ANalysis Of VAriance ANOVA table

## 1. Introduction

Welding is an ancient craft that combines art, science and human skill. It can be traced back to around 3000 BC, with the Sumerians and the Egyptians. The Sumerians use swords with parts joined by hard soldering. The Egyptians found that after heating iron, it was much easier to work with, or apply pressure” welding on solid-state”, welding just by hammering the parts to join. Several objects were found in tombs, excavations, etc., indicate the exploiting of several welding techniques, such as “pressure” (hammering) welding, applied with several metal materials (gold, iron, bronze, copper, etc.), in those ancient times.

In the sixteenth century, the basic welding techniques were well known but not used to any great extent. In 1540, the Italian Engineer Vannoccio Biringuccio (as cited in Smith and Gnudi, 1990) explains in his book “The Pirotechnia”, published in Venice, that welding “seems to me an ingenious thing, little used, but of great usefulness”. During these middle ages, the art of blacksmithing was further developed and it was possible to produce any items of iron welded by hammering. The welding, as we know it today, was not invented until the nineteenth century.

A number of different processes can be used for joining studs to sheets or structure: resistance, friction and arc welding (stud arc welding or manual metal arc welding). Manual metal Arc Welding is sometimes used, but often only fillet welds are possible, and it is very slow. Stud Arc Welding (SAW) was invented just prior to World War II at the New York Navy Yard and developed for necessity to attach wood planking to naval aircraft carriers, and later it was used in theshipbuilding and construction industries.To undertake a weld, the welder first cleans the workpiece to bright shining metal. A stud is fitted with its ferrule into the chuck. The gun is pressed against the workpiece in the correct position and the trigger squeezed. There are four steps of SAW process. First step the automatic solenoid of gun is energized, withdrawing the stud from the workpiece and starting the current to create an arc. The arc melts the end of the stud and the workpiece. When the preset time is complete, the current cut off. The spring in the gun plunges the stud into the molten pool to complete the weld. Once the weld is done, the welder removes the gun, breaks off the ferrule and inspects the weld. Figure (1) illustrates a stud arc welding processsteps (Miller Welds Electrical Mng. Co., 2005).

Stud arc welding process includes the same electrical, mechanical and metallurgicalprinciples as other arc welding processes (Lee and et al, 2009). The quality of weld joint at Drawn ArcWelding (DAW) process with ceramic ferule depends on number of factors such as: type of basemetal and stud material, welding position, welding time and others parameters, but proper selection of welding parametershave important role. The literature survey shows due to short time of welding cycle, simplicity in equipment use and cost efficiency, the application ofstud arc welding process is well known in various manufacturing fields. Reviewing previous literature surveys show the researchers concerned with search for this process in two directions: First direction is examining of process factors affecting the mechanical properties such as tensile stress weld or strain pieces influenced by multiple factors such as welding current, welding time, stud plunge and lift, and other factors, see references (Klarić and et al*,* 2009). References (Bursi O.S. & Gramola G., 1999) and (Lee and et al*,* 2009) describe the ability of studs to develop full strength welds and discuss the fact that, in some cases, some welds were less than full strength. Reference (Anderson N. S. &Meinheit D. F, 2000) documents embedment shear and tension tests of deformed bar anchors where no weld failures occurred and summarizes the results of extensive testing and studies from many sources on the performance of stud welded anchor and other types of anchors devices. Reference (Hsu C. &Mumaw, 2011)presents the findings of a weldability study of drawn arc stud welding of various advanced high-strength steels (AHHS) including two grades of boron steel, and one grade of dual-phase steel of various thicknesses and coatings from several automakers, and benchmarked against mild steel. Researchers like (Strigel R. M., Pincheira J. A., & Oliva M. G, 2000) also consider examining the failure in stud welding joint and they show that 19 percent of samples examined fail, the weld fail in the vicinity of the weld area. Eşme (2009) Reports on an investigation of the effect and optimization of welding parameters on the tensile shear strength in the resistance spot welding (RSW) process. The experimental studies were conducted under varying electrode forces, welding currents, electrode diameters, and welding times. The settings of welding parameters were determined by using the Taguchi experimental design method. The confirmation tests indicated that it is possible to increase tensile shear strength significantly by using the Taguchi method. The experimental results confirmed the validity of the used Taguchi method for enhancing the welding performance and optimizing the welding parameters in the resistance spot welding process.

Second direction of researchers studies application of automated systems in the control procedure regarding interest research on development of technology, previous research indicates the evolution trend especially since the procedure can be work with automation such as robot, see (Samardžić I. & Klari Š., 2007), (Hsu et al, 2007), and (Hsu et al, 2008). As well as researcher studied the possibility of using neural network systems for optimization process parameters (RiyadhMohammed Ali Hamza, 2011).

In this chapter, the experimental study is conducted under varying welding time, sheet thickness, sheet coating, welding current, stud design, stud material, preheat sheet and surface condition. The effectiveness of welding parameters levels on the joint tensile strength is determined via analysis of variance (ANOVA). The optimum welding parameter combination is obtained using the analysis of signal-to-noise (S/N) ratio and quality loss function. The confirmation tests indicated that it is possible to increase the tensile strength significantly by using Taguchi method, where in which 225 samples are tested.

Due to the mentioned importance of proper parameter selection, the main aim of this optimization technique is to ascertain the assumption that the specific selection of welding parameters will influence weld tensile strength and that the proper selection of parameters will give weld joint a desiredtensile strength.

