Theoretical and Numerical Analysis of deformation in fixture body plates

Authors

North Sazman Barnameh Ave Unit 30, No.18, East 7th Alley

Abstract

A fixture body consists of the base, second, and third plates, which are connected perpendicular to each other. The design of these plates is conducted based on the amount of their elastic deformation under the applied loads. Modeling of deformation in these plates is done specifically for each plate due to their different boundary and loading conditions. In the present study, two distinct analytical models are presented based on the theory of plates and shells to calculate the elastic deformation in the base, second, and third plates of the fixture body. Navier’s method (double series solution) was used to calculate the base plate deformation, in which the plate deformation was modeled by Fourier series, the coefficients of which were calculated based on the intensity and position of the external forces and moments. The deformations of the second and third plates were calculated by developing the differential equation governing the problem using Lagrange’s theory and applying loading and boundary conditions to it. Numerical analysis was conducted in the finite element analysis software to validate the theoretical predictions. The maximum elastic deformation of the base plate was obtained as 2.021 mm from the simulation, showing the maximum error of 4.7% in the theoretical predictions. Also, the maximum elastic deformation for the second and third plates was calculated as 0.0412 mm and 0.0391 mm from the numerical analysis, respectively. It can be concluded that the maximum error in theoretical predictions of deformation in the second and third plates was equal to 1.4%.

Keywords

Main Subjects

References

[1]  Mehta NK (2012) Machine Tool Design & Numerical Control. Tata McGraw Hill Education, India.
[2] Nategh MJ (2012) Machine tools jig and fixture design. Tarbiat Modares University Press, Tehran.
[3]  Satyanarayana S, Melkote S (2004) Finite element modeling of fixture–workpiece contacts: single contact modeling and experimental verification. Int J Mach Tools Manuf 44: 903–913.
[4] Parvaz H, Nategh MJ (2013) A pilot framework developed as a common platform integrating diverse elements of computer aided fixture design. Int J Prod Res 51: 6720–6732.
[5] Nategh MJ, Parvaz H (2018) Development of computer aided clamping system design for workpieces with freeform surfaces. Comput Aided Des 95: 52–61.
[6] Parvaz H, Nategh MJ (2018) Development of locating system design module for freeform workpieces in computer-aided fixture design platform. Comput Aided Des 104: 1–14.
[7] Hoffman EG (2004) Jig and Fixture Design, Fifth edn. Delmar Cengage Learning, New York.
[8] Siebenaler SP, Melkote SN (2006) Prediction of workpiece deformation in a fixture system using the finite element method. Int J Mach Tools Manuf 46: 51–58.
[9] Gameros A, Lowth S, Axinte D, Nagy-Sochacki A, Craig O, Siller HR (2017) State-of-the-art in fixture systems for the manufacture and assembly of rigid components: A review. Int J Mach Tools Manuf 123: 1–21.
[10] Aoyama T, Kakinuma Y (2005) Development of fixture devices for thin and compliant workpieces. CIRP Ann 54: 325–328
[11] Raffles MH, Kolluru K, Axinte D, Llewellyn-Powell H (2013) Assessment of adhesive fixture system under static and dynamic loading conditions. Proc Inst Mech Eng Part B J Eng Manuf 227: 267–280.
[12] Mironova A, Mercorelli P, Zedler A (2016) Robust control using sliding mode approach for ice-clamping device activated by thermoelectric coolers. IFAC-PapersOnLine 49(25): 470–475.
[13] Mironova A (2018) Effects of the influence factors in adhesive workpiece clamping with ice: experimental study and performance evaluation for industrial manufacturing applications. Int J Adv Manuf Technol 99: 137–160.
[14] Chou Y-C, Chandru V, Barash MM (1989) A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis. J Eng Ind 111: 299–306.
[15] Lee SH, Cutkosky MR (1991) Fixture Planning With Friction. J Eng Ind 113: 320–327.
[16] Kang Y, Rong Y, Yang JC (2003) Computer-Aided Fixture Design Verification. Part 3. Stability Analysis. Int J Adv Manuf Technol 21: 842–849.
[17] Parvaz H (2020) Analytical and Numerical Investigation of Reaction Forces in Fixturing of Rigid Workpiece with Polyhedral Geometry. J Solid Fluid Mech 10:17–29.
[18] Parvaz H, Mahdavi M, Sepehry N (2020) Experimental investigation of the jamming phenomenon in fixturing of workpiece using the peg-in-hole mechanism. Solid Fluid Mech 10: 77–89.
[19] Parvaz H, Sepehry N, Yazdi MK (2020) Theoretical and experimental analysis of jamming of workpiece in the fixture by using the block and palm study. Solid Fluid Mech 10:45–58
[20] Ventsel E, Krauthammer T (2001) Thin plates and shells: theory, analysis and applications. CRC Press, Dekker, Abingdon
[21] Timoshenko S, Woinowsky-Krieger S (1987) Theory of plates and shells, Second edn. McGraw-Hill, United States
[22] Zhang J, Liu S, Ullah S, Gao Y (2020) Analytical bending solutions of thin plates with two adjacent edges free and the others clamped or simply supported using finite integral transform method. Comput Appl Math 39: 266-278.
[23] Marks CR (1941) The Analysis of Cantilever Plates with Concentrated Loads. PhD thesis, University of Tennessee.
 
 
 
 
Journal of Solid and Fluid Mechanics
Volume 12, Issue 3
September and October 2022
Pages 13-32

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