Design Considerations of Gudgeon Pin in Reciprocating Air Compressors by Semi Analytic Approach
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Journal of Mechanical Engineering Research Vol. 4(3), pp. 75-88, March 2012 Available online at http://www.academicjournals.org/JMER DOI: 10.5897/JMER11.009 ISSN 2141-2383 ©2012 Academic Journals Full Length Research Paper Design considerations of Gudgeon pin in reciprocating air compressors by semi analytic approach V. Ramamurti1*, S. Sridhar2, S. Mithun2, B. Kumaravel2 and S. Lavanya2 1The Indian Institute of Technology Madras, India. 2WABCO-TVS India, Chennai, India. Accepted 17 March, 2011 The deformation and stress experienced by the Gudgeon pin of a reciprocating compressor used in air brake system is scientifically predicted when the pin is fully floating with lubricating oil surrounding it and when starved of oil. Both semi analytical approach in finite element method and simple bending theory of beams are used. Inadequacy of the beam approach is highlighted. The results obtained by both the approaches are compared. Role of clearance in piston bore and small end of connecting rod and effectiveness of lubrication are examined. Factor of safety associated with the design of Gudgeon pin is also looked into. Key words: Gudgeon pin, semi and fully floating pin, semi analytic method, role of lubricant, factor of safety. INTRODUCTION Reciprocating air compressors in vehicles compress air modal superposition technique was reported by the and supply it to the air brakes. Many of the components authors (Ramamurti et al., 2011). In the present constituting the reciprocating air compressor are having investigation, the design considerations connected with design features based more on standard practices rather the Gudgeon pin of reciprocating air compressors are than on sound scientific analysis. One of the systematic presented. This is motivated by lack of scientific analysis investigations reported recently is on the pressure in literature and the inadequacies in the design variation inside the air compressor as a function of the procedure. crank angle (Venkatesan et al., 2009). An experimental investigation using optical probes was also reported (Brun et al., 2005). The dynamic analysis of the response Relevance of investigation of the inlet and discharge valves of the compressor using Gudgeon pin (Figure 1) connects the small end of the connecting rod with the piston providing a turning pair; Gudgeon pin can either turn relative to the connecting rod *Corresponding author. E-mail: [email protected]. or relative to the piston bore or turn relative to both(Ramamurti, 2009). Nomenclature: C, Clearance in the piston bore; d, l ,D-Inner Prerequisite for this function is that the Gudgeon pin diameter, one-third length and outer diameter of the Gudgeon has a sliding fit with the other two. Since the Gudgeon pin pin; n, Fourier index; pr, pθ, radial and circumferential pressure transmits the load from the connecting rod to the piston, on the pin; r1,r2, inner and outer radii of the pin; w, load per unit the deformation that it suffers during the operation must length on the pin (F/ ℓ); A1, A2, B1, B2, C, salient locations on be such that it does not have surface contact with both the Gudgeon pin; E, Young’s modulus; F, force on the simultaneously. This will lead to seizure. Besides, the connecting rod; F1, Reaction at the end of the Gudgeon pin; I, Gudgeon pin should not be stressed beyond its second moment of area of the beam; M, Bending moment of the endurance limit. beam; OX,OY,OZ, radial , axial, circumferential; coordinates in semi analytical approach; Z, Modulus of section of the pin; The Gudgeon pin is either a hollow or solid steel ,Semi contact angle (in radians); σX, σY, σZ, Stresses in cylinder of length roughly five times its outer diameter. radial, axial and circumferential directions; θ, Angular position in This is subjected to lateral load from the connecting rod the pin. (Figure 2). The load acts for the full width of the 76 J. Mech. Eng. Res. Figure 1. Cross section of the piston assembly. Figure 2. Force on the gudgeon pin. connecting rod (for nearly one third of the axial length of other hand, assumed fixed, it ignores the fact that there is the Gudgeon pin) acting over a substantial arc of the a radial clearance between the piston bore and the outer cylindrical surface of the pin. A very simple method cylindrical surface of the Gudgeon pin. However, when of analysis is to treat the pin as a simply supported beam assumed simply supported, beam approach is very easy subjected to lateral load of uniform intensity from the to analyse since the structure is statically determinate. connecting rod. This approach has two basic deficiencies. (i) The Gudgeon pin does not