Mechanical Engineering Design III assignment involving the design of a geared industrial roll (two high). The roll is driven at 350 rev/min by a force F acting on a driven gear. The roll exerts a normal force of 60kN/m of roll length and a pull of 50kN/m on the material being processed. The material passes under the roll. The coefficient of friction is 0.40. A design life of 35 kh is desired. Use angular-contact ball bearings for the support to get a combined reliability of at least 0.92. Select standard size for the shaft. The drive gear is spur having 20° pressure angle. Assume suitable reduction ratio and select the drive motor for the mill. Please use this file as guide. For similar projects, please visit http://www.topengineeringsolutions.com/

2. Table of Contents
Table of Contents ............................................................................................................................ ii
List of Figures ................................................................................................................................ iv
List of Abbreviations ...................................................................................................................... v
Abstract ......................................................................................................................................... vii
Declaration ................................................................................................................................... viii
Acknowledgement ......................................................................................................................... ix
1
Introduction ............................................................................................................................. 1
2
Literature Review .................................................................................................................... 2
2.1
Basic Rolling Process ....................................................................................................... 2
2.2
Roll Mill Configurations .................................................................................................. 4
3
Forces, Moments, Free-body Diagrams and Transmitted Power ............................................ 5
4
Sizing of the Shaft ................................................................................................................. 12
5
Gears Design for Tooth Bending and Wear .......................................................................... 14
5.1
5.2
Gear Tooth Bending ....................................................................................................... 20
5.3
Pinion Tooth Wear ......................................................................................................... 20
5.4
Gear Tooth Wear ............................................................................................................ 20
5.5
6
Pinion Tooth Bending .................................................................................................... 18
Gear Rim Size ................................................................................................................ 21
Bearing Selection ................................................................................................................... 21
ii

3. 7
Design Drawings ................................................................................................................... 22
8
Conclusion ............................................................................................................................. 25
9
References ............................................................................................................................. 26
iii

4. List of Figures
Figure 1: Basic Rolling Process (De Garmo, Black and Kohser, 2012) ......................................... 3
Figure 2: Different Roll Mill Configurations.................................................................................. 5
Figure 3: The Roll Mill to be designed ........................................................................................... 6
Figure 4: Free Body Diagram for the Loads in the X-Y Plane ....................................................... 7
Figure 5: Free Body Diagram for the Loads in the X-Z Plane ....................................................... 7
Figure 6: The Roll Mill Assembly ................................................................................................ 22
Figure 7: Work Piece .................................................................................................................... 23
Figure 8: The Roll ......................................................................................................................... 23
Figure 9: The Roll ......................................................................................................................... 24
Figure 10: The assembly and the parts list.................................................................................... 24
iv

5. List of Abbreviations
MB =the backup ratio
Cma = The mesh alignment factor
Cpm =Pinion proportion modifier
Cmc = Load correction factor (Cmc)
Ce =Face alignment correction factor
Cmf = face load-distribution factor
MN= is the load-sharing ratio
𝛷t = Transverse pressure angle
Wt = tangential transmitted load, (N)
K0 = overload factor
Kv = dynamic factor
Ks =the size factor
b = face width of the narrower member, in mm
mt = transverse metric module
YJ =geometric factor for bending strength
KH = load-distribution factor
KB = rim-thickness factor
St = allowable bending stress (N/mm2)
YN = stress cycle factor for bending stress
Y 𝜭 = temperature factor
YZ = reliability factor
SF = AGMA factor of safety
v

6. ZE = elastic coefficient √
ZR = surface condition factor
dω1 = pitch diameter of the pinion in mm
Z1 = geometric factor for pitting resistance
FD = the desired radial load
af = application factor,
𝜭= the characteristic parameter corresponding to the 63.2121 percentile value of the variate
x0 = the minimum value of the variate
vi

