Evrim Berk 030060161 9th Week

1-) Muda ( Production)


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Muda is a japanese word referring to work or to elements of production that do not add value to the product. Therefore, it is important to eliminate muda. The job attitude of looking for muda and finding ways to eliminate it is called kaizen. Kaizen is central to the TPS (Toyota production system) way of thinking. In TPS, muda has been classified into a number of categories such as correction (rework), overproduction, processing, conveyance, inventory, motion and waiting.

(Handbook of design, manufacturing, and automation, Richard C. Dorf,Andrew Kusiak, p.568)

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The philosophy of JIT is much broader. It was developed as a reaction against waste, known by Japanese word Muda. One of the founders of JIT manufacturing, Taichi Ono, identified seven types of Muda. The first three - wait, movement and material handling - are similar to some industrial engineering concerns. The next two; over-production and higher-than-minimum inventories, relate to strategy.  the final two, overprocessing caused by poor designs and defects, are concerned with product quality and design.

(Wiersema W., Manufacturing, Distribution and Retail Guide, Pg: 1.04)

2-) Bicubic Surface ( CAD )

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The Bezier bicubic surface patch uses the basis matrix. The vector coefficients are given by a 4 × 4 matrix of position vectors for sixteen points forming a characteristic polyhedron. Fig. 6.31 shows the characteristic polyhedron for a Bezier surface. The four corner points R (0,0), R (3,0), R (3,3) and R (0,3) lie at the corners of the surface patch itself whereas remaining points do not lie on the patch. The four points along each edge of the polyhedron define the four edge curves of the patch. The four interior points determine the cross derivatives at the corner and cross slopes along the nearest edges to them.

(P.Radhakrishnan,CAD/CAM/CIM,page 165-166)

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The parametric cubic (PC) curve, Equation (3.1), is useful, since it can be used when either four points, or two points and two tangent vectors, are known. The latter approach is the topic of Chapter 4. The PC curve can easily be extended to a bicubic surface patch by means of the cartesian product. A PC curve has the form P(t)= I:3 ai ti . Two such curves, P(u)  and P(w), can be combined to form the Cartesian product surface patch

This is a double cubic polynomial (hence the name bicubic) with 16 terms, where each of the 16 coefficients aij is a triplet [compare with Equation (3.21)]. When w is set to a fixed value w0, Equation (3.25) becomes P(u,w0), which is a PC curve. The same is true for P(u0, w). The conclusion is that curves that lie on this surface in the u or in the w directions are parametric cubics. The four boundary curves are consequently also PC curves. Notice that the shape and location of the surface depend on all 16 coefficients. Any change in any of them produces a different surface patch. Equation (3.25) is the algebraic representation of the bicubic patch. In order to use it in practice, the 16 unknown coefficients have to be expressed in terms of known geometrical quantities, such as points, tangent vectors, or second derivatives. Two types of bicubic surfaces are discussed here. The first is based on 16 data points and the second is constructed from four known curves. A third type—defined by four data points, eight tangent vectors, and four twist vectors.


(Solomon D., Curves And Surfaces for Computer Graphics, Pg: 89)


3-) Miner's Rule ( Predictive Method )


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Several attempts have been made to predict the fatigue strength for such variable stresses using S/N curves for constant mean stress conditions. Some of the predictive methods available are very complex but the simplest and most well known is "Miner's Law."

