Optimal Tolerance Allocation for Tolerance Stack-Ups

1993 ◽  
Author(s):  
Thomas L. Dresner ◽  
Philip Barkan
Keyword(s):  
Lagrange Multiplier ◽  
Cost Allocation ◽  
Mechanical Design ◽  
Minimum Cost ◽  
Tolerance Allocation ◽  
Basic Method ◽  
Worst Case ◽  
One Dimensional ◽  
Sensitivity Functions ◽  
Multiple Tolerance

Abstract The allocation of individual tolerances that form critical stack-ups is an important task in mechanical design. It is desirable, but difficult in practice, to allocate tolerances to obtain all required stack-ups at minimum cost. A minimum-cost allocation method is proposed here that works for both a single tolerance stack-up and for multiple tolerance stack-ups that share one or more individual tolerances. Tolerances can be optimally allocated for both worst case and a variety of 6σ statistical cases. The method is applicable to one-dimensional stack-ups and to multi-dimensional stack-ups with known sensitivity functions. It is a numerical Lagrange multiplier method that is more general than the Lagrange multiplier methods that have often been proposed. The basic method will almost always provide the lowest cost result when the manufacturing process to produce each toleranced dimension has been firmly established in advance. An exact method for efficiently extending the basic method to determine the lowest cost process for producing each dimension is also introduced.

Optimal Tolerance Allocation Over Multiple Manufacturing Alternatives

1992 ◽  
Author(s):  
Jonathan Cagan ◽  
Thomas R. Kurfess
Keyword(s):  
Simulated Annealing ◽  
Optimization Problem ◽  
Simulated Annealing Algorithm ◽  
Minimum Cost ◽  
Tolerance Allocation ◽  
Hyperbolic Function ◽  
Manufacturing Processes ◽  
Worst Case ◽  
Annealing Algorithm ◽  
Manufacturing Alternatives

Abstract We introduce a methodology for concurrent design that considers the allocation of tolerances and manufacturing processes for minimum cost. Cost is approximated as a hyperbolic function over tolerance, and worst-case stack-up tolerance is assumed. Two simulated annealing techniques are introduced to solve the optimization problem. The first assumes independent, unordered, manufacturing processes and uses a Monte-Carlo simulation; the second assumes well known individual process cost functions which can be manipulated to create a single continuous function of cost versus tolerance with discontinuous derivatives solved with a continuous simulated annealing algorithm. An example utilizing a system of friction wheels over the manufacturing processes of turning, grinding, and saw cutting bar stock demonstrates excellent results.

A claims problem approach to the cost allocation of a minimum cost spanning tree

2021 ◽  
Author(s):  
José-Manuel Giménez-Gómez ◽  
Josep E. Peris ◽  
Begoña Subiza
Keyword(s):  
Spanning Tree ◽  
Cost Allocation ◽  
Minimum Cost ◽  
Claims Problem ◽  
The Cost

Using Tolerance-Maps to Generate Frequency Distributions of Clearance and Allocate Tolerances for Pin-Hole Assemblies

2007 ◽  
Vol 7 (4) ◽  
pp. 347-359 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Mathematical Model ◽  
Statistical Method ◽  
Frequency Distribution ◽  
Probabilistic Representation ◽  
Worst Case ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Material Condition ◽  
Geometric Tolerances ◽  
Case Basis

A new mathematical model for representing the geometric variations of lines is extended to include probabilistic representations of one-dimensional (1D) clearance, which arise from positional variations of the axis of a hole, the size of the hole, and a pin-hole assembly. The model is compatible with the ASME/ ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (T-Map) (Patent No. 69638242), a hypothetical volume of points that models the 3D variations in location and orientation for a segment of a line (the axis), which can arise from tolerances on size, position, orientation, and form. Here, it is extended to model the increases in yield that occur when maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis; the statistical method includes the specification of both size and position tolerances on a feature. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled pin and hole. A comparison is made between the effects of choosing the optional material condition MMC and not choosing it with the tolerances that determine the allowable variations in position.

