Kinematic and dynamic modeling and simulation of crank mechanism of automobile engine

Nguyễn Khắc Tuân và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 139(09): 19 - 24 KINEMATIC AND DYNAMIC MODELING AND SIMULATION OF CRANK MECHANISM OF AUTOMOBILE ENGINE Nguyen Khac Tuan*, Hoang Anh Tan, Nguyen Minh Chau College of Technology - TNU SUMMARY The study aims to conduct the kinematic and dynamic simulation of the four stroke engine in MATLAB software. A method of modeling which allows calculating the dynamics and kinematics of crank mechanism of automobile engine has been developed. Typical dynamic and kinematic performance characteristics of 4-cylinders engine are shown. Key words: kinematics, dynamics, crank mechanism, simulation INTRODUCTION* the following discussion, we refer to the The principle behind an internal combustion kinematics and dynamics of the crank engine (ICE) is that air and fuel are mixed mechanism, performed with the aid of and burnt inside the cylinder to generate MATLAB software. work. The combustion pushes the piston, KINEMATICS AND DYNAMICS OF which transfer the translational movement CRANK MECHANISM through the connecting rod, to a rotational Figure 1 shows a diagram of a central crank movement on the crank shaft. During each mechanism in which the axis of the cylinder cycle, the piston moves continuously back intersects that of the crankshaft [1,2]. The fol- and forth between its top and bottom lowing notation is used in this figure:  – positions, commonly known as the Top Dead angle of crank travel counted from the Center (TDC) and the Bottom Dead Center cylinder axis in the direction of clockwise (BDC), respectively. Kinematic analysis is crankshaft rotation, when  =0° the piston is important to understand the position, velocity at TDC (point A'),  = 180° the piston is at and acceleration of each linkage during the BDC (point A");  —angle between the working of mechanism. The essentiality of connecting rod and the cylinder axis; ω – dynamic analysis is to understand dynamic angular velocity of crankshaft rotation; S = behavior of each link, during the working of 2R – piston stroke; R – crank radius; l— mechanism. connecting rod length;   Rl/ –ratio Analysis of the publications [7-15] showed between crank radius and connecting rod that most of works focus on computational length. simulation and thermodynamic cycle [11, 12] The expression for the piston travel s from its or calculate the parameters of the engine with initial position at TDC when the crank turns valve timing, valve-contour or contour gas through the angle , According to Fig. 1 can distribution [13, 14]. Some other works using be expressed as: specialized software such as Adams, Saber, 11    Scilab, GT-power... to simulate the entire s( R  l )  ( R cos  l cos  )  1     c os   c os   R  engine [9,10] or crank mechanism [7,8].     Nonetheless, there is no a complete study of Determined s with an accuracy up to and the kinetics and dynamics of the 4-stroke including small quantities of the second order, engine with different numbers of cylinder. In has the following form [1-5]:  sR1  cos  1  cos2  (1) * 4 Tel: 0912 262771, Email: tuannkcn@gmail.com  19 Nguyễn Khắc Tuân và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 139(09): 19 - 24 The piston velocity can be determined by divided into three groups with respect to the taking the derivative of equation (1) with nature of their motion: respect to time (a) Parts reciprocating along the cylinder ds ds d vRp   sin   sin 2  (2) axis (the piston group). The mass of the dt d dt 2 piston with the rings and pin is assumed to be The can be obtained by piston acceleration lumped on the axis of the piston pin and is taking the derivative of expression (2) with respect to time designated by mp. (b) Rotating parts of the crankshaft. Their dvpp dv d aR  2 cos    cos 2   (3) dt d dt masses are replaced by a mass mcr. reduced to the crank radius R . The mass of the crankpin During the operation of an engine the crank m with adjacent parts of the webs (Fig. 2a) is mechanism parts are acted upon by gas cp assumed to be lumped along the center of the pressure in the cylinder, inertia forces of the crankpin axis and, since its center of gravity is reciprocating masses, centrifugal forces, crankcase