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Kinematics and Kinetic Analysis of the Slider-Crank Mechanism in Otto Linear Four Cylinder Z24 Engine

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Kinematics and Kinetic Analysis of the Slider-Crank Mechanism in Otto Linear Four Cylinder Z24 Engine Journal of Mechanical Engineering Research Vol. 3(3), pp. 85-95, March 2011 Available online at http://www.academicjournals.org/jmer ISSN 2141 - 2383 ©2011 Academic Journals Full Length Research Paper Kinematics and kinetic analysis of the slider-crank mechanism in otto linear four cylinder Z24 engine Mohammad Ranjbarkohan 1*, Mansour Rasekh 2, Abdol Hamid Hoseini 3, Kamran Kheiralipour 4 and Mohammad Reza Asadi 1 1Department of Mechanical Engineering, Islamic Azad University, Buinzahra branch, Qazwin, Iran. 2Department of Agricultural Machinery, University of Mohaghegh Ardabili, Ardabil, Iran. 3Mechanic Engineering in Megamotor Company, Tehran, Iran. 4Department of Mechanical Engineering of Agricultural Machinery, University of Tehran, Karaj, Iran. Accepted 26th November, 2010 Nissan Z24 is one of the numerous vehicles in Iran. MegaMotor's reports show high rate damaging in the crankshaft and connecting rod of this engine vehicle. It is necessary to carry out a complete research about slider-crank mechanism because of high expensive repairs and replacement of these parts and their reverse effects on the other parts such as cylinder block and piston. Results of initial researches show that an important reason of these parts’ damaging is using of downshifting in driving. In this research, we are concerned on the analysis of kinematics and kinetic of slider-crank mechanism of the engine in maximum power, maximum torque and downshifting situation. The influence of different parameters such as engine RPM and downshifting effects were investigated on crankshaft and connecting rod loads. Two methods for analyzing of slider-crank mechanism were used: solving Newton's law and MSC/Adams/Engine software. Key words: Engine, slider-crank mechanism, kinematics and kinetic, downshifting, Newton's Law, engine rpm. INTRODUCTION The base of dynamic mechanism operation of engine is a slider-crank mechanism. They, for this purpose, used slider-crank mechanism, which consist of crankshaft, Hamilton’s principle, Lagrange multiplier, geometric connecting rod and piston. Combustion pressure constraints and partitioning method (Ha et al., 2006). transferred from piston (the part merely has reciprocating Their formulation was expressed by only one motion) to the connecting rod (the part has both linear independent variable. Finally to obtain the best dynamic and rotation motion) and finally to the crankshaft (the part modeling, they compared obtained results and numerical has merely rotation motion). simulations. Cveticanin and Maretic (2000) have studied dynamic Also, a new identification method based on the genetic analysis of a cutting mechanism which is a special type of algorithm was presented to identify the parameters of a the crank shaper mechanism (Cveticanin and Maretic, slider-crank mechanism. Koser (2004) investigated on 2000). The influence of the cutting force on the motion of kinematic performance analysis of a slider-crank the mechanism was considered. They used Lagrange mechanism based on robot arm performance and equation to obtain boundary values of the cutting force dynamics (Koser, 2004). He analyzed kinematic analytically and then numerically. performance of the robot arm using generalized Jacobian Ha et al. (2006) have derived the dynamic equations of matrix. It was obtained that the slider-crank mechanism based robot arm had almost full isotropic kinematic performance characteristics and its performance was much better than the best 2R robot arm. He used *Corresponding author. E-mail: [email protected]. complex algebra to solve that classical problem and he 86 J. Mech. Eng. Res. obtained solution as the root of a cubic equation within a And thus: defined range. Another research about transmission angle was carried 2 2 x = r cos( θ ) + l 1 − n sin (θ ) (4) by Shrinivas and Satish (2002). They have summarized importance of the transmission angle for most effecti ve Using Taylor series in Equation 4: force transmission. In this regard, they investigated 4-, 5-, 6- and 7-bar linkages, spatial linkages and slider-crank 1 1 1 mechanisms. 1−n2 (sin(θ)) 2 =1− (n.sin(θ)) 2 + (nsin(θ)) 4 − (nsin(θ)) 6 +... 