Für neue Kunden:
Für bereits registrierte Kunden:
Masterarbeit, 2020
57 Seiten, Note: 7.69
ACKNOWLEDGEMENT
ABSTRACT
CONTENTS
LIST OF TABLES’
LIST OF FIGURES
Chapter-1 INTRODUCTION
1.1 Surface roughness
1.1.1 Surface roughness measurement
1.1.2 Roughness parameters
1.2 Laser cutting process
1.3 Problem statement
1.4 Thesis objective
Chapter-2 LITERATURE REVIEW
Chapter-3 DESIGN OF EXPERIMENT
3.1 Experimental studies
3.2 Why design of experiment
3.3 Central composite design
3.4 Response surface methodology
3.4.1 RSM step-by-step application
Chapter-4 EXPERIMENTAL WORK
4.1 Selection of input factors and output response
4.2 Sample
4.3 Instruments used
4.4 Methodology
4.4.1 Problem formulation
4.4.2 Literature survey
4.4.3 Trial runs
4.4.4 Design matrix creation
4.4.5 Conduction of experiment
4.4.6 Data analysis and interpretation
4.4.7 Confirmation experiment
4.4.8 Conclusion
Chapter-5 Results and discussion
5.1 Development of mathematical model
5.1.1 Validation of model
5.2 Effect of process parameters on response
5.2.1 Contour plots
5.3 Optimization
5.4 Confirmation test
5.4.1 Percentage error
Chapter-6 Conclusion and future scope
6.1 Conclusions
6.2 Future scopes
Appendices
Appendix 1 Literature presented
Appendix 2 Design Expert Documentation
Appendix 3 Numerical Optimization algorithm
Chapter-7 REFERENCE
Table 3.1 Types of Central Composite Design (CCD)
Table 3.2 ANOVA table for full model
Table 4.1 Laser system specification
Table 4.2 Roughness measuring instrument specification
Table 4.3 Design matrix
Table 5.1 Responses recorded from the roughness measuring experiment
Table 5.2 Fit Statistics
Table 5.3 ANOVA for reduced quadratic model
Table 5.4 Measured values of confirmation test
Fig 1.1 Laser cutting process
Fig 3.1 Central Composite Design generation
Fig 4.1 CO_{2} laser cutting and engraving machine with the computer system
Fig 4.2 Stylus type surface roughness measuring system
Fig 4.3 Trials runs on the sample
Fig 4.4 CCD options window
Fig 4.5 CCD design window
Fig 4.6 Engraved channels
Fig 5.1 Scatter diagram showing the relationship between the actual and predicted values for each responses.
Fig 5.2 Perturbation plot showing the effect of process parameters on surface roughness
Fig 5.3(a) Contour plot of combined effect of laser power and speed
Fig 5.3(b) 3D surface plot of combined of laser power and speed
Fig 5.4(a) Contour plot of combined effect of speed and DPI
Fig 5.4(b) 3D surface plot of combined of speed and DPI
Fig 5.5(a) Contour plot of combined effect of laser power and DPI
Fig 5.5(b) 3D surface plot of combined of laser power and DPI
Fig 5.6 Ramp function graph Ramp function graph for optimal setting of input parameters and optimized value of response
Fig 5.7 Roughness evaluation graph obtained for serial no. 01
Fig 5.8 Roughness evaluation graph obtained for serial no. 02
Fig 5.9 Roughness evaluation graph obtained for serial no. 03
The success in conducting experiments and writing this report required a lot of guidance and assistance from many people and I am extremely privileged to have got this all along the completion of my project report. All that I have done is only due to such supervision and assistance and I would not forget to thank them.
I respect and thank to our HOD, Prof. (Dr.) Parimal Bakul Barua, Department of Mechanical Engineering, Jorhat Engineering College for providing me an opportunity to do the project work in CSIR-North East Institute of Science & Technology, Jorhat and giving me all support and guidance which made me complete the project duly.
I owe my deep gratitude to my project guide Mr. Dipankar Neog, Principal Scientist, CSIR-North East Institute of Science & Technology, who took keen interest on my project work and guided me all along by providing all the necessary information for developing a good system.
I heartily thank my internal project guide, Mr. Nagendra Kushwaha, Assistant Professor (TEQIP), Department of Mechanical Engineering, Jorhat Engineering College, for his guidance and suggestions during this project work.
I am thankful to and fortunate enough to get constant encouragement, support and guidance from all teaching staffs and project staffs of our Department of Mechanical Engineering, Jorhat Engineering College and North East Institute of Science & Technology. Also, I would like to extend my sincere esteems to all staff in laboratory and all my classmates and friends for their timely support.
