Industrial Enginnering Assignment-Industrial Engg Research paper

Summary On 
A Mathematical Programming Model for Flow Shop Scheduling Problems for Considering Just in Time Production.

R. Ramezanian, M.B. Aryanezhad & M. Heydari*
R. Ramezanian: MSc in Department of Industrial Engineering, Iran University of Science and Technology.
M.B. Ariyanezhad: Professor in Department of Industrial Engineering, Iran University of Science and Technology.
M. Heydari: Assistant Professor in Department of Industrial Engineering, Iran University of Science and Technology.

Introduction
This paper is primarily concerned with industrial scheduling problems, where one has to sequence the jobs on each resource over time.

In a flow shop environment, a set of jobs must be processed on a number of sequential machines, processing routes of all jobs are the same, that is the operations of any job are processed in the same order, whereas a flow shop with bypass model, a generalization of the ordinary flow shop model, is more realistic, and it assumes that at least one job does not visit one machine.

This is the scheduling of n jobs in a m machine flow shop, where some jobs do not require processing on the some machines. The objective is to minimize the sum of earliness and tardiness costs. Just in time concept for the scheduling environment can be provided by considering minimization of the sum of earliness and tardiness costs as the objective function.

Problem Description

The FSSP with bypass can be described as follows: Each of n jobs from set J={1,2,..., n} will be sequenced through m machines (i=1, 2,...,m). Job has a sequence of lj operations through a subset m machines (jobs may have zero processing time on some machines) and a given due date dj.

Mathematical Formulation

• The objective function (1) considers the minimization of the earliness cost and the tardiness cost and the considered objective function provides just in time production in manufacturing systems. 
• The constraint set (2) determines earliness and tardiness of each job. 
• The constraint set (3) corresponds to the computation of the completion time of job (if job j is not processed on machine i, its completion time is the same as completion time on previous machine).
• The constraint set (4) forces to start the processing of each job only when it has been completed on the precedent machine. 
• The constraint set (5) forces to start the processing of each job only when its precedent job has been completed on the same machine. 
• The constraint sets (6-11) determine sequence of jobs for any machine. The constraint set (12) bounds the job starting times to be after job release times in the system. 
• The constraint set (13) insures that the job finishing times on the first machine to be after job release times (if job j does not require processing on the first machine, 
• C1j=Rj. (14) is logical constraint.

The Genetic Algorithm 
Genetic algorithms have been proven to be powerful techniques for constrained optimization and
combinatorial optimization problems.
The GA was proposed by Holland (1975) [15] to encode the factors of a problem by chromosomes, where each gene represents a feature of the problem. The GA’s structure and parameter setting affect its performance.
The overall structure of our GA can be described as follows:
1. Coding: The genes of the chromosomes describe the jobs, and the order in which they appear in the chromosome describes the sequence of Jobs. Each chromosome represents a solution for the problem.
2. Initial population: The initial chromosomes are obtained by a Random dispatching rule for sequencing.
3. Fitness evaluation: The sum of earliness and tardiness cost is computed for each chromosome in the current generation.
4. Selection: In any iteration, chromosomes are chosen randomly for crossover and mutation.
5. Offspring generation: The new generation is obtained by changing the sequencing of operations (reproduction, enhanced order crossover and mutation). These rules preserve feasibility of new individuals. New individuals are generated until a fixed maximum number of individuals is reached.
6. Stop criterion: Fixed number of generations is reached. If the stop criterion is satisfied, the algorithm ends and the best chromosome, together with the corresponding schedule, are given as output. Otherwise, the algorithm iterates again steps 3–5.
Based on bypass consideration GA is adapted to consider operation with zero processing time on some machines.



Conclusions
In this paper, we presented a mathematical formulation model for minimizing sum of the earliness and tardiness costs in flow shop scheduling problem with bypass consideration (some jobs may not process on some machines) which is often occurring in shop environment of real world. We proposed genetic algorithm to solve this problem with medium and large size. Computational experiments have been performed to demonstrate that the proposed GA is efficient and flexible.

Industrial Engineering Assignment-Engineering Research paper on connecting rod

Summary On:
DESIGN OF CONNECTING ROD OF INTERNAL COMBUSTION ENGINE:
A TOPOLOGY OPTIMIZATION APPROACH
M.S. Shaari  , M.M. Rahman , M.M. Noor , K. Kadirgama  and A.K. Amirruddin
Faculty of Mechanical Engineering, Universiti Malaysia Pahang
26600 UMP, Pekan, Kuantan, Pahang, Malaysia
Phone: +6094242246, Fax: +609-4242202
E-mail: shamilshaari@yahoo.com; mustafizur@ump.edu.my
Automotive Engineering Centre, Universiti Malaysia Pahang

Introduction

This paper presents the design connecting rod of internal combustion engine using the
topology optimization.
The objectives of this paper are to develop structural modeling,finite element analyze and the optimization of the connecting rod for robust design.

