Document Sample

12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx Thermodynamic and dynamic analysis of an internal combustion engine with a noncircular-gear based modified crank-slider mechanism H. F. Quintero* C. A. Romero† L. V. Vanegas Useche‡ Associate Professor Titular Professor Associate Professor Universidad Tecnológica de Pereira Pereira, Colombia Abstract—This paper presents a model for the calculation mechanisms, pumps, flow meters, and instruments. New of in-cylinder parameters in an internal combustion engine with applications have also been reported. Doege et. al. [1] a noncircular gear based modified crank-slider mechanism. present a new press concept using noncircular gears in the With the introduction of noncircular gears, the instantaneous driving mechanism. Dooner [2] and Yao and Yan [3] velocity of the piston can be accommodated to improve combustion performance. The displacement law of the propose using noncircular gears to reduce any undesired noncircular gears is obtained using a B-spline curve, so that the torque and speed fluctuations in rotating shafts. Fam et. appropriate instantaneous velocity of the piston is obtained. The al. [4] design a mechanical device consisting of a gas pressure and temperature required for the determination of noncircular gear pair that acts as a variable-ratio mechanical and thermal loads on engine components are found. transmission between an electro-mechanical actuator and The influence of the noncircular gears on the loads that act on a flexible structure. Han et. al. [5] design a noncircular all the components of the crank-slider mechanism, as well as the front gear to maximize the mechanical power output of a theoretical output torque for a given geometrical structure and driving system for a conventional bicycle. Dooner [6] uses inertial properties, are presented. To obtain the pressure and a noncircular gear pair to achieve a two degree of freedom temperature inside the cylinder, under different operating parameters, such as air fuel ratio and spark angle advance, a function generator. Librovich [7] uses noncircular gears in Zero dimensional model is applied. The proposed mechanism a torque transmission mechanism of a rotary vane engine. enables the optimisation of the combustion cycle; therefore, Voelkner [8] explains the advantages of using these tooth greater power may be achieved. bodies in press-driving mechanisms in the metal-forming *†‡ field. Vanegas Useche et. al. [9] develop a noncircular Keywords: noncircular gears, internal combustion engine gear pair for minimising shaft accelerations of the driven gear. This paper proposes a novel modified crank-slider I. Introduction mechanism of an internal combustion engine, by Non-uniform rotation mechanisms are required in many introducing a noncircular gear pair. The noncircular tooth applications. Noncircular gear wheels can be used to bodies enable to adjust the piston speed throughout the produce rotary motion with variable transmission ratio entire cycle, so that the performance of the engine can be and, compared to linkages, provide a number of design improved. advantages such as accurate transmission, ease of In spark ignition engines, the improvement of balancing, and compact size. Furthermore, they are very performance is constrained by the non-variability of the versatile because of the great flexibility to obtain a desired piston velocity law in accordance with the needs of the transmission function. combustion process. With the introduction of a Research on noncircular gears has been very limited. noncircular gear pair in the engine mechanism, the Most of the research on these tooth bodies have duration of the portion during which the non burned concentrated on (i) the development of pitch curves for charge is subjected to high pressures and temperatures can different applications or to satisfy specific requirements be diminished. Thus, the knock tendency of the engine [1-9], as reviewed in the next paragraph; (ii) the would be reduced. This modification also reduces the development of new tooth profiles; and (iii) the derivation rejected heat. of mathematical models to describe and manufacture teeth Since, to the knowledge of the authors, a mathematical of noncircular gears and their cutters. Reviews on model for piston velocity that optimizes the combustion noncircular gears have been presented in previous works process has