## Probabilistic design approach

Figure 4.41 shows the Stress-Strength Interference (SSI) diagrams for the two assembly operation failure modes. The instantaneous stress on the relief section on first assembly is composed of two parts first the applied tensile stress, s, due to the pre-load, F, and secondly, the torsional stress, r, due to the torque on assembly, M, and this is shown in Figure 4.41(a) (Edwards and McKee, 1991). This stress is at a maximum during the assembly operation. If the component survives this stress, it...

## D Conformability matrix

Component assembly process reference Component assembly process description Failure Mode Description and FMEA Severity Rating (5) Figure 2.34 Hub analysis results The analysis indicated that the conformance problems associated with the hub design had a cost of failure of more than 30 . This would represent at the annual production quantity required and target selling price, a loss to the business of several million pounds. As a result of the study the business had further detailed discussions...

## Selecting the pump shaft material

The torque capacity of the pump shaft must be greater than the torque capacity of the shear pin in all cases. We assume that failure of the pump shaft occurs at the interference of these two torque distributions. From equation 4.89, the torque capacity of the shear pin can be determined by substituting the ultimate shear strength of the weak link material, ruwL for L, giving mwl 0.785398a d2 ruWL (4.92) Solving equation 4.92 using Monte Carlo simulation for the variables involved, the torque...

## Stress concentration factors and dimensional variability

Geometric discontinuities increase the stress level beyond the nominal stresses (Shigley and Mischke, 1996). The ratio of this increased stress to the nominal stress in the component is termed the stress concentration factor, Kt. Due to the nature of manufacturing processes, geometric dimensions and therefore stress concentrations vary randomly (Haugen, 1980). The stress concentration factor values, however, are typically based on nominal dimensional values in tables and handbooks. For example,...

## Example determining the failure costs for product design

We will now consider calculating the potential costs of failure in more detail for the cover support leg shown earlier. The process for calculating the failure costs for a component is as follows Determine the value of qm or qa Obtain an FMEA Severity Rating (S) Estimate the number of components to be produced (N) Estimate the component cost (Pc). For example, the characteristic dimension 'A' on the cover support leg was critical to the success of the automated assembly process, the potential...

## Case study

Consider the example of fluid flow through a filter, where the objective is to maximize flow rate. Assume that the relevant control factors are filter, fluid viscosity and FljI failg'iifl exploring n wmtinalcons erf vsnabtes and 1he*r levels. This approach ran prcwe to be cosily and lime consuming. FljI failg'iifl exploring n wmtinalcons erf vsnabtes and 1he*r levels. This approach ran prcwe to be cosily and lime consuming. Orthogonal array involving s irials Here ins afecL of rJifiererit...

## Finite difference method

Substituting y (x1, x2, , xn) into the variance equation for the output of the function, and expanding for n variables gives The finite difference method can be used to approximate each term in this equation by using the difference equation for the first partial derivative (see Figure 2). The values of the function at two points either side of the point of interest, k, are determined, yk +1 and yk _ 1, which are equally spaced by an increment Ax. The finite difference equation approximates the...

## Example fitting a Normal distribution to a set of existing data

We will next demonstrate the use of the linear rectification method described above by fitting a Normal distribution to a set of experimental data. The data to be analysed is in the form of a histogram given in Figure 4.9. It shows the distribution of yield strength for a cold drawn carbon steel (SAE 1018). The data is taken from ASM (1997a), a reference that provides data in the form of histograms for several important mechanical properties of steels. Data collated in this manner has been...

## Simpsons Rule for numerical integration

Typically in engineering we are required to find the area under a curve where y f (x) between limits as shown in Figure 1. Direct integration is sometimes difficult, and the use of numerical integration techniques helps in this respect. One commonly used technique which gives high accuracy is Simpson's Rule (more correctly called Simpson's 3 Rule). Here the area under the curve is divided into equal segments of width, h. For an even number of segments, m, we can divide the range of interest...

## 45 Elements of stress analysis and failure theory

The calculated loading stress, L, on a component is not only a function of applied load, but also the stress analysis technique used to find the stress, the geometry, and the failure theory used (Ullman, 1992). Using the variance equation, the parameters for the dimensional variation estimates and the applied load distribution, a statistical failure theory can then be formulated to determine the stress distribution, f (L). This is then used in the SSI analysis to determine the probability of...

