Alessandro Freddi

In vitro measured strains in the loaded femur: Quantification of experimental error

Abstract The application of strain gauges to bone surfaces has been extensively employed as a method of determining, strain fields in response to implanted devices in orthopaedics. The aim of this study was to determine some of the experimental errors associated with the use of strain gauges in in vitro experimental investigations of the loaded femur. An experimental protocol was devised to obtain strain data at 20 strain gauged locations on the proximal femur. These data were interpolated using a parametric model. The parametric model was then used to estimate the errors associated with mispositioning of the gauges and deviations in their direction of application to the bone. This sensitivity analysis was also supported by a finite element analysis for the purposes of comparison and cross-validation. The results indicated that the nature of the loading normally employed in the literature can contribute to making the readings for some of the gauges (anterior and posterior) unreliable and redundant, even for small positioning errors. The greatest predicted errors for the lateral and medial gauges were due to misalignment of the gauge as opposed to mispositioning. The size of the gauge had a negligible effect on the errors predicted relative to those caused by misalignment.

Introduction to Inverse Problems

Experimental Stress Analysis has been traditionally applied—through a direct or forward approach—for solving structural mechanical problems as an alternative and complementary methodology to the theoretical one. The great development of numerical methods has largely overruled this task. In addition, the increased accuracy of numerical tools has confined the forward approach to the role of experimental verification restricted to cases of complex and non-conventional numerical modeling, such as stress states resulting from singularities, material anisotropy, etc. If, however, causes (such as forces, impressed temperatures, imposed deformations) or system parameters such as geometry, materials and boundary conditions are unknown, the case is totally different, and the experimental inverse approach has no alternatives. Through measurements of the effects like displacements, strains and stresses, it is possible to find solutions to these inverse problems by identifying the unknown causes, integrating a series of experimental data into a theoretical model. The accuracy of data together with a proper selection of the quantities that must be measured are a necessary premise for limiting the experimental errors that can influence the accuracy of the inversely estimated results.

Introduction to the Taguchi Method

We now introduce a further powerful engineering tool: the Robustness concept. It is inextricably linked to the name of Genichi Taguchi, a Japanese engineer. Although his approach is based on what was outlined in the previous chapter on Design of Experiment, it contains strong innovation of those concepts. Significant improvements are proposed for three design phases: system design, parameters design and tolerance design. It is not possible to draw a comprehensive picture of the method here. Only the main concepts are introduced, leaving any more complex treatment of the method to specialized books. This method is a real improvement of the application of statistical methods to design applications. This chapter describes the basic concepts, among which the Quality Loss Function that better than other interpretations clarifies the term, often ambiguous, of quality. In this way, the link between robustness, reliability and design of quality becomes obvious. We tried to give emphasis to ideas more than to technicality, but a limited mathematical formalism is necessary.

Invention and Innovation

Up to this point we met design methods with a predominantly technical approach, according to which the design process is developed as a sequence of actions related to the invention of solution principles. Through the previous approach we learned how to perform certain functions, i.e. with the invention of functional variants and also in certain cases, the construction of prototypes. However, especially design guidelines and the ISO 9001 standards now open up a broader scenario, in which a technical design is oriented to an industrial mass production. In this case, the problem-solving choices are no longer only a problem of technical invention. Mass-production requires the study of another coordinate of the problem: the design development within an industrial company. It concerns the “innovation concept” that is the core value played primarily within company strategies.

Embodiment Design of the Packaging Machine: Prototype Development

This chapter is devoted essentially to the embodiment design of the SASIB ALFA Packer Prototype, following the topic dealt with in the previous chapter. The embodiment design is the part of the design process in which, starting from the main decisions made in conceptual design, the product plan is concretely developed, dealing with technical and economic criteria. This step moves from logical to physical solutions, to define shape and size. In the example shown, the embodiment design is essentially an illustration of the main constructive solutions adopted. However, unlike conceptual design, embodiment design requires many corrective actions in which analysis and synthesis alternate. It is a less systematic process that gives rise to many reviews. In any case, we do not deal with the detailed design phase.

Design of a Packaging Machine: General Description and Conceptualization

This Chapter is devoted to the description of the conceptual design of an industrial product, the SASIB ALFA Packer (Sasib S.p.a., Bologna, now part of the COESIA Group, Italy), an automatic machine for the packaging industry, developed in the eighties, under the direction of one of the authors. The Dante Alighieri motto “It is true that, as a form is frequently discordant with the intention of an art, because its matter in response is deaf”, reminds us that in any human activity a gap always exists between theory and practical implementation. Design of artifacts shows a deep gap between conceptual phase and realization inside a business oriented organization. While theory gives guidelines for the design of a product, industrial practice is product oriented, i.e. its goal is to “develop a new product” taking into account any related activity “from cradle to grave”; while theory takes into account essentially “physical” constraints, a real mass production must consider human and social constraints such as time, expenditure, human resources, customers, and stakeholders, psychology, etc.

Requirements and Specifications

Subjects involved in the design and production of goods have to build their decisions on market data. Collecting and organizing information is then the preliminary activity, necessary in understanding the complexity of the customer needs, often not “clear and distinct”, but on the contrary, expressed in a confused and interrelated way. Users can play an active role that must be taken into account: user-driven design versus user-centered design is a controversial position that it is worth analyzing. The design process starts by the identification of the needs of potential customers and proceeds with conceptual design, then embodiment and finally detail design, and the knowledge and satisfaction of user real needs is crucial in any phase. The tools developed for acquiring this knowledge are far from being formalized (i.e. mathematically formulated) but, nevertheless, are consistent and based on principles of logic, cognitive sciences and on the human experience of all the subjects that collaborate in the design process. This great work of interpretation and translation leads, at the end of the conceptual design, to fundamental documents which are called “product (or service) specifications” and which are the starting points for all the following design phases.

One-Off Product Design

In the seminal conceptual idea that things derive from other things, in this chapter we will show examples of design that have been developed at the level of useful prototypes. They remained at this level, since they were designed as single units and it was considered not suitable at that time to transform them into large batch products. Only later, did some of them become first models of others, but outside the responsibility of the authors. Nevertheless, these prototypes have received confirmation of their usefulness in special environments, (as equipment in national laboratories and private companies’ research centers).

Engineering Design and Industrial Design

Engineering designers and industrial designers are the main actors called to collaborate, within their jurisdiction, in the design of products/service through creative choices that define functions, structures and forms together with manufacturing processes. In spite of different cultures and practical approaches of the two categories of professionals, design accomplishes a common goal: development of new products and services. Each design process runs from a conceptualization phase and moves towards an embodiment phase, trying to meet the customers’ real needs, and at the same time to satisfy business requirements, in respect of health-, safety- and environmental constraints [32]. Obviously, it is necessary to distinguish between the end user and the industrial customer that have requirements that must be met differently.

Introduction to the Application of Strain Gages

This chapter reviews the basic formulas of electrical resistance strain gages and related circuits, as well as some concepts that are not always emphasized in specialized books. Some sections of the chapter deal with the limits of the maximum and minimum values of the measurable strain, the choice of the resistance of the commercial gages series, the linearity and the drawbacks of the basic measuring circuits and some properties of a piezo-resistive gages. Classic formulas are given for principal strain and stress calculation for single strain gages and for rosettes, as well as for the application of the Wheatstone bridge circuit to biaxial strain state. A final issue concerns load cells. This topic is tackled from the point of view of design for high sensitivity and high stiffness which are especially required for fatigue tests. The calibration procedure is also described and applied to several cases, for uni- and multi-axial cells.