Miner postulated that whilst a component was being fatigued, internal damage was taking place. The nature of the damage is difficult to specify but it may help to regard damage as the slow internal spreading of a crack, although this should not be taken too literally. He also stated that the extent of the damage was directly proportional to the number of cycles for a particular stress level, and quantified this by adding, "The fraction of the totaldamage occurring under one series of cycles at a particular stress level, is given by the ratio of the number of cycles actually endured n to the number of cycles N required to break the component at the same stress level". The ratio n/N is called the "cycle ratio"and Miner proposed that failure takes place when the sum of the cycle ratios equals unity.

i.e. when ∑ n/N=1

or n1/N1+n2/N2+n3/N3+...+ etc =1 (11.14)

If equation (1 1.14) is merely treated as an algebraic expression then it should be unimportant whether we put n3/N3 before n l / N I etc., but experience has shown that the order of application of the stress is a matter of considerable importance and that the application of a higher stress amplitude first has a more damaging effect on fatigue performance than the application of an initial low stress amplitude. Thus the cycle ratios rarely add up to 1, the sum varying between 0.5 and 2.5, but it does approach unity if the number of cycles applied at any given period of time for a particular stress amplitude is kept relatively small and frequent changes of stress amplitude are carried out, i.e. one approaches random loading conditions. A simple application of Miner's rule is given in Example 11.4.

(Hearn, E. J., Mechanics of materials: an introduction to the mechanics of elastic and plastic deformation of solids and structural materials, 3rd Edition, pg. 455)

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The most widely quoted hypothesis for fatigue damage aggregation to date is known as Miner's Rule. None of the alternatives have achieved the same level acceptance or the status of being incorporated into Standards such as BS 5400: Part 10 and BS 7608, although it is recognized that in practice the rule is not unequivocally successful. But the simplicity of the rule is one of its attractions and variants of the rule appear to show no clear advantages. Miner’s rule is normally expressed in the form:


∑ ni/np = 1

where 1 ≤ i ≤ k. ni is the number of repetitions of the applied stress range, si and nip is the number of repetitions of the same applied stress range to failure. This formula is normally associated with the empirical s–n fatigue correlation discussed in Chapter 6. In Equation (7.1) the ni are not constrained to any particular sequence, nor is each of the ni necessarily in monobloc form according to BS 5400: Part 10 and BS 7608 and any of the other available publications. It is found in practice that the summation in Equation (7.1) may be more or less than unity by as much as 20% or more. There is, of course, significant scatter in the experimental results and nip is not easy to determine. The stress range content, or wave form, is not specified, although in practice, much of the laboratory test data is gathered under sinusoidal load (or deformation) conditions.

Both the above Standards also identify a threshold stress range, so, which is the stress range at a specific endurance and is considered to be the boundary of the “non-propagating stress range” below which the material can sustain an indefinitely large number of cycles in clean air (or more generally, a passive environment). It is noted this does in fact depend upon any modifying factors required to the (s–n) relationship due to material thickness, the effect of the environment on any unprotected joints and the effect of weld grinding in steel structures. For example, for unprotected joints in sea water the recommendation is that so = 0, that is, there is no fatigue limit. For 0 < s < so the index of the s–n relation is modified to (m + 2). In the case where the applied fluctuating load is of varying magnitude such that some of the si < so will cause crack propagation, resulting in an earlier fatigue failure than if all si < so were non-contributory. Both Standards advocate the use of a weight factor (si/so)2 applied to the appropriate cycle ratio. Thus the effect of (si/so)2 becomes vanishingly small as si/so approaches zero.

The Standards also specify that for acceptability, the summation in Equation (7.1) should not exceed 1.0 at any design point. In the case where the limit is exceeded it is recommended that the artefact design should be amended by strengthening or redesigning until new stress ranges is found that are less than the original stresses divided by α1/m and α1/(m+2), where α represents the summation in Equation (7.1). BS 7910 for fusion welded structures is another Standard which refers to Miner’s rule. It specifies 2∗106 cycles on the standard (s–n) correlation at constant stress range (sr ) as a reference for mixed stress ranges. It also defines an equivalent stress (se) for mixed stress ranges.

(Harris J., Fuzzy Logic Applications in Engineering Science, Pgs: 87 - 88)

4-) Chemical Reduction Process ( Chemical Reaction )

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Chemical reduction is a reaction in which one or more electrons are transferred to the chemical being reduced (reductant) from the chemical initiating the transfer (the reducing agent). Chemical reduction can also be defined as a change in oxidation states where the oxidant (reducing agent) is an electron donor. The reductant is the substance which accepts electrons. The overall reaction is called a reduction-oxidation (redox) reaction.