DEBASHISH GOGOI Dept. of Mechanical Engineering
Jorhat Engineering College
In today's production and manufacturing industries, the laser cutting method is the broadly used nonconventional, advanced, non-contact type machining process. It has various advantages in using to cut or engrave almost all kinds of materials. In this study the effect of laser engraving parameters on filter paper were quantified using mathematical model. The main objective of this study was to assess the individual and interaction effect of the input parameters on the surface quality of engraved portion under the experimental conditions that were based on the experimental design. From the experiment it was found that the laser power has the significant effect on the surface roughness. The interaction effect of the speed and number of dots per inch created by nozzle of the laser engraving machine and the quadratic effect of speed also have the significant effect on the output surface quality. It is seen that the roughness increases with the increase in the laser power. Also, it was found that the combination of low laser power and mid engraving speed can results in the good surface quality. Similarly, combination of low speed and DPI results in the good surface quality. Accordingly, interaction effect of low power and high DPI results the better surface quality. The best optimal setting was at 8W of laser power, 205.895 mm/sec of engraving speed and 299.9 numbers of dots per inch, the roughness was found as 5.5693 µm with the percentage error of 0.53%.
The invention of laser was the landmark inventions of the mid 20th century which is often grouped with the invention of transistor and computer. The 1st conceptual building block of laser was the proposal given by Albert Einstein in 1916 that photons could stimulate emission of identical photons from excited atoms. Laser is abridged as "Light Amplification by Stimulated Emission of Radiation." [1-2]. Helium-Neon(He-Ne) laser was the first gas laser developed at Bell Telephone Laboratories in 1961. Since then, newer types of reliable and powerful lasers have been developed but a few types of lasers are only in use for material processing. Mostly, CO_{2} and the Nd-YAG laser have been used frequently in most of the material processing applications. [3]. A laser generates high intensity beam of infrared light which is focussed on the surface of the material to be processed. The focussed beam melts the surface locally and the molten material is blown away with the help of assist gas pressure that acts coaxially to the beam. The common assist gases are oxygen and nitrogen [4]. The CO_{2} laser operates in the middle infrared on rotational-vibration transitions in the 10.6 and 9.6 wavelength regions. [5]. There are various applications of CO_{2} laser processing that includes cutting, welding marking or engraving etc. It also has many industrial applications for both metallic and non-metallic materials. The laser processing can be applied in tougher and robust material and also in the material like thin paper. The main application of CO_{2} laser processing on paper is marking or engraving. [6].
Laser cutting in general is an effective way to reduce production and manufacturing costs. This is due to the advantage of high production rates as well as the fact that lasers can be mechanised, computer controlled and integrated into assembly lines. Many industries have been revolutionized by the application of laser equipment in their production lines. This is because of the high-quality and low distortion characteristics of the cutting action which can be achieved. Most materials can be cut by the process including metals, wood, plastics, rubber and composites etc. On the other hand, some materials cannot be cut by this process due to safety reasons [4].
Paper based microfluidics is one of the widely used techniques in the field of microfluidics. Paper has the capability of transporting fluid through capillary action or wicking. It eliminates the need of pump or other similar equipments. The paper based microfluidics technique has various advantages such as inexpensive, rapid, biodegradability, mass production and faster response etc. [7]
Surface roughness is nothing but the component of the surface texture. It is measured by taking the measurement of the deviation of real surface from its ideal surface in the normal direction. [8-9]
The measurement of surface roughness is the measurement of the small-scale variations in the height of a surface. This is in contrast to larger-scale variations such as form and waviness that are typically part of surface geometry. [10]
The different parameters of roughness are discussed below. It is to be mentioned that in our experiment, we have used arithmetic mean value of roughness as our response minimization of which is our intended goal.
- Mean roughness (Ra): The Mean Roughness (Roughness Average Ra) is the arithmetic average of the absolute values of ordinates for roughness profile. Ra is one of the most important tests of surface roughness typically taken in general engineering practice. It gives a clear general explanation of surface height fluctuations. Ra's units are micrometers, or micro inches.
- Root mean square roughness (Rq): Root Mean Square roughness (Rq) is the root mean square average of ordinates for roughness profiles.
- Mean roughness depth (Rz): The Mean Roughness Depth (Rz) is the mean arithmetic value of consecutive sampling lengths of the single roughness depths.
- Rt- Total roughness profile height: difference between height Zp of the highest peak and depth Zv of the deepest valley within the assessment length
- Rzi – the maximum height of the roughness profile: the sum of the highest profile peak and the depth of the lowest profile valley, relative to the mean line, within the length of the study.
The laser cutting process is carried out by using précised laser beam through the hich we are concentrating on. It delivers an accurate and smooth finish of the work.