An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

1993 ◽  
Author(s):  
B. K. Kannan ◽  
Steven N. Kramer
Keyword(s):  
Lagrange Multiplier ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Continuous Optimization ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Augmented Lagrange Multiplier

Abstract An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

Mechanical Design for Accuracy of Linkage Servo Press for Near-Net Shape Forming

2018 ◽  
Author(s):  
Jing Tao ◽  
Huanan Qian ◽  
Suiran Yu
Keyword(s):  
Mechanical Design ◽  
Structure Design ◽  
Tolerance Allocation ◽  
Component Level ◽  
Eccentric Load ◽  
Servo Press ◽  
Near Net Shape ◽  
Net Shape Forming ◽  
Heavy Loads

The accuracy of machine is important to achieving highly accurate shapes. This paper is focused on mechanical design of highly accurate mechanical linkage servo press applicable to (near-)net shape forming. The effects of geometric errors, deformations under heavy loads and ram tilting are analyzed. A top-down design for accuracy approach is proposed: First, accuracy model for identification of inaccuracy-causing factors and their interlinking relations is developed. Then, based on this model, top accuracy index are decomposed and translated into structure design specifications at component level. Both analytic and simulation methods are employed for design for accuracy in aspects of dimensional and geometric tolerance allocation, stiffness synthesis and anti-eccentric load capability. A case study of mechanical design for accuracy of a six-linkage mechanical servo press is also presented to demonstrate and test the proposed design approaches.

Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models

2014 ◽  
Author(s):  
Erasmo Carrera ◽  
Enrico Zappino
Keyword(s):  
Mechanical Design ◽  
Computational Cost ◽  
Advanced Materials ◽  
Complex Structures ◽  
Displacement Fields ◽  
One Dimensional ◽  
Classical Models ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Dimensional Models

One-dimensional models are widely used in mechanical design. Classical models, Euler-Bernoulli or Timoshenko, ensure a low computational cost but are limited by their assumptions, many refined models were proposed to overcome these limitations and extend one-dimensional models at the analysis of complex geometries or advanced materials. In this work a new approach is proposed to couple different kinematic models. A new finite element is introduced in order to connect one-dimensional elements with different displacement fields. The model is derived in the frameworks of the Carrera Unified Formulation (CUF), therefore the formulation can be written in terms of fundamental nuclei. The results show that the use variable kinematic models allows the computational costs to be reduced without reduce the accuracy, moreover, refined-one dimensional models can be used in the analysis of complex structures.

Process Capability Based Tolerance Allocation in Pneumatic Percussive Riveting

2020 ◽  
Author(s):  
Hua Wang ◽  
Jialei Zhang ◽  
Junyang Yu
Keyword(s):  
High Efficiency ◽  
Load Transfer ◽  
Process Capability ◽  
Tolerance Analysis ◽  
Tolerance Allocation ◽  
Hole Drilling ◽  
Case Method ◽  
Pneumatic Hammer ◽  
Worst Case ◽  
Mating Conditions

Abstract Pneumatic percussive riveting is an important way to join the sheet metals. In order to ensure the load transfer and the fatigue performance of riveted joint, the interference of the rivet/hole is strictly specified. The interference of the rivet/hole is highly correlated with the process capability of the pneumatic hammer and the diameter of the pre-hole. It is a critical step to choose the appropriate pneumatic hammer to ensure the interference requirements. Energy per blow of the pneumatic hammer is a proclaimed parameter from the riveting hammer manufacturer. It is difficult for the designer to choose the riveting hammer in practical riveting scheme based on energy per blow. Tolerance analysis is an efficient way to model the manufacturing variation and implement process control. This paper presents the tolerance allocation of the pneumatic percussive riveting based on the process capability of the pneumatic hammer. In order to obtain the designed interferences of the rivet/hole, a tolerance chain is built with the process capability of the pneumatic hammer, the diameter of the pre-hole and the diameter of the rivet shank. The process capability of the pneumatic hammer is represented with the interferences of the rivet/hole after riveting. It is an intuitive parameter for the designer to choose the riveting hammer in practical riveting scheme. The process capability of the pneumatic hammer is obtained from the designed riveting experiments with the pneumatic percussive riveting platform. The diameter of the pre-hole affects the interference of the rivet/hole also. The tolerance for manual hole-drilling should be determined to assure the interference requirements and high drilling operation efficiency simultaneously. The variation of the pre-hole is obtained from the manual drilling experiments and diameter measurements. Different hole-drilling results in different mating conditions between the pre-hole and the rivet. The fit conditions of different pre-holes are modeled and the final interferences after riveting are analyzed. Worst case method and statistical analysis method are two common methods for tolerance analysis. For the manual hole-drilling and the pneumatic percussive riveting, worst case method is employed to analyze the constructed tolerance chain in order to accomplish the interferences of the rivet/hole. The different analyzed dimensions, rivet-hole clearances and pre-hole drilling variation, are investigated respectively. The reported work enhances the understanding of the tolerance allocation for the pneumatic percussive riveting. The interference based process capability of the pneumatic hammer provides good reference for pneumatic hammer choosing in riveting scheme. The reported tolerance chain of the interference could be used for the tolerance determination of manual hole-drilling with good quality and high efficiency.

