Nominal Shapes Research Articles

Method for the consideration of statistically distributed geometrical deviations in the design of cylindrical roller bearing arrangements

Rolling bearings are of great importance in all areas of mechanical engineering due to their precise and low-friction guidance of rotating components at low cost. The design of rolling bearing arrangements is usually based on approximately ideal geometries of bearings and adjacent parts on which the bearing seats are located. However, real components inevitably show statistically distributed deviations from their nominal shapes, which are limited by tolerances. Tight tolerances result in high manufacturing costs while on the other hand their expansion leads to an increase of occurring geometrical deviations which cause changes in the bearing-internal contact and load conditions and can thus impair the operating behavior of the bearing, e.g. with regard to fatigue life, frictional torque or vibration behavior. By taking these effects into account in the design stage, potential problems in operation can be identified early during development and countermeasures can be taken, e.g. by adjusting bearing and seat tolerances. This enables an improvement of overall product quality and a reduction of costs. This paper presents a method for the integration of component deviations in the computation of the fatigue life (Lnmr) and dynamic behavior of cylindrical roller bearing arrangements—both of which are crucial design criteria—based on a combination of statistical tolerance analysis and multi-body simulations. The method is applied to an exemplary use case for illustration.

Separable shape tensors for aerodynamic design

AbstractAirfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of two-dimensional (2D) and three-dimensional (3D) aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, and translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers: (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.

Development of high-performance hypodermic needle penetration resistance flexible cotton fabric using patterned thermoplastic adhesive film

Injuries caused by needle stick puncture are common and a concern in many industries, such as health services and waste collection. Personal protection against needle stick punctures currently use high-cost materials like high-density polyethylene (HDPE) woven fabric and Kevlar which compromises flexibility. In this paper, a low-cost, easy to produce, needle puncture resistant material is developed. Here, cotton fabric is overlaid by patterned Ethylene-Vinyl Acetate (EVA) based adhesive film and multiple layers are used that increase the needle penetration resistance by up to 478% as compared to a single layer of laminated fabric, while the flexibility decreased by only 12–49 %. Patterns of different shapes (hexagons and hexagons mixed with triangles) and sizes with nominal diameters ranging from 2.6 to 13.5 mm were tested, with the smaller nominal dimensional shapes having a greater flexibility. Patterned hot film had a similar needle penetration resistance as plain hot film but was significantly more flexible. Increasing the number of laminated fabric layers from 1 to 3 resulted in an increase in needle penetration resistance force from 2 N up to 8 N.

Comparison of nominal and real 2D contours of manufactured products using Ant Colony Optimisation of shape landmarks

In studying manufacturing processes it is often necessary to compare nominal or reference product shapes that are expected to be ideally achieved after applying a nominal set of process parameters and the actual product shape achieved. The latter is usually obtained by metrological equipment such as profilometers, tomographs and 3D scanners, whilst the former may also result from manufacturing process numerical simulation software. In this work, comparison of 2D contours is studied by adopting the well-established Procrustes method. The method relies on minimizing deviation of landmark points belonging to the shapes under scrutiny. Landmarks that need to be compared pairwise should be chosen in an optimal way, especially when the contours contain different numbers of points, when they differ locally etc. Optimal determination of landmarks and as a result implementation of contour comparison is performed through ant colony optimization implemented on MatlabTM platform. Indicative results are shown where deviations discovered signify shrinkage of a die-cast clay part.

Stress-strain state prediction for statically indeterminate system with accounting for malfunctioning of rod elements production

The use of pre-tension as a regulating mechanism in structures that are statically indeterminate rod systems usually implies the absence of initial forces and stresses. It is necessary to take into account its initial stresses from probabilistic positions and adjust the pre-tension parameters accordingly. The laws of distribution of deviations of rod elements or shipment-sized sets of details from nominal sizes and shapes are usually known. The technique of determination of reliable enough value of initial effort in the certain connection of interest of the statically indeterminate system (SIS) because of deviations of rod elements or shipment-sized sets of details from their nominal sizes and forms is presented. Thus, deviations of both rod elements and dispatch brands from the nominal sizes and forms are known to be random variables with symmetric laws of distribution. The task is solved in linear statement with result of research giving the opportunity to determine the value of initial effort using just one static design calculation.