## 11 Statement of the problem

In order to improve business performance, manufacturing companies need to reduce the levels of non-conformance and attendant failure costs stemming from poor product design and development. Failure costs generally make up the largest cost category in a manufacturing business and include those attributable to rework, scrap, warranty claims, product recall and product liability claims. This represents lost profit to a business and, as a result, it is the area in which the greatest improvement in...

## Monte Carlo Simulation code written in Visual Basic

Dim L() As Variant Dim SUM As Variant Dim VAR As Variant Dim MEAN As Variant Dim STD As Variant Dim F As Variant Dim a As Variant Dim b As Variant ReDim L(10000) Let F 68605.5+(103530.2 _ 68605.5) * ((_Log(1 _ Rnd)) 0.2907) (inverse CDF's for Let a 0.02906+ (0.03011 _ 0.02906) * ((_Log(1 _ Rnd)) 0.2907) each variable) Let b 0.04874+ (0.05014 _ 0.04874) * ((_Log(1 _ Rnd)) 0.2907) Let L(I ) F (a * b) (function goes here) Let VAR VAR + (L(I ) _ MEAN) 2 Next I Let STD Sqr(VAR 10000) Label1 .Caption...

## Application of the technique

The following factors are assessed in an FMEA Potential Failure Mode. How could the component, product, process or system element fail to meet each aspect of the specification Figure 1 General ratings for FMEA Occurrence, Severity and Detectability Potential Effects of Failure. What would be the consequences of the component, product, process or system element failure Potential Causes of Failure. What would make the component, product, process or system fail in the way suggested by the...

## 271 Electronic power assisted steering hub design

Under this heading, a flexible hub design for an automotive steering unit is analysed. The application of CA resulted from the requirement to explain to a customer how dimensional characteristics on the product, identified as safety critical, could be produced capably. A key component in this respect is the hub. The component is made by injection moulding, the material being unfilled polybutylene terephthalate (PBT) plastic. The moulding process was selected for its ability to integrate a...

## Determining the stress variable

The stress, L, due to pure bending at the section A-A on the pedal is given by equation 4.81 y distance from x x axis to extreme fibre 7xx second moment of area about the axis x x F load * couple length d depth of section. For the elliptical cross-section specified, the second moment of area, I, about x-x axis Therefore, substituting equation 4.82 into equation 4.81 gives Equation 4.83 states that there are four variables involved. We have already determined the load variable, F, earlier. The...

## Example process capability and failure prediction

The component shown in Figure 4 is a spacer from a transmission system. The component is manufactured by turning boring at the rate of 25000 per annum and the component characteristic to be controlled, X, is an internal diameter. From the statistical data in the form of a histogram for 40 components manufactured, shown in Figure 5, we can calculate the process capability indices, Cp and Cpk. It is assumed that a Normal distribution adequately models the sample data. The solution is as follows 2...

## 53 Tools and techniques in product development 531 Overview of tools and techniques

A summary of each of the key tools and techniques considered to be important in the product development process is given in Appendix III. This covers such techniques as FMEA, QFD, DFA DFM and DOE. Included for each is a description of the tool or technique, placement issues in product development, key issues with regard to implementation, and the benefits that can accrue from their use, and finally a case study. It would be advantageous next, however, to determine exactly what a tool or...

## 52 Product development models 521 Overview of product development models

Product development models are the driving force for delivering the product to market on time and at the right cost. In general, the models in the literature can be divided into just two types sequential and concurrent. Each has its own characteristics, but there are several requirements that a new product development model should fulfil (Sum, 1992) It must be scaleable as organizations change size constantly The model will probably be introduced incrementally, perhaps into one team, and then...

## 36 Case study revisiting the solenoid design

A familiar case study is presented next to illustrate the use of the key elements of the CAPRAtol methodology. Figure 3.6 shows the tolerance stack on the solenoid end assembly design as first encountered in Chapter 2. The key requirement was that the plunger displacement, from the sealing face through the solenoid tolerance stack to the plunger end seal, must be within a tolerance of 0.2mm, otherwise fuel flow restriction could occur. The product will be in the warranty return category as it...

