Tolerance Synthesis Research Articles

A New Approach for Synthesis of 3D Tolerances with Consideration of Flatness Defects in Mechanical Assembly Using Jacobian Torsor Model

A New Approach for Synthesis of 3D Tolerances with Consideration of Flatness Defects in Mechanical Assembly Using Jacobian Torsor Model

Jacobian Torsor Model for Statistical Synthesis of Three-Dimensional Tolerances in Mechanical Assemblies

Jacobian Torsor Model for Statistical Synthesis of Three-Dimensional Tolerances in Mechanical Assemblies

Unified approach for tolerance analysis, synthesis, and compensator selection.

Tolerancing is a necessary task for practical designs. The system Jacobian is utilized here for the three sub-tasks of tolerancing. The first is tolerance analysis, which is evaluation of the perturbed system. Second is tolerance allocation, also known as tolerance budgeting and more widely known as error budgeting. The automatic allocation of tolerances is tolerance synthesis. The algorithm described accomplishes this by fitting an orthotope inside an ellipsoid. Third is compensator selection. Metrics are presented that correlate with the looseness of the allocated tolerances and hence with the effectiveness of the compensator set, thus enabling identification of the most optimum combination of compensators.

Serum Amino Acid Profile Changes After Repetitive Breath-Hold Dives: A Preliminary Study

BackgroundThe aim of this work was to investigate the serum amino acid (AA) changes after a breath-hold diving (BH-diving) training session under several aspects including energy need, fatigue tolerance, nitric oxide (NO) production, antioxidant synthesis and hypoxia adaptation. Twelve trained BH-divers were investigated during an open sea training session and sampled for blood 30 min before the training session, 30 min and 4 h after the training session. Serum samples were assayed for AA changes related to energy request (alanine, histidine, isoleucine, leucine, lysine, methionine, proline threonine, valine), fatigue tolerance (ornithine, phenylalanine, tyrosine), nitric oxide production (citrulline), antioxidant synthesis (cystine, glutamate, glycine) and hypoxia adaptation (serine, taurine).Main resultsConcerning the AA used as an energy support during physical effort, we found statistically significant decreases for all the investigated AA at T1 and a gradual return to the basal value at T2 even if alanine, proline and theonine still showed a slight significant reduction at this time. Also, the changes related to the AA involved in tolerance to physical effort showed a statistically significant decrease only at T1 respect to pre-diving value and a returned to normal value at T2. Citrulline, involved in NO production, showed a clear significant reduction both at T1 and T2. Concerning AA involved in endogenous antioxidant synthesis, the behaviour of the three AA investigated is different: we found a statistically significant increase in cystine both at T1 and T2, while glycine showed a statistically significant reduction (T1 and T2). Glutamate did not show any statistical difference. Finally, we found a statistically significant decrease in the AA investigated in other hypoxia conditions serine and taurine (T1 and T2).ConclusionsOur data seem to indicate that the energetic metabolic request is in large part supported by AA used as substrate for fuel metabolism and that also fatigue tolerance, NO production and antioxidant synthesis are supported by AA. Finally, there are interesting data related to the hypoxia stimulus that indirectly may confirm that the muscle apparatus works under strong exposure conditions notwithstanding the very short/low intensity of exercise, due to the intermittent hypoxia caused by repetitive diving.

T-Maps-Based Tolerance Analysis of Composites Assembly Involving Compensation Strategies

Abstract Clamping force and shimming are two important compensation processes in the composite assembly. Their effects on variation propagation should be investigated in tolerance analysis. The paper presents a tolerance analysis method for composites assembly based on the T-Maps method, mainly concerning the anisotropic variations accumulation and propagation where there is the clamping force modification and the shimming. Variations of the composite parts in different directions are represented by the T-Maps. Since the different axial deviations are represented in the same Euclidean point-space, the T-Maps-based tolerance analysis of the composite parts assembly provides more accurate and reliable results. Compensation processes, the clamping force, and the shimming, on assembly tolerance synthesis of the composite parts, are analyzed clearly in the T-Map. This procedure is found to be effective for the anisotropy-oriented assembly tolerance analysis, especially concerning about effect of the clamping force and the shimming on variations accumulation and propagation. The assembly of an aircraft composite elevator is considered to demonstrate the effectiveness of the T-Maps-based method. The procedures outlined in the paper are quite general and can be used for assembly tolerance analysis of anisotropic parts.

