Open Access Open Access  Restricted Access Subscription or Fee Access

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


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/irea.v12i3.23557

Abstract


This research introduces a novel and practical approach to statistical tolerance synthesis in mechanical assemblies that adheres to ISO/ASME standards. The approach combines the unified Jacobian torsor model with Monte Carlo simulation and integrates flatness defects, dimensional, and geometric tolerances. The model is built using the Functional Requirements (FR) of an assembly and the starting tolerance values of the Functional Elements (FE) that make up the tolerance chain. While the model initially produces deterministic results, Monte Carlo simulation transforms it into a statistical model. Iterative simulations are conducted to evaluate the model. Random values for the torsor components corresponding to the functional elements are employed in each simulation until the predetermined maximum number of iterations is reached. Then, a set of values that represents the components of the Functional Requirement (FR) torsor is generated by repeatedly multiplying the model. A percentage that indicates the contribution of each Functional Element (FE) to the total Functional Requirement (FR) is calculated. This percentage aids in identifying the critical tolerance value that requires modification to ensure that the calculated functional requirement equals the desired functional requirement value. The significance of tolerances for flatness defects in ensuring the quality and precision of manufactured parts is emphasized in ISO/ASME standards. However, statistical studies on geometric tolerances often overlook these defects, leading to a decrease in tolerance analysis accuracy. The proposed approach employs additional torsors to model flatness defects and uses small displacement torsors to model tolerance zones. To demonstrate the application of this approach, an example of positioning and holding a milling part assembly is provided. This novel approach is expected to offer a practical and efficient solution for tolerance redesign, particularly in complex engineering systems where the performance of the entire system is reliant on the interplay between different components.
Copyright © 2024 Praise Worthy Prize - All rights reserved.

Keywords


Tolerances Synthesis; Jacobian Torsor Model; Flatness Defects; Monte Carlo Simulation; Functional Requirement

Full Text:

PDF


References


G. R. Cogorno, Geometric Dimensioning and Tolerancing for Mechanical Design, McGraw Hill, 2006.

S. Talebi, L. Koskela, P. Tzortzopoulos, et al., Deploying geometric dimensioning and tolerancing in construction, Buildings, vol. 10, no. 4, 2020.
https://doi.org/10.3390/buildings10040062

J. Xiao et al., Geometric Models and Standards for Additive Manufacturing : A Preliminary Survey, Virtual Concept Workshop, no. March 2016, pp. 1-4, 2017.

X. Zhang, H. Wang, S. Chen et al., A novel two-stage optimization approach to machining process selection using error equivalence method, J Manuf Syst, vol. 49, pp. 36-45, 2018.
https://doi.org/10.1016/j.jmsy.2018.07.009

D. Tsutsumi et al., Joint optimization of product tolerance design, process plan, and production plan in high-precision multi-product assembly, J Manuf Syst, vol. 54, no. June 2019, pp. 336-347, 2020.
https://doi.org/10.1016/j.jmsy.2020.01.004

D. Vignesh Kumar, D. Ravindran, N. Lenin et al., Tolerance allocation of complex assembly with nominal dimension selection using Artificial Bee Colony algorithm, Proc Inst Mech Eng C J Mech Eng Sci, vol. 233, no. 1, pp. 18-38, 2019.
https://doi.org/10.1177/0954406218756439

M. Hallmann, B. Schleich, and S. Wartzack, Tolerance allocation to tolerance-cost optimization: a comprehensive literature review, The International Journal of Advanced Manufacturing Technology, vol. 107, no. 11-12, 2020.
https://doi.org/10.1007/s00170-020-05254-5

H. A. Tinoco and S. Durango, Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM, Math Probl Eng, vol. 2019.
https://doi.org/10.1155/2019/9067624

J. Yu, Y. Zhao, H. Wang et al., Tolerance analysis of mechanical assemblies based on the product of exponentials formula, Proc Inst Mech Eng B J Eng Manuf, vol. 232, no. 14, pp. 2616-2626, 2018.
https://doi.org/10.1177/0954405417703425

A. Armillotta, Tolerance analysis of gear trains by static analogy, Mech Mach Theory, vol. 135, pp. 65-80, 2019.
https://doi.org/10.1016/j.mechmachtheory.2019.01.029

H. Zhang, Y. Cao, Y. Wei et al. A concurrent design method for functional tolerance and structure based on the principle of decomposition and reconstitution, Procedia CIRP, vol. 10, pp. 194-202, 2013.
https://doi.org/10.1016/j.procir.2013.08.031

H. Peng and B. Wang, A statistical approach for three-dimensional tolerance redesign of mechanical assemblies, Proc Inst Mech Eng C J Mech Eng Sci, vol. 232, no. 12, pp. 2132-2144, 2018.
https://doi.org/10.1177/0954406217716956

