Large deflection of a circular C-shaped spring

The theoretical analysis of a circular $\text{C-}\text{shaped}$ spring is presented. The analysis is based on the assumptions that the spring is perfectly elastic and that its deflection is plane under large deflections. The deformed shape of the spring is found to be a segment of a nodal elastica, and the load-deflection curve is almost linear over some range of deflection; this provides basic information for the design of the spring. Experimental verifications are performed using steel circular $\text{C-}\text{shaped}$ springs of flat rectangular cross section. There is no discrepancy between the calculated and observed results.     

Sampling error in ad conversion of the surface profile signal

A fundamental problem in a/d conversion of a measurment signal of surface profile id discussed from the viewpoint of a limit of sampling error in the time domain. A comparison is also made of the results of autocorrelation function, power spectrum and profile parameters such as R_max, R_a etc, obtained from the sampled surface profile in the time domain and in the longitudinal domain. It is suggested that the minimization of sampling error may be attained by the use of a digital displacement transducer attached to the usual surface measurement instrument.     

A displacement analysis of the general spatial 7-link, 7R mechanism

An input-output equation of degree 32 in the tan-half-angle of the output angular displacement is expressed in the form of a $\text{16 × 16}$ determinant equated to zero for the single-loop, single-degree-of-freedom linkage with seven links connected by seven turning pairs arbitrarily oriented in space. An algorithm is developed for computing values of the remaining angular displacements of the mechanism. The results are verified by numerical examples.The derivation of the input-output equation and the development of the algorithm are outlined before proceeding with the detailed algebraic analysis. The detailed analysis is performed using a unified theory for the analysis of spatial mechanisms [1,2] which was developed using a treatise on spherical trigonometry by Todhunter and Leatham [3].     

Rolling of I-section beams using lead as a model material: Some experimental results

Results of a series of tests rolling $\text{I-}\text{section}$ beams in the first two passes, using lead as a model material, are presented; they include measurements of relative spread, natural elongation, roll load, roll torque and the observed changes in deformation modes with variation in shape factors (height to width ratios) of the specimens and the relative draughts.A comparison of these results is made with those obtained using empirical formulae suggested by earlier research workers. The observed rolling loads are compared also with measurements made of the die loads when rectangular specimens with the same shape factors as in these rolling tests were compressed between shaped dies having grooves similar to that in rolling and compressed under conditions of plane strain and in open-die compression.     

The use of finite element creep solutions to obtain J integrals for plane strain cracked members

Numerical values are obtained for the path independent $\text{J}$ integral and for crack opening displacement δ, for internally and externally cracked tension members under conditions of plane strain. These parameters have been obtained, for an $\text{n-}\text{power}$ creeping material, from stationary state solutions using the finite element method. Values of $\text{J}$ and δ are compared with available results and are shown to be in good agreement.     

A tension-torsion machine for testing yield criteria and stress-strain relationships at T = 78°K

A tension-torsion machine in which aluminium and copper specimens are pulled and twisted while being immersed in liquid nitrogen is described. The incorporated load cell and extensometer offer very accurate readings at $\text{T = 78°}\text{K}$.The test materials are especially treated to approach conditions of isotropy and homogeneity. Stress-strain curves in simple tension and pure shear are obtained at $\text{T = 292°}\text{K}$ and $\text{T = 78°}\text{K}$. It can be seen that at 78°K the initial yield surface obeys the von Mises yield criterion.     

212 transmission electron microscopy applied to phase transformations in ball bearings

$\text{2}\text{1}\text{2}$D transmission electron microscopy has been applied to rolling contact-fatigued ball bearings. The $\text{2}\text{1}\text{2}$D technique implies that correlations between image features and the object lattice structure are transformed to a stereoscopic effect, using defocused dark-field image pairs. During contact fatigue, the martensite matrix may decay and be transformed to new phases. Particularly, a carbon-enriched phase has been studied. The findings indicate areas of probable nucleation sites and areas being dilated due to internal stresses. The phase is constituted of a lattice structure with minor and regular variations in the g-vector, involving vector orientation and magnitude.     

First-mode properties of N-story buildings

First-mode properties of N-story buildings determined from a standard computer program possess certain simple relationships which can be displayed graphically by straight lines. Structures investigated include uniform buildings and buildings with reduced first floor stiffness. Some of the results presented are verified analytically from difference equations.     

Influence of a low temperature sulphurizing process on lubricants in standard ep and fzg tests

The influence of the Sulf BT process, an anodic sulphurizing process, on the performance of a non-EP turbine oil and an EP gear oil has been tested. Both standard EP (four-ball, Timken and Falex) and gear-simulating (FZG) tests, were used on plain and sulphurized specimens. EP tests showed increased performance for the sulphurized specimens: the most remarkable result was noted in the four-ball and Timken tests, where the turbine oil attained a performance typical of commercial EP lubricants. FZG tests, however, showed no improvement, the sulphide film being progressively worn away during the tests and thereby having no influence on the results. The disagreement between EP and FZG determinations points to the fact that predictions from measurements of load-carrying capacity on the commonly used laboratory devices may not agree at all with behaviour on machines more closely simulating actual service.     

Multi-objective optimization of the ecm process

Optimization of process parameters is helpful in efficient working of the process and, hence, in lowering the cost of machining. Optimization of ECM process parameters has been achieved by considering only one objective at a time from metal removal rate, geometrical accuracy, and total process cost. From a practical point of view, a solution of the ecm problem satisfying all three objectives simultaneously is highly desirable.In the proposed model, a multi-objective problem involving the ecm process is formulated producing highly nonlinearized equations. These are then linearized by regression analysis and converted into a goal programming format. Finally, the problem is solved by the partitioning algorithm.It is concluded that the tool, or cathode, remains safe at the optimal values of design variables obtained in the examples discussed. The optimal value of voltage when metal removal rate is the only objective, is found to be higher than the case when the geometrical accuracy requirement is also to be satisfied.     

An investigation into yield surfaces and plastic flow laws for f.c.c. metals at room temperature and a low temperature (T = 78°K)

Experimental investigations are made into yield criteria and stress-strain relationships for aluminium and copper at room temperature and 78°K by tension-torsion testing of tubular specimens. Initial and subsequent yield surfaces are determined after prestrain in tension and torsion.The laws of normality and convexity and the possibility of the existence of corners on the yield surfaces are considered.     

Analysis of taper produced in side zone during ecd

The full capabilities of electrochemical machining (ecm) have not been utilized in production, mainly due to some inherent problems associated with tool design. For example, the side wall generated during electrochemical drilling (ecd) of a cylindrical hole is tapered. To study the effect of process parameters on the taper produced during ecd, experiments were performed using brass as cathode, low alloy steel forgings and castings as anode and aqueous solution of NaCl as electrolyte. From the analysis of the results, some useful conclusions have been derived that would be helpful in controlling the taper produced by bare tool, bare bit tool or coated tool.     

Plasma channel growth and the resolidified layer in edm

An analysis for the computation of the plasma channel size, is presented as a function of pulse-on duration in edm. It has been shown that accounting for the effects of the plasma growth leads to marked improvement in analytical results obtained. The paper also suggests a method for evaluating the thickness of the resolidified layer in edm machined workpieces. The analytical values of the resolidified layer thickness agree well with published experimental data.     

Statistical design of variable sample size and sampling interval $\bar{X}$\bar{X}control charts with run rules

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.