The topology optimization technique is used to achieve the objectives of optimization which is to reduce the weight of the connecting rod.

Optimization Approach

The objective of optimization technique is to minimize the mass of the connecting rod
and reduce the cost of production. The connecting rod subjected to tensile load at crank
end, while using factor of safety 3 as recommended by Shenoy (2004). The maximum
stress of the connecting rod monitored and make sure it is not over the allowable stress.
The load of the connecting rod optimized is comprised of the tensile load of 26.7 kN at
crank end. Linear buckling analysis was performed on the connecting is 26.7 kN. The
buckling load factor is considered also 3. The optimization technique methodology
flowchart is shown in Figure 1.

The Steps involved is as follows:

1. The initial design is compared to other design before performing the optimization.
2. A simple three-dimensional model of connecting rod was developed using SOLIDWORKS software and finite element model was created using TET10.
3. Mesh study was performed on the FE model to ensure sufficiently fines sizes are employed for accuracy of the calculated result depends on the CPU time.
4. FEA for both tensile and compressive loads were conducted. Two cases were analyzed for each case, Firstly, load applied at the crank end and restrained at the piston pin end, and secondly, load applied at the piston pin end and restrained at the crank end and the axial load was 26.7 kN in both tension and compression.

Optimization of connecting rod.

The optimization of the connecting rod carried out using topology optimization

technique. The optimization focused on the uncritical sections which need to be

reduced. From the topology optimization, it is suggest the unnecessary shape and design

of the connecting rod.  The main objective is to minimize the weight

of the connecting rod as well as the total production cost. It can be seen that the

optimized model is reduce the weight from initial design until the value converges.

Figure 8 shows the objective function history of the optimization. The convergence of

the design is immediately after cycle no. 9. The implementation of these optimizations

is to find out the best design and topology of the connecting rod to improve the

performance and the strength especially at the critical location. The possible

modification section of the optimized connecting rod is indicated in the figure. The

section with lower value than initial value considered as the suggestion to be optimized

in the new design. Table 4 shows the comparison between initial and optimize designs

on max principles stress and mass of the connecting rod. The optimize connecting rod

no 4 was choose as the best optimize design due to the lowest occurred stress and mass.

Even though the mass of the optimize connecting rod is not the lowest, but the decision

was also based on the maximum stress which is 320 MPa. 

The new design of the connecting rod and mass of the connecting rod is 0.464 kg compare to

initial design 0.577 kg which is 11.7% lighter.

CONCLUSION

The modeling of connecting rod and FE Analysis has been presented. Topology

optimization were analyzed to the connecting rod and according to the results, it can be

concluded that the weight of optimized design is 11.7% lighter and maximum stress

also predicted lower than the initial design of connecting rod. The results clearly

indicate that the new design much lighter and has more strength than initial design of

connecting rod. Material optimization approach will be considered for future research

Industrial Engineering Assignment-Component design

A project Report

On

Design of Connecting rod

For an Automobile industry.

Under the guidance of

Prof K.V.S.S Narayan Rao

                                                                  Prepared by: 
                                                                                 Pramod Kumar Moharana (Roll No 64)

                                                                                 Samay Singh Meena (Roll No 86)

                                                                                 PGDIE-42

                                                                                  Sec-B

                                   Content                                             

1.             Introduction                                                                                                                   

2.            Functioning of connecting rod                                                                                       

3.            Design process flow of connecting rod.                                                                  

4.            Manufacturing process flow of connecting rod.                    

5.            Conclusion                                                                          

6.            References                                                                       

           

      

           Introduction                                                    

In a reciprocating piston engine, the connecting rod or conrod connects the piston to the crank or crankshaft. Together with the crank, they form a simple mechanism that converts linear

motion into rotating motion. Connecting rods may also convert rotating motion into linear motion.

Historically, before   the development of   engines, they were first used in this way.

As a connecting rod is rigid, it may transmit either a push or a pull and so the rod may rotate the crank through both halves of a revolution, i.e. piston pushing and piston pulling. Earlier mechanisms, such as chains, could only pull. In a few two-stroke engines, the connecting rod is only required to push.