H. Peng, Z. Peng, and Z. Zhou, Manufacturing variation modeling and process evaluation based on small displacement torsors and functional tolerance requirements, Journal of Advanced Mechanical Design, Systems and Manufacturing, vol. 15, no. 3, pp. 1-16, 2021.
https://doi.org/10.1299/jamdsm.2021jamdsm0028

S. Ding, S. Jin, Z. Li, and H. Chen, Multistage rotational optimization using unified Jacobian-Torsor model in aero-engine assembly, Proc Inst Mech Eng B J Eng Manuf, vol. 233, no. 1, pp. 251-266, Jan. 2019.
https://doi.org/10.1177/0954405417703431

S. Ding, X. Zheng, J. Bao et al., An improved Jacobian-Torsor model for statistical variation solution in aero-engine rotors assembly, Proc Inst Mech Eng B J Eng Manuf, vol. 235, no. 3, pp. 466-483, 2021.
https://doi.org/10.1177/0954405420958769

H. Peng and S. Chang, Including material conditions effects in statistical geometrical tolerance analysis of mechanical assemblies, International Journal of Advanced Manufacturing Technology, vol. 119, no. 9-10, pp. 6665-6678, 2022.
https://doi.org/10.1007/s00170-021-08247-0

Y. Xi, Z. Gao, K. Chen et al., Error Propagation Model Using Jacobian-Torsor Model Weighting for Assembly Quality Analysis on Complex Product, Mathematics 2022, Vol. 10, Page 3534, vol. 10, no. 19, p. 3534, 2022.
https://doi.org/10.3390/math10193534

El Mouden, M., Chahbouni, M., Boutahari, S., An Efficient Method for Statistical and Deterministic Tolerances Synthesis Using the Jacobian Torsor Model, (2022) International Review of Mechanical Engineering (IREME), 16 (10), pp. 555-563.
https://doi.org/10.15866/ireme.v16i10.22505

M. El Mouden, M. Chahbouni, S. Boutahari, D. Amegouz Statistical Analysis of Three-Dimensional Tolerances by Integrating Form Defects Using the Jacobian Torsor Model, Advances in Integrated Design and Production II, pp. 35-46, 2023.
https://doi.org/10.1007/978-3-031-23615-0_5

W. Ghie, L. Laperrière, and A. Desrochers, A Unified Jacobian-Torsor Model for Analysis in Computer Aided Tolerancing, Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering, pp. 63-72, 2003.
https://doi.org/10.1007/978-94-017-0161-7_7

C. Rausch, M. Nahangi, C. Haas et al., Monte Carlo simulation for tolerance analysis in prefabrication and offsite construction, Autom Constr, vol. 103, no. March, pp. 300-314, 2019.
https://doi.org/10.1016/j.autcon.2019.03.026

E. Umaras, A. Barari, and M. D. S. Guerra Tsuzuki, Intelligent Design Tolerance Allocation for Optimum Adaptability to Manufacturing Using a Monte Carlo Approach, IFAC-PapersOnLine, vol. 52, no. 10, pp. 165-170, 2019.
https://doi.org/10.1016/j.ifacol.2019.10.017

J. Gao, K. W. Chase, and S. P. Magleby, Comparison of Assembly Tolerance Analysis by the Direct Linearization and Modified Monte Carlo Simulation Methods, Proceedings of the ASME Design Engineering Technical Conference, vol. 1, pp.

W. Xu, K. Wu, P. Li et al., Grouping Strategies of Discrete Elements for Efficient Power Pattern Tolerance Analysis of Antennas/Radomes Using Monte Carlo Method, IEEE Trans Antennas Propag, vol. 70, no. 10, pp. 9988-9993, 2022.
https://doi.org/10.1109/TAP.2022.3177548

C. Zhou, Z. Liu, C. Qiu et al., A quasi-Monte Carlo statistical three-dimensional tolerance analysis method of products based on edge sampling, Assembly Automation, vol. 41, no. 4, pp. 501-513, 2021.
https://doi.org/10.1108/AA-09-2020-0144

W. Ghie, L. Laperrière, and A. Desrochers, Re-design of mechanical assemblies using the unified Jacobian-Torsor model for tolerance analysis, Models for Computer Aided Tolerancing in Design and Manufacturing - Selected Conference Papers from the 9th CIRP International Seminar on Computer-Aided Tolerancing, pp. 95-104, 2007.
https://doi.org/10.1007/1-4020-5438-6_11

El Mouden, M., Chahbouni, M., Boutahari, S., Jacobian Torsor Model for Statistical Synthesis of Three-Dimensional Tolerances in Mechanical Assemblies, (2024) International Review of Aerospace Engineering (IREASE), 17 (1), pp. 29-38.
https://doi.org/10.15866/irease.v17i1.24643


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize