applied sciences Article Kinematic Conceptual Design of In-Line Four-Cylinder Variable Compression Ratio Engine Mechanisms Considering Vertical Second Harmonic Acceleration Seung Woo Kwak 1 , Jae Kyung Shim 2,* and Young Kwang Mo 1 1 Graduate School, Department of Mechanical Engineering, Korea University, Seoul 02841, Korea; [email protected] (S.W.K.); [email protected] (Y.K.M.) 2 School of Mechanical Engineering, Korea University, Seoul 02841, Korea * Correspondence: [email protected]; Tel.: +82-2-3290-3362 Received: 19 April 2020; Accepted: 27 May 2020; Published: 29 May 2020 Abstract: In the in-line four-cylinder engine, it is well known that the shaking force is due to the vertical second harmonic acceleration components of the pistons. This paper proposes a kinematic conceptual design method to determine the kinematic structure of a feasible in-line four-cylinder variable compression ratio (VCR) engine and its dimensions that would yield a lower vertical second harmonic acceleration at joints. Through type and dimensional synthesis, candidate VCR engine mechanisms are chosen and their dimensions satisfying design specifications are determined. Based on the analysis of the vertical second harmonic acceleration components at the joints, a feasible mechanism for an in-line four-cylinder VCR engine is selected. Then, the method finds the dimensions that yield a nearly minimized sum of the vertical second harmonic acceleration at each joint by adjusting the link lengths within specified tolerances. For validation, the result is compared with that of a constrained optimization using MATLAB. The proposed method would be useful at the conceptual design stage of multi-link multi-cylinder VCR and variable-stroke engine mechanisms where the second harmonic acceleration is an important design factor in the automotive industrial applications. Keywords: kinematic conceptual design; mechanism design; variable compression ratio (VCR) engine mechanism; harmonic acceleration analysis; vertical second harmonic acceleration 1. Introduction The general performance and thermal efficiency of the internal combustion engine have been improved by various technologies such as turbochargers, fuel injection systems, and variable valve actuation systems [1]. In addition to the above, the variable compression ratio (VCR) engine technology has been considered as a method for improving fuel efficiency and reducing pollutants [2–5]. Various approaches have been suggested for the variation of the compression ratio, which include moving the crankshaft axis or the cylinder head, varying the combustion chamber volume or the piston deck height, and modifying the connecting rod geometry [6–10]. Numerous VCR engine mechanisms have been proposed [11–13], and their kinematic structures have been identified [14]. In general, as the VCR engine mechanism has more links than the conventional fixed compression ratio engine, the design of a VCR engine mechanism could be a quite complicated problem: the kinematic structure and dimensions of the mechanism that fits within the internal space of the engine must be determined, and then the dynamic characteristics and the balancing of shaking force and shaking moment need to be considered. The latter problem on the balancing of the conventional engine has been studied extensively [15–17]. The vertical second harmonic acceleration components of the Appl. Sci. 2020, 10, 3765; doi:10.3390/app10113765 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 19 shaking force and shaking moment need to be considered. The latter problem on the balancing of the conventional engine has been studied extensively [15–17]. The vertical second harmonic acceleration Appl. Sci. 2020, 10, 3765 2 of 19 components of the pistons cause the shaking moments in the in-line three-cylinder, in-line five-cylinder, and V six-cylinder engines; the shaking forces in the in-line four-cylinder engine. In pistonsorder to cause balance the shaking the shaking moments forces, in the an in-lineextra three-cylinder,device, such as in-line a balancer, five-cylinder, which androtates V six-cylinder at double engines;engine speed, the shaking is used forces to balance in the the in-line shaking four-cylinder force [18,19]. engine. From In orderthis point to balance of view, the even shaking though forces, the ancomplete extra device, dynamic such analysis as a balancer, of a whichVCR engine rotates atunder double development engine speed, is isnot used possible to balance until the the shaking mass forceproperties [18,19 ].of From the parts this point are ofdetermined, view, even consider though theing completethe vertical dynamic second analysis harmonic of a VCRacceleration engine undercomponents development would isprovide not possible a good