The basic mechanism for laser cutting process consists of:
1. The laser generates high intensity beam of infrared light.
2. The beam is concentrated or focused on the surface of the material being cut or engrave by means of lens.
3. The focused beam heats the surface concentrating on and melting starts and localized position.
4. The molten material is ejected from the area by pressurized gas jet which acts coaxially with the laser beam. [10-11]
Abbildung in dieser Leseprobe nicht enthalten
Fig 1.1 Laser cutting process [11]
If a manufacturer wishes to introduce laser engraving as a way during a
manufacturing process, it's necessary to review the effect of the method during a new material. Variety of preferred characteristics like accuracy of the cut and quality of the surface finish are often specified and also process characteristics like high speed and low power usage are often also stipulated. It’s then necessary to vary the laser input parameters and test whether or not the specified quality features are achieved or not. This
procedure is typically performed by skilled workers. However, this procedure of selection of parameters is predicated on trial-and-error and is typically time-consuming. Moreover, the conventional one by one technique isn't systematic and typically doesn't cause an optimised combination of laser engraving parameters. A systematic study, supported Design of Experiment (DOE) techniques followed by the analysis of the results using Response Surface Methodology (RSM),
will allow the detection and visualisation of the interactive effects of the input
parameters on the results. Once a study of this type has been done, the optimum
combinations of laser cutting parameters are often selected then wont to produce the desired specifications.
The present work has been undertaken keeping into consideration the following problem:
- Smoother channel boundaries are required in the study of paper based system. Therefore micro-precision is required in order to get the smoother surface of the paper so that different investigations on the miniature system on paper can be done.
- It is difficult to engrave on paper due to different operating parameters of the engraving machines, so it is important to investigate the range of operating parameters to engrave on the paper.
- Optimal combinations of operating parameters need to be investigated to get the smoothened surface on paper.
The main objective of the present work is to use RSM to develop mathematical models, within the sort of function showing the relationships between the possible laser engraving parameters. These models would add a considerable knowledge to assist scientists and researchers in conducting experiments. It might also assist technicians and engineers to achieve the specified laser engraving characteristics particularly on paper based material.
Moreover, the models to be developed would be useful in predicting
responses. This is able to allow the choice of the optimal settings of the method input parameters to minimise or maximise certain responses. The response to be used here is the surface roughness of the engraved paper. The principal aims of this research are often summarized within the following points:
1) To build up mathematical models using RSM with the aid of Design Expert 12 statistical software to predict surface roughness on paper.
2) To identify the most influential laser cutting parameters and to clarify their interactions on the surface roughness.
3) To present the developed models in 3D plots.
4) To identify the optimal combinations of the process input parameters, using numerical and graphical optimisation, to achieve a specific target criterion.
The laser processing on paper is used mainly for the design and study of micro-system using techniques of microfluidics. G.Jenkins et al.[7] studied the new methodologies for health care using printed electronics integrated with paper based microfluidics and they found that the roughness has a significant effect on the flow of PDMS after deposition.
A considerable number of researches have been carried out to study the cut or engraved quality and the operating parameters by using laser processing on different metals and non-metals. A quantitative analysis was done by the J.N. Gonsalves and W W Duley [14] to examine the CW CO_{2} power required to cut a sheet of thin stainless steel of type 302 at varying cutting speeds. In their process of analysis, series of experiments were done for different incident laser power and in each different power level; the critical speed was examined by increasing the speed and noting down the width. During this series of experiments, it was found that all beams did not take part in the process of heating. It was seen in their experiment that the cutting width decreases with increasing velocity. It was also found that a fraction of beam used in the process of cutting also increases with increasing cutting speed.
Neimeyer et al. [15] studied the effect of laser cutting operating parameters on surface quality of mild steel and found better surface at high cutting speed and low assist gas pressure. It was also found that the thickness of work-piece has a nominal effect on the cut surface quality. It was mentioned that the despite the significant visual difference in the striation pattern, the profile of the cut surface of the top and bottom edge yield have the same values for the average surface roughness.
Pietro and Yao [16] have conducted an investigation into characterizing and optimizing to review the current status of laser cutting and associated quality techniques, including research efforts undertaken in the fields of modeling, regulation, diagnosis and monitoring. The quality of the laser cut was defined in terms of kerf width, cut edge, inner side slope of the kerf, HAZ extent, dross appearance and surface roughness. It was mentioned that for characterizing the cut profile, the arithmetic average roughness parameter Ra is the most reliable parameter. They also mentioned that a roughness profile can be measured when a complete cut surface is achieved.