Chemical reduction as a waste treatment process is an established and well-developed technology. The reduction of hevavalent chromiym’s valence state to decrease toxicity and encourage precipitation is presently used as a treatment technology in numerous electroplating facilities. Major advantages of chemical reduction when used to reduce hexavalent chromium is operation at ambient conditions, automatic controls, high reliability, and modular process equipment, ORP (oxidation-reduction potential) and pH controls and instrumentation, mechanical agitation, adequate venting, and separate tanks for subsequent precipitation and sedimentation. The retention time in the reduction tank is pH dependent but should be at least four times the theoretical time for complete reduction.

(Robert Noyes, Handbook of Pollution Control Process,p.285)

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Reduction in a chemical reaction in which one or more electrons are transferred to the chemical being reduced from the chemical initiating the transfer (the reducing agent). Chemical reduction may be necessary to convert metals from a higher valence state to a lower one to decrease toxicityor to encourage a given chemical reaction. 

The first step of the chemical reduction process is usually the adjustment of the pH of the solution. With sulfur dioxide treatment of hexavalent chromium, for instance, the requires a pH range of 2- 3. The pH adjustment is done with the appropriate acid. this followed by the addition of a reducing agent. Mixing is provided to improve contact between the reducing agent and waste.  The agent can be in form of a gas, a solution, or as finely sivided powder if there's adequate mixing. Reaction times vary for different wastes, reducing agents, temperatures, pHs, and concentrations. In commercial-scale operations treating chromium wastes, reaction times are on the order of minutes. Additional time is usually allowed to ensure complete mixing and reduction. Once reacted, the reduced solution is generally subjected to some form of treatment of settle, float or filter so that the reduced will precipitate from the solution. A treatment for the removal of what remains of the reducing agent may be included. this can be unused reducing agent or reducing agent in its oxidized state.

(Wang K.L. Hung. Y, Advanced Physicochemical Treatment Processes, Pgs: 483 - 484)

5-)Pressure Thermoforming ( Manufacturing Method )


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An alternative to vacuum forming involves positive pressure to force the heated plastic into the mold cavity. This called pressure thermoforming or blow forming: its advantage over vacuum forming is that higher pressures can be developed because the latter is limited to a theoretical maximum of 1 atm. Pressure forming pressures of 3 to 4 atm are common. The process sequence is similar to the previous, the difference being that the sheet is pressurized from above into the mold cavity.

(Groover M. P., Fundamentals of modern manufacturing: materials, process, and systems, Ed. 4th, p.363)


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Technically all thermoforming methods employ differantial pressure to stretch the sheet against the mold. Therefore, all thermoforming can be considered pressure forming. According to accepted technology however, thermoforming is considered to be pressure forming only when the differantial pressure across the sheet thickness exceeds 15 psi absolute.


Pressure thermoforming is employed when at its forming temperature the sheet is too stiff adequately stretch to the fartest regions of the mold or to adequately replicate the texture of the mold surface. Traditional pressure forming uses air pressure off up to 150 psi on the free side of the sheet and vacuum to extract the air between the sheet and the mold surface.


Typically pressure thermoforming employs a two-step process. The sheet is first drawn against the mold surface by evacuating the air from the mold cavity. Then a metal box called a pressure box, is clamped against the sheet and mold surface using bayonet or rotating clamps. Flexible air packs placed between the mold and machine platen are inflated to affect a seal. Then air pressure is introduced to force the sheet to replicate the mold surface. Once the formed part is cooled sufficiently , the air pressure is bled from the pressure box and air packs, the box is unclamped from the sheet and the mold.

(Throne J., Understanding Thermoforming, Pg: 19)