## 2. Characters of stud arc welding process

A process can be defined as a combination of inputs such as materials, machines, manpower, measurement, environment and methods that results at various outputs which are the measurements of performance (Conti, Kondo & Watson, 2003). The inputs x_{1}, x_{2}…x_{p} are controllable factors, such as temperature, pressures, feed rates, and other process variable. The inputs z_{1}, z_{2}…z_{q} are uncontrollable (or difficult to control) input factors, such as environmental factors or properties of a raw materials provided by the supplier as shown in figure (2). The manufacturing process transforms these inputs into a final product that has several quality characteristics(Schmidt & Launsby, 1992).

There are two types of arc-stud welding processes: Capacitor Discharge Welding and Arc Stud Welding.

### 2.1. Capacitor discharge welding

In this process Direct Current (DC) produced by the rapid discharge of stored electrical energy from a bank of capacitors is used to create an arc between a stud and the sheet or structure. Pressure is applied immediately following electrical discharge to form the weld and no flux or ferrule is required.The arc –stud processes are quick and access to the other side of the joint is not required, as is necessary for bolted connections.Because of the short welding cycle, HAZs are narrower than for other arc processes.(Samardžić, 2007) explains Capacitor Discharge Stud Welding (CD) can be accomplished by a special drawn-arc stud welding process known as“short cycle”process,where stud welding to sheet metal is characterized by the use of high current and short time.

The stud is held in a gun. When the trigger is operated, the capacitor is discharged to fuse the end of the stud and the base material, and then the stud plunged into the weld pool. Welds are produced using very high currents (6000A) for very short duration 3 to 15 millisecond. Because of the percussive nature of the process, surface coatings are removed more effectively than the arc stud process. More dissimilar combinations can be welded (e.g. brass to steel), than for the arc stud process because of the short duration. The process is also suitable for welding studs to thin sheet without damaging the surface coating on the opposite side.

The capacitor discharge method is limited to studs of 8 mm and less for economic reasons. It is less tolerant to rust and scale. Because of these limitations, this process is used less than the arc stud welding process for heavy fabrication. The most common application of capacitor discharge welding is to join thermocouple to steel structure for monitoring preheat and post weld heat treatment. The scar that remains after removal of the thermocouples is insignificant(Taylor, 2001).

### 2.2. Arc stud welding process

In this process, an arc is established between the stud and the work piece using a conventional welding power source. After a brief time, the stud is plugged into the weld pool and the current shut off. The process is quick and there is little time for detrimental phases to form. The main limitation is that it is intolerant to contamination and the surface to be welded should be free of rust, scale, paint and other contamination.

The welding parameters (current and arc time) depend on the material type and size of the stud base. The current used is 250 to 600 Ampere and the cycle time 0.13 second to 1 second for stud of diameter 3 mm to 22 mm. An average of about six studs can be welded per minutes.

#### 2.3.The. required process equipment

The most basic equipment is a stud gun connected to a control unit, which is connected to a source of DC power. Some modern stud welding equipment includes the controller and the power source as one unit, but it is possible to obtain a controller and gun utilize an existing DC welding power source. Figure 3 illustrate the process equipment consists of a stud gun, a control unit for timing the weld, a direct current power source and suitable weld cable.

The stud gun consists of the following components(Taylor, 2001):

A spring-load chuck for holding the stud.

An adjustable spacer for holding the stud gun against the workpiece.

A solenoid coil to lift the stud away from the workpiece by a preset distance of approximately 3 mm.

A trigger for initiating the welding cycles.

Most welding is undertaken using a hand-held gun. An automatic stud gun, which is fixed to robot arm or other fixture, can be used to automate the process.The controller has a solenoid switch to turn the current on and off rapidly, timers to control the automatic welding cycle and adjustment of current and cycle time.

#### 2.3.1. Studs and ferrules

Studs can have circular, square or rectangular bases. If the base is rectangular, the width should not be more than five times the thickness. It must have a shape that is capable of being held in chuck; otherwise, the form of the stud is limitless. The most common stud types are screw fasteners and shear studs, but hooks, rings, rings, brackets and many other items can be made.Studs are available in a variety of materials. Carbon steel studs are semi-killed or fully killed carbon steel grads 1010 to 1020 in the cold drawn condition(Taylor, 2001).

The studs for must materials have a flux tip. They have to be supplied by reputable stud- welding supplier, who is required by the code to perform qualification tests. Those from other than a reputable supplier may not produce satisfactory welds. Studs and ferrules should be from the same supplier.

Each stud is supplied with a matching ceramic ferrule to:

Protect the arc by restricting air flow ,

Concentrate the arc heat to the weld area

Mould the weld flash , and

Prevent charring of adjacent materials

The ferrule is broken off when the weld is complete.

### 2.4. Application ofstud arc welding process

Arc stud welding process is applied in different production areasas boiler production, motor vehicle industry, bridge construction and shipbuilding, due to the efficiency of such a process.

In addition, arc stud welding process is currently applied in different production areas. Theapplication of Draw Arc Welding with ceramic ferrule has important role in steam boilerproduction. This process issuccessfully used in ship building, automobile industry etc. Stud welding process uses for fixating of cryogenic insulation of membrane tanks in ship building (Lee et al, 2009). Also, stud welding is widely used in the contraction industryand bridge construction (composite steel/concrete structures). There are many different stud welded products that are commonly used in the manufacture of precast/pre-stresses components, including threaded, headed, and deformed bars(Bursi & Gramola, 1999).