not been developed, this work proposes a [9,10]. design for the displacement law of the noncircular gear set Classical applications of noncircular gears are found in based on B-spline curves. These curves provide a automatic machinery, packaging machines, quick return powerful tool for designing displacement laws, because they give the designer a higher-level interface and the curve design is thus more intuitive. * E-mail: hquinte@utp.edu.co The primary input in mechanical design analyses is the † E-mail: cromero@utp.edu.co data of the dynamic pressure of the cylinder. In the engine ‡ E-mail: lvanegas@utp.edu.co 1 12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx design process, a predictive model for the combustion where: process has to be selected. For simplicity, a Zero- dQrech is the overall rejected heat transfer (W/m2) dimensional or single zone model has been chosen in this A is the cylinder area (m2) work, in accordance with the approach found in Zhelezko Tg is the effective gas temperature, typically 800 °C [11]. With a Zero-dimensional model, the cylinder charge Tcool is the coolant temperature, typically 80 °C is assumed to be homogeneous in both temperature and hg is the film coefficient or heat transfer coefficient (W/ composition. m2 ºC). Models for in-cylinder thermodynamics and dynamics The heat transfer coefficient depends on the engine of the crank-slider mechanism are integrated in this work geometric parameters, such as the exposed cylinder area to configure a concise methodology for an easy simulation and bore, as well as the piston speed. The coefficient of an internal combustion engine. Based on this varies with location and piston position. In this research, methodology, a computer program to analyze pressure, to model the heat exchange between gas and cylinder temperature, heat release, forces, and torques is wall, the Woschni equation has been used [14]. In this developed. The program is written in the MathematicaTM model, applied to the internal combustion engine, the software language. Results for an example case are equation has the form: presented, with an angular resolution of 0,25 degree of crank angle (2880 data points per engine cycle) and under − hg = 1, 2 ⋅10−2 ⋅ D −0.2 ⋅ p0.8 ⋅ Tg 0.53 ⋅ w0.8 (5) steady operation conditions. Finally, a noncircular gear pair is designed in order to optimise the operation of the where engine. V ⋅T w = (Cw1 ⋅ cm + Cw 2 ⋅ cu ) + C2 T CA ⋅ ( p − p0 ) (6) II. Thermodynamic modelling pCA ⋅ VCA The first law of thermodynamics for engine cylinder systems states that D is the cylinder diameter in m p is the instantaneous pressure in N/m2 dUs = dQ + dW (1) Tg is the instantaneous temperature of the gas in K where cm is the mean velocity of the piston in m/s dW = pdV cu is specific heat of the gas in J/ kg K dUs = mcv dT VT is the displaced volume in m3 dT = d(pV)/mR TCA is the charge temperature at intake valve closing in K R/cv = k – 1 (2) pCA is the charge pressure at intake valve closing in N/m2 VCA is the charge volume at intake valve closing in m3 where dUs is the change in internal energy, dQ is the heat p0 is the instantaneous pressure for motored engine in added to the system, dW is the mechanical work done by N/m2. the system, m is the working charge mass, cv is the The constants Cw1, Cw2, and C2 take the values given in constant volume specific heat, p is the pressure, V is Tables 1 and 2. volume, T is temperature, k is adiabatic constant, and R is Table 1. Coefficients Cw1 and Cw2 (Source: [15]) the gas constant. Using the ideal gas law (neglecting the change in gas Cw1 Cw2 constant R and gas leakages), and after some Gas exchange process 6,18 0,417 transformations, the following expression for the heat Compression-expansion release is obtained: 2,28 0,308 process k 1 Table 2. Coefficient C2 (Source: [15]) dQhr = p dV + V dp + dQrech (3) k −1 k −1 C2 Open chamber 3,24 × 10-3 This is the traditional equation for the evaluation of the Divided chamber 6,22 × 10-3 heat release, which can be inferred from Gatowski et al. [12] and Brunt and Platts [13]. The combustion process is dealt with in accordance with For the average overall heat transfer from the gas to the the approach in Zhelezko [11]. cylinder coolant, convection type heat transfer equations The combustion process starts with the spark ignition are used: (neglecting the retarding period of the combustion process), point y in Fig. 1. During this phase, the pressure ( dQrech = Ahg Tg − Tcool ) (4) increases as a result of two factors: the geometrical compression and the heat release corresponding to the fraction of the mass burned [15]. 