Bekir Yilbas[17] studied the relationships among the parameters involved in the CO_{2} Laser cutting processes and the cutting quality. The cutting parameters were taken as work-piece thickness, laser output power, cutting speed and assisting gas pressure taking the Mild Steel as the work-piece. The experiment extended to monitor whether any surface plasma formed during the cutting process or not. Through the experiment, it was found that at very low cutting speed the self burning occurred in the cutting surface and increased with the increased oxygen pressure. At very high cutting speed, heat spread from the zone of cutting decreased. Curved strias developed near the undersurface of cut once the cutting speed exceeds critical speed. It was also found that a considerable amount of surface plasma caused the surface erosion.
Yilbas[18] et al investigated the CO_{2} laser cut quality by using Taguchi method on different sheets of stainless steel. The flatness and waviness were observed with respect to cutting speed, oxygen pressure, and workpiece thickness. It was found that the oxygen gas pressure and cutting speed had the significant effect on the cut quality. However, the thickness had a significant effect on flatness. On extended study on detection of light emission from surface plasma, it was seen that the microcracks appeared on cut edge surfaces due to the rapid solidification of the molten oxide layer formed on the surface.
The performance of cutting operation by CO_{2} laser on a mild steel plate of 3mm thickness with assistant-gas pressure of maximum of 10 bar was studied by S.L Chen[19] . The assistant gases were nitrogen, oxygen, argon, and air. A coaxial nozzle with very high pressure was designed to perform the experiment that was capable to withstand pressure to the maximum limit 12 bar. It was found that, in the inert laser cutting process, the cutting quality can be significantly improved by using high cutting gas pressure but it is opposite in case of high-pressure oxygen and air laser cutting resulted in poor quality cutting. It was also observed that on the top of the cut surface the side burning appeared.
Wang and Wong [20] have investigated the cut quality by using laser system on sheet of steels coated with zinc and aluminium with thickness ranging from 0.55 to 1 mm. Good-quality cuts are found at a high cutting speed of 5000 mm/min by proper control of the cutting parameters. It was reported that high laser power above 500 W results in a poor- quality cut. It was also found that the kerf width generally increases with increasing gas pressure and laser power, and with a decrease in cutting speed.
Chen and Yao [21] investigated on the interactive nature of the melt flow and oxidation in cutting of mild steel using laser. They found that the increase in the cutting speed leads to the increase in liquid film thickness which increases the interfacial velocity. It increases the striation frequency. Cutting speed has significant effect on striation wavelength. They have reported that the striation depth get reduced with increasing striation frequency and cutting speed.
Yilbas [22] investigated the process parameters of the CO_{2} laser cutting on kerf width . He found that with increase in energy coupling factor and laser power,the size of the kerf also increases. He also found that energy coupling factor, laser power, energy and cutting speed have the considerable effect on the size of kerf that can be modified remarkably even with the minimal variation of the of these parameters Although among these parameters laser power has the highest impact on size of kerf width. He reported that the size of the kerf increases with increasing energy coupling factor at a lower cutting speed with high power.
The cut quality of 4130 steel by using CO_{2} laser cutting system was investigated by Rajaram et al [23]. They have found that increasing the feed rate and decreasing the laser power leads to the decrease in kerf width and HAZ. They have reported that the increase in feed rate increases the surface roughness and striation frequency. It was concluded that the power has the small effect on the surface roughness but it does not have any effect on the striation frequency.
An investigation on laser cutting quality and thermal efficiency analysis has been carried out by Yilbas [24]. To identify the effect of cutting parameters on the resulting cut quality, a statistical method based on factorial analysis was introduced. It was found that increasing laser cutting speed reduces the kerf width, while the kerf width increases with increasing laser power.
Powell and Kaplan [25] found CO_{2} laser cutting technique is the most effective techniques among the available laser cutting technique. For very fine and detailed work, Nd:YAG lasers are only preferred. It was found that the employed pressure of the gas depends upon which materials are being cut. The lasers involved usually got to have smaller focused spots than are possible using infrared CO_{2} and standard Nd:YAG lasers.
I Uslan[26] investigated the influences of laser power and cutting speed on kerf width size in CO_{2} laser cutting operation on a sample of mild steel. It was found that power intensity had a significant effect on the size of kerf width.
Evaluating the optimum parameters of laser cutting process for cutting samples of austenitic stainless steel with a thickness of 1.2 mm, has been investigated by Abdel Ghany and Newishy [27]. It was found that cut quality is affected by all the input process parameters. The paper also mentioned that the optimal cutting conditions are: power 210 W, frequency from 200 to 250 Hz, speed 1.5 m/min, focus position from -1 to 0.5, pressure of nitrogen ranges from 9 to 11 bar and pressure of oxygen ranges from 2 to 4 bar. They also found that the roughness and kerf width decreases with increase in frequency and cutting speed but with increase in power and gas pressure increases the kerf width and the roughness. It was found that using nitrogen as an assist gas, it produces brighter and smoother cut surfaces with smaller kerf.