### 2.5. Stud welding failures

The stud fully butt welds with the base material, so there is no unfused central area that is a feature of fillet welded attachments. Because the weld is full penetration, the small amount of flash interference much less with an attachment than a fillet weld would.For the full strength of the stud, the base metal thickness should be at least 1/3 of the stud base diameter. Studs can be closer to a flange edge than for threaded connections. The basis for loading is the smallest cross section of the stud (Taylor, 2001)..

When the proper operation of stud welding equipment is combined with good quality control and inspection procedures, full strength welds can be obtained consistently and result in optimal performance of the stud. But improper stud welding process parameter causes stud failure. The root causes for weld or stud failures can usually be attributed to one or more of following factors (Chambers, 2001):

Unacceptable base plate material or plate surface condition.

Inappropriate weld setting.

Malfunctioning or obsolete equipment.

Little or no formal training for stud welding operators.

Lack quality control and inspection procedures.

## 3. Taguchi experimental design methodology

Experimental design is a subject with a set of techniques and knowledge to help investigators conduct experiments in a better way, analyze results of experiments, and find optimal parameter combinations to achieve the intended objectives (Montgomery D.C, 2009) and (Antony J.& Kaye M., 1999). Stud arc welding technology has mostly continued to grow vigorously because of new applications. Tensile strength quality is one of the key factors in achieving good welding process performance, so the purpose of this study is to improve the tensile strength of stud joint by using Taguchi Experimental Design Technique. In the following sections, some of the important concepts in design of experiment technique will be explain.

### 3.1. Measure of variation (measure of dispersion)

It describes how the data are spread out or scattered in each side of the central value (mean). The measures of dispersion are:

#### 3.1.1. the Range of data

For a series of numbers, the range is the difference between the largest and smallest values of observation. The range equation:

Where

*r*= rangex

_{h}= highest observation in a datax

_{l}= lowest observation in a data

#### 3.1.2. Standard Deviation

Which of a set of (n) numbers x_{1}, x_{2},…..,x_{n} denoted by (S) and defined by:

Where (S) is the root mean square of the deviations of each number x_{i} from the mean

### 3.2. Target value

In the data analysis, the target value or an objective value is a parametric quantity identified as the standard against which all measurements or calculations of the same parameter are to be evaluated. The target value is represented by T (Buyske S. & Trout R., 2003).

### 3.3. Sum of Squares (SS)

Sum of squares (*SS*) of factor *i* at level *k* was calculated according to the equation (Buyske S. & Trout R., 2003):

Where *N* is the total number of experiments, *N*_{k}isthe number of levels and *Y*_{j}is the mean response. The total sum of squares (SS_{T}) is calculated using equation:

Experimental error (*S*e) is calculated from:

### 3.4. Degree of freedom

Degree of freedom, an integer associated with a statistic, is the number of available independent squares of the associated statistic. If the independent sum of squares is *n* then the number of degrees of freedom denoted by ƒ is equal to *n-1*.

### 3.5. Variance

Variance is defined as the sum of the squares of the deviations of a parameter from a specific value, divided by the degrees of freedom, ƒ. variance, sometimes called the mean square, is denoted by V (Steiner S.H. & MacKay R. J.,2005).

#### 3.5.1. Analysis of variance

The relative magnitude of the effect of different factors can be obtained by the decomposition of variance; called analysis of variance (ANOVA) is given in table (1). Experimental design permits the effects of numerous factors to be investigated at the same time. When many different factors dynamically affect a given quality characteristic, ANOVA is a systematic, meaningful way of statistically evaluating experimental results (Montgomery D.C, 2009).

Sources of variation | Degrees of freedomF | Sum of squares SS | Mean square V | Pure sum of squares Ś | F-ratio | Percent contribution (%) |

Factor(a) | 1 | s_{a} | v_{a} | ś_{a} | F_{a} | á |

Error(e) | n-1 | s_{e} | V_{e} | ś_{e} | 1 | é |

Total(t) | N | s_{t} | ś_{t} | 100.0 |

Where:

Variance ratio

Sum of squares

Percent contribution:

After *n* piece of experimental data is collected and after the values of á andé are calculated, significant testing provides the criterion for making such decisions. The F-tests are used to statistically determine whether the constituents, total sum of squires is decomposed, are significant with respect to the components that still remain in the error variance. The specific numerical confidence levels (usually 5% or 1%) depending on which F-table is used where the number, 5% is called the level of significance. When the variance ratios Fa, are larger than the F-table at the 5% level, then the effect is called significant at the 5% level (Montgomery D.C, 2009).

### 3.6. Larger-the-better Signal to Noise (S/N) ratio

ASignal-to-Noise (S/N) ratio is a measure of performance, which estimates the effect of the noise factors on the quality characteristic (Taguchi G., Chowdhury S., & Wu Y., 2005 ;Ross, P.J, 1986). The S/N is defined as:

Where y= Response, *n*= run experiment number.

### 3.7. Taguchiloss function

The Taguchi quality losses function for larger the better is (Taguchi G., Chowdhury S., & Wu Y., 2005; Ross, P.J, 1986):

A_{o} is the loss (stated in monetary or scaled monetary units) at a specified distance, Δ_{o}, from target, m, and y is performance measure.

### 3.8. Orthogonal Array (OA)

Orthogonal Arrays (OA) are a special set of Latin squares, constructed by Taguchi to layout the product design experiments. For each of the orthogonal array's a code is available in the form of L_{a}b^{c}, where (a) is the number of experiments, (b) the number of levels for each factor and (c) is the number of columns in the array (Taguchi G., Chowdhury S., & Wu Y., 2005 ; Ross, P.J, 1986).

## 4. Experimental work

Taguchi experimental design is a statistical technique that allows running the minimum number of experiments to optimize the process.

### 4.1. (The DABOTEK stud welding)machine

These two steps were mentioned in (1) and (1.2). The experiment work was executed by using the DABOTEK stud welding equipment. Welding current can be set in five grades such as (350, 540, 750, 900, 1250 Amperes). Welding time can be set in grades of 0.05 second (from0.05-1second). The machine that was used in experiments is shown in figure (4).

### 4.2. Identification of process parameters

Problem identification is very critical for any industrial experiment, as the experimental and analysis part is based on this. One of the most used methods for identifying the problem is brainstorming. Brainstorming is an activity that promotes team participation, encourages creative thinking and generates many ideas in a short period of time. For an investigation into the possible causes of the undesirable variability in stud welding process, the researcher modify a cause-and-effect diagram that lists several suspected causes of this variability, figure (5) illustrates the cause and effect of the problem under study. The researcher used brainstorming in conjunction with Cause and Effect Analysis (CEA) to identify the control factors which are to be considered for the experiment.

Figure 5 shows that many factors play an important role in stud welding process; they are separated in five main groups:

The sheet group

The factors that can be distinguished for these groups are:

sheet material

sheet thickness

sheet coating

sheet preheating

The stud group

The factors that can be distinguished for this group are:

Stud design

Stud material

Stud diameters

The welding machine group

The factors that can be distinguished for this group are:

The power supplies properties (voltage, current, machine power type (Continues Electric arc or Direct Capacitor arc).

The pistol properties (gun wear (new or used), polarity of machine, gun wire length).

The setup welding operations group

The factors that can be distinguished for this group are:

The welding time adjustment.

The quantity of studs welding.

The operator performance.

The environment

The arc machine pistol group

The factors that can be distinguished for this group are:

Polarity of the machine

Plunge depth

Gun wire

Collect wear

To implement experimental welds samples, eight independent control factors was choice to improve the stud welding process. These factors are welding time, sheet thickness, sheet material, welding current, stud design, stud material, preheat sheet and surface cleaning.

### 4.3. Selection of factor levels and range of factor setting

The selection of a number of levels depends on how the outcome (tensile strength) is affected due to different level of settings. The levels for control factors are shown in table (2).

### 4.4. Method of measurement

The researcher took a sample containing ten pieces for stud welding depending on the value for welding time and current to define the variety of this response, the results are in table (3). The dotplot for the data is shown in figure (6). Mean is 330.53 N/mm², standard division is 57.560 N/mm² and the range is 189.90 N/mm².

Piece Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Tensile Strength (N/mm^{2}) | 310.5 | 377.8 | 352.1 | 243.1 | 350.3 | 342.4 | 253.8 | 354.6 | 432.4 | 289.7 |

#### 4.5.The. Orthogonal Array (OA) design

The number of degrees of freedom required for the experiment must be greater than 14 (7+7). A Taguchi’s L_{16}2^{7}1^{8} orthogonal array (OA) design, with seven in two levels and one in eight levels which table (4) shows the code design matrix.

run | welding time | sheet thickness | sheet material | welding current | stud design | stud material | preheat | surface cleaning |

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

3 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 2 |

4 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |

5 | 3 | 1 | 1 | 2 | 2 | 1 | 1 | 2 |

6 | 3 | 2 | 2 | 1 | 1 | 2 | 2 | 1 |

7 | 4 | 1 | 1 | 2 | 2 | 2 | 2 | 1 |

8 | 4 | 2 | 2 | 1 | 1 | 1 | 1 | 2 |

9 | 5 | 1 | 2 | 1 | 2 | 1 | 2 | 1 |

10 | 5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |

11 | 6 | 1 | 2 | 1 | 2 | 2 | 1 | 2 |

12 | 6 | 2 | 1 | 2 | 1 | 1 | 2 | 1 |

13 | 7 | 1 | 2 | 2 | 1 | 1 | 2 | 2 |

14 | 7 | 2 | 1 | 1 | 2 | 2 | 1 | 1 |

15 | 8 | 1 | 2 | 2 | 1 | 2 | 1 | 1 |

16 | 8 | 2 | 1 | 1 | 2 | 1 | 2 | 2 |

#### 4.6.Experimental. preparation and process run

In this step, the main task was to construct the uncoded design matrix for the experiment. The uncoded design matrix is shown tables (5).

