A new approach to tolerance analysis based on tracking local coordinate systems

Zhai, Xiaochen; Du, Qiang; Wang, Wenxi; Qi, Wen; Baoshan, Liu; Zhu, Dongwen

doi:10.1299/jamdsm.2017jamdsm0021

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…For shaft-hole fit (Figure 1), the cylinder tolerance zone is acquired by expressing clearance value at the axis, so the variation of shaft in the hole is equivalent to the variation of the axis in the cylinder tolerance zone in Figure 2. During tolerance analysis, the error transformation matrix D i reflects variation of TF [18]. D i is gained from homogeneous transform matrix (HTM) based on DOF.…”

Section: Error Transformation Matrix Of Axis Tfmentioning

confidence: 99%

“…The mapping relationship between the area coordinate system and Cartesian coordinate system was further established for each TF on the dimension chain. A tolerance analysis model based on tracking local coordinate systems [18], as proposed previously, was combined to obtain analytic expression of pose decoupling of the axis TF as expressed by the area coordinate system. This method not only accurately obtained the ultimate error of the target feature through permutation and combination of ultimate area coordinate values, with a greatly reduced calculated quantity when compared with the T-Map method, but also obtained the sole deviation value of TF on arbitrary DOF within the tolerance domain by changing the corresponding area coordinate value.…”

Section: Introductionmentioning

confidence: 99%

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Study of the Ultimate Error of the Axis Tolerance Feature and Its Pose Decoupling Based on an Area Coordinate System

Zhai

2018

Applied Sciences

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Manufacturing error and assembly error should be taken into consideration during evaluation and analysis of accurate product performance in the design phase. Traditional tolerance analysis methods establish error propagation model based on dimension chains with tolerance values being regarded as error boundaries, and obtain the limit of target feature error through optimization methods or conducting statistical analysis with the tolerance domain being the boundary. As deviations of the tolerance feature (TF) on degrees of freedom (DOF) have coupling relations, accurate deviations on all DOF may not be obtained, even though these deviations constitute the basis for product performance analysis. Therefore, taking the widely used shaft-hole fit as an example, a pose decoupling model of the axis TF was proposed based on an area coordinate system. This model realized decoupling analysis of any pose of the axis TF within the tolerance domain. As proposed by the authors, by combining a tolerance analysis model based on tracking local coordinate systems, ultimate pose analysis of the closed-loop system, namely the target feature, as well as statistical analysis could be further implemented. This method contributed to analysis of true product performance with arbitrary error in the product design phase from the angle of tolerance, therefore, shortening the product research and development cycle. This method is demonstrated through applying it to a real-life example.

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Section: Error Transformation Matrix Of Axis Tfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study of the Ultimate Error of the Axis Tolerance Feature and Its Pose Decoupling Based on an Area Coordinate System

Zhai

2018

Applied Sciences

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“…During the assembly process of flexible parts, a three-dimensional (3D) precision analysis approach was used to obtain rigid and flexible displacements (Wang and Hua, 2011). Zhai et al (2017) proposed a thermal deformation model, coupling a small displacement torsor (SDT) to improve the accuracy of the tolerance analysis model. Mei et al (2019) simulated the compliant aeronautic part (ribs) deformation as warpage and torsion using FEM to perform assembly variation analysis.…”

Section: Introductionmentioning

confidence: 99%

Assembly variation analysis of the non-rigid assembly with a deformation gradient model

Ajani

2021

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Purpose This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process. Design/methodology/approach First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process. Findings Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored. Originality/value In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.

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“…Wang and Hua (2011) proposed a three-dimensional (3D) precision analysis method of rigid displacement and flexible displacement based on the flexible parts assembly process. Zhai et al (2017) improved a small displacement torsor method and incorporated thermal deformation into the tolerance analysis model. Yildiz (2013) integrated the statistical tolerance design with finite element analysis, and then used the multi-objective genetic algorithm to design tolerance, but it did not consider the deviation caused by the deviation accumulation in the assembly process.…”

Section: Introductionmentioning

confidence: 99%

3D tolerance modeling and geometric precision analysis of plane features for flexible parts

Sun

et al. 2018

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Purpose The traditional precision design only takes the influence of geometric tolerance of the parts and does not involve the load deformation in the assembly process. This paper aims to analyze the influence mechanism of flexible parts deformation on the geometric precision, and then to ensure the reliability and stability of the mechanical system. Design/methodology/approach Firstly, this paper adopts the N-GPS to analyze the influence mechanism of flexible parts deformation on the geometric precision and constructs a coupling 3D tolerance mathematical model of the geometric tolerance and the load deformation deviation based on the SDT theory, homogeneous coordinate transformation theory and surface authentication idea. Secondly, the least square method is used to fit the deformation surface of the mating surface under load so as to complete the conversion from the non-ideal element to the ideal element. Findings This paper takes the horizontal machining center as a case to obtain the deformation information of the mating surface under the self-weight load. The results show that the deformation deviation of the parts has the trend of transmission and accumulation under the load. The terminal deformation cumulative amount of the system is up to –0.0249 mm, which indicated that the influence of parts deformation on the mechanical system precision cannot be ignored. Originality/value This paper establishes a comprehensive 3D tolerance mathematical model, which comprehensively considers the effect of the dimensional tolerance, geometric tolerance and load deformation deviation. By this way, the assembly precision of mechanical system can be accurately predicted.

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A new approach to tolerance analysis based on tracking local coordinate systems

Cited by 3 publications

References 9 publications

Study of the Ultimate Error of the Axis Tolerance Feature and Its Pose Decoupling Based on an Area Coordinate System

Study of the Ultimate Error of the Axis Tolerance Feature and Its Pose Decoupling Based on an Area Coordinate System

Assembly variation analysis of the non-rigid assembly with a deformation gradient model

3D tolerance modeling and geometric precision analysis of plane features for flexible parts

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