Today, connecting rods are best known through their use in internal combustion piston engines, such as car engines. These are of a distinctly different design from earlier forms of connecting rods, used in steam engines and  steam locomotives.

         Functioning of connecting rod

         Design steps of Connecting rod.

                                    

                                                                                            

  Need or Aim:

   The Primary purpose of connecting rod is to transmit gas forces applied on the piston due to      ignition to crankpin of crankshaft assembly.

                                        

   Synthesis(Mechanism)

                                                    

    The above mechanism will give the required motion to the connecting rod.

                                        

   Analysis of Forces in connecting rod.

    The various forces acting on the connecting rod are as follows:

    1. Force on the piston due to gas pressure and inertia of the reciprocating parts,

    2. Force due to inertia of the connecting rod or inertia bending forces,

    3. Force due to friction of the piston rings and of the piston,       

    4. Force due to friction of the piston pin bearing and the crankpin bearing.

1.  Force on the piston due to gas pressure and inertia of reciprocating parts

Consider a connecting rod PC as shown in Fig

                                        

Forces on the connecting rod

Let p = Maximum pressure of gas,

D = Diameter of piston,

A = Cross-section area of piston = (π /4)D2

mR = Mass of reciprocating parts, = Mass of piston, gudgeon pin etc. + 1/3 rd mass of connecting rod,

ω = Angular speed of crank,

φ = Angle of inclination of the connecting rod with the line of stroke,

θ = Angle of inclination of the crank from top dead centre,

r = Radius of crank,

l = Length of connecting rod, and

n = Ratio of length of connecting rod to radius of crank = l / r.

We know that the force on the piston due to pressure of gas,

FL = Pressure × Area = p . A = p × (π /4)D2
and inertia force of reciprocating parts,

FI = Mass × *Acceleration = mR .ω2. r (cos n  θ + (cos 2 θ)/n)

It may be noted that the inertia force of reciprocating parts opposes the force on the piston when

it moves during its downward stroke (i. e. when the piston moves from the top dead centre to bottom

dead centre). On the other hand, the inertia force of the reciprocating parts helps the force on the piston when it moves from the bottom dead centre to top dead centre.

Net force acting on the piston or piston pin (or gudgeon pin or wrist pin),

               

FP = Force due to gas pressure   Inertia force = FL    FI

The –ve sign is used when piston moves from TDC to BDC and +ve sign is used when piston

moves from BDC to TDC.

When weight of the reciprocating parts (WR = mR . g) is to be taken into consideration, then

         FP = FLF1 ±WR

2. Force due to inertia of the connecting rod or inertia bending forces
Consider a connecting rod PC and a crank OC rotating with uniform angular velocity ω rad / s. In order to find the acceleration of various points on the connecting rod, draw the Klien’s acceleration diagram CQNO as shown in Fig. 32.11 (a). CO represents the acceleration of C towards O and NO represents the acceleration of P towards O. The acceleration of other points such as D, E, F and G etc.,on the connecting rod PC may be found by drawing horizontal lines from these points to intresect CN at d, e, f, and g respectively. Now dO, eO, fO and gO respresents the acceleration of D, E, F and G all towards O. The inertia force acting on each point will be as follows:

Inertia force at C = m × ω2 × CO

Inertia force at D = m × ω2 × dO

             Inertia force at E = m × ω2 × eO, and so on.                

       

                                                                   

Inertia force per unit length at the crankpin = m1 × ω2 r

and inertia force per unit length at the piston pin = 0

Inertia force due to small element of length dx at a distance x from the piston pin P,

    dF1 = m1 × ω2r ×x/l × dx

Resultant inertia force,=m /2 × ω2 r  
3. Force due to friction of piston rings and of the piston.

The frictional force ( F ) of the piston rings may be determined by using the following expression :

F = π D · tR · nR · pR · μ

where D = Cylinder bore,

tR = Axial width of rings,

nR = Number of rings,

pR = Pressure of rings (0.025 to 0.04 N/mm2), and

μ = Coefficient of friction (about 0.1).

Since the frictional force of the piston rings is usually very small, therefore, it may be neglected.

The friction of the piston is produced by the normal component of the piston pressure which varies from

3 to 10 percent of the piston pressure. If the coefficient of friction is about 0.05 to 0.06, then the frictional force due to piston will be about 0.5 to 0.6 of the piston pressure, which is very low. Thus, the frictional

force due to piston is also neglected.