Run | welding time | sheet thickness | sheet material | welding current | stud design | stud material | preheat | surface cleaning |

1 | 0.15 | 1.6 | K14358 | 350 | Small | 54NiCrMoS6 | Preheat | Clean sheet |

2 | 0.15 | 3.175 | K52355 | 540 | Large | 40CrMnMoS8-6 | No Preheat | Oil sheet |

3 | 0.2 | 1.6 | K14358 | 350 | Small | 40CrMnMoS8-6 | No Preheat | Oil sheet |

4 | 0.2 | 3.175 | K52355 | 540 | Large | 54NiCrMoS6 | Preheat | Clean sheet |

5 | 0.25 | 1.6 | K14358 | 540 | Large | 54NiCrMoS6 | Preheat | Oil sheet |

6 | 0.25 | 3.175 | K52355 | 350 | Small | 40CrMnMoS8-6 | No Preheat | Clean sheet |

7 | 0.3 | 1.6 | K14358 | 540 | Large | 40CrMnMoS8-6 | No Preheat | Clean sheet |

8 | 0.3 | 3.175 | K52355 | 350 | Small | 54NiCrMoS6 | Preheat | Oil sheet |

9 | 0.35 | 1.6 | K52355 | 350 | Large | 54NiCrMoS6 | No Preheat | Clean sheet |

10 | 0.35 | 3.175 | K14358 | 540 | Small | 40CrMnMoS8-6 | Preheat | Oil sheet |

11 | 0.4 | 1.6 | K52355 | 350 | Large | 40CrMnMoS8-6 | Preheat | Oil sheet |

12 | 0.4 | 3.175 | K14358 | 540 | Small | 54NiCrMoS6 | No Preheat | Clean sheet |

13 | 0.45 | 1.6 | K52355 | 540 | Small | 54NiCrMoS6 | No Preheat | Oil sheet |

14 | 0.45 | 3.175 | K14358 | 350 | Large | 40CrMnMoS8-6 | Preheat | Clean sheet |

15 | 0.5 | 1.6 | K52355 | 540 | Small | 40CrMnMoS8-6 | Preheat | Clean sheet |

16 | 0.5 | 3.175 | K14358 | 350 | Large | 54NiCrMoS6 | No Preheat | Oil sheet |

Run | actual run order | Tensile strength (N/mm² ) | Mean N/mm² | Standard deviation N/mm² | |||||

1 | 5 | 175.73 | 213.23 | 143.66 | 195.09 | 210.50 | 155.60 | 182.302 | 28.860 |

2 | 9 | 288.70 | 251.20 | 330.40 | 284.99 | 225.90 | 300.70 | 280.315 | 36.946 |

3 | 13 | 284.39 | 198.56 | 225.89 | 245.87 | 276.24 | 263.54 | 249.082 | 32.539 |

4 | 3 | 359.99 | 420.50 | 428.42 | 300.03 | 387.38 | 367.54 | 377.310 | 46.790 |

5 | 12 | 190.70 | 245.87 | 235.90 | 298.46 | 164.33 | 289.46 | 237.453 | 52.977 |

6 | 11 | 370.45 | 392.68 | 191.74 | 360.38 | 288.70 | 383.26 | 331.202 | 77.637 |

7 | 8 | 321.60 | 139.00 | 349.05 | 310.00 | 362.93 | 457.50 | 323.375 | 104.318 |

8 | 1 | 331.96 | 326.32 | 331.15 | 401.60 | 387.26 | 314.78 | 348.828 | 36.095 |

9 | 4 | 388.10 | 233.60 | 372.20 | 287.95 | 225.43 | 278.00 | 297.547 | 68.611 |

10 | 2 | 530.00 | 460.72 | 549.85 | 375.12 | 410.53 | 375.89 | 450.352 | 76.343 |

11 | 15 | 305.40 | 383.20 | 456.00 | 378.00 | 478.00 | 375.00 | 395.933 | 62.388 |

12 | 7 | 152.09 | 160.74 | 170.76 | 166.80 | 250.88 | 132.45 | 172.287 | 40.835 |

13 | 16 | 219.19 | 152.97 | 250.85 | 257.16 | 266.78 | 198.75 | 224.283 | 43.258 |

14 | 10 | 155.65 | 180.45 | 289.40 | 220.68 | 225.35 | 248.78 | 220.052 | 47.705 |

15 | 14 | 289.36 | 215.62 | 318.43 | 256.84 | 288.23 | 145.63 | 252.352 | 62.900 |

16 | 6 | 185.32 | 178.45 | 223.21 | 155.82 | 298.33 | 188.43 | 204.927 | 50.651 |

## 5. Results, analysis and discussions

The results of the experiments conducted depends on the L_{16}2^{7}1^{8} OA with randomized order are shown in the table (6).

### 5.1. Determination optimum condition of process

One objective is to reduce the variability in tensile strength and to bring the mean as close as possible to the target. The target is 728.48 N/mm^{2} which is the tensile strength of the stud. The optimization procedure by Taguchi for the study is:

Stage (1):calculate the SNR for each experimental design point. The SNR for the larger-the-best quality characteristic is calculated by the equation (12). Substitute the values into the above equation. The SNR values for experimental trials are shown in table (7).

Trial no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

S/N (dB) | 44.9 | 48.7 | 47.7 | 51.3 | 46.9 | 49.4 | 48.1 | 50.7 | 48.9 | 52.7 | 51.6 | 44.2 | 46.5 | 46.3 | 47.0 | 45.7 |

After obtaining the SNR values, the next step was to obtain the average response values of a SNR at low and high levels of each factor and hence the effect of each factor on the SNR. The results are shown in table (8) and table (9).