pressure exerted on the piston, and at a distance R from the shaft axis, this mass gravity. need not be reduced. The mass mcw of the middle portion of the crank web over the The pressure of the gases in the engine cylinder is usually preceded by thermal contour abcd with its center of gravity on the calculations [1,2]. radius  is reduced to the radius R  To determine the forces of inertia, it is m22 m R  whence m m necessary to know the masses of the crank cw cwR cwR cw R mechanism elements. To simplify the The reduced mass of crank calculations, the actual crank mechanism is  is: m m 22 m  m  m replaced by a dynamical equivalent system of cr cp cwR cp cw R lumped masses. All the moving parts are Fig. 1 Diagrams of central Fig. 2. Reduction of the crank gear system to a Fig. 3. Total forces crank mechanism two-mass one: acting in a crank gear a) reduction of crank mass; b)reduction of connecting rod mass; c) reduced system of crank mechanism 20 Nguyễn Khắc Tuân và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 139(09): 19 - 24 (c) Parts performing complex plane-parallel The centrifugal force of the rotating masses of motion (connecting rod group).The a crank mechanism 2 connecting rod is replaced with a certain NRR m R (5) approximation by a system of two masses NR is always directed along the crank radius. statically equivalent to its mass: the mass It is constant in magnitude and applied at the mrod.pp lumped on the piston pin axis, and the center В of the crankpin. The force NR rotates mass mrod.cr on the axis of the crankpin. For together with the crank and, not being ba- this purpose, the mass of the connecting rod lanced, is transmitted to the engine supports mrod is divided into two masses (Fig.2b): that through the shaft bearing, and the crankcase. referred to the piston pin axis: The total force P acting on the piston is the initial force lrod. cr mmrod. pp rod and that refered to the PPPgt (6) lrod l The force P acting along the cylinder axis rod. pp (Fig, 3) can be resolved into two components: crank axis mmrod. cr rod lrod QP tan  (7) To obtain a dynamically equivalent system KP / cos  (8) the following three conditions should be The force can be transferred along the line observed: (i). A constant total mass K of its action to the center of the crankpin (K' m m m ; (ii). A constant rod.. pp rod cr rod = K) and resolved into two components: position of the center of gravity of the system cos( ) m l m l 0 ; (iii) A NKPcos(  )  (9) rod.... pp rod pp rod cr rod cr cos  constant moment of inertia of the system with sin( ) respect to the center of gravity [1-2]. FKPt sin(  )  (10) Thus, the entire crank mechanism (Fig. 3c) is cos  replaced by a system of two lumped masses Transfer the normal force N along the line of connected by rigid weightless links; the its action to the center of the shaft and denote reciprocating mass at point A: it as N' (i.e., N=N'). The tangential force Ft m m m and the rotating mass at will also be transferred to the shaft center (Ft t p rod. pp point В: mR m cr m rod. cr = F’t = F”t). Here a couple of forces (Ft and In conformity with the adopted system of two F’t) appear with the torque T: masses dynamically equivalent to the crank sin( ) TFRPRPRt  (sin  tan  cos  ) (11) mechanism, the forces of inertia are reduced cos  to two forces: the force Pt induced by the Since the angle  is small, replace tan by reciprocating masses and the centrifugal force sin  sin  NR induced by the rotating ones.  TPRsin sin 2 The force of inertia due to reciprocating 2 masses can be represented as the sum of the The forces N' and F " may be summated. forces of inertia of the first and second t Their resultant K” equal to the force K acting order PP; , which change according to the ii12 along the connecting rod axis loads the main harmonic law: bearings of the shaft. The force K” may be 2 Pi  m i a   m i Rcos    cos2   P i12  P i (4) resolved into two components: Q’ per- where: P m R2 cos and pendicular to the cylinder axis and P’ acting ii1 2 along it. P m R cos 2  ii2 The forces Q’ and Q form a tilting moment Mtilt: 21 Nguyễn Khắc Tuân và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 139(09): 19 - 24 sin( ) where: 1 the crank angle of first cylinder; Mtilt   hQ'   hP tan   P tan R   TR   T Ci