7. Abstract
This report represents a detailed and systematic procedure for designing a geared roll
mill. The report first provides a brief introduction on the principles and terminologies used in
metal rolling. This includes the general mechanics of rolling, classification and configuration of
rolling mills as well as the main components of a rolling mill. The report then provides the
general procedure for designing the selected elements of a rolling mill such as the gears, the
shafts, the motor and the bearings.
The design process in this report begins with the determination of all the forces and
moments present in the roll mill in order to determine the required power and the stresses in the
main components. The analysis revealed that the required power was approximately 183kW.
Consequently, the closest commercially available motor was identified to be 185kW at a
rotational speed of 1500 rpm. Based on this power and speed as well as on the forces and
moments present, the shaft diameter was determined to be 90mm. The shaft was sized on the
basis of maximum shear theory. On the other hand, the designed driven gear had a module of
6mm, a pitch diameter of 462mm, and 77 teeth while the pinion had 18teeth, a pitch diameter of
108mm and a module of 6mm. On the other hand, the selected gear had a load rating of 106kN.
The matching angular contact ball bearing for this rating had a bore diameter of 90mm and an
outer diameter of 160mm. Upon completing the design process, the roll mill was modeled in
Solidworks 2014.
vii

8. Declaration
I declare that:
This design report presents work carried out by myself and does not incorporate without
acknowledgment any material previously submitted for a degree or diploma in any university;
To the best of my knowledge it does not contain any materials previously published or written by
another person except where due reference is made in the text; and all substantive contributions.
Name:………………………………..Signature:………………………
viii

9. Acknowledgement
ix

10. 1
Introduction
Metal rolling has been around for several centuries from as early as the late 1500s. It is
the most common and most important bulk deformation method. It accounts for over 90% of all
metals manufactured by metal working processes. It is usually used to form intermediate
products for various metal working processes. For instance, it reduces the cross-section of ingots
into blooms, billets, slabs, plates, and sheets among other semi-finished products. These semifinished products are then used in other metal working processes to produce the desired finished
products. The predominant type of rolling is flat rolling which reduces the cross section of flat
work-pieces such as blooms and ingots into slabs and billets among other flat products
(Boljanovic, 2010). However, there are other types of rolling such as thread rolling, shape
rolling, gear rolling and ring rolling.
Thread rolling is a rolling technique that is used to form threads on cylindrical workpieces by rolling the work-piece between two dies. It the most common technique used for mass
production of threaded parts. It is extremely fast compared to thread cutting because it can
produce up to 8 in a second. In addition, it allows for economical use of material, produces
stronger threads due because of work hardening, the threads have a relatively smoother surface
and the produced part has increased fatigue resistance.
Shape rolling is another important rolling process in which the work piece is plastically
deformed to achieve a contoured cross section. In this case, the work-piece is rolled between
among others. On the other hand, gear rolling is a rolling process used to manufacture gears. The
setup of the rolls in this case is similar to that used in thread rolling but the deformed feature of
the cylindrical blank is either oriented parallel or an angle to the blanks axis depending on
1

11. whether spur gears or helical gears are desired. Rolled gears are better than gears manufactured
by alternative methods because rolling is much faster, the gears have higher fatigue strength and
there is efficient material utilization.
Ring rolling on the other hand is a rolling process that is used to reduce the thickness of a
thick-walled ring to form a thin-walled ring with a larger diameter.
There are different sizes of rolling mills depending on the type of rolling, the magnitude
of deformation and the desired production rates among other parameters. These rolling mills
have different power requirements. Therefore, each rolling mill must be carefully designed to
achieve the desired performance and capacity without premature failure. Such a design can only
be achieved if all the forces, power and moments present in the rolling mill are identified. Failure
to identify these forces might lead to failure of critical rolling mill parts such as shafts, gears,
rolls, supports and bearings. This report provides a detailed design procedure for various parts of
a rolling mill including shafts, gears and bearings. Some of the design considerations include
bending stresses, shear stresses, fatigue life, contact stresses in gears, appropriate material
selection among others. The report also provides an overview of the terminologies used in
rolling. The designed parts are then modelled using solidworks 2013.
2
2.1
Literature Review
Basic Rolling Process
The basic rolling process is illustrated in figure 1 below:
2

12. Figure 1: Basic Rolling Process (De Garmo, Black and Kohser, 2012)
The basic rolling process refers to flat rolling. In this process, the metal is passed
between two rolls where it is reduced in cross section due to the compressive forces exerted by
the rolls (Boljanovic, 2010). The two rolls rotate in opposite directions and generate frictional
forces that pull the material through the roll gap. The rolls are arranged in such a way that the
roll gap is less than the thickness of the material to be rolled. The frictional forces generated
during rolling are caused by the difference in velocity between the work piece and the surface
velocity of the rolls. It is worth noting that when the material is introduced at the roll gap, its
velocity is less than the surface speed of the rolls. However, as the material exits the roll gap as a
finished product its speed is higher than the surface velocity of the rolls. There is a transition
3