Completeness of ceramic bricks’ quality control

The method of quality control of building materials is proposed taking into account the indicator of completeness of control. The completeness of the control calculated as the percentage of checked failures. By the example of quality control of ceramic bricks of brand 100, it is shown that the completeness of control of ceramic bricks of grade 100 is from 46.7 to 48.3%. This confirms the requirements of normative document on conducting performance checks (appearance, dimensions, deviations from nominal sizes and shapes, tensile strength in compression and bending, average density) during acceptance tests. Proposed to exclude verification of the width of the brick, which will reduce the complexity of the control.

Focal depth measurement of scanning helium ion microscope

When facing the challenges of critical dimension measurement of complicated nanostructures, such as of the three dimension integrated circuit, characterization of the focal depth of microscopes is important. In this Letter, we developed a method for characterizing the focal depth of a scanning helium ion microscope (HIM) by using an atomic force microscope tip characterizer (ATC). The ATC was tilted in a sample chamber at an angle to the scanning plan. Secondary electron images (SEIs) were obtained at different positions of the ATC. The edge resolution of the SEIs shows the nominal diameters of the helium ion beam at different focal levels. With this method, the nominal shapes of the helium ion beams were obtained with different apertures. Our results show that a small aperture is necessary to get a high spatial resolution and high depth of field images with HIM. This work provides a method for characterizing and improving the performance of HIM.

Transcatheter Heart Valve With Variable Geometric Configuration: In Vitro Evaluation

Clinically, the current transcatheter aortic valve (TAV) technology has shown a propensity for paravalvular leakage; studies have correlated this flaw to increased calcification at the implantation site and with nonideal geometry of the stented valve. The present study evaluated the hydrodynamics of different geometric configurations, in particular the intravalvular considerations. Three TAV devices were made to create a representative, size 26 mm TAV. Hydrodynamics were assessed using a pulse duplicator. The geometries tested were composed of the nominal, elliptical, triangular, and undersized shapes; along with half-constriction, a conformation in which only a portion of the stent was constrained. The TAVs were assessed for transvalvular pressure gradient (TVG), effective orifice area (EOA), and regurgitant fraction. The nominal-sized shape posed a larger TVG (6.2 ± 0.3 mm Hg) than other configurations (P < 0.001) except the undersized valves. EOA of the nominal sized TAV (1.7 ± 0.1 cm(2) ) was smaller than that of the triangular and half-elliptical versions (P < 0.001). The half- and full-undersized geometries had EOAs smaller than the nominal type (P < 0.001). Nominal shape had smaller regurgitation (6.7 ± 1.4%) than all configurations (P < 0.001) except for the half-undersized (4.0 ± 0.7, P < 0.001) with no statistically significant difference from the full-undersized (6.8 ± 1.3, P = 0.724). The testing of variable geometries showed significant differences from the nominal geometry with respect to TVG, EOA, and regurgitant fraction. In particular, many of these nonideal configurations demonstrated an increased intravalvular regurgitation.

Springback control in sheet metal bending by laser-assisted bending: Experimental analysis, empirical and neural network modelling

The present investigation deals with the control of springback phenomena in the bending process of aluminium sheets by hybrid forming process. Metal substrates were pre-bent to nominal shapes on a built-ad-hoc mould after being constrained on it. Then, they were post-treated by high power diode laser to prevent the deformation of the pre-bent sheets after the release of the constraints. The extent of springback phenomena were estimated by measuring the difference between the nominal bending angles and those achieved on the unconstrained substrates after laser post-treatments. Analytical models, aimed at predicting the springback by varying the setting of the operational parameters of the forming process, were developed. Neural network solutions were also proposed to improve the matching between experimental and numerical data, with the Multi-Layer Perceptrons trained by Back-Propagation algorithm being the fittest one. On this basis, a control modulus very useful to practitioners for automation and simulation purposes was built-on.

Functional muscle synergies constrain force production during postural tasks

We recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations. This characterization depended critically upon the assumption that the endpoint force vector (synergy force vector) produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane. Here, we used a detailed, 3D static model of the hindlimb to confirm that this assumption is biomechanically plausible: as we varied the model posture, simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane ( r 2=0.94±0.08). We then tested whether a neural strategy of using these five functional muscle synergies provides the same force-generating capability as controlling each of the 31 muscles individually. We compared feasible force sets (FFSs) from the model with and without a muscle synergy organization. FFS volumes were significantly reduced with the muscle synergy organization ( F=1556.01, p≪0.01), and as posture varied, the synergy-limited FFSs changed in shape, consistent with changes in experimentally measured active forces. In contrast, nominal FFS shapes were invariant with posture, reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone. We propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates, and this reduced-dimension control scheme reduces the set of forces available for postural control.