An investigation on laser cutting to investigate the different cut quality on Polycarbonate, Polyethylene and Polypropylene have been carried out by Caiazzo et al [28]. They took the thickness of the plastics ranging from 2 mm to 10 mm and found that for the entire considered polymer sample, the quality of cutting edge is significantly affected by the cutting speed. They have also mentioned that the high cutting speed may not always lead to better process efficiency. They have found that the 200 Watt of laser power may be the sufficient power to cut these considered plastic which obviates the need of high power laser. When working with Polypropylene and Polyethylene, the quality of edge and faces have been found better.
Radovanovic and Dasic [29] investigated the surface roughness of mild steel sheets when CO_{2} laser is used to cut the sheets. It was found that there are two zones on the cut surface, uppur one and lower zone. The laser beam enters the sample is defined as the upper zone and where the laser beam leaves the sample is defined as the lower zone. It was found that the surface roughness decrease with increasing laser power but increase with increasing sheet thickness.
Lamikiz et al. [30] have investigated the influence of the laser cutting parameters on different metallurgical characteristics of different series of advanced high strength steels. They found that the high quality cut for sheet thickness of 0.7mm and 0.8mm can be achieved by using a large range of cutting speeds between 2000 mm/min and 7000 mm/min. It was also mentioned that a level of power of 200W is sufficient to working at a speed of 4000 mm/min and 300 W for speed of 8000 mm/min. They also found that if sheet thickness is more than 1 mm, then high quality cut can be obtained by using oxygen pressure of 4 bar, power of 300W and speed of 3000 mm/min . It also reported that the gas pressure of 6 bars is sufficient for all the speeds mentioned above.
Li et al. [31] have conducted an investigation to achieve striation-free laser cutting of 2 mm thick EN43 mild steel. They used a 1 kW single mode fibre laser in their investigation. A theoretical model to predict the cutting speed at which striation- free cutting occurs was proposed by them. It was found that above the critical speed of 33 mm/s striation occurs and the surface roughness increases.
An experiment to investigate the quality of cut taking as the sample of Polymethyl-Methacrylate by using a CO_{2} laser have been conducted by Davim et al. [32]. It was presented that the size of HAZ increases with increasing the laser power but it is inversely proportional to the cutting speed. They also found that the laser power is inversely proportional to the surface roughness but the cutting speed is directly proportional to it.
Riveiro et al [33] investigated the influence of processing parameters and optimal condition for CO_{2} laser cutting on the specimen of Aluminum-Copper alloy (2024-T3) and evaluated the results in terms of it was found that in the pulsed mode of cutting, the best quality of cut can be obtained under the combination of high laser power, high frequency, and moderate duty cycle. On the other hand, in the case of cw mode of cutting it was found that it substantially increased the cutting speed as compared to pulsed mode. In this mode high-quality cut and cutting speed can be found by applying high laser power and focusing the laser beam onto the surface. They also pointed out that the assist gas pressure and nozzle exit diameter must be correctly adjusted to have a better quality cut.
Choudhury and Shirley [34] have carried out an experiment to investigate the effect of the process parameters in cutting three polymeric materials those are Polypropylene, Polycarbonate, and Polymethyl-Methacrylate. They mentioned that good quality cut can be achieved when cutting the Polymethyl-Methacrylate than in case of the Polycarbonate and Polypropylene. They mentioned that roughness increases with the decreasing laser power, compressed air pressure and laser cutting speed. Comparatively the compressed air pressure and laser cutting speed have higher effect on roughness. They also found that HAZ is smaller n case of Polymethyl-Methacrylate. It is followed by Polycarbonate and Polypropylene. The dimension of HAZ decreases with decreasing laser power and increases with decreasing cutting speed and pressure.
Choudhary and Patel [35] evaluated processing parameters of fibre laser in cutting of mild steel and found that the cutting speed as the most significant factor for sheet of thickness 5mm.
Kotadiya and Pandya [36] did a parametric analysis of CO_{2} laser machining on sample of stainless steel sheet of thickness 5mm. They found that the laser power has the significant effect on achieving the better surface roughness as compare to the cutting speed and the gas pressure.
B. Bhardwaj and V. Sharma [37] optimized the effect of parameters involved in the CO_{2} laser cutting to get minimum kerf width in the cutting of AISI304L steel. Taking the gas pressure, cutting speed, laser power and position of focal point as the input parameters and Kerf width as the outcome, it was found that that minimum value of kerf width can be achieved at lowest level of laser power, lowest level of gas pressure, highest level of cutting speed and highest level of focal point position. Among these parameters, cutting speed was found as the most dominating factor in response to kerf width.