## 541 Team approach to engineering design

Even with the aid of tools and techniques, engineering is still a task that requires creative solutions (Urban and Hauser, 1993). Companies recognizing the importance of product development have searched to resolve this problem, with most opting for some kind of 'team approach', involving a multitude of persons supposedly providing the necessary breadth of experience in order to obtain 'production friendly products'. Research (Urban and Hauser, 1993) has shown that teams produce better...

## 361 Paperbased analysis

This entails assigning design tolerances for each characteristic in the assembly stack based on those given by the process capability maps (Appendix IV), but including the effects of processing the material and geometry of each through the Component Manufacturing Variability Risk Analysis, qm. The reader is referred to Chapter 2 for a detailed explanation of this part of the analysis. For example, the dimension of 12mm for characteristic number 1, we can refer to the turning boring map (Figure...

## Stress Strength Interference SSI models

A statistical representation of the yield strength for BS 220M07 is not available however, the coefficient of variation, Cv, for the yield strength of steels is commonly given as 0.08 (Furman, 1981). For convenience, the parameters of the Normal distribution will be calculated by assuming that the minimum value is 3 standard deviations from the expected mean value (Cable and Virene, 1967) The yield strength for 220M07 can be approximated by In the stress rupture case, the interference of the...

## 47 Application issues

The reliability analysis approach described in this text is called CAPRAstress and forms part of the CAPRA methodology (CApabilty and PRobabilistic Design Analysis). Activities within the approach should ideally be performed as capability knowledge and knowledge of the service conditions accumulate through the early stages of product development, together with qualitative data available from an FMEA. The objectives of the approach are to Model the most important design dependent variables...

## Example determining the stress distribution using the coefficient of variation

When dimensional variation is large, its effects must be included in the analysis of the stress distribution for a given situation. However, in some cases the effects of dimensional variation on stress are negligible. A simplified approach to determine the likely stress distribution then becomes available. Given that the mean load applied to the component assembly is known for a particular situation, the loading stress can be estimated by using the coefficient of variation, Cv, of the load and...

## 266 Completing the Conformability Matrix

The final part of the analysis is based around the completion of a Conformability Matrix relating variability risk indices for component manufacturing assembly Figure 2.32 Conformability matrix symbols and their quantification processes to potential failure modes, their severity and the costs of failure. A blank Conformability Matrix is provided in Appendix VII. The final results of an analysis are best displayed in the Conformability Matrix to provide a traceable record of the costs of failure...

## Later mechanical deformation

Is the process automated or performed manually (1 ) Is the joint easily accessible to the process (3) What is the skill level required for process set-up or operation (2) What is the type of tool motion used for deformation (4) Is heat simultaneously applied to the part to be deformed during processing (5) 0 Automated processes use close control of time for deformation, tool positioning forces to provide consistent joint quality. (2) Process capability is dependent on the attention of skilled...

## Simple to perform

Assumes tolerance distribution on maximum or minimum limit Little information generated for redesign purposes Popular as a safeguard, leading to unnecessarily tight tolerances and, therefore, increased costs. The 'statistical' tolerance stack approach is characterized by More difficult mathematically (computer necessary) Assumes tolerances are random variables Opportunities for optimization of tolerances in the assembly Can perform sensitivity analysis for redesign purposes Can include effects...

## 51 Introduction

Effective product development can be the single most important driving force behind creating successful products. The objective is to develop a product that has been systematically optimized to meet the customers' needs as early as possible (Dertouzos et al., 1989). Fierce competition and higher customer expectations are forcing manufacturing businesses to improve quality, reduce costs, and shorten time to market and this places new pressures on the product development process. In today's...

## 35 Application issues

A flow chart for the tolerance stack methodology CAPRAtol is shown in Figure 3.5. Elements of FMEA, CA, process selection methodology, assembly sequence diagrams (through DFA techniques or CA) and, of course, adequate tolerance stack models, should be used in order to provide a complete solution to the assembly stack problem. Additionally, an understanding of geometric tolerancing, process capability indices and selection of key characteristics is useful (Leaney, 1996a). Initially, it is...

