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The Dynamics of the Otto Engine

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American Journal of Engineering and Applied Sciences Original Research Paper The Dynamics of the Otto Engine 1Relly Victoria Virgil Petrescu, 2Raffaella Aversa, 3Taher M. Abu-Lebdeh, 2Antonio Apicella and 1Florian Ion Tiberiu Petrescu 1ARoTMM-IFToMM, Bucharest Polytechnic University, Bucharest, (CE), Romania 2Advanced Material Lab, Department of Architecture and Industrial Design, Second University of Naples, 81031 Aversa (CE), Italy 3North Carolina A and T State University, USA Article history Abstract: The dynamic calculation of a certain mechanism and of the Received: 29-01-2018 piston crankshaft mechanism, used as the main mechanism for Otto Revised: 03-02-2018 internal combustion engines, also implies the influence of external Accepted: 14-02-2018 forces on the actual, dynamic kinematics of the mechanism. Take into Corresponding Author: account the strong and inertial engine forces. Sometimes weight forces Florian Ion Tiberiu Petrescu can also be taken into account, but their influence is even smaller, ARoTMM-IFToMM, Bucharest negligible even in relation to inertial forces that are far higher than Polytechnic University, gravitational forces. In the present paper, one carry out an original Bucharest, (CE), Romania method of determining the dynamics of a mechanism, applying to the Email: [email protected] main mechanism of an Otto or diesel engine. The presented method of work is original and complete. Relationships (1) express the velocity of the center of gravity to calculate the moment of inertia (mechanical or mass, of the whole mechanism) reduced to the crank (2). In dynamic calculations, the first derivative of the reduced mechanical inertia moment, derived by the angle FI (relations 3-4), is also required. For dynamic calculation, it is also necessary to determine the expression of the total torque momentum and crank-resistance forces (relations 5-6). The differential equation of the machine (7) is arranged under the more convenient forms (8) to solve it. It is easily observed that a second-degree equation has been reached, which is solved by the known formula (9). Keywords: Machines, Mechanisms, Applied Computing, Forces, Velocities, Powers, Dynamics, Engines, Thermal Engines Introduction Karikalan et al ., 2013; Leidel, 1997; Petrescu, 2012a; 2012b; Rahmani et al ., 2013; Ravi and Subramanian, The gasoline engine wears us every day about of 2013; Ronney et al ., 1994; Sapate and Tikekar, 2013; 150 years. The Old Engine Otto (and his brother, Sethusundaram et al ., 2013; Zahari et al ., 2013). Diesel) is today: Younger, more robust, more There is a lot of discussion about the removal of dynamic, stronger, more economical, more the Otto engine, but nothing has yet been prepared to independent, more reliable, quieter, cleaner, more take its place. compact, more sophisticated and especially still Let's talk a little about electric motors. An electric necessary. At the global level, we can eliminate motor is an electrical machine that converts electricity roughly 60,000 cars a year, but millions of new cars into mechanical energy. If we talk in reverse, we are appear annually (Table 1), (Amoresano et al ., 2013; dealing with converting mechanical energy into Anderson, 1984; Bishop, 1950; Choi and Kim, 1994; electricity and is made by an electric generator. De Falco et al ., 2013a; 2013b; Ganapathi and Generators and electric motors are extremely Robinson, 2013; Heywood, 1988; Hrones, 1948; important, today more than ever. © 2018 Relly Victoria Virgil Petrescu, Raffaella Aversa, Taher M. Abu-Lebdeh, Antonio Apicella and Florian Ion Tiberiu Petrescu. This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license. Relly Victoria Virgil Petrescu et al . / American Journal of Engineering and Applied Sciences 2018, 11 (1): 273.287 DOI: 10.3844/ajeassp.2018.273.287 Table 1: World cars produced The Otto engine still remains more dynamic than Year Cars produced in the world electric motors. 