We Have Numbers Of Free Samples

Table of Contents

1. Abstract
2. Introduction
   • 2.1 Simulation Model
   • 2.2 System Simulation Model
   • 2.3 Multi-Stage Production System
3. Material & Methods
   • 3.1 Simulation Methods
   • 3.2 Probability Distribution
   • 3.3 Continuous Distribution
   • 3.4 Discrete Distributions
   • 3.5 Randomness in Systems and Models
   • 3.6 Random # Generation
   • 3.7 Witness Simulation Model
4. Simulation Results
   • 4.1 Optimization
   • 4.2 Breakdown of Machinery
5. Discussion
6. Conclusion
7. References
8. Appendices

1 Abstract

The simulation project for the execution of an industrial Gearbox that portrays all its features and functions are a rare event that can be simulated over an industrial workshop for the understanding of its operation for approximately 10 days according to the prospected consumers that need to be dispatched on. The Gearbox produced by the manufacturing plant have to be designed and optimized. The Gearboxes are comprised of the different components and these gearboxes are well produced in a separate plant and are arrived at the point of assemble through a conveyor belt. The casting required for the Gearboxes are taken from the available stock and hence it is loaded up to a CNC workstation for the additional tasks involved like machining and boring. Thus each of these castings of the Gearboxes are loaded to the workstation by an operator.

Whereas to be specific about the entire procedure of the Gearbox manufacturing, the assembly process of the Gearbox is performed manually by an operator Thus the bearings of the gearboxes re always assumed to be available in the Stock. These manufactured Gearboxes have huge practical utility and applications in the industry of different machineries. As they have a huge loading capabilities, so they can be used in the commercial vehicles, specialty vehicles, military vehicles, etc. They also have their huge utility in the cranes, land mowers, tractors, pumps, etc. The most important application of the Gearboxes in the practical world is that it can be used in a hybrid car.

2 Introduction

The main purpose of the project is to create a simulated model of the manufacturing plant that produces Gearboxes that has to be designed and optimized. This is a discrete event simulation coursework that might be simulated in an environment of an industrial workshop with a time period of approximately 10 days. Different kinds of modeling and simulation methods have been used to carry out the discrete event-simulation work for manufacturing of the industrial Gearboxes. In the whole process, the stochastic modeling that is used for the estimation and forecasting purpose are described here. As per the stochastic modeling, the mathematical modeling has been recognized to be an essential form of modeling in the certain areas of the applied sciences.

To be in useful application, the model has to be simple conceptually and in addition to being consistent with the numerical and statistical observations. Some tests for the validation of the models need to be performed. The methods that are considered for the purpose of modeling are the exponential regression, linear regression, polynomial curve fittings, autoregressive and moving mean models of the several orders thus assuming the stationary position with following the theories of Box and Jenkins and even the non-stationary models of the time-series of the integrated moving average of auto-regressive. Thus using these different methods twelve different kinds of models are obtained.

To discuss briefly about these modeling techniques are like —-Linear Regression which is a method that depends on the simplifying assumption and for that the observed series of data must be approximated by the linear equation relationship:  y_k= a + bk + w_k, where k= 1, 2,……N and where, y_k = the value of the k^th observation, w_k= the random error in the model. In relation to this the series of Polynomial model is assumed to have the form of — y_k= a₀ + a₁k + a₂k² +……..+a_mk^m. It is quite evident from this equation that the equation of the linear regression is considered as a special case with m=1. Thus for a given value of m, the coefficients a₀, a_1,…a_m may be obtained through a set of the simultaneous equations. To indicate the estimation model of the exponential regression, it can be given by the equation, y_k= ae^βk, where a and β are the consonants. There are other such methods and modeling techniques that would be discussed later in this report.