2 12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx proposed modification, the curve of the piston speed can be defined as a function of the angle of rotation of the crankshaft, and it is not limited to the modification of the dimensions of the crank-slider mechanism. crank slider mechanism driving gear driven gear Fig. 2. Modified crank slider mechanism Following Lagrangian analysis, as in [16], the vector of generalized coordinates of the mechanism is q = {ϕ, β, sp}T, where ϕ, β and sp are the angular position of the Fig. 1. Indicator diagram, p-ϕ. crank, the angular position of the connecting rod, and the position of the piston respectively. These and other The combustion heat release can be expressed in terms variables are shown in Figure 3. Vector q gives the of the lower heating value of the fuel, Hi, and the fuel configurations of the mechanism. The constraint equation burning rate; the lower heating value can be found in fuel vector, f(q) = 0, is the set of equations that impose the tables. The burning fuel rate is calculated as the product of geometrical constraints of the linkage mechanism: induced fuel mass, mf, and mass fraction burned. The induced fuel mass can be calculated from the specific fuel f1 : r cos ϕ + L cos β − sp = 0 consumption and maximum power at a given speed, while (8) f 2 : r sin ϕ − L sin β = 0 the mass fraction burned is estimated by a Wiebe function [11]: ω1 ϕ − ϕ0 x = 1 − exp −6,908 (7) L ϕz r ϕ β p .G In expressions (1) and (6), it is important to note that 6m since the gas pressure in the cylinder is dependent on the Ip piston displacement law, the heat release, and the heat losses, any variation in the piston displacement law affects Fig. 3. Kinematics of a crank-slider mechanism the in-cylinder pressure and heat losses, which in turn affect the output performance of the engine. Therefore, a The vector q is usually subdivided into an independent manner in which the piston displacement law can be modified is needed. coordinates vector {qi} = {ϕ} and a dependent coordinates vector {qd} = {β, sp}T. III. Noncircular gear based modified crank slider The velocity analysis can be carried out after mechanism differentiating the system of constraint equations with respect to time: Nowadays big efforts are devoted to the improvement of the combustion process of internal combustion engines. d ∂f Although combustion models have been refined, few f (q, t ) = ⋅q = 0 & (9) movements have been made towards changing the piston dt ∂q kinematics. In order to improve the performance of the internal combustion engine, a novel concept is explored in The Jacobian matrix is the partial derivation of the this work: the introduction of noncircular gears in the constraint equation with respect to the generalized transmission of the engine. Figure 2 presents the coordinates vector, J q = ∂ f i / ∂ q j : schematic representation of the proposed modified crank- slider mechanism that includes a noncircular gear pair. −r sin ϕ − Lsin β −1 The driven gear rotates with the crankshaft, and the Jq = (10) driving gear rotates with the power shaft. With the r cos ϕ − L cosβ 0 3 12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx The angular velocities of crank link and connecting rod and driven gear wheels, respectively. This work proposes (Fig. 2) are obtained by expressing the generalized the design for the displacement law of the noncircular velocity vector in terms of two components: a generalized gear set based on B-spline curves. The objective of the dependent vector, {qd } , and a generalized independent & curve designed is to obtain a higher piston velocity around the top dead centre. vector, {qi } : & Figure 5 presents a comparison of the piston displacement curves of the conventional crank-slider q & mechanism and the mechanism proposed in this paper. In J q,d | J q,i | d = J q,d {qd } + J q,i {qi } = 0 q & & the traditional mechanism (dashed line), the angular speed &i of the crank is considered constant and equal to that of the −1 {qd } = − J q, d & ⋅ J q , i ⋅ ω1 (11) crankshaft. This produces an Sp-ϕ1 curve of sinusoidal −1 form. The coordinate ϕ1 represents the angular position of ω2 − L sin β −1 −rsin ϕ the crankshaft. v = − ⋅ ⋅ ω1 p − L cos β 0 rcosϕ sp [m] Differentiation of Equation (11) with respect to time 0,5 allows finding the angular accelerations of both links: 0,4 modified mechanism 0,3 J q,d {qd } + {qd }T ⋅ J q , d ⋅ {qd } & && & & 0,2 conventional + {qi } J q , i ⋅ {qi } = 0 T & & & mechanism 0,1 −1 α 2 − Lsin β −1 (12) = − ⋅ 0 ap − L cos β 0 0 1 2 3 4 5 6 ϕ [rad] −ω2 Lcos β 0 ω2 −r cos ϕ 2 Fig. 5. Piston displacement + ⋅ ω1 ω2 L sin β 0 ω3 −r sin ϕ In the proposed mechanism with noncircular gears, it is IV. Displacement law design considered that the angular speed of the crankshaft is constant. Based on this, the angular velocity of the crank In this section, a noncircular gear set is designed. The would be given by the product of the angular velocity of gear pair is positioned between the crankshaft and the new the crankshaft and the gear ratio. In this case, the output shaft with the aim of increasing the piston velocity coordinate ϕ1 represents the angular position of the before and after the top dead centre. This has the twofold driving gear. objective of reducing the area of convective heat transfer during the main combustion period and enabling the vp [m/s] compression ratio to increase beyond the limits imposed 50 conventional by the knocking phenomena to conventional engines. mechanism 25 ϕ2 [rad] 6 0 5 -25 modified 4 mechanism -50 3 0 1 2 3 4 5 6 ϕ [rad] 2 Fig. 6. Piston speed 1 V. Dynamic loads 0 The primary input needed for mechanical design 0 1 2 3 4 5 6 ϕ1 [rad] analyses is the dynamic cylinder pressure data. In the Fig. 4. Displacement law of the noncircular gear pair thermodynamic model, the combustion process is considered to occur in the same displacement interval of Figure 4 shows a displacement law of noncircular gears, the piston for both the conventional and modified where ϕ1 and ϕ2 are the angles of rotation of the driving mechanisms. 4 12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx The torque of the engine is obtained from the study of VI. Results the power in the system. Neglecting the friction forces, the Figure 7 shows the curves of the torque in the crankshaft forces that act in the mechanism are the inertial force against ϕ1 for both the conventional and the modified mechanism. F0 = −∑ mi aGi (13) Tm [Nm] and the force due to the pressure of the gas, Fg; the torque 1000 modified that acts in the mechanism is the torque in the crankshaft, mechanism Tm. Therefore: conventional d Ec = − Fg ⋅ vp + Tm ω1 (14) 500 mechanism dt On the one hand, the total kinetic energy of the conventional mechanism is the sum of the kinetic energy 0 of the crank, the connecting rod, and the piston: 0 0,5 1 1,5 ϕ [rad] 1 2 1 1 2 1 Fig. 7. Torque in the engine for both conventional and modified Ec = 2 J 01ω1 + J 2 ω2 + m2 v2 + mp vp 2 (15) mechanisms 2 2 2 2 Considering an engine of 8 cylinders, the energy The derivative of the kinetic energy is: available in a thermodynamic cycle is 482 N m, for the conventional engine, and 498 N m, for the modified d Ec = ( J 2 ω2 α 2 + m2 vG2 ⋅ aG2 ) + mp vp ⋅ ap (16) engine. Therefore, there is an increase of the energy dt available in a cycle. The curves for the pressure against ϕ1 for both On the other hand, assuming that the crankshaft and, configurations are shown in Figure 8. The pressure in the consequently, the driving gear rotate at constant speed, the modified mechanism configuration is slightly higher than total kinetic energy of the proposed mechanism is: that in the conventional configuration. p [MPa] 1 2 1 2 Ec = J dr ωdr + J driven ωdriven 7 2 2 (17) 6 1 2 1 2 1 2 1 2 J 01ω1 + J 2 ω2 + m2 v2 + mp vp 2 2 2 2 5 4 The derivative of the kinetic energy is: conventional 3 mechanism modified 2 mechanism d Ec = ( J driven + J 01 ) ω1α1 + dt (18) 1 ( J 2 ω2 α 2 + m2vG2 ⋅ aG2 ) + mp vp ⋅ ap 0 0 2 4 6 8 10 12 ϕ1 [rad] The external force that acts in the mechanism is the Fig. 8. Pressure force produced by the pressure of the gas, Fg; the torque that acts in the mechanism is the torque in the crankshaft, Figure 9 presents the heat flux due to losses by Tm. Hence: convection at the engine. As may be inferred from Figure 9, the magnitude of heat transferred to the combustion d Ec chamber walls has the biggest changes during combustion = − Fg ⋅ vp + Tm ωdr (19) dt and expansion. With the modified mechanism, the behaviour of the heat flux has the same sharp rise as that of the conventional mechanism, but the maximum is followed by a more rapid decrease, resulting in a lower amount of heat loss. 5 12th IFToMM World Congress, Besançon (France), June18-21, 2007 CK-xxx Q [kW] References 250 [1] Doege, E., Meinen, J., Nuemaier, T., and Schaprian, M. conventional mechanism Numerical design of a new forging press drive incorporating 200 noncircular gears. Proc of the Inst. of Mech. Eng, J. of Engineering Manufacture Part B, 215(4): 465-471, 2001. 