Zhou et. al [38] investigated the role of supersonic nozzle in laser cutting process and found that the supersonic nozzle helps in fibre laser cutting of stainless steel by stabilizing the effect of feed rate.
Nikolidakis et. al [39] investigated the cutting conditions for laser engraving of stainless steel and found that with increase in laser power and with decrease in scanning speed at same time increases the material removal rate. It was also found that the material removal rate increases with increase in scanning speed and decrease in repetition at a time.
Parthiban et. al [40] developed a mathematical model for heat affected zone when processed using CO_{2} laser cutting system. They found that response surface methodology is very effective method and quadratic model can be used for the prediction of the heat affected zone.
Thus from the literatures we have seen that many researchers have done numerous researches to investigate the operating parameters of CO_{2} laser processing for better intending output. It has been applied in different kind of materials including metals and non-metals. We have also come to know that cut quality is one of the most important output factors that most of the researchers have intended to achieve better. It has been also cleared that surface roughness is one of that factor which we want to achieve according to our need. As we knew from the literature that in paper based microfluidics, surface roughness of the paper plays a vital rule in the intended study of the micro system. Therefore, here we are interested to have a smoother channel that is engraved on filter paper. Because of this reason, we’ll use CO_{2} laser for engraving our sample and optimize the operating parameters to get smoother engraved channels.
After going through the literatures we have decided to take the operating parameters of CO_{2} laser engraving process as laser power, cutting speed and dot per inch (DPI) of the nozzle. To measure the surface roughness after the engraving the sample, stylus type roughness measuring instrument will be used. We have also decided to use response surface methodology to create the mathematical model for the optimization of the parameters. For this purpose, statistical software Design Expert 12 will be used to analyze the experimental data.
This chapter describes about design of experiment, all the related terms and methodologies along with the equations that are being used in developing mathematical models.
In experimental studies the researcher can control many aspects of the environment in which the experiment is being conducted. They can change the values of common variables, and then calculate responses. By controlling the environment the researcher can attempt to minimize factors that might obscure the results of the experiment.
There are three main elements of an experimental study:
1) Experimental units: These are the objects or subjects which are under investigation.
2) Treatments: This refers to the procedures which are used in the experimental study for each unit.
3) Responses: This refers to the scales by which the various treatments are compared.
The aim of any experimental study is to clearly demonstrate the difference in response when different treatments are applied to the experimental units (assuming, of course, that the hypothesis of the researchers is correct and that there is a difference indeed). Variations in responses that are due to factors other than the treatments under investigation will obscure differences. Good experimental design reduces obscuring variation. [41]
Previously, the experiments used to be conducted by changing one-factor-at- time, this type of experimental approach required a huge number of runs to determine the effect of a single factor. This creative method is no longer being pursued, because it is expensive and would take longer. Another downside is that by using this method, the interaction variables cannot be identified. [42-43]. Therefore, other strategies that resolve these barriers, such as DOE, ANN etc., have to replace it. For these reasons, a DOE approach was chosen for implementation here. Many designs exist among DOE's, the typical designs are two level factorial design and Taguchi method, which have the less number of runs to test a process with multifactor and multi responses such as laser engraving. However, owing to the limitation of this design as a screen design, the quadratic effect of each factor cannot be determined using 2-level FD. By comparison, due to the aliased structures, some of the interactions between the factors influencing the process cannot be calculated using Taguchi method, meaning that not all the interaction effects can be estimated. RSM, on the other hand, will find out all of the effects of the factor and their interactions. The following Eq 3.1 is composed of three capital-sigma notations.
Abbildung in dieser Leseprobe nicht enthalten
The first summation term represents the main factor effects, the second term describes the quadratic effects and the third term reflects the results of the two factor interaction. [44]. RSM was therefore chosen by Central Composite Design (CCD) implementation.
The CC designs (designs from Box and Wilson) consist of a full, factorial or fractional design. The points at the centre of the experimental domain and the "star" points outside this domain allow estimation of the response surface curvature.
Abbildung in dieser Leseprobe nicht enthalten
Fig.3.1 Central Composite Design generation
Here "Full" means that the design of the experiments consists of all possible factor combinations, "Factorial" means that all the levels of all the factors are coded and "Fractional" means that the design of the experiments consists solely of certain possible combinations. The factorial design points levels are ±1 and those on a "star" are ±α where is used. There are 3 forms of CC plans.
The value of the α parameter is determined by the calculation possibilities and the precision required for the surface response estimation. The position of the points determines the quality of the estimation. The calculation accuracy is determined by the setting of α value and the number of trails at the middle of the domain.