2.1 What is Simulation Model?

A Model that is defined as a mathematical business model and which combines both the logical as well as the mathematical concepts are known as the Simulation model. It tries to imitate a real life system via the use of computer software. The model helps in calculating the impact of uncertain decisions and inputs that is made on the results that is cared about such as profit and loss, environmental consequences, return of investment, and it’s alike. This kind of model can be developed by writing the code in the supported programming language, the formulas of the model is formulated in the Microsoft Excel spreadsheet, and the statements are constructed in the simulation modelling language.

Generally, a simulation model includes the inputs of the model that are uncertain numbers and which are called as the uncertain variables, then the calculations that is intermediate as required per solution, and the output of the model that depends on the input which are often known as the uncertain functions. It is quite essential to realize the fact that the outputs of the model that depend on the uncertain inputs are itself uncertain in their values and functions. The various numeric values are tested for the uncertain variables and thus several numeric values for the uncertain functions are obtained. Thus the statistics are used to summarize and also analyze all the values for the uncertain functions.

2.2 System Simulation Model

The System Simulation is considered as a set of several techniques that is used by the computers to emulate the operations of the variety of the real-world process or tasks through the processes of Simulation. The computers are required to generate the numeric models with the objective of displaying or describing the complex interactions among the several kinds of variables within a system. Thus the complexity of the system appears from the nature of the events that is probabilistic, the rules for the interaction of the elements and thus the difficulty that arises in the perceiving of the behavior of the systems as a whole as the time passes by. One such instances for the System Simulation is the Video games and such notable example within such games is the Sim City video game that simulates the several systems of a functioning city that includes all the realictic function of a city like sewage, water, electricity, public transportation, etc. Thus there are two types of the System Simulation Model. They are Discrete and also the Continuous Simulation Models. A Discrete Simulation System is such a system in which the defined state variable changes only at a certain discrete set of the points in time. For example the system of a Bank can be considered as a discrete system. It can be illustrated in the graphical form as:

Fig.1 Graphical Representation of Discrete Simulation System

Whereas, a Continuous System is such a system in which the defined state variable changes continuously from time to time. One such example of such a system in real life can be mentioned as the Head of the water behind the dam. The illustration of a Continuous Simulation System in the graphical form is as follows:

Fig.2 Graphical Representation of Continuous Simulation System

2.3 Multi-Stage Production System

To define the complete procedure and each stages that is involved in the production of Gearboxes in a manufacturing plant, it needs to stated synchronously, one after the other as it proceeds. The gearbox that is produced needs to be designed and optimized at first. Before proceeding further it needs to be mentioned that the gearbox is comprised of the components like two bearings, two gears, and one casting. The Gears are thus produced at a different plant and so it is arrived at the assembly point through a 20m conveyor belt that depends on the time distribution that is pre-defined.

To define the conveyor it is of a kind of belt and the gears have a calculated footprint of 80 by 80 by 100mm. Thus the highest capacity of the conveyor is 180 parts and thus the speed of it is 5m per minute. The castings are done from the stock and it is loaded up to a CNC workstation for the supplementary function of machining and boring. An operator loads every casting to the workstation and the time taken by the loading operation is 0.5 to minutes. The maximum capacity of the bin for unloading is 50. The time taken for unloading is 0.5 to 0.9 minutes and the cycle of machining takes to complete in 2.3 minutes. Instead of loading to the bin, every 20^th machined casting is sent to a station where inspection is done.

Thus the operation cycle time of the inspection is distributed with a least of 0.8 minutes, a highest of 2.2 minutes, and a mode of 1.1 minute. The operators carry out the inspection manually. As per the previous tests it has been shown that, after the inspection of around 20 samples, there is a 78% probability that the dimensions that are critical are at the upper limit of tolerance. The operation time that is distributed with the least of the 2.5 minutes, the highest of 3.7, and a mode of 3.2 minutes. In the overall process the failed Gearbox is scraped.  The operator manually performs the assembly process of a Gearbox. The average mean time taken by the process is 3 minutes and the standard deviation is 0.7 minutes, whereas the minimum time that is required is 2.2 minutes and the most required time is 5 minutes. Finally every gearbox that is assembled is put into a buffer for testing.