Factor A | Average SNR at level 1 | Average SNR at level 2 | Average SNR at level 3 | Average SNR at level 4 | Average SNR at level 5 | Average SNR at level 6 | Average SNR at level 7 | Average SNR at level 8 | Effect of the factor | rank |

Factor Effect dB | 46.83 | 49.53 | 48.19 | 49.43 | 50.84 | 47.96 | 46.41 | 46.38 | 4.52 | 1 |

Factors | Average SNR at level 1 dB | Average SNR at level 2 dB | Effect of the factor dB | rank |

B | 47.73 | 48.69 | 0.96 | 6 |

C | 47.10 | 49.31 | 2.21 | 2 |

D | 48.18 | 48.23 | 0.05 | 8 |

E | 48.23 | 48.46 | 0.23 | 7 |

F | 47.41 | 49.00 | 1.69 | 3 |

G | 48.98 | 47.43 | -1.65 | 4 |

H | 47.55 | 48.86 | 1.31 | 5 |

Table (8) and table (9) show that factors A and C have a dominant effect on the SNR, followed by factors F, G, H, B, E, and D. The main effects plot for the SNR is shown in figure (7).

The calculations of ANalysis Of VAriance for the factors by using Minitab software are showing in table (10):

Source of variation | Sum of Squares | df | Mean Square | F-ratio |

A | 37.384 | 7 | 5.341 | 0.88 |

B | 3.529 | 1 | 3.529 | 0.58 |

C | 19.769 | 1 | 19.769 | 3.26 |

D | 0.004 | 1 | 0.004 | 0.00 |

E | 1.129 | 1 | 1.129 | 0.19 |

F | 9.899 | 1 | 9.899 | 1.63 |

G | 9.402 | 1 | 9.402 | 1.55 |

H | 6.679 | 1 | 6.679 | 1.10 |

error | 6.070 | 1 | 6.070 | 1 |

Total | 93.865 | 15 | 6.257 |

The second column in Table (10) was calculated by using equations 3, 4 and 5, the fourth column with equation 6, and fifth from equation 7. The ANOVA table has shown that the most dominant factor effects are D (welding current), E (stud design) and A (welding time). The optimal conditions setting of factors, which will maximize the SNR (i.e. the best control factor settings) based on the SNR are A_{5}, B_{2}, C_{2}, D_{2}, E_{2}, F_{2}, G_{1}and H_{2.}

Trial no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

S N/mm^{2} | 28.8 | 36.9 | 33.1 | 46.7 | 52.9 | 77.6 | 104.3 | 36.1 | 68.6 | 76.3 | 62.3 | 40.8 | 43.2 | 47.7 | 62.9 | 50 |

The following step was studying the effect of the factors on standard deviation(S) of the process. The standard deviationfor each experimental design trials are shown in table (11). The average response affects values of factor A on the standard deviation is shown in table (12), and at low and high levels of other factors are in table (13).

Factor A | Average St. at level 1 | Average St. at level 2 | Average St. at level 3 | Average St. at level 4 | Average St. at level 5 | Average St. at level 6 | Average St. at level 7 | Average St. at level 8 | Effect of the factor | rank |

Factor Effect N/mm^{2} | 32.9 | 39.6 | 65.3 | 70.2 | 72.4 | 51.6 | 45.4 | 56.7 | 39.5 | 1 |

Factors | Average St at level 1 N/mm^{2} | Average St at level 2 N/mm^{2} | Effect of the factor N/mm^{2} | rank |

B | 56.98 | 51.62 | -5.36 | 6 |

C | 54.27 | 54.32 | 0.05 | 8 |

D | 50.56 | 58.04 | 7.48 | 5 |

E | 49.80 | 58.79 | 8.99 | 4 |

F | 46.01 | 63.1759 | 16.58 | 2 |

G | 51.75 | 56.84 | 5.09 | 7 |

H | 59.70 | 48.9 | -10.8 | 3 |

Table (12) and table (13) show that factors A and F have dominant effect on the St, followed by factors H, E, D, B, and C. the main effects plot for the St as shown in figure (8).

In order to obtain the statistical significance of the effects, ANOVA table for the standard deviation was performed, as shown in table (14).

Source of variation | Sum of Squares | df | Mean Square | F-ratio |

A | 2935.4 | 7 | 419.34 | 0.538 |

B | 114.7 | 1 | 114.7 | 0.147 |

C | 0.0 | 1 | 0.0 | 0.00 |

D | 224.1 | 1 | 224.1 | 0.287 |

E | 323.3 | 1 | 323.3 | 0.415 |

F | 1100.6 | 1 | 1100.6 | 1.413 |

G | 103.7 | 1 | 103.7 | 0.133 |

H | 467.2 | 1 | 467.2 | 0.599 |

error | 778.9 | 1 | 778.9 | 1 |

Total | 6047.9 | 15 | 403.193 |

It can be seen from Table (13) that C (Sheet material) has a large affect on the tensile strength standard deviation, while the F (Stud material) has a less effect. The next step was to determine the optimal settings for these factors, which will minimize the standard deviation. The optimum conditions (i.e. the best control factor settings) based on the standard deviation are A_{1}, B_{2}, C_{2}, D_{1}, E_{1}, F_{2}, G_{2} and H_{2}. Comparing this result with the result of SNR setting it was found that for factors (B, C, F and H) it was the same. While for factor A it was found that there is a big differences in the values between the tow choices and A_{6} gets a balance between the two criterions. For factor D the effect of this factor on the SNR is very small while having more effect on standard deviation, so the choice for the factor level is D_{1}.The same is for factor E, so the choice for this factor level is E_{1}. For factor G the effect of this factor on SNR is less than on standard deviation, so the level of this factor is G_{2}. After analyzing SNR, standard deviationtables the best setting for the factor levels were:

A_{6}, B_{2}, C_{2}, D_{1}, E_{1}, F_{2}, G_{2} and H_{2}

Stage (2): Performing the SNR analysis and standard deviation analysis, the next step was to identify the factor effects that have significant impact on the mean response. The average response values at each level of the factor A and the effects are present in table (15) and the average response values at low and high level for the other factors and their effects are present in table (16).