is the crank angle of ith cylinder relative sin  to the crank of cylinder 1; Si is the angle of In a multi-cylinder engine there must be a rotation of the crankshaft for the current state sequence in which the powers troke of each of the ith cylinder; cylinder takes place, one after another. In order to evaluate the net engine torque, RESULTS AND DISCUSSION information on the firing order must be The analysis of kinematics and dynamics of available. Successive firings cause a the crank mechanism is normally carried out continuous torque delivery to the crankshaft by graphical method [1,2]. This section output. Since the torque generated by every presents some simulation results that were individual cylinder is dependent on the crank generated using models and equations that angle, the resultant engine torque is a have been outlined. In order to study combination of all individual torques from all kinematics and dynamics of crank cylinders and can be determined in the mechanism, MATLAB software is used with following form: a set of parameters of IEC [1]: mp= 430 g; n mrod =440 g; l= 140 mm; R=49 mm; piston TT(,,)   (12) area 5800 mm2   i1 Ci Si 1 20 3000 rpm 10 2000 rpm 0 1000 rpm -10 Piston speed Piston (m/s) -20 0 50 100 150 200 250 300 350 400 Crank angle (deg) Fig. 4 Piston speed Results for the piston speed are plotted in Figures 4. Positive values refer to the downward direction and negative values to the upward direction. 20000 Pg 15000 10000 P=Pi+Pg 5000 0 Pi -5000 Forceson the piston (N) 0 100 200 300 400 500 600 700 800 Crank angle (deg) Fig. 5 Forces acting on the piston P – Total force Pi – inertia force Pg- Gas force The total force curve P = f () in Fig. 5 shows that at the end of the compression stroke and the beginning of the power stroke the forces of inertia reduce the effort produced by gas pressure on the piston. The total force acting on the piston is important for the further calculations and the power source of the engine. 22 Nguyễn Khắc Tuân và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 139(09): 19 - 24 500 400 n=3000 rpm 300 200 n=4000 rpm 100 0 Enginetorque (Nm) -100 -200 0 100 200 300 400 500 600 700 800 Crank angle (deg) Fig. 6a Single cylinder Engine Torque at speed of crank shaft 3000 rpm and 4000 rpm 1000 n=4000rpm 500 n=3000rpm 0 -500 Totalengine torque (Nm) 0 100 200 300 400 500 600 700 800 First cylinder crank angle (deg) Fig.6b. Four cylinder engine torque at speed of crank shaft 3000 rpm and 4000 rpm In Fig. 6a presents the torque of a single 2. Чистяков В.К. Динамика поршневых и cylinder engine and in Fig. 6b presents the комбинированных двигателей внутреннего total torque of a four-cylinder engine with 1– сгорания, М.: Машиностроение, 1989. — 256 3–4-2 firing order. From Fig. 6a and Fig.6b, it с.: ил. 3. Richard Van Basshuysen , Fred Schafer , can be seen that the differences in the overall Internal Combustion Engine Handbook: Basics, smoothness of torque delivery of a single and Components, Systems, SAE, 2004, 448 p. four- cylinder engine. 4. Guzzella, L. and Onder, C. (2009) Introduction CONCLUSIONS to Modelling and Control of Internal Combustion The analysis of kinematics and dynamics of Engine Systems, 2nd edn. Springer. 5. Pulkrabek, W.W. (2004) Engineering the crank mechanism is normally carried out Fundamentals of the Internal Combustion Engine. by graphical method. The study aims to Prentice Hall, conduct the kinematic and dynamic 6. Chaturvedi D.K. Modeling and Simulation of simulation of the four stroke engine in Systems Using MATLAB and Simulink, CRC MATLAB software. The study results showed Press, 2010. 733 p. that the use of MATLAB software allows 7. 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Một phương pháp mô hình hóa cho phép tính toán động học và động lực học của cơ cấu thanh truyền trục khuỷu của động cơ ô tô đã được xây dựng. Các kết quả nghiên cứu về động học và động lực học của cơ cấu thanh truyền truyền trục khuỷu động cơ 4 kỳ cũng được trình bày chi tiết trong bài báo. Từ khóa: động học, động lực học, cơ cấu thanh truyền trục khuỷu, mô phỏng Ngày nhận bài:20/6/2015; Ngày phản biện:06/7/2015; Ngày duyệt đăng: 30/7/2015 Phản biện khoa học: PGS.TS Vũ Ngọc Pi - Trường Đại học Kỹ thuật Công nghiệp - ĐHTN * Tel: 0912 262771, Email: tuannkcn@gmail.com 24