2 8 16 One of the numerous vehicles in Iran is Nissan Z24, 1 n4 n6 produced by MegaMotor's company. This company =1− n2 sin(θ)2 + sin(θ)4 − sin(θ)6 +... reports show high rate damaging in the crankshaft and 2 8 16 connecting rod of this engine vehicle. As investigation on (5) phenomena like vibration, resonance, fatigue, noise . , Because n is less than 1(about 0.3), we con eliminate high degree and optimization of these parts, kinematics and kinetic of sentences. Thus: slider-crank mechanism must be known, it is necessary to carry out a complete research about slider-crank 2 2 1 2 2 1 2 1 2 mechanism because of high expensive repairs and 1− n sin (θ ) ≅ 1− n sin (θ ) = 1− n − n cos( 2θ ) 2 4 4 replacement of these parts and their reverse effects on (6) the other parts such as cylinder block and piston. Results of initial researches show that an important reason of From Equations1 and 6, one can obtain: these parts’ damaging is using of downshifting in driving. So, in this research, we concerned on analysis of 1 2 1 2 x = r cos( θ) + l 1( − n − n cos( 2θ)) (7) kinematics and kinetic of slider-crank mechanism of the 4 4 engine in maximum power, maximum torque and downshifting situation. The influence of different For simplification in calculation we use these notations: parameters such as engine rpm and downshifting effects were investigated on crankshaft and connecting rod Q1 = .ln loads. n 2 .l Q = 2 4 MATERIALS AND METHODS 2 n Q = l 1( − ) (8) At first stage the combustion chamber pressure curve of Nissan 3 4 Z24 engine was measured in MegaMotor's power test lab (Engine, 2 Gearbox and Axel Manufacturing located in Tehran province in Iran, n info @megamotor.ir). These experimental data have been shown in Q4 = 1+ Figure 1. 4 Because of different type of motion in this mechanism; such as: n2 linear, linear-rotation and rotation, there is inertial force in the Q5 = system. The inertial force has important role in engine slider-crank 4 mechanism, so behavior of this force must be known. For analyzing of inertia force, the kinematics of mechanism should be defined. Equation 7 and 8 will result: x = Q cos( θ ) + Q cos( 2θ) + Q Kinematics analysis of slider-crank mechanism 1 2 3 (9) The engine slider-crank mechanism has been shown in Figure 2. Where ω is the crankshaft rotational velocity. Piston speed obtained The piston has linear motion in x direction in this figure: from derivation of Equation (9): v = −Q cos( θ ). ω − 2Q cos( 2θ). ω x = r cos( θ) + l cos( β) (1) P 1 2 (10) Where, r is the crank radius, L is the connecting rod length, θ is the And for piston acceleration: crank rotation angle and β is the connecting rod angle with x axis. From Figure 1, one can obtain that: 2 2 aP = −Q1 cos( θ)ω − Q1 sin( θ )α − 4Q2 cos( 2θ )ω − 2Q2 sin( 2θ )α (11) r.sin( θ ) = l.sin( β ) (2) where α is the crankshaft rotational acceleration. r From Equation 11 and Taylor series, for other parts, can reached n = (3) l the following result: Ranjbarkohan et al. 87 Combustion pressure on 2800 Rpm(Full load) Combustion pressure on 2400 Rpm(Full load) 6 Combustion pressure(Idel) 5 4 3 Pressure (Mpa) 2 1 0 0 100 200 300 400 500 600 700 800 Crank angle (Deg) Figure 1. Combustion pressure in different rpms and loads. could be calculated from Figure 3: r r r ag = a p + ag / p (14) where ag / p is acceleration vector of connecting rod’s C.G relative the piston, as follow: r r r r r r ag / p = η × rg / p + λ × (λ × rg / p ) (15) where r g/p is the displacement vector of connecting rod’s C.G relative the piston, that (Meriam and Kraige, 1998): r rg / p = s(− cos( β ) i + sin( β ) j) = (−e (Q3 + Q2 cos( 2θ )) i + ( e Q1 sin( θ )) j Figure 2. Slider crank mechanism. (16) where s is the distance between connecting rod’s C.G and piston, and e= s/l . For vertical acceleration of C.G: λ = nω cos( θ )(Q −Q cos( 2θ)) (12) 4 5 2 2 acx = (−Q1 cos( θ )ω − Q1 sin( θ )α − 4Q2 cos( 2θ )ω 2 η=nαcos(θ)(Q −Q cos(2θ))−nω sin(θ) − 2Q2 sin( 2θ )α − (−nα cos( θ )( Q4 − Q5 )cos( 2θ )) + 4 5 2 Q Q nQ 2 1 3 2 ( 4 − 5 cos(2θ))+2 5ω cos(θ)sin(2θ) n sin( )( Q Q cos( 2 )) n cos( )sin( (13) ω θ 4 − 5 θ − ω θ r 2 λ η 2 2 2 2 That is, is the connecting rod rotational velocity and is the sin( 2θ )) eQ 1 sin( θ ) + n ω cos (θ )( Q4 − Q5COS 2( θ )) connecting rod rotational acceleration. r Now the velocity and acceleration of connecting rod’s C.G e(Q + Q cos( 2θ ))) i 3 2 (Center of gravity) could be calculated. Connecting rod acceleration (17) 88 J. Mech. Eng. Res. The force diagram of connecting rod was shown in Figure 5 and Equations 21 and 22: ∑ Fx = mc .acx N x − Rx = mc acx (21) N x = Rx + mp .a p + mc.acx (22) Engine torque can be obtained from Figure 6 as follow: T = N x r.. sin( θ ) + N y r.. cos( θ ) (23) For N y: ∑ M A = I A.η (24) N x r.. sin( θ ) − I A .η N y = Q3 + Q2 .cos( 2θ ) (25) Where I A is Inertia of connection rod.
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