Equivalence Classes for Shape Synthesis of Moving Mechanical Parts

Moving parts in contact have been traditionally synthesized through specialized techniques that focus on completely specified nominal shapes. Given that the functionality does not completely constrain the geometry of any given part, the design process leads to arbitrarily specified portions of geometry, without providing support for systematic generation of alternative shapes satisfying identical or altered functionalities. Hence the design cycle of a product is forced to go into numerous and often redundant iterative stages that directly impact its effectiveness. We argue that the shape synthesis of mechanical parts is more efficient and less error prone if it is based on techniques that identify the functional surfaces of the part without imposing arbitrary restrictions on its geometry. We demonstrate that such techniques can be formally defined for parts moving in contact through equivalence classes of mechanical parts that satisfy a given functionality. We show here that by replacing the completely specified geometry of the traditional approaches with partial geometry and functional specification, we can formally define classes of mechanical parts that are equivalent, in the sense that all members of the class satisfy the same functional specifications. Moreover, these classes of functionally equivalent parts are computable, may be represented unambiguously by maximal elements in each class, and contain all other functional designs that perform the same function.

Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions

The Hertz type contact problems and the analytical treatment of depth-sensing nanoindentation are under consideration. Fundamental relations of nanoindentation tests are derived for various boundary conditions within the contact region. First, a frictionless contact problem for a convex punch of revolution is studied and the connection between Galin and Sneddon solutions is shown. The Bulychev–Alekhin–Shorshorov (BASh) relation that is commonly used for evaluation of elastic modulus of materials by nanoindentation, is discussed. An analogous relation is derived that is valid for adhesive (no-slip) contact. Similarly to the Pharr–Oliver–Brotzen frictionless analysis, the obtained relation is independent of the geometry of the punch. Further, we study solutions to adhesive contact for punches whose shapes are described by monomial functions and obtain exact solutions for punches of arbitrary degrees of the monoms. These formulae are similar to the formulae of the frictionless Galin solutions and coincide with them when the material is incompressible. Finally, indenters having some deviation from their nominal shapes are considered. It is argued that for shallow indentation where the tip bluntness is on the same order as the indentation depth, the indenter shapes can be well approximated by non-axisymmetric monomial functions of radius. In this case problems obey the self-similar laws. Using one of the authors’ similarity approach to three-dimensional contact problems and the corresponding formulae, other fundamental relations are derived for depth of indentation, size of the contact region, load, hardness, and contact area, which are valid for both elastic and non-elastic, isotropic and anisotropic materials for various boundary conditions. In particular, it is shown that independently of the boundary conditions, the current area of the contact region is a power-law function of the current depth of indentation whose exponent is equal to a half of the degree of the monomial function of the shape.

405 幾何公差域内におけるフィーチャの存在確率に関する研究 : 公差の重畳の扱いについて(GS-1.12.14 生産システム・システム設計)

This paper deals with stochastic analysis of geometric features within tolerance zone. The geometric features and their tolerance zone are firstly analyzed based on the JIS standards, and the parameters are established to represent the deviations of the geometric features from the nominal shapes. A systematic method is then proposed to analyze the existing probability of the geometric features within the tolerance zone, considering concatenation of a series of tolerances.

Analytical study of fundamental nanoindentation test relations for indenters ofnon-ideal shapes

Nanoindentation techniques provide a unique opportunity to obtain mechanicalproperties of materials of very small volumes. The load–displacement andload–area curves are the basis for nanoindentation tests, and their interpretationis usually based on the main assumptions of the Hertz contact theory andformulae obtained for ideally shaped indenters. However, real indenters have somedeviation from their nominal shapes leading researchers to develop empirical ‘areafunctions’ to relate the apparent contact area to depth. We argue that for bothaxisymmetric and three-dimensional cases, the indenter shape near the tip can bewell approximated by monomial functions of radius. In this case problemsobey the self-similar laws. Using Borodich’s similarity considerations ofthree-dimensional contact problems and the corresponding formulae, fundamentalrelations are derived for depth of indentation, size of the contact region,load, hardness, and contact area, which are valid for both elastic andnon-elastic, isotropic and anisotropic materials. For loading the formulaedepend on the material hardening exponent and the degree of the monomialfunction of the shape. These formulae are especially important for shallowindentation (usually less than 100 nm) where the tip bluntness is of thesame order as the indentation depth. Uncertainties in nanoindentationmeasurements that arise from geometric deviation of the indenter tipfrom its nominal geometry are explained and quantitatively described.