Table 3.1 Types of Central Composite Design (CCD) [45]
Abbildung in dieser Leseprobe nicht enthalten
In the early 1920 's Sir R. A. Fisher invented the DOE method. Fisher developed a system for conducting agricultural experiments to assess the impact on a crop of properties such as fertilizer, sunlight and heat. DOE method has been applied over a wide range of disciplines since the 1920's. Since then, a range of different DOE methods have been developed including factorial experiments and techniques of Response Surface Methodology, such as Central Composite Design and Box-Behnken Design. The approach chosen for a particular experiment depends on criteria such as the aims of the experiment, the number of factors to be examined and the available funds [46]. Engineers frequently search for conditions to optimize the process interested. In terms of process input parameters, the optimum could be either a minimum or a maximum of a given function. RSM is one of the optimisation techniques currently used to explain the laser cutting process performance.
RSM is a collection of mathematical and statistical techniques useful for modelling and predicting the interest response influenced by multiple input variables in order to optimize this response. [47]
RSM also sets out the relationships between one or more calculated responses and key controllable input factors [48.]
If all independent variables are measurable and can be replicated with negligible error, the response surface can be expressed with:
Abbildung in dieser Leseprobe nicht enthalten
Where: k is the number of independent variables
To optimize the "y" response, an appropriate approximation must be found for the true functional relationship between the independent variables and the response surface. A second-order polynomial Eq.3.1 is normally used in RSM.
It is usually considered in sequential steps for performing any RSM problem. In order to build a mathematical model in the case of laser engraving, the following steps are thus taken:
1) Determining the parameters of critical input operation:
These critical parameters may be specified from past literatures or by performing a factorial design based preliminary analysis (i.e. screening test). The process parameters from past literatures were determined in this research. The parameters of the process inputs are: laser power, engraving speed and dot per inch (DOI).
2) Finding the limits of each factor:
To find the range of each parameter, trial laser engraving runs were performed to find out the range of each parameter by varying one of the process parameters at-a-time.
3) Development of design matrix:
In the current research the design matrix was built using Design Expert 12 statistical software for each experiment. 40 numbers of experimental runs will be carried out and these experimental runs are sufficient to estimate the Eq.3.1 coefficients.
4) Performing the experiment:
The laser cutting experiments were accomplished in a random order according to the design matrix to avoid any systematic errors in the experiment.
5) Measuring the responses:
Surface roughness as the response in this project was measured at different levels of parameters.
6) Development of mathematical model:
The functional relationship for three factors, representing any response of interest can be expressed as y = f (A, B, C) and Eq. 3.1 becomes as follows:
Abbildung in dieser Leseprobe nicht enthalten
7) Estimation of the coefficients
To estimate the values of the coefficients in Eq 3.3, regression analysis is used .Nevertheless; the computer software was used to estimate the coefficients for all experiment responses.
8) Testing the adequacy of the developed models
The Analysis of Variance (ANOVA) has been used to test the adequacy of the model developed. The statistical significance of the models developed and the sequential F-test, non-fit test and other adequacy measures (i.e. R2, Adj-R2, Pred. R2 and Adeq. precision ratio) were examined for each term in regression equation using the same software to obtain the best fit. The model's Prob.>F (sometimes called p-value), which can be measured using ANOVA for each term in the model. If the model's Prob.>F and each term in the model does not reach the significance point (say α= 0.05), then within the confidence interval of (1-α) the model can be considered adequate. The lack of fit could be considered insignificant for the non-fit test if the Prob.>F of the lack of fit exceeds the significance level. A summary of the ANOVA table is given below in table 3.2 [48-49]
9) Model reduction:
The complete mathematical model shown in Eq. 3.3 normally contains terms which are not significant that need to be eliminated (i.e. terms with p-value greater than α). This removal can be achieved manually or automatically by selecting one of the software's selection procedures.
10) Development of the final reduced model:
At this stage it is possible to build up the final reduced model, as determined by applying the above steps. This model contains only the significant terms and conditions that are necessary for hierarchical maintenance. It can also be produced with reduced quadratic table ANOVA.
11) Post Analysis:
By using the adequate model it is possible to predict the response within the ranges of factors. Moreover, using the developed model, it is feasible to find the optimum laser engraving conditions which could optimize the process and lead to the desired surface quality.
Table 3.2 ANOVA table for full model
Abbildung in dieser Leseprobe nicht enthalten
This chapter explains the selection of input factors and output responses, requirements of the sample, the experimental methods that have been followed and the equipment used in the current study.
From the literatures we have come to know that cut quality is one of the most important output factors that most of the researchers have intended to achieve better. It has been cleared that surface roughness is one of that factor which we want to achieve according to our need. As we knew from the literature that in paper based microfluidics, surface roughness of the paper plays a vital rule in the intended study of the micro system. Therefore, here we have taken surface roughness as our output response. From literatures it has also been found that input factors such as laser power, engraving speed, and dots produced by laser has different effect on different materials. Therefore here we have decided to take the input factors as laser power, cutting speed and dot per inch (DPI) of the nozzle.