150 [2] Dooner, D. B. Use of noncircular gears to reduce torque and modified speed fluctuations in rotating shafts. Journal of Mechanical 100 mechanism Design, 119(2): 299–306, 1997. [3] Yao, Y. A. and Yan, H. S. A new method for torque balancing of 50 planar linkages using non-circular gears. Proceedings of the 0 Institution of Mechanical Engineers, 217(5): 495-502, 2003. [4] Fam, Y. L., Sang, C. M., and Nan, J. J. Concurrent mechanism 5 6 7 8 9 ϕ1 [rad] and control design for the slewing of flexible space structures. Journal of Mechanical Design, 116(3): 944-951, 1994. Fig 9 Heat lost by convection [5] Han, P. S., Thomlinson, M. A., and Tu, Y. S. Kinematics and kinetics of a noncircular bicycle drive system. Mechanisms and Machine Theory, 26(4): 375–388, 1991. Even though the amount of energy saved in this case is [6] Dooner, D. B. A geared 2 DOF mechanical function generator. not impressive, an optimized design can be attempted to Journal of Mechanical Design, 121(3): 65–70, 1997. reduce further heat losses. [7] Librovich, B. V. Dynamics of rotary vane engine. Journal of In Figure 10, the noncircular gears designed are Mechanical Design, 125(3): 498–508, 2003. [8] Voelkner, W. Present and future developments of metal forming: illustrated. The number of teeth of each gear is 40, and the selected examples. Journal of Materials Processing Technology, pressure angle of the rack cutter is 30º. 106: 236–242, 2000. [9] Vanegas Useche, L. V., Abdel Wahab, M. M., and Parker, G. A. driven Design of noncircular gars to minimise shaft accelerations. 8th driving gear wheel Biennial ASME Conference on Engineering Systems Design and gear wheel Analysis, Proceedings of ESDA2006, ASME paper ESDA2006- 95560, Turin, Italy, July 2006. [10] Quintero, H. F., Cardona, S., and Jordi, L. Engranajes no circulares: aplicaciones, diseño y manufactura. Scientia et Technica, 24: 133-138, 2004. -0.5 [11] Zhelezko, B. A. Construction and design fundamentals for automobiles and tractors engines, Superior School Minsk, 1988. [12] Gatowski, A., Balles, E. N., Chun, K. M., Nelson, F. E., Ekchian, J. A., and Heywood, J. B. Heat release analysis of engine pressure data. SAE Technical Paper 841359, 1984. [13] Brunt, M. and Platts, K. Calculation of heat release in direct injection diesel engines. SAE Paper 1999-01-0187, 1999. [14] Woschni, G. A. A universally applicable equation for the Fig. 10. Gear wheels instantaneous heat transfer coefficient in the internal combustion engine. SAE Paper, No. 670931, 1967. VII. Conclusion [15] Romero, C. A. and Quintero, H. F. Prediction of in-cylinder pressure, temperature, and loads related to the crank slider This paper proposed a modified crank-slider mechanism mechanism of I. C. engines: a computational model. SAE of an internal combustion engine, through the introduction Congress, Detroit, 2003. of a noncircular gear pair; the driven gear rotates with the [16] Cardona, S. and Clos, D. Teoría de máquinas, Ediciones UPC, Barcelona, España, 2001. crankshaft and the driving gear is coupled to the output power shaft. With these gears, the piston speed can be adjusted to obtain the desired performance of the engine. The thermodynamic and kinematic analyses of the proposed mechanism were presented. A noncircular gear pair was designed using B-spline curves, based on the optimisation of engine performance. The results of the example presented indicate that the performance of the engine can be improved with the proposed mechanism. VIII. Acknowledgements The authors would like to thank the support of the Universidad Tecnológica de Pereira, at which H. F. Quintero and L. V. Vanegas are Associate Professors and C. A. Romero is Titular Professor. 6

DOCUMENT INFO

Shared By:

Categories:

Tags:
Blast Waves, No. 4, Combustion and Flame, No. 2, Combustion Institute, SAE Paper, New York, No. 1

Stats:

views: | 37 |

posted: | 4/5/2010 |

language: | English |

pages: | 6 |

OTHER DOCS BY fdjerue7eeu

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.