2011 59,929,016 Globally, two out of three jobs depend directly or 2010 58,264,852 indirectly on the automotive and machine-building 2009 47,772,598 industries, in particular of the Otto classical engines. 2008 52,726,117 If the current mode of production suddenly changed, 2007 53,201,346 2006 49,918,578 almost half of the world's jobs would disappear, resulting 2005 46,862,978 in an extremely serious global social crisis (Aversa et al ., 2004 44,554,268 2016a; 2016b; 2016c; 2016d; 2017a; 2017b; 2017c; 2003 41,968,666 2017d; 2017e; Berto et al ., 2016a; 2016b; 2016c; 2016d; 2002 41,358,394 Mirsayar et al ., 2017; Cao et al ., 2013; Dong et al ., 2013; 2001 39,825,888 Garcia et al ., 2007; Garcia-Murillo et al ., 2013; He et al ., 2000 41,215,653 2013; Lee, 2013; Lin et al ., 2013; Liu et al ., 2013; 1999 39,759,847 Padula and Perdereau, 2013; Perumaal and Jawahar, 2013; Most electric motors work by interacting with a Petrescu, 2012a; 2012b; Petrescu and Petrescu, 1995a; magnetic field of an electric motor and the winding currents 1995b; 1997a; 1997b; 1997c; 2000a; 2000b; 2002a; 2002b; to generate force. In some applications, such as regenerative 2003; 2005a; 2005b; 2005c; 2005d; 2005e, 2016a; 2016b; braking with traction motors in the transport industry, 2016c; 2016d; 2016e; 2013; 2012a; 2012b; 2011; electric motors can also be used in the reverse direction as Petrescu et al ., 2009; 2016a; 2016b; 2016c; 2016d; 2016e; generators to convert mechanical energy into electricity, 2017a; 2017b; 2017c; 2017d; 2017e; 2017f; 2017g; that is, they recover energy that otherwise would lose. 2017h; 2017i; 2017j; 2017k; 2017l; 2017m; 2017n; Electric motors can be found in as diverse applications 2017o; 2017p; 2017q; 2017r; 2017s; 2017t; 2017u; as industrial fans, blowers and pumps, machine tools, 2017v; 2017w; 2017x; 2017y; 2017z; 2017aa; 2017ab; household appliances, power tools and disc drives, electric 2017ac; 2017ad; 2017ae; Petrescu and Calautit, 2016a; motors can be powered by DC sources such as Be batteries, 2016b; Reddy et al ., 2012; Tabaković et al ., 2013; cars or rectifiers; through AC (AC) sources, such as from the mains, inverters or generators. Small motors can be Tang et al ., 2013; Tong et al ., 2013; Wang et al ., 2013; found in electric watches. General purpose motors with Wen et al ., 2012; Antonescu, 2000; Antonescu and very standardized dimensions and features provide a Petrescu, 1985; 1989; Antonescu et al ., 1985a; 1985b; convenient mechanical power for industrial use. 1986; 1987; 1988; 1994; 1997; 2000a; 2000b; 2001). The largest of the electric motors are used for ship propulsion, pipe compression and pumping-storage Materials and Methods applications with a rating of 100 megawatts and today are increasingly used in industrial robots and in mechatronic Figure 1 shows the kinematic scheme of an Otto mobile systems. Electric motors can be classified by types internal combustion engine (Petrescu, 2012b). of power sources, internal construction, applications, Relationships (1) express the velocity of the center output type of motion and so on. of gravity to calculate the moment