESULTS AND CONCLUSION

The behaviour of the profiles under loading is just as studied from various references. With

the flat profile generating edge stresses and hence going above the limits, it is not preferred

for the present applications. Spherical profile if properly designed, will give the desired

results with stresses lesser than the flat profile.

It has been noted in circular and logarithmic profiles, the variation of the contact stresses with

the load is not linear. As the radius of the crown of roller surface increases the maximum

stress decreases for the same applied load. In the trend is same in logarithmic profile also i.e.

the maximum stress decreases with the increases design load for the profile up to a particular

limit, afterwards it increases. In the circular crowned profile as the load increases the

uniformity of the stress along the length of the roller vanishes rapidly. In logarithmic profiled

roller as the load increases the length of the contact increases. If we keep the logarithmic

design load at 3 times the load acting at the centre of the roller, then logarithmic profile will

suffice any requirement.

On comparing spherical and logarithmic profile, it can be stated that the stress increase, after

the optimal profile, begins at an earlier stage in a spherical profile than in logarithmic profile.

There are no existing formulae to confirm the optimal crowning radius for a spherical profile.

Hence logarithmic profile can be preferred over spherical and flat profile.

Even though at the dimensions recommended shear stress is not under the tested endurance

limit, the design is still safe. It is not wrong to advocate the design as the stresses are much

lesser than the stresses in the competitor’s product which has sustained the required number

of testing hours, with the roller having a flat profile. This is due to the difference in the

material used for testing and the material used in the component. The roller material is a

cleaner material with lesser non metallic impurities.

Hence at the end, it can be recommended to design rollers with logarithmic profile with a

load factor of 2.75 to 3, which is the commonly used profile by the leading bearing

manufacturer.



REFERENCES

1. Brian L. Vlcek, Georgia Southern University, Statesboro, Georgia, Robert C.

Hendricks and Erwin V. Zaretsky, Glenn Research Center, Cleveland, Ohio,

DETERMINATION OF ROLLING-ELEMENT FATIGUE LIFE FROM

COMPUTER GENERATED BEARING TESTS, 2003 Annual Meeting and

Exhibition sponsored by the Society of Tribologists and Lubrication Engineers, New

York City, New York, April 28–May 1, 2003.

2. P.V.V.N. Prasad and Rajiv Tiwari, Department of Mechanical Engineering, Indian

Institute of Technology Guwahati, Guwahati, EFFECT OF CONTOURED PROFILE

ON CONTACT STRESSES OF THE CYLINDRICAL ROLLER.

3. Y. Nakasone and S. Yoshimoto, Department of Mechanical Engineering, Tokyo

University of Science, Tokyo, Japan, T. A. Stolarski, Department of Mechanical

Engineering, School of Engineering and Design, Brunel University, Middlesex, UK,

ENGINEERING ANALYSIS WITH ANSYS SOFTWARE, Elsevier Butterworth-

Heinemann, Linacre House, Jordan Hill, Oxford OX2 8DP,30 Corporate Drive,

Burlington, MA 01803.

4. Joseph V. Poplawski, Steven M. Peters, J.V. Poplawski and Associates, Bethlehem,

Pennsylvania, Erwin V. Zaretsky, Glenn Research Center, Cleveland, Ohio, EFFECT

OF ROLLER PROFILE ON CYLINDRICAL ROLLER BEARING LIFE

PREDICTION, 2000 Annual Meeting, sponsored by the Society of Tribologists and

Lubrication Engineers, Nashville, Tennessee, May 7–11, 2000, National Aeronautics

and Space Administration, Glenn Research Center.

5. David H. Johnson, P.E., Penn State-Erie, Erie, Pennsylvania, USA, PRINCIPLES OF

SIMULATING CONTACT BETWEEN PARTS USING ANSYS.

6. Robert L. Norton, Worcester Polytechnic Institute, Worcester, Massachusetts,

MACHINE DESIGN, AN INTEGRATED APPROACH, Second Edition, 490-536.

7. A presentation by Rich Bothmann, IMPACT Engineering Solutions, Inc. Brookfield,

WI, www.impactengsol.com.



8. Lech Pawlowski, Ecole Nationale Sup´erieure de Chimie de Lille, THE SCIENCE AND ENGINEERING OF THERMAL SPRAY COATINGS, Second Edition, John Wiley & Sons Ltd.

9. Gwidon W. Stachowiak, Andrew W. Batchelor, Department of Mechanical and Materials Engineering, University of Western Australia, Australia, ENGINEERING TRIBOLOGY, 427-441, Butterworth Hienmann.

10. Hiroki Fujiwara, Tatsuo Kawase, Elemental Technological, R&D Center, LOGARITHMIC PROFILES OF ROLLERS IN ROLLER BEARINGS AND OPTIMIZATION OF THE PROFILES, NTN TECHNICAL REVIEW No.75, 2007.

11. ASM Journal, FATIGUE AND FRACTURE. Published in 1996.

12. STRUCTURAL ANALYSIS GUIDE, ANSYS Release 8.1.

13. ANSYS CONTACT TECHNOLOGY GUIDE, ANSYS Release 9.0.

14. www.wikipedia.org.

15. World Wide Web.


Main Report

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