Factor A | Average mean at level 1 | Average mean at level 2 | Average mean at level 3 | Average mean at level 4 | Average mean at level 5 | Average mean at level 6 | Average mean at level 7 | Average mean at level 8 | Effect of the factor | rank |

Factor Effect N/mm^{2} | 231.3 | 313.1 | 284.3 | 336.1 | 382.3 | 284.1 | 222.1 | 228.6 | 160.6 | 1 |

Factors | Mean response at level 1 N/mm^{2} | Mean response at level 2 N/mm^{2} | Effect N/mm ^{2} | rank |

B | 270.29 | 298.16 | 29.96 | 6 |

C | 257.07 | 313.47 | 56.4 | 3 |

D | 278.73 | 291.81 | 13.08 | 8 |

E | 278.43 | 292.11 | 13.68 | 7 |

F | 255.61 | 314.93 | 59.32 | 2 |

G | 310.17 | 260.37 | -49.8 | 4 |

H | 269.55 | 300.99 | 31.44 | 5 |

Fig.7 Shows factors A, C, E and F have a significant impact on the mean response (i.e. mean tensile strength).

Source of variation | Sum of Squares | Df | Mean Square | F-ratio | Percent contribution (ρ) |

A | 42644 | 7 | 6092 | 42.35 | 40.11 |

B | 3107 | 1 | 3107 | 21.6 | 2.92 |

C | 13686 | 1 | 13686 | 95.14 | 12.87 |

D | 482 | 1 | 482 | 3.35 | 0.51 |

E | 9099 | 1 | 9099 | 63.25 | 8.55 |

F | 13095 | 1 | 13095 | 91.04 | 12.31 |

G | 9099 | 1 | 9099 | 63.25 | 8.55 |

H | 3444 | 1 | 3444 | 23.94 | 3.23 |

error | 11651 | 81 | 143.84 | 1 | 10.95 |

total | 106307 | 95 | 1119.02 | - | 100 |

It can be seen from table (17) that factor A (welding time) has a large affect on the mean of stud welding tensile strength (40.11% fraction of importance), see equations 10 and 11, the factor C (sheet material) and F (stud material) has just (12.87%) and (12.31%) respectively. Added the factors B, D, E, G and H can be pooled. A new table without these factors was constructed table (19). The sum of squares of pooled factors was added to the error term. The new mean square of the error term was calculated using equation:

Where superscript p is indicates the pooled factors.

Source of variation | Sum of Squares | df | Mean Square | Variance ratio (F-ratio) | Percent contribution (ρ) |

A | 42644 | 7 | 6092 | 14.2 | 40.36 |

C | 13686 | 1 | 13686 | 31.91 | 13.5 |

F | 13095 | 1 | 13095 | 30.53 | 12.89 |

error | 28779 | 86 | 428.86 | 1 | 33.25 |

total | 98204 | 95 | 1033.72 | 100 |

Since the degree of freedom of the factor A is 7 and of the error term is 86, from F-table at level of significance (95% confidence) we obtain F_{7, 86=} 2.11.

Because the computed values of variance ratio in the table (18) are bigger than the value from F–table, there is 95% of confidence that this factor (welding time) has an effect on stud welding process. For factor (C and F) the degree of freedom is 1, then the F_{1, 86}= 3.97, science the computed F-ratio is 31.91 and 30.53 respectively is higher than from F-table, then these two factors also have in effect in the stud welding process. After identifying the significant factor effects, the next step was to determine the optimal setting for these factors which will bring the mean response as close as possible to the target. The optimum condition (i.e. the best control factor settings) based on the mean response figure was:

A_{5}, B_{2}, C_{2}, D_{2}, E_{2}, F_{2}, G_{1} and H_{2}

Here the factors B, C, F and H are the same with the last setting. While for factor A there is high deference when we choose A_{5} or A_{6}, when we choose A_{5} (the welding time is0.35 second) the tensile strength will be 382.341N/mm^{2} and the standard deviationis 72.47 N/mm², while when choosing A_{6} (the welding time is 0.4 second) the tensile strength will be 284.110 N/mm^{2} and the standard deviationis 51.61N/mm^{2}. Because the welding time is continues values, the researcher choice the new level for this factor be intermediate between tow this value that is Ẩ_{6}=0.38 second. For factor D the effect for standard division of this factor is more and opposite than for mean, so the level for this factor is D1. The same thing is for factor E_{1}. For factor G the effect of this factor on the mean is more and opposite for the standard deviation, so the level of this factor is G_{1}. The factor levels are:

Ẩ_{6}, B_{2}, C_{2}, D_{1}, E_{1}, F_{2}, G_{1} and H_{2}

In order to arrive at the optimal factor settings, the factor setting is the one, which yields minimum quality loss. The Taguchi quality losses function for larger the better is shown in equation (13). The summarized calculation is shown in table (19).

