Statistical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation

Bruyère, Jérôme; Dantan, Jean‐Yves; Bigot, Régis; Martin, Patrick

doi:10.1016/j.mechmachtheory.2006.11.003

Cited by 74 publications

(40 citation statements)

References 32 publications

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“…5. Tooth Contact Analysis (TCA) [4], [6], program computes a simulated transmission error then F' I and f' I are calculated. Secondly, the estimation of the probability distribution of the transmission error of a studied gear (Approach 2) is detailed in Figure 1 3'.…”

Section: Global Approachmentioning

confidence: 99%

Gear Metrology of Statistical Tolerancing by Numerical Simulation

Vincent¹,

Baudouin²,

Bruyère³

et al. 2009

Series on Advances in Mathematics for Applied Sciences

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Tolerance verification permits to check the product conformity and to verify assumptions made by the designer. For conformity assessment, the uncertainty associated with the values of the measurands must be known. In the ISO TS 17450 part 2, the notion of the uncertainty is generalized to the specification and the verification. The uncertainty is divided into correlation uncertainty, specification uncertainty and measurement uncertainty. Correlation uncertainty characterizes the fact that the intended functionality and the controlled characteristics may not be perfectly correlated. Therefore, we propose a new specified characteristics based on the statistical tolerancing approach which is directly in relationship with the design intent: the probability distribution of maximum range of the transmission error (the transmission error is the main source of vibratory and acoustic nuisances), and the evaluation of this characteristic based on 3D acquisition by Monte Carlo simulation and Tooth Contact Analysis. Moreover, the measurement uncertainty of the evaluation of this characteristic is estimated by Monte Carlo Simulation.

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Section: Global Approachmentioning

confidence: 99%

Gear Metrology of Statistical Tolerancing by Numerical Simulation

Vincent¹,

Baudouin²,

Bruyère³

et al. 2009

Series on Advances in Mathematics for Applied Sciences

Self Cite

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“…In the case of the GD&T standards, the profile deviations are the deviations normal to the transverse involute profiles, measured within the profile evaluation range L1 : F1, ff1, fH1, [4] … These profile characteristics can easily be measured but they are not adapted for tolerance analysis [6]. Therefore, we propose a set of flank form specifications like flank topography [4], [1] (Figure 3).…”

Section: "Profile or Form Tolerances"mentioning

confidence: 99%

“…• a mathematical representation of the geometrical specifications which are detailed in section 2, • a digital simulation tool based on Tooth Contact Analysis [9] which enables one to evaluate functional characteristics as kinematic error, position of contact point, , … (the result is similar to the tangential composite test [6], but the cost of a digital simulation is lower than the cost of an experimental simulation), • a tolerance analysis tool by Monte Carlo simulation, which computes the probability that the product can be assembled and will function (respect of requirements on the kinematic error, …) for given individual tolerances. The result of a statistical tolerance analysis [6] is a set of meshing simulations (Figure 7), the probability distribution of each functional characteristics like kinematic error (Figure 8 …”

Section: Gear Tolerance Analysismentioning

confidence: 99%

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Geometrical Specification Model for Gear - Expression, Metrology and Analysis

et al. 2007

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To ensure the gear precision, industries need a coherent model to express, to analyse and to check geometrical specifications. Most gear tolerance representations are directly driven by the convenience of dimensional metrology and not by the convenience of the set of activities of the tolerancing process. Therefore, to ensure the coherence of all tolerancing process activities, there is a necessity to develop a complete gear tolerance model which should: represent standard tolerance practices; be integrated in the Computer-Aided systems of design, manufacturing and metrology; be controlled by CMM; and support automated tolerance analysis. The proposed model extends capabilities of a vectorial dimensioning & tolerancing model in order to satisfy the four requirements. This model is based on GeoSpelling [1]. Its coherence is illustrated by two applications: gear tolerance analysis and gear tolerance verification by CMM. Keywords:Tolerancing Model, Functional Metrology, Gear INTRODUCTIONAs technology increases and performance requirements continually tighten, the cost and required precision of assemblies increase as well. There is a strong need for increased attention to tolerance design to enable highprecision assemblies to be manufactured at lower costs. Indeed, tolerance analysis is a key element in industry for improving product quality. Designers want tight tolerances to assure product performance; manufacturers prefer loose tolerances to reduce cost. There is a critical need for a quantitative design tool for specifying tolerances. Tolerance analysis brings the engineering design requirements and manufacturing capabilities together in a common model, where the effects of tolerance specifications on both design and manufacturing requirements can be evaluated quantitatively. The inherent imperfections of manufacturing processes (forging, cutting or grinding) involve geometrical variations and a degradation of product quality. The geometrical variations of each part must be limited by geometrical specifications (tolerances) to ensure a certain level of product quality, which is defined by the functional requirements. In the case of gears, their geometrical variations impact the transmission error, the tooth contact position, meshing interference, and gap. To ensure a quality level, designers limit these parameters by requirements. Tolerancing decisions can profoundly impact the quality and cost of gears. To assess the impact of tolerance on gear quality, designers need to simulate the influences of tolerance with respect to the functional requirements. To do so, they use AGMA [2] or ISO tables. These tables are a set of discrete associations between tolerances and meshing quality. They do not take into account all tolerances, and they focus on the pitch error and the misalignment. In the case of a forged gear or not classical gear like WILDHABER-NOVIKOV, designers can not use them to allocate the gear tolerances to

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“…As an important transmission device, the bevel gear transmission system contains a variety of failure modes. Although research literatures on bevel gear pair addressing design optimization and reliability can be found [3,19,21], there is still a need for more in-depth research on the joint failure modelling of the bevel gear transmission system.…”

Section: Introductionmentioning

confidence: 99%

The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction

Lü

Zhencai

2017

EiN

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Article citation info: IntroductionGenerally, multiple failure modes may occur in a gear transmission system. Due to the common-source of the input random variables of the system, such as the external loads, the geometric parameters and the material properties, the existing failure modes would be correlated to a certain extend [2,13]. From another perspective, it means that a failure may cause another failure occurs more rapidly, or just the opposite. Actually, whether the dependence of different failure modes is considered during the reliability design process may affect the system reliability estimation greatly. The commonly used independent assumption between failure modes usually leads to defects in gear HAO L, ZHENCAI Z. The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction. Eksploatacja i Niezawodnosc -Maintenance and Reliability 2017; 19 (2): 220-228, http://dx.doi.org/10.17531/ein.2017.2.9. Lu HAO Zhu ZHENCAIThe probabilisTic analysis and opTimal design of a bevel gear Transmission sysTem wiTh failure inTeracTion probabilisTyczna analiza i opTymalne projekTowanie układu przekładni sTożkowej z uwzględnieniem inTerakcji między uszkodzeniami

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Statistical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation

Cited by 74 publications

References 32 publications

Gear Metrology of Statistical Tolerancing by Numerical Simulation

Gear Metrology of Statistical Tolerancing by Numerical Simulation

Geometrical Specification Model for Gear - Expression, Metrology and Analysis

The probabilistic analysis and optimal design of a bevel gear transmission system with failure interaction

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