After the final assembly process, before the dispatching the Gearboxes, a test bench execute the Gearboxes for 10 minutes and thus it can be initially taken up to five at a time. It is loaded and unloaded to the test points by an operator. Thus the unloading and loading both take from 0.2 to 0.4 minutes for every gearbox. The probability of passing the Gearbox towards shipping is 93%, whereas the failed gearboxes are directly sent to the station where they are disassembled and the operator removes the gear and again puts them on the conveyor belt at a distance of 5m from the end. The bearings and castings of the Gearbox are discarded instead. The disassembly takes a mean time of 2.3 minutes, with a standard deviation of 0.4, thus the least time taken is 1.7 minutes and the most is 3.5 minutes. The operators who are employed in the manufacturing plant are trained in all the activities. The entire flowchart of the Gearbox production process in the manufacturing plant can be depicted diagrammatically as follows:

Fig.3 Flowchart of the Simulation Model

3 Materials & Methods

As discussed earlier the materials that are required for running the entire process are the raw materials including the components of the Gearbox like two bearings, two gears, and one casting. After from this the materials sections also includes the assembly devices, testing devices, casting devices, and even the machineries required for the processes like machining, and boring. The methods that are employed in the entire production flowchart are also mentioned earlier as such the Simulation methods which in turn involve the Discrete Event Simulation, Petri nets, and Simulation Environments. The probability distribution and the Continuous distribution also form an essential part of the methods of simulation process. These systems further have several sectional operations and other distributions that are to be discussed later in this section.

3.1 Discrete Event Simulation 

The process of discrete event simulation can be utilized by the computers to simulate the operations of the complex system and hence is also used to study their performance. Thus Discrete Event Simulation is an extensively used technique in any of the simulation process. In this procedure a computer oriented program is developed to simulate the behavior of the system under the study.  If taken the example of a computer system, the system can be a cluster of CPUs or a single CPU, a large communication network or a network switch. Thus with the progress of time the system traces the state of the system.  In terms of the other simulation methods, in the discrete event simulation, there is a constraint that is placed on how the state of system can change. Thus in this case the system state changes at an instant of time.

Therefore, depending on the system understanding which is under study and the objectives of the study, and also on determining the suitable state variables and events, the algorithm of discrete event simulation can be applied in the simulation program. Thus the pseudo-code for the algorithm is as given below:

Fig.4 Pseudo-code for the Discrete Event Simulation Algorithm

The Petri net methods of the Discrete Event Simulation System are a method of the analysis that is often called as the parallel process net with the resources. The proposed analysis method that is based on the reduced reachability graph that is required for the verification of the correspondence between the specification required by the manufacturing system and its PN representation. For reducing the reachablility graph a new kind of technique is proposed that incorporates the transition vectors for determining all the transitions that are enabled at a given state of the system and requires recognizing them as dependent or independent.

The Simulation environment is the created place where the simulated event occurs be it a manufacturing event or any other system. It usually consists of both the contents and the physical space that is required to perform an event. The simulation process can replicate the clinical scenarios in a realistic environment. It basically offers an environment for the trainees to improve and develop their skills through the deliberate and sustained self-practice and even the appropriate feedback.

3.2 Probability Distribution

In the theory of probability and statistics, it is a function that is mathematically denoted and that provides the probabilities of the occurrence of the various possible results in an experiment. To define it more technically it is thus a description of a random phenomenon which is explained in terms of the probabilities of the events. If a random variable say X, is used to denote the result of a coin toss, then the probability distribution of the variable X would take the value as 0.5 for X, that is taken as heads, and the 0.5 for X assumed as tails.  A probability distribution is usually divided into two classes i.e. Discrete Probability distribution and Continuous Probability Distribution.

3.3 Continuous Distributions

A state of a variable can be defined as continuous probability distributions, if only a random variable is a continuous variable and a continuous probability distribution differs from a discrete probability distribution in different ways.  A continuous probability distribution can be described by using an equation or formula as the probability of a continuous random variable will assume the particular value to be as zero. The equation that is used to describe it as a continuous probability distribution is often called a probability density function and it satisfies the conditions like

Fig.5 The conditions satisfying the Probability Density Function

The Uniform distribution is often known as the rectangular distribution that has constant probability.

