Allocation of geometric tolerances in one-dimensional stackup problems

Many tolerancing problems on mechanical assemblies involve a functional requirement depending on a chain of parallel dimensions on individual parts. In these one-dimensional cases, simple methods are available for the analysis and the allocation of dimensional tolerances. However, they are difficult to extend to geometric tolerances, which must be translated into equivalent dimensional tolerances; this allows the analysis but makes the allocation generally impossible without Monte Carlo simulation and complex search strategies. To overcome this difficulty, the paper proposes a way of dealing directly with geometric tolerances in the allocation problem. This consists in expressing the functional requirement as a linear model of geometric tolerances rather than equivalent dimensional tolerances; the coefficients of the model (sensitivities) are calculated considering both the dimension chain and the standard definition of the geometric tolerances. The approach can be combined with any constrained optimization method based on sensitivities. The optimal scaling method, previously proposed for dimensional tolerances, is extended to geometric tolerances and used in two examples to demonstrate the simplicity of the overall workflow and the quality of the optimal solution

An experimental approach for dimensional tolerance analysis using 3D printed parts

In 2D or 3D tolerance analysis, a dimension chain involves a complex propagation of random deviations from individual parts to the controlled assembly requirement. This can be calculated by setting up complex mathematical models, possibly with the help of CAD-based software tools. The paper studies the feasibility of an alternative approach, which uses measurements on assemblies of 3D printed parts to estimate the coefficients of a linearized error propagation model. The analysis is structured as a designed experiment, where each dimension is varied in two levels resulting in two different printed parts. The experimental plan consists of building assemblies from selected combinations of parts and measuring the assembly dimension on each combination. Among the possible designs of the plan, the paper compares two methods based on finite differences and least squares. The comparison includes both simulations with randomly generated dimension chains and physical tests on simple cases. The results show that a least squares plan allows a significant improvement in the accuracy on the estimation of model coefficients compared to a finite difference plan, with just a marginally higher number of assembly combinations. However, dimensional and geometric deviations in the 3D printing process are shown to play a critical role, and criteria are suggested to reduce or compensate them

Estimating the cost of functional requirements for tolerance allocation on mechanical assemblies

When allocating tolerances to geometric features of machine parts, a target variation must be specified for some functional requirements on the assembly. Such decision, however, is usually made from experience without consideration of its effect on manufacturing cost. To allow such an assessment, the paper describes a method for estimating the cost of a requirement as a function of its variation. The estimation can be done before solving a tolerance allocation problem, at the time the variation on the requirement is chosen as an optimization constraint. A simple expression for the cost of requirements of various types is obtained using the extended reciprocal-power function for the cost of part tolerances, and the optimal scaling method for tolerance allocation. As a result, the costs of both requirement variations and part tolerances can be treated in the same way; this allows a hierarchical approach to tolerance allocation, which can simplify the problem when dealing with complex dimension chains. Furthermore, simple calculations based on the proposed method suggest general cost reduction criteria in the design of assemblies

Solving basic problems of compliant tolerance analysis by static analogy

Predicting the geometric variation of sheet metal assemblies is a complex task, because deformation during joining operations influences the propagation of initial part deviations. To consider this effect, the paper proposes a method that formulates tolerance analysis as an equivalent problem of static analysis. Previously proposed for rigid parts, the static analogy is extended to compliant parts and applied to two-dimensional problems modeled with straight beams under the assumptions of small displacements and normal distributions of errors. For such simple cases, the method solves the problem by linearization, avoiding the use of Monte Carlo simulation and the related computational burden. Compared to existing linearization methods, the static analogy is less efficient in the integration with a finite element solver. However, it features an especially simple procedure that does not require the calculation of deflections, thus allowing a streamlined solution and even manual calculations. The comparison with alternative methods provides a first verification of the feasibility of the method, in view of further developments with the aim of dealing with cases of realistic complexity