## 443 Reliability determination with multiple load application

The approach taken by Carter (1986, 1997) to determine the reliability when multiple load applications are experienced (equation 4.34) is first to present a Safety Margin, SM, a non-dimensional quantity to indicate the separation of the stress and strength distributions as given by This is essentially the coupling equation for the case when both stress and strength are a Normal distribution. A parameter to define the relative shapes of the stress and strength distributions is also presented,...

## Material properties and temperature

A number of basic material properties useful in static design depend most notably on temperature (Haugen, 1980). For example, Figure 4.15 shows how high temperatures alter the important mechanical properties of a low carbon steel, and the variation that can be experienced. Temperature dependent materials properties are sometimes available in statistical form, as shown in Figure 4.16 where the 3-parameter Weibull distribution is used to model the tensile strength of an alloy steel over a range...

## 343 Model for shifted distributions

Other factors can further enhance equation 3.16, such as factors to account for the type of distributions anticipated and the shift in the component distributions from the target. When components with shifted distributions are assembled, a large percentage of rejects would result if a model which does not effectively handle nonsymmetrical distributions is used (Chase and Greenwood, 1988 Lin et al., 1997), particularly when one component distribution is dominant in its variance contribution as...

## The 6 mm end seal dimension will be used in the analysis not 28 mm

Figure 3.11 Solenoid end assembly redesign least risk are optimized to near equal value as shown in Figure 3.12. The risk values determined at this stage are very low, close to unity in fact, and the situation looks more promising. Figure 3.13 shows the effects of the material processing and geometry risks for each component from the component manufacturing variability risk, qm, and these are taken into consideration in the calculation of the final estimates for Cpk and Cp for each tolerance....

## Monte Carlo simulation

Monte Carlo simulation is a numerical experimentation technique to obtain the statistics of the output variables of a function, given the statistics of the input variables. In each experiment or trial, the values of the input random variables are sampled based on their distributions, and the output variables are calculated using the computational model. The generation of a set of random numbers is central to the technique, which can then be used to generate a random variable from a given...

## 221 Process capability maps

As can be seen from the above, central to the determination of qm is the use of the process capability maps which show the relationship between the achievable tolerance and the characteristic dimension for a number of manufacturing processes and material combinations. Figure 2.6 shows a selection of process capability maps used in the component manufacturing variability risks analysis and developed as part of the research. There are currently over 60 maps incorporated within the analysis...

## The concepts of static design

The most significant factor in mechanical failure analysis is the character of loading, whether static or dynamic. Static loads are applied slowly and remain essentially constant with time, whereas dynamic loads are either suddenly applied (impact loads) or repeatedly varied with time (fatigue loads), or both. The degree of impact is related to the rapidity of loading and the natural frequency of the structure. If the time for loading is three times the fundamental natural frequency, static...

## 544 External supplier quality

A key success factor for reducing the costs and lead times for vehicle manufacturers, for example, is the degree of integration of the suppliers within the product development process. This is seen as a natural extension to concurrent engineering principles (Wyatt et al., 1998). For many years, in engineering companies, a substantial proportion of the finished product, typically two thirds, consists of components or subassemblies produced by suppliers (Noori and Radford, 1995). An effective...

## 223 Validation of the Component Manufacturing Variability Risks Analysis

Validation of the Component Manufacturing Variability Risk, qm, is essential to CA in determining Cpk estimates for component characteristics at the design stage. Collecting component parts from various industrial sources with known statistical histories was central to this. The components were taken from a number of collaborating companies which had produced the components and had measured a critical characteristic using SPC, therefore the process capability indices Cpk and Cp could be...

## 22 Component Manufacturing Variability Risks Analysis

In the development of the Component Manufacturing Variability Risk Index, qm, it was found to be helpful to consider a number of design manufacture interface issues, including Material to process compatibility Component geometry to process limitations Process precision and tolerance capability Surface roughness and detail capability. In the formulation of qm, it has been assumed that there is a basic level associated with an 'ideal' design for a specific manufacturing process, factors listed...

## 486 Bimetallic strip deflection

Bimetallic elements are widely used in instruments such as thermostats to sense or control temperatures. There are several bimetallic element types available, such as straight strips, coils and discs, but all rely on the same working principle. In its most basic form, the bimetallic strip comprises of two dissimilar metal strips bonded together, usually of the same surface area, but not necessarily of the same thickness thermostat. The composite metal strip is clamped at one end to act as a...