Application of Variational Geometry to the Analysis of Mechanical Tolerances

1989 ◽  
Author(s):  
P. M. Martino ◽  
G. A. Gabriele
Keyword(s):  
Mechanical Design ◽  
Worst Case Analysis ◽  
Prototype System ◽  
Tolerance Design ◽  
Worst Case ◽  
Geometric Tolerances ◽  
Solid Models ◽  
The Cost ◽  
Selection Of

Abstract The proper selection of tolerances is an important part of mechanical design that can have a significant impact on the cost and quality of the final product. Yet, despite their importance, current techniques for tolerance design are rather primitive and often based on experience and trial and error. Better tolerance design methods have been proposed but are seldom used because of the difficulty in formulating the necessary design equations for practical problems. In this paper we propose a technique for the automatic formulation of the design equations, or design functions, which is based on the use of solid models and variational geometry. A prototype system has been developed which can model conventional and statistical tolernaces, and a limited set of geometric tolerances. The prototype system is limited to the modeling of single parts, but can perform both a worst case analysis and a statistical analysis. Results on several simple parts with known characteristics are presented which demonstrate the accuracy of the system and the types of analysis it can perform. The paper concludes with a discussion of extensions to the prototype system to a broader range of geometry and the handling of assemblies.

THE PRICE OF NASH EQUILIBRIA IN MULTICAST TRANSMISSION GAMES

2010 ◽  
Vol 11 (03n04) ◽  
pp. 97-120 ◽  
Author(s):  
VITTORIO BILÒ
Keyword(s):  
Nash Equilibrium ◽  
Cost Sharing ◽  
Price Of Anarchy ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Price Of Stability ◽  
Common Source ◽  
Cost Share ◽  
Worst Case ◽  
The Cost

We consider the problem of sharing the cost of multicast transmissions in non-cooperative undirected networks where a set of receivers R wants to be connected to a common source s. The set of choices available to each receiver r ∈ R is represented by the set of all (s, r)-paths in the network. Given the choices performed by all the receivers, a public known cost sharing method determines the cost share to be charged to each of them. Receivers are selfish agents aiming to obtain the transmission at the minimum cost share and their interactions create a non-cooperative game. Devising cost sharing methods yielding games whose price of anarchy (price of stability), defined as the worst-case (best-case) ratio between the cost of a Nash equilibrium and that of an optimal solution, is not too high is thus of fundamental importance in non-cooperative network design. Moreover, since cost sharing games naturally arise in socio-economical contests, it is convenient for a cost sharing method to meet some constraining properties. In this paper, we first define several such properties and analyze their impact on the prices of anarchy and stability. We also reconsider all the methods known so far by classifying them according to which properties they satisfy and giving the first non-trivial lower bounds on their price of stability. Finally, we propose a new method, namely the free-riders method, which admits a polynomial time algorithm for computing a pure Nash equilibrium whose cost is at most twice the optimal one. Some of the ideas characterizing our approach have been independently proposed in Ref. 10.

scholarly journals Stochastic Phenomena in One-Dimensional Rulkov Model of Neuronal Dynamics

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Irina Bashkirtseva
Keyword(s):  
Period Doubling ◽  
Neuronal Dynamics ◽  
One Dimensional ◽  
Sensitivity Functions ◽  
Stochastic Sensitivity ◽  
Random Disturbances ◽  
Transient Zone ◽  
Stochastic Regimes ◽  
Stochastic Phenomena ◽  
Stochastic Bifurcations

We study the nonlinear Rulkov map-based neuron model forced by random disturbances. For this model, an overview of the variety of stochastic regimes is given. For the parametric analysis of these regimes, the stochastic sensitivity functions technique is used. In a period-doubling zone, we analyze backward stochastic bifurcations modelling changes of modality of noisy neuron spiking. Noise-induced transitions in a zone of bistability are considered. It is shown how such random transitions can generate a new neuronal regime of the stochastic bursting and transfer the system from order to chaos. A transient zone of values of noise intensity corresponding to the onset of noise-induced bursting and chaotization is localized by the stochastic sensitivity functions technique.

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