until starting the mass point properties at the conceptual of the parts design are determined, stage of consideringa new VCR theengine vertical mechanism. second harmonic acceleration components would provide a good starting point at the conceptualIn the designcase of stage the fixed of a new compre VCRssion engine ratio mechanism. engine, the crank can be shortened to decrease the magnitudeIn the caseof the of second the fixed harmonic compression acceleration ratio engine,of the piston, the crank but sh canortening be shortened the crank to length decrease causes the magnitudea change in of the the stroke. second For harmonic the VCR acceleration engine mechanis of the piston,m, since but more shortening links can the be crank used length to connect causes the a changepiston and in the the stroke. crank, Forthe second the VCR harmonic engine mechanism,acceleration sincecan be more reduced links by can adjusting be used the to connectlink lengths the pistonwithout and scarifying the crank, a desired the second stroke harmonic and top acceleration dead center can(TDC) be reducedposition. by adjusting the link lengths withoutIn scarifyingthis paper, a desireda kinematic stroke conceptual and top dead design center process (TDC) position.of in-line four-cylinder VCR engine mechanismsIn this paper,considering a kinematic the vertical conceptual second design harmonic process acceleration of in-line component four-cylinder at VCReach enginejoint is mechanismsproposed. The considering proposed method the vertical includes second the harmonictype and accelerationdimensional componentsynthesis of atcandidate each joint VCR is proposed.engine mechanisms, The proposed harmonic method includesacceleration the typeanalysis, and dimensional selection of synthesis a feasible of candidatemechanism, VCR and engine the mechanisms,minimization harmonic of the vertical acceleration second analysis, harmonic selection acceleration of a feasible sum in mechanism, the selected and mechanism. the minimization For the oftype the synthesis, vertical second the atlas harmonic of ki accelerationnematic chains sum inis theused selected to choose mechanism. appropriate For the candidates. type synthesis, The thedisplacement atlas of kinematic equations chains of candidate is used to choosemechanisms appropriate are derived candidates. and used The displacementto determine equationsthe initial ofdimensions candidate of mechanisms links that satisfy are derived prescribed and design used tospecifications. determine the Then, initial the dimensionsFourier series of expression links that satisfyfor the prescribeddisplacement design of each specifications. joint is determined Then, the numerically Fourier series and expressiondifferentiated for to the obtain displacement the vertical of eachharmonic joint isacceleration determined components. numerically Among and diff theerentiated candidates, to obtain a feasible the vertical mechanism harmonic is selected acceleration based components.on the vertical Among second theharmonic candidates, acceleration a feasible analysis mechanism when they is selected are used based in the on in-line the vertical four-cylinder second harmonicengine, and acceleration then by varying analysis the when link lengths they are of used the ininitially the in-line designed four-cylinder mechanism engine, within and prescribed then by varyingtolerances, the the link final lengths dimensions of the initially of the mechanism designed mechanism that yields withina nearly prescribed minimized tolerances, sum of the the second final dimensionsharmonic acceleration of the mechanism are determined. that yields a nearlyThe resu minimizedlt is compared sum of the with second that harmonic of a accelerationconstrained areoptimization determined. for Thethe validati result ison compared of the proposed with that method. of a constrained optimization for the validation of the proposed method. 2. Understanding of Harmonic Acceleration in the In-Line Four-Cylinder Engine 2. Understanding of Harmonic Acceleration in the In-Line Four-Cylinder Engine A slider-crank mechanism used in the conventional fixed compression ratio internal combustionA slider-crank engine mechanismis shown in usedFigure in 1. the The conventional displacement fixed of compressionthe piston pin, ratio s, can internal be derived combustion as engine is shown in Figure1. The displacement of the piston pin, s, can be derived as − θ 2 =+−8 θ lers cos 9 sr>sin 1> , (1) > rll e r cos θ2> s = r<sin θ + 1 =, (1) > − > :> r − l ;> where θ is the crank angle, r is the crank length, l is the connecting rod length, and e is the piston whereoffset.θ is the crank angle, r is the crank length, l is the connecting rod length, and e is the piston offset. FigureFigure