418 Modeling and Analysis of Geometric Feature Deviation in Tolerance Zone

The paper deals with statistical analysis of geometric features within tolerance zone. The geometric features and their tolerance zone are firstly analyzed based on the JIS standards, and the parameters are established to represent the deviations of the geometric features from the nominal shapes. A systematic method is then proposed to analyze the probability that the geometric feature is included in the tolerance zone and to estimate the standard deviations of the deviation parameters that satisfy the constraints specified by the tolerance zones. The statistical properties of the deviation parameters of the geometric features are analyzed, and the statistical distributions of the deviation parameters of the geometric features are theoretically clarified.

Modeling the assembly of compliant, non-ideal parts

All manufactured parts and tooling have unavoidable variations from their nominal shapes. During assembly, compliant parts are further deformed by the relatively rigid assembly tooling. Lack of knowledge regarding variations and deformations often results in expensive problems. Since most current computer-aided design (CAD) systems today are based on ideally sized, ideally located, and rigid geometry, they are unable to model or predict the effects of variations in parts and tooling. This paper proposes a model for the assembly of compliant, non-ideal parts.

Uncertainty of a Least Squares Curve Fit through Points with Known Uncertainties

Uncertainties in least squares curve fits to data with uncertainties are examined. First, experimental data with nominal curve shapes, representing property profiles between boundaries, are simulated by adding known uncertainties to individual points. Next, curve fits to the simulated data are achieved and compared to the nominal curves. By using a large number of different sets of data, statistical differences between the two curves are quantified and, thus, the uncertainty of the curve fit is derived. Studies for linear, quadratic, and higher-order nominal curves with curve fits up to fourth order are presented herein. Typically, curve fits have uncertainties that are 50% or less than those of the individual data points. These uncertainties increase with increasing order of the least squares curve fit. The uncertainties decrease with increasing number of data points on the curves.

Relative positioning of variational part models for design analysis

A collection of functionally oriented assembly relations serves as an implicit representation for part positions in an assembly. The actual determination of part positions from the assembly relations has been extensively researched for assemblies in which parts are at their nominal shapes and sizes. However, design-analysis algorithms such as those used in tolerance analysis require the determination of the final assembly configuration, where the individual part geometries incorporate simulated manufacturing variations. The paper describes a constrained-optimization technique for the determination of part positions in assemblies of nonideal parts. Because the manufacturing variations are relatively small, the authors' technique linearizes the rotational elements in the constraint formulation. The constraint-optimization formulation seeks to satisfy the assembly relations to the maximum extent possible that is consistent with their relative functional significance. Noninterference constraints between the mating parts are enforced.

Frequency based localisation of structural discrepancies

The intent of modal analysis is to develop a reliable model of a structure by working with the analytical and experimental modal properties of frequency, damping and mode shape. In addition to identifying these modal properties it would be desirable to determine spatially which parts of the structure are modeled poorly or well. This information could be used to improve the finite element model, or to point to faults in the structure and hence help to evaluate mechanical integrity. This paper shows how the pattern of discrepancies in the pole and the driving point zero frequencies of a structure can be linked to discrepancies in the mass or stiffness of the structural elements. Only nominal mode shapes, as opposed to mode shape discrepancies, are required. Because first-order errors in mode shape cause only second-order localisation errors, the nominal mode shapes need not be measured, but can be taken from a finite element model. The success of this procedure depends on the numerical conditioning of a modal reference matrix. Strategies to ensure adequate numerical conditioning require a formulation which avoids geometric and energy storage symmetries of the structure, and ignores structural elements which contribute negligibly small potential or kinetic energy to the excited modes. Physical insight into the numerical conditioning problem is provided by a numerical example and by the localisation of a mass discrepancy in a real structure based on laboratory tests.