qualify to be treated as a beam since its length is much less than ten FORCE ANALYSIS OF GUDGEON PIN times its outer diameter. (ii) Besides the beam, when assumed as simply supported at the ends, ignores the The Gudgeon pin assembly is subjected to uniform fact that its support is along an arc of a circle. If, on the intensity of pressure in the region of the connecting rod Ramamurti et al. 77 Figure 3. Close up view of Gudgeon pin and its salient locations. due to air compressed on the top flat face of the piston. Analytical procedure Besides it is prevented from moving axially by the circlips. The deformation of the Gudgeon pin is to be within elastic Beam approach limits under the action of the force along the width of the connecting rod for various angular positions. The This corresponds to a problem ignoring the presence of bending deformation of the Gudgeon pin is to be oil in the annular space and assuming direct contact assessed to address the adequacy of clearance between between the piston bore and the Gudgeon pin and the pin and the small end of the connecting rod and also between the Gudgeon pin and connecting rod. In this between the Gudgeon pin and piston bore. approach, even though the beam length is only five times The Gudgeon pin, in reality, is a cylinder of roughly the diameter, Euler beam theory is assumed to be valid. length 5 times its diameter, supported by lubricating oil present in the clearance on the piston bore for roughly two thirds its length with the middle one third subjected to Case (i): Contacts at B1 and B2 lubricating oil pressure on the annular space of the small end of connecting rod. The load that gets communicated Figure 3 shows the close up view of the Gudgeon pin. to the Gudgeon pin from the connecting rod acts on the The length 3ℓ of the pin is roughly divided into three parts, outer circumference along the middle one third of its namely, one third from either end housed in the piston length. The piston bore on both sides supports this pin bore and the middle one third inside the small end. When through the lubricating oil. The pin oscillates through this is subjected to the bending load from the connecting approximately 10° about its mean position. There are two rod, the middle one third can deform as shown in Figure aspects to be considered for the load distribution, one 4. In Figure 3 the supports on either side are at the along the length of the pin and other along its locations B1 and B2.The two parts of the deformed neutral circumference. Along the circumference, due to the axis (Figure 4) A1 B1 and A2 B2 are assumed to be not lubricating oil pressure, it is periodic with the resultant touching the piston bore. The deformed neutral axis B1C along the line joining small end and the big end and along B2 is not also touching the small end bore of the the width of the connecting rod, with uniform intensity. To connecting rod. meet these two requirements, semi analytical approach This is possible, only when there is adequate clearance can be used (Ramamurti, 2009; Ramamurti and Gupta, available in both the piston bore and the small end of the 1978; Ramamurti and Narayanan, 1989; Quing et al., connecting rod. The Gudgeon pin is treated as a beam 2006; Zienkiewicz, 1991). In this connection, the following carrying uniformly distributed load over one third of its papers that have similar connected applications can be length as shown in Figure 3 and analysis carried out. For cited. this first case, the beam is assumed to be simply Ramamurti and Gupta (1978) have assumed the load supported in locations B1 and B2. Area moment method of a kiln tyre supported by rollers to act over a small arc, (Papov, 1978) is used to compute the deflections and whereas in another paper, Ramamurti and Narayanan axial stress at its salient locations. The beam deflects as (1989) have assumed that the load is transferred along shown in Figure 4. several short arcs for a roller clutch. Quing et al. (2006) have determined the natural frequencies of a shell system by semi analytical approach in finite element Case (ii): Contacts at A1, B1, B2 and A2 method. In this paper, both beam and semi analytical approaches are attempted and results compared. In the second case (Figure 5), the free ends A1 and A2 of 78 J. Mech. Eng. Res. Figure 4. Deformation of a Gudgeon pin when not touching the piston bore. Figure 5. Deformation of the Gudgeon pin when it exceeds clearance in the piston bore. the beam physically touch the piston bore. If the available the locations A1 and A2 .One can, then, calculate the tolerance between the piston bore and the Gudgeon pin deflections and stresses on the pin. is less than the difference in deflection between the ends A1 & B1 or A2 & B2, the Gudgeon pin will touch the piston bore.