4. Force due to friction of the piston pin bearing and crankpin bearing

The force due to friction of the piston pin bearing and crankpin bearing, is to bend the connecting rod and to increase the compressive stress on the connecting rod due to the direct load. Thus, the maximum  compressive stress in the connecting rod will be
 σc (max) = Direct compressive stress + Maximum bending or whipping stress due to inertia bending stress.

      Material Selection.

The connecting rods are usually manufactured by drop forging process and it should have adequate strength, stiffness and minimum weight. The material mostly used for connecting rods varies from mild carbon steels (having 0.35 to 0.45 percent carbon) to alloy steels (chrome-nickel or chrome molybdenum steels). The carbon steel having 0.35 percent carbon has an ultimate tensile strength of about 650 MPa when properly heat treated and a carbon steel with 0.45 percent carbon has a ultimate tensile strength of 750 MPa. These steels are used for connecting rods of industrial engines. The alloy steels have an ultimate tensile strength of about 1050 MPa and are used for connecting rods of  aeroengines and automobile engines. 
                                                                                          

Design of Connecting Rod

In designing a connecting rod, the following dimensions are required to be determined :

1. Dimensions of cross-section of the connecting rod,

2. Dimensions of the crankpin at the big end and the piston pin at the small end,

3. Size of bolts for securing the big end cap, and

4. Thickness of the big end cap.

The procedure adopted in determining the above mentioned dimensions is discussed as below :

                                                                        

# Design a connecting rod for an I.C. engine running at 1800 r.p.m. and developing a maximum pressure of 3.15 N/mm2. The diameter of the piston is 100 mm ; mass of the reciprocating parts per cylinder 2.25 kg; length of connecting rod 380 mm; stroke of piston 190 mm and compression ratio 6 : 1. Take a factor of safety of 6 for the design. Take length to diameter ratio for big end bearing as 1.3 and small end bearing

as 2 and the corresponding bearing pressures as 10 N/mm2 and 15 N/mm2. The density of material of the rod may be taken as 8000 kg/m3 and the allowable stress in the bolts as 60 N/mm2 and in cap as 80 N/mm2. The rod is to be of I-section for which you can choose your own proportions. Draw a neat dimensioned sketch showing provision for lubrication. Use Rankine formula for which the numerator

constant may be taken as 320 N/mm2 and the denominator constant 1 / 7500.

Given : N = 1800 r.p.m. ; p = 3.15 N/mm2 ; D = 100 mm ; mR = 2.25 kg ; l = 380 mm

= 0.38 m ; Stroke = 190 mm ; *Compression ratio = 6 : 1 ; F. S. = 6.                                           

The connecting rod is designed as discussed below :

1. Dimension of I- section of the connecting rod

Let us consider an I-section of the connecting rod, as shown in Fig. 32.14 (a), with the following

proportions :

                                                                                            

Flange and web thickness of the section = t

Width of the section, B = 4t

and depth or height of the section, H = 5t

First of all, let us find whether the section chosen is satisfactory or not.

The connecting rod is considered like both ends hinged for buckling about X-axis and both ends fixed for buckling about Y-axis. The connecting rod should be equally strong in buckling about both the axes. We know that in order to have a connecting rod equally strong about both the axes, Ixx = 4 Iyy

where Ixx = Moment of inertia of the section about X-axis,  and Iyy = Moment of inertia of the section about Y-axis.

 In actual practice, Ixx is kept slightly less than 4 Iyy. It is usually taken between 3 and 3.5 and the connecting rod is designed for buckling about X-axis.

Now, for the section as shown in Fig.  area of the section,

Now let us find the dimensions of this I-section. Since the connecting rod is designed by taking the force on the connecting rod (FC) equal to the maximum force on the piston (FL) due to gas pressure, therefore,   

                                                                                                                             

We know that the connecting rod is designed for buckling about X-axis (i.e. in the plane of

motion of the connecting rod) assuming both ends hinged. Since a factor of safety is given as 6, therefore the buckling load,

WB = FC × F. S. = 24 740 × 6 = 148 440 N

We know that radius of gyration of the section about X-axis,

Length of crank, r = Stroke of piston/2 = 190/2= 95 mm

Length of the connecting rod, l = 380 mm ...(Given)

Equivalent length of the connecting rod for both ends hinged,

L = l = 380 mm

Now according to Rankine’s formula, we know that buckling load (WB),

                                                                             

Thus, the dimensions of I-section of the connecting rod are :
Thickness of flange and web of the section 

= t = 7 mm Width of the section, B = 4 t = 4 × 7 = 28 mm
and depth or height of the section,