A triangular distribution that is featured as a continuous probability distribution consists with a probability density function which is shaped like a triangle. It is usually defined by three values: the maximum value (a), the minimum value (b), and the peak value (c).

Fig.6 The graphical representation of probability density function of a triangular distribution

3.4 Discrete Distributions

A Discrete Distributions is a statistical method of distributions that shows the probabilities of the results with the finite values. A statistical distribution can either be continuous or discrete. By the nature of the outcomes, the statisticians can identify the development of either a continuous or discrete distribution. There is finite number of results for the discrete distributions. The concept of discrete distribution can also arise in the Monte Carlo Simulation. It is a modeling technique that identifies the probabilities of the different outcomes through the programmed technology.

3.5 Randomness in Systems and Models

The randomness in the systems and models is an essential portion in the discrete event world as it often incorporates the random kinds of components in two different ways, i.e. internal and external. The system itself is based on stochastic in the internal randomness and in case of external, with all the usual Monte-Carlo explorations of uncertainty either from the internal randomness or through replacing constant but the unknown parameters also prevails with the probability distributions as a form of the sensitivity analysis. In the randomness of the system dynamics there is also a several kind of the probabilistic flavor to the deterministic simulations.

3.6 Random # Generation

The random way of number generation is the process of generating a certain sequence of numbers or the symbols which cannot be predicted reasonably well than by a random probability. This done by the device called random number generator that can be a true hardware of random-number generators or the pseudo-random number generators that usually generate numbers that looks like random numbers but they are actually deterministic.

3.7 Witness Simulation Model  

The Witness is a software or modeling tool that is deployed and implemented for creating and designing the simulation model of the manufactured Gearboxes in the associated manufacturing plant. The Simulation Model which created by the Witness modeling tool is as depicted below:

Fig.7 Witness Simulation Model

The Dimensions of all the elements that are involved in the creation of the Witness Simulation Model are as mentioned below:

4. Simulation Results

The simulation based results for optimization helps in integrating the optimization techniques into the simulation analysis of the simulation model that has been converted in the form of projects. The objective function of the project might be difficult as well as expensive to evaluate, due to the complexity of the evaluation.

4.1 Optimizations

The optimizations of the Simulation Model are basically mathematically modeled system, in which the computer-based simulations provide the entire information about its behavior. In such cases the parametric simulation Models can also be used to improve the overall performance of a system.  The specific Simulation-based optimization methods can be chosen based on the decision variable types and it exists in two main branches of the operational research that is Optimization Parametric and Optimization control.

5. Discussion

The Simulated model can be discussed with respect to the Optimized simulation results of the production model that has been created so far. The gearbox that is manufactured in the simulated environment has developed the need to be designed and optimized at first. The budget constraints and the entire production costs involved in the simulated production process is a mathematically modeled system that is expected for the optimized simulation results that begins from the manufacturing of the Gear box at a separate belt to the dispatch of the complete product of Gearbox after test matching the optimized outcomes.

6. Conclusion

The research and study that is conducted in the creation and design of this  simulation model of the Gearbox manufacturing that involved the several mathematical and statistical analysis and study thus leading to an optimized simulation-based outcome that proves the necessity of the simulation variables, several used models, and techniques, and even the simulation environment that resulted in the optimum budgeting and costs generation of the entire manufacturing process of Gearbox for a minimum duration of the production time. The progressive model that is created is the representative of the Gearbox and drives the standard of the industry thus making it a successful experimentation of the manual assembling of the various internal components of the Gearboxes that could used for the further, more-detailed analysis and that could be better integrated into the design process. As experimented, the expected outcomes of the simulated productions of the Gearboxes have led a way to the feasibility study of its optimized outcomes in the future ahead.

[Download not found]

Download