13. point where the surface velocity of the rolls is equal to the velocity of the work piece. This point
is referred to as the neutral point.
The frictional force determines the magnitude of deformation that can be achieved. When
the friction required to achieve a particular deformation is too high, the rolls simply skid on the
surface of the material. In such a case, several passes can be used to gradually deform the
material until the desired thickness is achieved. On the other hand, small deformations per pass
increase the number of passes which eventually increase the cost of production.
2.2
Roll Mill Configurations
Roll mills can be configured in several ways depending on the level of deformation as
well as the material to be rolled. Some of the most commonly used configurations include 2-high
reversing mill, 2-high non-reversing mill, 3-high mill, 4-high mill, planetary rolling mill and
cluster mills. 2-high non-reversing mills have a simple arrangement and they allow the material
to pass between the rolls in one direction only. In this case, the rolls are placed one over the other
(De Garmo, Black and Kohser, 2012). 2-high reversing mills have a similar arrangement to that
used in 2-high non-reversing mill. However, the rolls are driven by different motors to allow for
reversing (H. Gupta, R. Gupta and Mittal, 2009).
3-high roll mill configuration consists of three rolls that are arranged one over the other.
This arrangement allows the material to be passed between the top two rolls during the forward
pass and for the semi-finished product to be passed through the bottom two rolls during the
reverse pass. On the other hand, the four-high mill has four rolls arranged one over the other.
Unlike in 2-high and 3-high roll mills, this roll mill has rolls with different diameters. The rolls
that are in contact with the work piece are smaller in diameter than the other pair of rolls. The
small rolls are referred to as working rolls while the rolls with a larger diameter are known as
4

14. working rolls. Using small diameter rolls allow for greater deformation and has relatively lower
roll force requirement. The backup rolls are meant to apply a constant force on the working rolls
to prevent deflections (De Garmo, Black and Kohser, 2012). Finally, cluster rolling mill has two
working rolls and four or more backup rolls. The different roll mill configurations are shown in
figure 2 below:
Figure 2: Different Roll Mill Configurations
3
Forces, Moments, Free-body Diagrams and Transmitted Power
Before sizing the critical parts of the rolling mill, the relevant forces and moments were
determined. To determine the forces, important assumptions were made. The assumptions were
made after considering the available rolling mill data outlined below:
i.
The rolls are driven at 350rpm
5

15. ii.
Power is transmitted through spur gears with a pressure angle of 20°
iii.
The rolls exert a normal force with a magnitude of 60kN/m of roll length
iv.
The rolls exert a pull with a magnitude of 50kN/m on the material
v.
The coefficient of friction is 0.40
vi.
The design life is 35 kilo hours
The roll mill to be designed is shown in figure 3 below:
Figure 3: The Roll Mill to be designed
By observing the roll mill configuration in figure 3 above, it can be seen that there exists
a clearance between the roll and the support. However, only the roll length is provided, that is,
0.8m. Since the shaft length is not provided, it assumed that the distance from the roll end to the
point of support in the bearings is 10cm.
In order to have a clear understanding of the magnitude and orientation of the forces and
moments acting on the rolling mill, the free body diagram was drawn. However, the rolls and the
6

16. shafts are loaded both in the X-Y plane and the X-Z plane. The free body diagram for the loading
in the X-Y plane and the X-Z plane are shown in figure 4 and figure 5 below:
Figure 4: Free Body Diagram for the Loads in the X-Y Plane
Figure 5: Free Body Diagram for the Loads in the X-Z Plane
The support reactions were then calculated as shown below:
Sum of moments about A
7

17. ∑
∑
Sum of vertical forces
∑
(
∑
)
It is evident that the load is shared equally between the two supports. Therefore, the
reactions in the X-Z plane will also be equal:
The two reactions can be combined to determine the total reaction:
)
√(
√(
)
(
√(
)
(
)
√
)
8
(
)

18. √(
)
(
)
The Maximum Bending Moment
It is necessary to determine the magnitude and location of the maximum bending moment
in the shafts in order to calculate the induced stresses and the appropriate size. The maximum
bending moment is obtained by subdividing the beam into sections then writing the equation of
the bending moment for each section. The location of maximum bending moment is obtained by
considering that at the point of maximum bending moment the shear force V=0.
In the beam segment above, 0≤x≤L
Sum of moments about the right end
(
( )
( )
(
9
)
)