Tolerance analysis by static analogy on 2D assemblies with fits and fasteners

In tolerance analysis, the effect of clearance fits is especially difficult to estimate because the mating parts are not necessarily in actual contact and can take an infinite number of relative positions. The treatment of these situations is allowed in most of the available methods, possibly introducing additional elements in the dimension chains with appropriate statistical assumptions. The paper provides a similar extension for the static analogy, a previously proposed method that converts the tolerance analysis problem into an equivalent problem of force analysis. The procedure represents each fit, possibly between patterns of features (e.g., fasteners and holes), with a proper constraint in the equivalent static model. The ability of the constraint to transmit forces and torques is determined according to the types and directions of misalignments allowed by the joint clearance. With simple rules, this avoids complications in the static model, which must include only the constraint between parts rather than the geometric details of the mating features. The extended method, currently limited to 2D dimension chains, is demonstrated on examples involving both dimensional and geometric tolerances. The comparison with existing methods shows the correctness of the proposed procedure. The simplicity of the workflow confirms the possibility, already demonstrated for the static analogy, of avoiding numerical simulations or even the use of computer-based tools

Estimation of cost reduction by tolerance optimization

Tolerance allocation is a design task with a strong potential impact on manufacturing choices. In practice, however, it is often carried out with simple heuristics rather than with an optimization approach like those available in research literature. One reason could be the difficulty in predicting the economic benefits resulting from optimization. To allow for such considerations, the paper proposes a procedure to estimate the cost reduction that optimization allows compared to three traditional allocation methods (equal tolerances, precision factor, proportional to nominal). The chosen optimization method is based on the closed-form solution of a problem of cost minimization with a stackup constraint, using the extended reciprocal power cost-tolerance function. Compared to other methods, it provides analytical expressions of both the allocated tolerances and the associated costs. When applied to specific cases, these help recognize the conditions in which optimization allows a significant reduction in manufacturing costs. The results show that this occurs when the features of the same dimension chain have very different properties regarding a set of design variables with particular influence on the amount of machining required

Ligation of Carbon Monoxide at Cobalt Single-Metal-Atom Sites in a Surface-Confined Metal–Organic Network: Oxidation State, Anharmonicity, and Long-Range Lateral Interactions

Ligation of carbon monoxide at the single metal atom cobalt sites of a surface-confined tetra-pyridyl porphyrin coordination network is investigated under near-ambient pressure conditions at room temperature. It is found that (anti-)cooperative effects associated with network-mediated lateral interactions allow tuning of the adduct adsorption energy and of its coverage dependence. The mechanism involves charge and geometric distortions, induced upon ligation, that are transferred to proximal sites of the network as far as few nanometers away through deformation of the pyridinic residues. Anharmonic contributions to the ligation potential are evidenced via the light-induced population of the vibrational hot-band of the internal C-O stretching mode, known to play a role in the C-O dissociation energy barrier and, thus, in the CO activation towards reaction

The origin of the high-velocity cloud complex C

High-velocity clouds consist of cold gas that appears to be raining down from the halo to the disc of the Milky Way. Over the past fifty years, two competing scenarios have attributed their origin either to gas accretion from outside the Galaxy or to circulation of gas from the Galactic disc powered by supernova feedback (galactic fountain). Here we show that both mechanisms are simultaneously at work. We use a new galactic fountain model combined with high-resolution hydrodynamical simulations. We focus on the prototypical cloud complex C and show that it was produced by an explosion that occurred in the Cygnus-Outer spiral arm about 150 million years ago. The ejected material has triggered the condensation of a large portion of the circumgalactic medium and caused its subsequent accretion onto the disc. This fountain-driven cooling of the lower Galactic corona provides the low-metallicity gas required by chemical evolution models of the Milky Way's disc.Comment: 6 pages, 4 figures, 1 table; accepted by MNRA

Testosterone decreases adiponectin levels in female to male transsexuals

Aim: To evaluate the effect of testosterone (T) on adiponectin serum levels in transsexual female patients. Methods: We measured adiponectin, leptin, luteinizing hormone and follicle stimulating hormone, T, estradiol, lipid profile, biochemical parameters and body composition in 16 transsexual female patients at baseline and after 6 months of T treatment (100 mg Testoviron Depot /10 days, i.m.). Results: Adiponectin levels were 16.9 ± 7.3 mg/mL at baseline and 13.5 ± 7.4 mg/mL at month 6 of T treatment (P < 0.05). Leptin and high-density lipoprotein cholesterol decreased significantly, whereas body mass index, waist circumference and lean body mass increased significantly after 6 months of T treatment. No changes in insulin or Homeostasis Model Assessment were detected. Conclusion: T can significantly reduce adiponectin serum levels in transsexual female patients