## 24 Component Assembly Variability Risks Analysis

In the development of the assembly variability risks analysis, expert knowledge, data found in many engineering references and information drawn from the CSC DFA MA practitioner's manual (CSC Manufacturing, 1995) were collated and issues related to variability converged on. Much of the knowledge for the additional assembly variability risks analysis was reviewed from the fabrication and joining data sheets called PRocess Information MAps (PRIMAs) as given in Swift and Booker (1997). Product...

## 21 Manufacturing capability

One of the basic expectations of the customer is conformance to specification, that is, the customer expects output characteristics to be on target with minimum variation (Abraham and Whitney, 1993 Garvin, 1988). Assessing the capability of designs early in product development therefore becomes crucial. The designer must aim to achieve the standards demanded by the specification, but at the same time not exceed the capabilities of the production department. This may not be an easy task because...

## 423 The algebra of random variables

Typically, if the stress or strength has not been taken directly from the measured distribution, it is likely to be a combination of random variables. For example, a Figure 4.11 Normal distribution linear rectification for SAE 1018 yield strength data Figure 4.12 Normal distributions from various sources for SAE 1018 yield strength data Figure 4.12 Normal distributions from various sources for SAE 1018 yield strength data failure governing stress is a function of the applied load variation and...

## 41 Deterministic versus probabilistic design

For many years, designers have applied so called factors of safety in a deterministic design approach. These factors are used to account for uncertainties in the design parameters with the aim of generating designs that will ideally avoid failure in service. Load and stress concentrations were the unknown contributing factors and this led to the term factor of ignorance (Gordon, 1991). The factor of safety, or deterministic approach, still predominates in engineering design culture, although...

## 487 Design of a conrod and pin

This case study discusses the design of a reciprocating mechanical press for the manufacture of can lids drawn from sheet steel material. The authors were involved in the early stages of the product development process to advise the company designing the press in choosing between a number of design alternatives with the goal of ensuring its reliability. The authors used a probabilistic approach to the problem to provide the necessary degree of clarity between the competing solutions. The press...

## 26 Objectives application and guidance for an analysis

A short review of the CA process is given before proceeding with the applications of the technique to several industrial case studies. The three key stages of CA are shown in Figure 2.24 within the simplified process of assessing a design scheme. Component Manufacturing Variability Risks Analysis - As mentioned previously, the first of the three key stages in CA is the Component Manufacturing Variability Risks Analysis. When detailing a design, certain characteristics can be considered...

## References

Abbot, H. 1993 The Cost of Getting it Wrong. Product Liability International, February. Abraham, B. and Whitney, J. B. 1993 Management of Variation Reduction Investigations. In Advances in Industrial Engineering No. 16 - Quality Through Engineering Design. Amsterdam Elsevier Science Publishers. Albin, S. L. and Crefield, P. J. 1994 Getting Started - Concurrent Engineering for a Medium Sized Manufacturer. Journal of Manufacturing Systems, 13(1), 48-58. Alexander, C. 1964 Notes on the Synthesis...

## Solenoid end assembly Initial design

The initial design is analysed using CA at a component level for their combined ability to achieve the important customer requirement, this being the tolerance of 0.2mm for the plunger displacement. Only those characteristics involved in the tolerance stack are analysed. The 'worst case' tolerance stack model is used as directed by the customer. This model assumes that each component tolerance is at its maximum or minimum limit and that the sum of these equals the assembly tolerance, given by...

## 431 Material strength

The largest design dependent strength variable is material strength, either ultimate tensile strength Su , uniaxial yield strength Sy , shear yield strength ry or some other failure resisting property. For deflection and instability problems, the Modulus of Elasticity E is usually of interest. Shear yield strength, typically used in torsion calculations, is a linear function of the uniaxial yield strength and is likely to have the same distribution type Haugen, 1980 . With mass produced...

## 222 Surface roughness chart

Figure 2.8 shows the range of surface roughness values likely for various manufacturing processes. The ranges determined are bounded within the risk index, A, in the same way as the process capability maps, because a similar cost-surface finish relationship exists, as suggested for tolerance and cost. This is shown in Figure 2.14 for several machining processes. The finer the surface finish required, the longer the manufacturing time, thereby increasing the cost Kalpakjian, 1995 . Select...