19. ( )
(
)
( )
Sum of Vertical Forces
(
∑
(
)
)
To determine the location of the maximum moment, V is equated to zero.
Therefore;
For the remaining part of the beam;
10

20. Sum of moments about the left end
(
)
(
)
For x=0.5m;
(
)
Sum of moments about the left end for the loading in the X-Z plane,
(
)
(
)
The Combined Bending Moment
√(
√(
)
)
(
)
The Torque
11
(
)

21. The torque on the shaft is due to the 50kN/m force.
(
4
)
Sizing of the Shaft
The shafts in this case are subjected to combined loading, particularly combined bending
and twisting. Tresca’s failure theory is used in this case. The mathematical representation of this
theory is shown below (Khurmi and Gupta, 2008):
⁄
τmax = maximum shear stress
τy = shear stress at yield point
S = safety factor
Another mathematical representation of this failure theory is shown below:
σy is the tensile yield stress
Tresca’s failure criterion is usually preferred when designing components that will be
manufactured from ductile material. In addition to being conservative, this failure theory is also
simple to apply (Khurmi and Gupta, 2008). Tresca’s failure theory can be easily used to design
shafts subjected to combined loading as shown below:
√(
12
)

22. However,
( )
√(
)
(
)
[√(
)
)
√(
Substituting these values in the equation
(
)
]
)
√(
But;
In order to solve the equation above, the appropriate material must be selected. The yield
stress for the selected material can be used to determine the maximum shear stress using the
Tresca’s failure theory. Annealed AISI 4620 was the preferred shaft material. This material has a
yield stress of 372Mpa. AISI 4620 is a Nickel-molybdenum steel. This steel has sufficient wear
and creep resistance necessary in hot rolling (Grote and Antonsson, 2009).
)
√(
13

23. However, the standard shaft diameter is 90mm (Khurmi and Gupta, 2008).
5
Gears Design for Tooth Bending and Wear
The driven gear and the pinion were designed according to the American Gear
Manufacturers Association (AGMA) procedure. Budynas and Nisbett (2006) provide a
systematic explanation of gear design based on AGMA procedure. The conventional way of
sizing a gear starts by identifying the power to be transmitted as shown below:
It is important to note that it is almost impossible to get a commercially available motor
with a power rating of 183.26kW. Therefore, an alternative motor with a rating closer to the
calculate power was selected. The selected motor was rated 185kW and 1483 rpm (Siemens,
2013). Since the pinion is directly fixed on the motor shaft, its rpm will be 1483. For a single
step reduction, the gear ratio will be:
Since few data about the desire gears is available, several assumptions, decisions and trial
values are required. The first decision to be made is the appropriate gear material. Since the
design is based on AGMA principles outlined by Budynas and Nisbett (2006), the selected
material will also be obtained from the same reference in order to obtain all the required
properties of the material. Nitralloy 135M grade 1 was selected because of its outstanding wear
resistance and mechanical strength.
14

24. After selecting the material, the number of teeth on the pinion was selected. According to
Budynas and Nisbett (2006), the minimum number of teeth to avoid interference for a spur gear
with 200 pressure angle is 18. Therefore, the gear has (18*4.24) teeth =76.32. This was rounded
off to 77. After determining the number of teeth, Yp ,YG , Jp and JG can be obtained from tables.
YP =0.309, YG = 0.436, JP=0.32, JG=0.42. Also, overload factor Ko = 1, Quality number (Qv) =6,
Backup ratio MB ≥1.2, KB =1.
In order to determine the pitch diameter of the gear, an appropriate gear module was
selected, that is, 6.0mm. Therefore;
The pitch line velocity
Tangential transmitted load Wt
(
)
(
)
The dynamic factor
15

25. √
(
)
(
)
(
(
)
)
⁄
(
)
√
(
⁄
)
The reliability factor YZ
(
(
)
)
(
)
The stress cycle factors (YN and ZN)
In order to determine the stress cycle factors, it necessary to obtain the desired load cycles. This
can be obtained from the given design life in khs.
(
(
)
)
(
(
(
⁄
(
)
)
)
(
)
)
⁄
(
Face Width
16
)