Run | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

(yˆ)² | 299094.4 | 202216.8 | 230924.9 | 125509.6 | 243914.1 | 163858.9 | 174992.3 | 145438.5 | 190410.7 | 83183.4 | 160655.2 | 290938.1 | 256371.3 | 260776.3 | 230653.3 | 276680.6 |

L(y)/K (money unit/piece) | 3.3* 10 ^{-6} | 4.9*10^{-6} | 4.33*10^{-6} | 7.97*10^{-6} | 4.1* 10 ^{-6} | 6.1* 10 ^{-6} | 5.71*10^{-6} | 6.89*10^{-6} | 5.25*10^{-6} | 1.2* 10 ^{-5} | 6.22*10^{-6} | 3.43*10^{-6} | 3.9*10^{-6} | 3.83*10^{-6} | 4.33*10^{-6} | 3.61*10^{-6} |

From table (19), run (1) (represented in bold) yield the minimum loss. The optimal factor settings based on the loss-function analysis was therefore obtained as:

A_{1}, F_{1}, C_{1}, G_{1} and H_{1}

For factor A level 1 will yield a very low tensile strength (182.302N/mm^{2}), so this level is not taken, for the three factors F, C and G the level is the same, for factor H in level 1 the tensile strength is (269.55N/mm^{2}), while in level 2 it is (300.99N/mm^{2}) the reduction is also high, so the final optimum stetting is:

Ẩ_{ 6}, B_{2}, C_{2}, D_{1}, E_{1}, F_{2}, G_{1} and H_{2}.

These factors are summarized in table (20).

factor | Ẩ_{ 6}: welding time | B_{2} :sheet thickness | C_{2} :sheet material | D_{1}: welding current | E_{1}: stud design | F_{2}: stud material | G_{1} | H_{2}: Surface cleaning |

level | 0.38 second | 3.175 mm | non- galvanized (K14358steel) | 350 Ampere | Small stud | 40CrMnMoS8-6 steel | Preheating | Clean sheet |

The predicted mean response at the optimal condition is estimated only from the significant main and interaction effects. For the study, the main factor effects, which has a significant impact on the mean response were A, F, C, G and H. The predicted mean response based on the optimal factor levels of A, F, C, G and H is given by:

Where

R= predicted mean response at the optimal condition

T = overall mean of all observation in the data

Then: R = 284.225 + (310.5-284.225) + (313.47-284.225) + (314.93-284.225) + (310.17-284.225) + (300.99-284.225)

R=413.185 N/mm^{2}

#### 5.2.Experimental. conclusions and confidence interval for the predicted mean response

The confidence interval (CI) is the variation of the estimated result at the optimum condition, and it is calculated as:

MSE = error variance =143.84 N/mm2, F_{1}, _{96} = 3.96,

Therefore, the 99 percent confidence interval for the mean tensile strength is given by:

Therefore the result at the optimal condition is 413.185±8.43 N/mm^{2}at the 99 per cent confidence level.

#### 5.3.Confirmation. run

A confirmatory run is necessary in order to verify the results from the statistical analysis. A confirmatory run should be carried out to confirm the optimal factor settings obtained from step10. A sample taken contains ten pieces were produced under the optimal condition that is in table (21):

Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Tensile strength N/mm ^{2} | 443.52 | 421.32 | 410.63 | 390.48 | 472.40 | 422.67 | 398.93 | 431.88 | 408.33 | 524.55 |

The mean tensile strength from the confirmation run was 432.47 N/mm^{2}; the standard deviation is 39.950 N/mm^{2} and the range is134.07 N/mm^{2}. The distribution of this data is explained in figure (10):

## 6. Conclusion

The reduction in standard deviation was approximately (30.06 per cent) and for the range the reduction was as approximately (29.39per cent). In the other side the increase in the tensile strength mean was as approximately (30.84 per cent). The parameters that affect the tensile strength of their influence, the factor welding time have an major effect on stud welding process, followed by factor C (sheet coating) and factor F (stud material). Specific conclusions from this study are as follows:

Dominant factors in the Performance of Stud Welds — the performance of stud welds in this (welding time), (sheet material) and (stud material) dominated study. In this case, the attached sheet thickness was found to be the dominant variable, with the thicker material demonstrating nearly double the strength compared to using the thinner material. In such cases, thicker materials will have implied higher strengths. This, in fact, appears to be the case with tensile strengths varying nearly in proportion to the attached sheet thickness

Effect of preheating sheet — the preheating has positive effects on the increasing of the tensile strength with reducing variability.

Effect of Stud design — Increasing stud area appeared to decrease of measures of mechanical performance. This was true though the levels of internal porosity also increased with the larger studs.

Effect of Sheet Thickness — increasing thickness led to increases in mechanical measure (tensile strength) of weld quality. The benefits appeared to come from increased stiffness of the joint as well as increased peel strengths associated with the thicker material.

Effect of Sheet Material — Welding onto galvanized sheets appears to result in substantial porosity in the joint, so the non-galvanized sheets get better tensile strength.

## 7. Future work

Actually, there are two tracks to be followed for the use of the proposed Taguchi experimental design. First, to use the output of experiment to be input to the artificial intelligence techniques like neural network, fuzzy logic or other technique to get a processes relationship between input and output. Especially, if this relationship between input and output cannot be represented by lower order equation, then these techniques can result accurate parameter level for optimization.

Secondly is to extend the work of this chapter in the multi objective optimization. This could be optimizing with respecting of torque testing and bending testing.