Kinematic error analysis and tolerance allocation of cycloidal gear reducers

Lin, Ken-Shin; Chan, Kuei-Yuan; Lee, Jyh‐Jone

doi:10.1016/j.mechmachtheory.2017.12.028

Cited by 78 publications

(53 citation statements)

References 23 publications

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“…Some researchers have proposed numerical optimization approaches with several objective functions (convex hull volume, Euclidean distance, weighted unsigned distance, weighted signed distance) [23], experimental and theoretical investigations using the SDT and clearance domain (gap hull) models [24], the Fast Fourier Transform and the Conjugate Gradient Method in case of elastic contact of rough surfaces [25,26], development of an optimization algorithm and geometric interference relationships [27] and some other methods in [28][29][30]. Moreover, some others researchers proposed to study the floating contacts by means of a regularized closure function and a constrained optimization problem [31], Virtual Work Principle and a contact model of joints to determine the displacements at each node and relative displacements/rotations of the kinematic pairs [32], constrained registration techniques and difference surface in a sequential positioning problem [33], Tooth Contact Analysis algorithm [2,34], the Gap Hull estimation [35]. Among all the previous methods, the Signed Distance Approach [17,18,20,23] combined with an optimization technique is selected to characterize the fixed and sliding contacts assembly in the mechanical system.…”

Section: Mathematical Formulation Of the Assembly Feasibility Of The mentioning

confidence: 99%

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

Goka

Beaurepaire

Homri

et al. 2019

Mechanism and Machine Theory

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Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis. Mechanism and Machine Theory, Elsevier, 2019, 139, pp. AbstractThe statistical tolerance analysis has become a key element used in the design stage to reduce the manufacturing cost, the rejection rate and to have high quality products. One of the frequently used methods is the Monte Carlo simulation, employed to compute the non-conformity rate due to its efficiency in handling the tolerance analysis of over-constrained mechanical systems. However, this simulation technique requires excessive numerical efforts. The goal of this paper is to improve this method by proposing a probabilistic model of gaps in fixed and sliding contacts and involved in the tolerance analysis of an assembly. The probabilistic model is carried out on the clearance components of the sliding and fixed contacts for their assembly feasibility considering all the imperfections on the surfaces. The kernel density estimation method is used to deal with the probabilistic model. The proposed method is applied to an over-constrained mechanical system and compared to the classical method regarding their computation time. 1.

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Section: Mathematical Formulation Of the Assembly Feasibility Of The mentioning

confidence: 99%

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

Goka

Beaurepaire

Homri

et al. 2019

Mechanism and Machine Theory

View full text Add to dashboard Cite

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“…Tolerance analysis applied to transmissions has been considered by Armillotta [18] and Lin et al [19]. An analogy from static analysis to tolerance analysis (analytic model) have been presented by [18], in which external forces correspond to assembly-level errors and calculated forces (reactions, internal forces which guarantee equilibrium) correspond to the sensitivity of the gearing part tolerances on the total error.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…An analogy from static analysis to tolerance analysis (analytic model) have been presented by [18], in which external forces correspond to assembly-level errors and calculated forces (reactions, internal forces which guarantee equilibrium) correspond to the sensitivity of the gearing part tolerances on the total error. Kinematic error and tolerance analysis of cycloidal transmissions were performed by Monte Carlo simulations in [19], by mapping geometric and manufacturing parameters to the transmission performance through gearing theory. Resulting kinematic error distributions allows optimizing the tolerance of the geometric parameters to minimize manufacturing costs with reliable gearing performance.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

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Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Tinoco

Durango

2019

Mathematical Problems in Engineering

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The kinematic performance of mechanisms is affected by different uncertainty sources involved in the manufacturing and assembling cycle; among these are the geometric variations. It is known that the effects of these variations produce position errors which are not usually included in the design process. With this objective, a complementary method for the tolerance analysis of planar mechanisms that incorporate geometric variations is presented in this paper. The approach is based on Direct Linearization Method (DLM) that does not consider all the kinematically admissible solutions. DLM naturally minimizes a residual functional ; however it is possible to maximize the residual by means of a proposed complementary method called H-Based Residual Method (RMH). From the proposed methodology, local and global error domains can be defined to predict the maximum and minimum position errors caused by the input variations. DLM and RMH were applied in a four-bar mechanism with dimensional and angular variations to estimate positioning errors. The results show intervals where output positions were invariant with respect to angular variations of the crank. These computations were performed through a distance ratio established with the output deviations determined with nominal angular variations. Furthermore, domain errors were predicted for a set of positions generated by a multivariate normal random algorithm with 1000 combinations of input variations (links lengths). These domains delimited all solutions created in each position stage. It means that by applying the proposed methodology it is possible to estimate the geometric errors of any combination of variations.

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“…The study of kinematic accuracy and the estimation of the effect of manufacturing errors on the load-carrying capacity of transmissions were performed [10][11][12]. In order to improve their kinematic and dynamic characteristics, new designs and computer models were developed based on the analysis of patents and literature in the subject area [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Geometrical Parameters and Estimation of Kinematic Accuracy of Resource Effective Planetary Transmission

Kapitonov¹

2018

Proceedings of the International Conference "Aviamechanical Engineering and Transport" (AVENT 2018)

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The purpose of the research is to study how the shape of a geometric profile of the periodic raceway affects kinematic accuracy and smooth operation of the resourceeffective planetary radial plunger transmission with intermediate rolling bodies. The shape and computer model for a geometric profile of the periodic raceway of the planetary radial plunger transmission are proposed. The profile under study is constructed from the equation of a periodic curve in the form of a circle with an offset center. The transmission with the proposed profile is characterized by increased kinematic accuracy and smoothness of operation. A comparative analysis of kinematic errors of the planetary radial plunger transmission was performed for two profiles of raceways having different geometric shapes, and diagrams were constructed. Kinematic parameters of the transmission with the periodic raceway profile in the form of an eccentrically offset circle were improved. It was established that the use of the planetary radial plunger transmission with the periodic raceway profile constructed from the equation of a periodic curve in the form of a circle with an offset center significantly improves (three times or more) such transmission characteristics as kinematic accuracy and operation smoothness compared to the geometric profile in the form of arcs of circles. Keywords-planetary transmission, periodic raceway, kinematic accuracyThe following equations can be used to determine kinematic characteristics of the planetary transmission with the raceway which is a circle with a center offset by the value A.

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Kinematic error analysis and tolerance allocation of cycloidal gear reducers

Cited by 78 publications

References 23 publications

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

Probabilistic-based approach using Kernel Density Estimation for gap modeling in a statistical tolerance analysis

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

Optimization of Geometrical Parameters and Estimation of Kinematic Accuracy of Resource Effective Planetary Transmission

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