Three-Dimensional Synthesis of Manufacturing Tolerances Based on Analysis Using the Ascending Approach

The present paper develops a new approach for manufacturing tolerances synthesis to allow the distribution of these tolerances over the different phases concerned in machining processes using relationships written in the tolerance analysis phase that have been well developed in our previous works. The novelty of the proposed approach is that the treatment of non-conventional surfaces does not pose a particular problem, since the toleranced surface is discretized. Thus, it is possible to study the feasibility of a single critical requirement as an example. During the present approach, we only look for variables that influence the requirements and the others are noted F (Free). These variables can be perfectly identified on the machine, which can be applied for known and unknown machining fixtures; this can be the base for proposing a normalized ISO specification used in the different machining phases of a mechanical part. The synthesis of machining tolerances takes place in three steps: (1) Analysis of the relationship’s terms, which include the influence of three main defects; the deviation on the machined surface, defects in the machining set-up, and the influence of positioning dispersions; then (2) optimization of machining tolerance through a precise evaluation of these effects; and finally (3) the optimization of the precision of the workpiece fixture, which will give the dimensioning of the machining assembly for the tooling and will allow the machining assembly to be qualified. The approach used proved its efficiency in the end by presenting the optimal machining process drawing that explains the ordered phases needed to process the workpiece object of the case study.

On Robust Mechanical Design of a PAR2 Delta-Like Parallel Kinematic Manipulator

Abstract Sensitivity analysis of manipulators aims at studying the influence of variations in its own geometric parameters on its performance. This information is useful for evaluating the position error of the end-effector as well as for the synthesis of tolerances. Indeed, the synthesis of tolerances is a very important issue in the design and manufacturing of robot manipulators. In this paper, a sequential procedure for modeling, dimensioning, and tolerance synthesis of the Parallel Kinematic Manipulator (PKM) PAR2 is proposed. For optimal dimensional design, an approach based on the optimization of the workspace is proposed, taking into account several constraints, followed by a numerical matrix analysis-based deterministic method for sensitivity analysis whose performance is studied in terms of accuracy. To calculate the optimal dimensional tolerances, a new tolerance synthesis method is used. The effect of geometric tolerance on accuracy is analyzed.

Tolerance synthesis for lost motion requirement of planetary gear train based on a mechanism model

In this paper, an original equivalent mechanism with parallel linkages is proposed for lost motion behavior analysis and tolerance synthesis of planetary gear train (PGT). The parallel linkages are equivalent in kinematics of PGT to depict the multiple branches of sun-planet-ring gears with a driving link/sun gear and an output platform/carrier, a slider-block with two strokes in the circle curve guide rail of the platform is introduced in each linkage to intuitively express the lag rotation of output platform driven by the parallel linkages under error condition, and the errors are described by the deviations of link lengths. With the mechanism model, the lost motion expression of PGT is explicitly derived and then the tolerance synthesis method is formulated to allocate the optimum tolerances for satisfying the lost motion requirement with the minimum manufacturing cost. The lost motion behavior of PGT was simulated and the tolerances of errors were allocated involving tooth thickness reduction, planet position errors and gear eccentricity errors. The lost motion tests of two PGTs with the allocated tolerances were conducted. The results well agree with the simulations’, which validated the effectiveness of the developed tolerance synthesis method by the proposed mechanism model.

Speeding up Statistical Tolerance Analysis to Real Time

Statistical tolerance analysis based on Monte Carlo simulation can be applied to obtain a cost-optimized tolerance specification that satisfies both the cost and quality requirements associated with manufacturing. However, this process requires time-consuming computations. We found that an implementation that uses the graphics processing unit (GPU) for vector-chain-based statistical tolerance analysis scales better with increasing sample size than a similar implementation on the central processing unit (CPU). Furthermore, we identified a significant potential for reducing runtime by using array vectorization with NumPy, the proper selection of row- and column- major order, and the use of single precision floating-point numbers for the GPU implementation. In conclusion, we present open source statistical tolerance analysis and statistical tolerance synthesis approaches with Python that can be used to improve existing workflows to real time on regular desktop computers.

Assignment of dimensional accuracy parameters of parts during assembly of aircraft repair engines

The article considers the existing models and methods of analysis and synthesis of geometric tolerances of products with assembly dimensional chains. There proposed a method to define the rational tolerances for the linear dimensions of parts during assembly of aircraft repair engines. The developed methodology is based on the use of computer simulation technology for assembling the assemblies with actual geometry, and a model for calculating the labor input and cost of parts manufacturing based on the assigned tolerances. The main advantages of the technique are considered by the example of assigning rational tolerances to the parts of the repair rotor of a high-pressure compressor, which have the greatest influence on the functional characteristics of the aircraft engine. The results of the relationship between the dimensional accuracy parameters of parts and assembly parameters are presented, and the dependence of the cost of refinement or manufacturing of the part on the assigned tolerance is obtained.