In our study, we have used filter paper of diameter 125mm. The thickness of the paper is 0.23mm. The filter paper which has varieties application such as removal of precipitates, preparation of qualitative analysis, environmental monitoring etc has been used in our study to have the usefulness in making smoother channels in study of paper based microfluidics system. The input parameters of CO_{2} laser engraving process have to be controlled to get intended engraved surface quality and therefore filter paper is taken as our sample for study.
In this experiment, we have used basically two instrumental systems. Those are -
1. CO_{2} laser cutting or engraving machine:
This machine has mainly two parts; one is the software part and another one is the hardware. The software used here is the L Solution.
The hardware part of laser system mainly has three components.
i. Computers
ii. Laser cutting machine
iii. Exhaust pump
Table 4.1 Laser system specification
Abbildung in dieser Leseprobe nicht enthalten
Abbildung in dieser Leseprobe nicht enthalten
Fig 4.1 CO_{2} laser cutting and engraving machine with the computer system
2. Surface roughness measuring instruments.
A stylus type roughness measuring instrument has been used in this experiment. The specifications are as follows
Table 4.2 Roughness measuring instrument specification
The instrumental setup of this measuring system is shown in the fig 4.2
Abbildung in dieser Leseprobe nicht enthalten
Fig 4.2 Stylus type surface roughness measuring system
Different steps and methods are used in this experiment. These methodologies and steps that are being used in conducting this experiment are described below:
The first step of any study is the formulation of the problem on which the researchers intended work for solution. In this study the problems that are taking into consideration have been already discussed in chapter 1.
Extensive survey on previous works has been done and described in the chapter 2. This is the 2nd step of this work. After going through the literatures, it has been decided to take the input process parameters of laser engraving process as the laser power, engraving speed and the dot per inch. It has been also decided to use RSM to develop mathematical models, within the sort of function showing the relationships between the possible laser engraving parameters. These models would add a considerable knowledge to assist scientists and researchers in conducting experiments. Filter paper is used as the sample for our experiment. From the literatures it has been found that the engraving of smooth surface is most needed element for any paper based microfluidics study. Therefore, the process parameters are optimized to get the smoothened engraved surface on the paper.
[...]
Masterarbeit, 132 Seiten
Doktorarbeit / Dissertation, 263 Seiten
Doktorarbeit / Dissertation, 180 Seiten
Medien / Kommunikation - Public Relations, Werbung, Marketing, Social Media
Bachelorarbeit, 85 Seiten
Doktorarbeit / Dissertation, 143 Seiten
Masterarbeit, 106 Seiten
Chemie - Materialchemie, Werkstoffchemie
Doktorarbeit / Dissertation, 191 Seiten
Masterarbeit, 70 Seiten
Diplomarbeit, 115 Seiten
Diplomarbeit, 88 Seiten
Doktorarbeit / Dissertation, 194 Seiten
Doktorarbeit / Dissertation, 115 Seiten
Masterarbeit, 132 Seiten
Doktorarbeit / Dissertation, 263 Seiten
Doktorarbeit / Dissertation, 180 Seiten
Medien / Kommunikation - Public Relations, Werbung, Marketing, Social Media
Bachelorarbeit, 85 Seiten
Doktorarbeit / Dissertation, 143 Seiten
Masterarbeit, 106 Seiten
Chemie - Materialchemie, Werkstoffchemie
Doktorarbeit / Dissertation, 191 Seiten
Masterarbeit, 70 Seiten
Diplomarbeit, 115 Seiten
Diplomarbeit, 88 Seiten
Doktorarbeit / Dissertation, 194 Seiten
Doktorarbeit / Dissertation, 115 Seiten
Der GRIN Verlag hat sich seit 1998 auf die Veröffentlichung akademischer eBooks und Bücher spezialisiert. Der GRIN Verlag steht damit als erstes Unternehmen für User Generated Quality Content. Die Verlagsseiten GRIN.com, Hausarbeiten.de und Diplomarbeiten24 bieten für Hochschullehrer, Absolventen und Studenten die ideale Plattform, wissenschaftliche Texte wie Hausarbeiten, Referate, Bachelorarbeiten, Masterarbeiten, Diplomarbeiten, Dissertationen und wissenschaftliche Aufsätze einem breiten Publikum zu präsentieren.
Kostenfreie Veröffentlichung: Hausarbeit, Bachelorarbeit, Diplomarbeit, Dissertation, Masterarbeit, Interpretation oder Referat jetzt veröffentlichen!
Kommentare