26. A face width (b) that is 4 times the circular pitch is selected basing on Budynas and Nisbett
(2006).
Size Factor ks
√
(
√
(
)
)
Assume Cpm =1, Cma =0.175, Cmc =1, Ce = 1
(
(
√
)
)
(Budynas and Nisbett, 2006)
The geometry factor ZI
𝛷
𝛷
MN = 1 for spur gears
17

27. 5.1
Pinion Tooth Bending
From;
the desired face width
But;
Since Nitralloy 135M grade 1 has a Brinell hardness of about 320 (Budynas and Nisbett, 2006),
the values of St and Sc are:
(
)
(
)
But;
For SF = 2
(
) ( ) (
( ) (
) (
) (
Also;
18
) (
) (
)( ) ( ) (
)
)

28. ( )
(
)( )(
(
(
) (√
)(
) (
)
)(
) [(
)( ) [
)(
(
) ( )(
)( )]
)]
The b value of 77.54mm is selected and rounded off to 78. The new face width value is then used
to correct KH and Ks
(
√
)
(
(
)
)
The bending stress for b=78mm is:
(
) ( ) (
) (
) (
)
(
) ( )
(
)
And:
(
) (
19
)

29. 5.2
Gear Tooth Bending
( )
(
( )
5.3
)
(
) (
)
Pinion Tooth Wear
√
[(
) ( ) (
(
) (
) (
(
) (
)(
)
)
SH2= 2.242= 5.02
5.4
Gear Tooth Wear
(
) (
)
(Wear is the probable cause of failure)
20
)]

30. 5.5
Gear Rim Size
Assuming a backup ratio greater than or equal to 1.2, the rim thickness is:
( )
( )
. Any
rim thickness greater than 15.48mm is
sufficient.
6
Bearing Selection
The most appropriate bearings for this application are determined based on the reaction at
the shaft support, that is, the radial load is the absolute reaction at the shaft support.
( )
√
The equation for determining C10 rating is:
⁄
[
(
)(
)
⁄
Assume af =1.25 and use an L10 life of 90(106)
(
)
But, 𝜭=4.48; x0 =0; b=1.5.
21
]

31. ⁄
[
(
)(
)
⁄
]
The calculated C10 value is then used to select the actual C10 value from manufacturer’s
catalogue. A C10 value of 106 kN was selected. The corresponding bearing dimensions are:
Bore= 90mm, Outer diameter =160mm, Fillet radius= 2mm, Shoulder diameter
dS=104mm and Shoulder diameter dH =146mm
7
Design Drawings
Some of the drawings for the assembly and critical roll mill components are provided in
this section.
Figure 6: The Roll Mill Assembly
22

32. Figure 7: Work Piece
Figure 8: The Roll
23

33. Figure 9: The Roll
Figure 10: The assembly and the parts list
24

34. 8
Conclusion
The aim of this design project was to design a geared two-high rolling mill and model it
using 3D modelling software. The report provided an overview of the operation, classification
and principles of a rolling mill. The critical components of the rolling mill, that is, the shafts, the
bearings, the motor and the bearings were then sized. The recommended shaft size was 90mm.
The sized gear had 462mm pitch diameter, 78mm face width, 6mm module and 77 teeth while
the pinion had 108mm pitch diameter, 78mm face width, 6mm module and 18 teeth. On the other
hand, the bearing had a bore of 90mm, an outer diameter of 160mm and a C10 rating of 106kN.
The shaft material was AISI 4620 Nickel-molybdenum steel while the gear and pinion material
was Nitralloy 135M grade 1 steel.
25

35. 9
References
Boljanovic, V. (2010). Metal shaping processes: casting and molding, particulate processing,
deformation processes, and metal removal. New York, Industrial Press.
Budynas, R. and Nisbett, K. (2006). Shigley’s Mechanical Engineering Design, 8Th Ed. New
York: McGraw-Hill
Grote, K. H., & Antonsson, E. K. (2009). Springer Handbook of Mechanical Engineering. New
York: Springer.
Gupta, H.N., Gupta, R.C. and Mittal, A. (2009). Manufacturing Processes, 2nd Ed. New Delhi:
New Age International.
Khurmi, R. S., & Gupta, J. K. (2008). A Textbook of Machine Design (S.I. Units). New Delhi:
Eurasia Pub. House.
Siemens. (2013).Products: Motors. Retrieved from <
http://www.industry.siemens.com/drives/global/en/motor/pages/default.aspx> [Accessed
22 December 2013]
26