Tolerance allocation: A reliability based optimisation approach

Tolerance analysis and allocation are two activities of great importance in product development. The mathematical formulation of the latter concerns the establishment and solution of a constraint optimisation problem. In this work, making one step forward, a probabilistic framework is developed and the tolerance synthesis problem is reformulated to a reliability based optimisation one introducing probabilistic constraints. Advanced reliability methods are merged with professional computer aided tolerance tools to estimate the distribution of the assembly key characteristic. Cost-tolerance relationships based on the variability of the manufacturing resources rather than on empirical formulas were adopted in a process based cost modelling methodology. The suggested framework is compared to the classical tolerance allocation approaches of the worst case scenario and the root sum square. It was found that despite the increased computational cost, further relaxation in the design tolerance can be achieved using reliability based optimisation techniques driving down the product cost.

Assembly Tolerance Design Based on Skin Model Shapes Considering Processing Feature Degradation

To increase the reliability and accuracy of tolerance design, more and more research works are considering not only orientation and position deviations; they are also forming errors in tolerance modeling. As a direct cause of form errors in industrial mass production, the processing features of the machining system degrade over time. Under the Industry 4.0 paradigm, an assembly tolerance design method based on Skin Model Shape is proposed to take the effect of degrading processing features into consideration. A continuous-time multi-dimensional Markov process is trained through maximum likelihood estimation based on the nodal sampling point set on the machined surface. Degradation of the machined surface is modeled based on the joint probability distribution of nodal displacements. Assembly force constraints and assembly entity constraints are applied to spatial assembly simulations. Tolerance synthesis takes the manufacturing cost and assembling probability as design objectives. A design example of the rotary feed component in a five-axis machine tool is proposed for explanation and verification.

Design of experiment-based tolerance synthesis for a lock-or-release mechanism of the Chinese Space Station Microgravity Platform

Abstract. This paper deals with the tolerance synthesis with the application for a typical Lock-or-Release (L/R) mechanism, used for Chinese Space Station Microgravity Platform (SSMP). The L/R mechanism is utilized to lock the SSMP maintaining space position during the launching stage, and to release the SSMP automatically during on-orbit stage. Manufacturing accuracy of L/R mechanism presents direct influence on its kinematic and dynamic behaviors. Tolerance synthesis can provide a reasonable assignment of tolerance, satisfying the critical assembly criteria while lowering manufacturing complexity. In this paper, based on the number-theory method (NTM), a Halton-set based Monte Carlo (MC) simulation is introduced in the accuracy model of the L/R mechanism, aiming at improving analytical precision and efficiency for tolerance synthesis. A design of experiment (DOE) based tolerance synthesis approach is proposed. With initial tolerance determined by capacity, sensitivities of different tolerance factors are generated through the first DOE stage, and then applied to determine feasible tolerance levels. The final tolerance assignments, like points scatted in high-dimensioned space with inherent uniformity, are then produced through uniform DOE in the second stage. Result shows that the majority of feasible tolerance assignments generated have more relaxed tolerance, which can facilitate the manufacturing process.

A multiple objective framework for optimal asymmetric tolerance synthesis of mechanical assemblies with degrading components

In order to produce the mechanical assemblies with the high quality, the finest functionality, and the low cost, the optimal tolerance synthesis can be a useful tool in the design stage. The degradation of components due to some operational or environmental factors (such as the thermal cycling, the mechanical deformation, and the wear) can lead to dimensional variations in components and fall-off of the functionality of the product. In addition, different manners of the degradation on the internal and external dimensions can cause asymmetric deviations in the dimensions. On the other hand, the effect of degradation on the product quality has not been considered in most researches. In this paper, a new multi-objective framework is proposed for optimal asymmetric tolerance synthesis of mechanical assemblies with degrading components. In this method, the optimal tolerances are allocated based on ensuring the fulfillment of the product’s functional requirements, maximizing the product quality, and minimizing the total cost over the lifetime of the product. To incorporate the degradation effect into the loss function concept, the present worth of the expected quality loss (PWL) is formulated in terms of asymmetric tolerances. Accordingly, the functional process capability and manufacturing cost are developed based on asymmetric tolerances and the degradation effects. In order to extract Pareto fronts of optimal solutions, the elitist Non-dominated Sorting Genetic Algorithm II as an evolutionary generating methodology is utilized. In solving multi-criteria tolerance synthesis problem by a generating method, selecting the best tolerances from the obtained optimal Pareto solutions is a significant challenge. In this paper, to find the best asymmetric tolerances from Pareto solutions, a combined Shannon’s entropy-based TOPSIS algorithm is used. Finally, a bi-directional non-back drivable roller clutch assembly as an industrial case study is considered to illustrate the efficiency of the proposed method, and the obtained results are compared and discussed for verification.