H = 5 t = 5 × 7 = 35 mm

These dimensions are at the middle of the connecting rod. The width (B) is kept constant throughout  the length of the rod, but the depth (H) varies. The depth near the big end or crank end is kept as 1.1H to 1.25H and the depth near the small end or piston end is kept as 0.75H to 0.9H. Let us take 

Depth near the big end, H1 = 1.2H = 1.2 × 35 = 42 mm and depth near the small end,

H2 = 0.85H = 0.85 × 35 = 29.75 say 30 mm 
Dimensions of the section near the big end = 42 mm × 28 mm .

and dimensions of the section near the small end = 30 mm × 28 mm

Since the connecting rod is manufactured by forging, therefore the sharp corners of I-section

are rounded off, as shown in Fig., for easy removal of the section from the dies.

2. Dimensions of the crankpin or the big end bearing and piston pin or small end bearing

Let dc = Diameter of the crankpin or big end bearing,

lc = length of the crankpin or big end bearing = 1.3 dc ...(Given)

pbc = Bearing pressure = 10 N/mm2 ...(Given)

We know that load on the crankpin or big end bearing = Projected area × Bearing pressure

= dc .lc . pbc = dc × 1.3 dc × 10 = 13 (dc)2

Since the crankpin or the big end bearing is designed for the maximum gas force (FL), therefore,

equating the load on the crankpin or big end bearing to the maximum gas force,

 i.e. 13 (dc)2 = FL = 24 740 N

∴ (dc )2 = 24 740 / 13 = 1903 or dc = 43.6 say 44 mm Ans.

and lc = 1.3 dc = 1.3 × 44 = 57.2 say 58 mm Ans.

The big end has removable precision bearing shells of brass or bronze or steel with a thin lining

(1mm or less) of bearing metal such as babbit.

Again, let dp = Diameter of the piston pin or small end bearing,

lp = Length of the piston pin or small end bearing = 2dp ...(Given)

pbp = Bearing pressure = 15 N/mm2 ..(Given)

We know that the load on the piston pin or small end bearing = Project area × Bearing pressure

= dp . lp . pbp = dp × 2 dp × 15 = 30 (dp)2

Since the piston pin or the small end bearing is designed for the maximum gas force (FL),

therefore, equating the load on the piston pin or the small end bearing to the maximum gas force,

i.e. 30 (dp)2 = 24 740 N

∴ (dp)2 = 24 740 / 30 = 825 or dp = 28.7 say 29 mm and lp = 2 


dp = 2 × 29 = 58 mm

The small end bearing is usually a phosphor bronze bush of about 3 mm thickness.

3. Size of bolts for securing the big end cap                                               

Let dcb = Core diameter of the bolts,

σt = Allowable tensile stress for the material of the bolts

= 60 N/mm2 ...(Given)

and nb = Number of bolts. Generally two bolts are used.

We know that force on the bolts

The bolts and the big end cap are subjected to tensile force which corresponds to the inertia

force of the reciprocating parts at the top dead centre on the exhaust stroke. We know that inertia force of the reciprocating parts,

We also know that at top dead centre on the exhaust stroke, θ = 0.

Equating the inertia force to the force on the bolts, we have

and nominal diameter of the bolt,

4. Thickness of the big end cap

Let tc = Thickness of the big end cap, bc = Width of the big end cap. It is taken equal to the length of the crankpin or big end bearing (lc) = 58 mm (calculated above)

σb = Allowable bending stress for the material of the cap = 80 N/mm2 ...(Given)

The big end cap is designed as a beam freely supported at the cap bolt centres and loaded by the inertia force at the top dead centre on the exhaust stroke (i.e. FI when θ = 0). Since the load is assumed to act in between the uniformly distributed load and the centrally concentrated load, therefore, maximum bending moment is taken as

                                            

                                            = Dia. of crank pin or big end bearing + 2 × Thickness of bearing  

liner + Nominal dia. of bolt + Clearance = (dc + 2 × 3 + db + 3) mm = 44 + 6 + 12 + 3 = 65 mm

     

   Detailed drawing.

Manufacturing Process of Connecting rod.

Conclusion

    The project on the design of connecting rod with respect to the Industrial engineering    gave us platform to understand the design process of connecting rod in detailed , also scope for further studies on advance research on connecting rod and usage of IE tools for the manufacturing process like JIT.

    References

    1. Machine Design book By R.S.Khurmi.

    2. www.google.com

    3. www.youtube.com