Sensitivity analysis of the equal angle divider mechanism kinematics with the synthesis of the joint gap tolerances

ABSTRACTTolerance analysis of mechanical components and assemblies is a key element in the industry for improving product quality and reducing overall cost. This paper is an attempt to propose a methodology to formulate and compute the kinematic assembly variations with respect to the critical dimensions (joint clearances) by calculating the homogeneous matrix of loops with considering the transforming and rotation matrix, the tolerance sensitivities, the geometrical responses to assembly variations, and the tolerance sensitivity of mechanism for clearance in the joints in different motion phases. The analysis is performed by the systematic methodology which is extended for kinematic sensitivity and positional error analysis with published results.

Tolerance synthesis of fastened metal-composite joints based on probabilistic and worst-case approaches

Variabilities in geometrical and material properties occur systematically after manufacturing and joining operations on different parts of an assembly. The behaviour and structural performance of composite/composite or composite/metal fastened joints are particularly sensitive to some of these variabilities. Controlling the effect of variabilities by tolerancing uncertain parameters is therefore crucial to avoid the failure of the structure. However, performing a variability study is generally costly because a large number of configurations need to be evaluated, especially when the behaviour model of the system is a numerical one.This paper presents an approach for tolerance synthesis of uncertain parameters in fastened metal-composite joints. The low time-cost of the approach is ensured by using a reduced finite element model of the joints and a strategy to reduce the number of calculations. Both probabilistic and worst-case approaches for the propagation of uncertainties can be applied through the proposed tolerancing synthesis. An allowable tolerance value for an uncertain parameter can then be easily calculated by identifying an analytical law which links tolerance to a structural performance criterion. The robustness of the proposed approach is illustrated by its application to a 4-bolt metal-composite single-lap joint where several sources of variability are introduced (i.e. hole-location error, pin/hole clearance, fastener preload).

Tolerance synthesis of 2R serial robot manipulator

tolerance synthesis of 2R serial robot manipulator

A Novel Tolerance Design Approach to Manufacturing and Quality Loss Cost Optimization in Mechanical Assemblies

Tolerance design has a profound impact on the manufacturability, ease of assembly, performance, quality and cost of mechanical components. However, assigning appropriate tolerances is still far from being a trivial engineering task. The optimization of dimensional and geometric tolerances for components that control functional dimensions in mechanical assemblies is receiving continuous attention from researchers. In this paper a novel tolerance design approach is introduced. The basic concept of the proposed approach is the transformation of an unconstrained optimization problem of multiple decision variables to a constrained optimization problem of a single variable in order to improve the convexity of the set of feasible solutions. Through the development of a Quasi-Newton algorithm, our objective is the optimization of both the manufacturing cost of each component and the quality loss cost of the mechanical assembly. A step-by-step mathematical formulation of the approach is presented by using the widely referenced example of the overrunning clutch assembly. The experimental results obtained for this application example are directly compared with alternative tolerance synthesis techniques that are found in technical literature, illustrating that the proposed approach is reasonable and effective.

Method to measure the position offset of multiple light spots in a distributed aperture laser angle measurement system.

In this paper, an accurate measurement method of multiple spots' position offsets on a four-quadrant detector is proposed for a distributed aperture laser angle measurement system (DALAMS). The theoretical model is put forward, as well as the corresponding calculation method. This method includes two steps. First, as the initial estimation, integral approximation is applied to fit the distributed spots' offset function; second, the Boltzmann function is employed to compensate for the estimation error to improve detection accuracy. The simulation results attest to the correctness and effectiveness of the proposed method, and tolerance synthesis analysis of DALAMS is conducted to determine the maximum uncertainties of manufacturing and installation. The maximum angle error is less than 0.08° in the prototype distributed measurement system, which shows the stability and robustness for prospective applications.

A bootstrap method for uncertainty estimation in quality correlation algorithm for risk based tolerance synthesis

A risk based tolerance synthesis approach is based on ISO9001:2015 quality standard’s risk based thinking. It analyses in-process data to discover correlations among regions of input data scatter and desired or undesired process outputs. Recently, Ransing, Batbooti, Giannetti, and Ransing (2016) proposed a quality correlation algorithm (QCA) for risk based tolerance synthesis. The quality correlation algorithm is based on the principal component analysis (PCA) and a co-linearity index concept (Ransing, Giannetti, Ransing, & James, 2013). The uncertainty in QCA results on mixed data sets is quantified and analysed in this paper.The uncertainty is quantified using a bootstrap sampling method with bias-corrected and accelerated confidence intervals. The co-linearity indices use the length and cosine angles of loading vectors in a p-dimensional space. The uncertainty for all p-loading vectors is shown in a single co-linearity index plot and is used to quantify the uncertainty in predicting optimal tolerance limits. The effects of re-sampling distributions are analysed. The QCA tolerance limits are revised after estimating the uncertainty in limits via bootstrap sampling. The proposed approach has been demonstrated by analysing in-process data from a previously published case study.