of inertia Electric motors are therefore used to produce linear (mechanical or mass of the whole mechanism) reduced or rotary forces and must be distinguished from devices to the crank (2). In fact, squares of the velocities weight such as magnetic solenoids and loudspeakers that centers ( S2 and S3) of the mechanism are required convert electric power into motion but do not generate (Mirsayar et al ., 2017; Cao et al ., 2013; Dong et al ., usable mechanical powers which are referred to as 2013; Garcia et al ., 2007; Garcia-Murillo et al ., 2013; actuators and transducers. He et al ., 2013; Lee, 2013; Lin et al ., 2013; Liu et al ., Perhaps the first electric motors were simple 2013; Padula and Perdereau, 2013; Perumaal and electrostatic devices created by the Scottish monk Jawahar, 2013; Petrescu and Petrescu, 1995a; 1995b; Andrew Gordon in the 1740s. Only today, after nearly 1997a; 1997b; 1997c; 2000a; 2000b; 2002a; 2002b; three hundred years of existence, the electric motors begin to be put to work at their full capacity. 2003; 2005a; 2005b; 2005c; 2005d; 2005e, 2016a; However, in transports, although they have gone a 2016b; 2016c; 2016d; 2016e; 2013; 2012a; 2012b; long way, electric motors could not take the place of the 2011; Petrescu et al ., 2009; 2016a; 2016b; 2016c; Otto motor home, obviously primarily due to technical 2016d; 2016e; 2017a; 2017b; 2017c; 2017d; 2017e; problems, then for reasons of dynamics and thirdly due 2017f; 2017g; 2017h; 2017i; 2017j; 2017k; 2017l; to social reasons. 2017m; 2017n; 2017o; 2017p; 2017q; 2017r; 2017s; Powering a car with electricity is difficult today, 2017t; 2017u; 2017v; 2017w; 2017x; 2017y; 2017z; compared to vehicles equipped with internal combustion 2017aa; 2017ab; 2017ac; 2017ad; 2017ae; engines. Petrescu and Calautit, 2016a; 2016b; Reddy et al ., 274 Relly Victoria Virgil Petrescu et al . / American Journal of Engineering and Applied Sciences 2018, 11 (1): 273.287 DOI: 10.3844/ajeassp.2018.273.287 2012; Tabaković et al ., 2013; Tang et al ., 2013; Tong et al ., 2013; Wang et al ., 2013; Wen et al ., 2012; Antonescu and Petrescu, 1985; 1989; 0 Antonescu et al ., 1985a; 1985b; 1986; 1987; 1988; y 1994; 1997; 2000a; 2000b; 2001): yrB =⋅sinϕ +⋅ l sin ψ ; r ⋅ cos ϕ +⋅ l cos ψ =⇒ 0 S3 2 2 l⋅cosψ =−⋅ r cos ϕψλϕψ ;cos =−⋅ cos ;sin =−⋅ 1 λ cos ϕ 3 sin ϕ −⋅lsinψψ ⋅=⋅& r sin ϕωψλ ⋅⇒=−⋅ & ⋅ ω B sin ψ ψ⋅sin ψψ +⋅2 cos ψ =−⋅ λ cos ϕω ⋅⇒ 2 && & 2 λ⋅−(1 λ2 ) ⋅ cos ϕω ⋅ 2 ψ&& = − 3 sin ψ vyrB≡& B =⋅cosϕω ⋅+⋅ l cos ψψ ⋅=& α l = l2 sinϕ sin( ψ− ϕ ) ' =r ⋅ cos ϕ ⋅⋅+⋅ωλ1 =⋅r ⋅=⋅⇒ ωω s B sinψ sin ψ 2 S2 ''sin(ψϕ− ) '2'22 sin ( ψϕ − ) ⇒≡=⋅ssrGB ⇒≡=⋅ ssr GB 2 3 sinψ3 sin ψ ψ = φ2 xr=⋅cosϕ +⋅ a cos ψ xr =−⋅ sin ϕω ⋅−⋅ a sin ψψ ⋅ S2 &S 2 & ⇒ a yr=⋅sinϕ +⋅ a sin ψ yr =⋅ cos ϕω ⋅+⋅ a cos ψψ ⋅ S2 &S 2 & l sin ϕ x= − r ⋅ sinϕω⋅+⋅⋅a λψ sin ωλ =−⋅−⋅ ( l a ) sin ϕω ⋅ A &S2 l sin ψ 1 l 2 sinϕ sin ϕ yrS =cosϕωλ + a cos ϕ ωλϕ = cos la +⋅ λ ω & 2 r = l1 l sinψ sin ψ 2 ω1 φ '2 '2 '2 2 22 2 2 sin ϕ sxyG=+=− S S λ( la ) sin ϕλϕ + cos la +⋅⋅ λ 2 2 2 sin ψ (1) 2 X sin ϕ '2 2 2 2 2 O S1 sG =⋅−λ( la ) ⋅ sin ϕ ++⋅⋅ la λ ⋅cos ϕ 2 sin ψ Fig.
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  • Gottlieb Daimler

    Gottlieb Daimler

    Gottlieb Daimler Gottlieb Wilhelm Daimler (German pronunciation: day morning classes. In 1853, Daimler, with Steinbeis’ [ˈɡɔtliːp ˈdaɪmlɐ]; 17 March 1834 – 6 March 1900[1]) assistance, got work at “the factory college”, F. Rollé und was an engineer, industrial designer and industrialist born Schwilque(R&S) in Grafenstaden, so-called because its in Schorndorf (Kingdom of Württemberg, a federal state manager, Friedrich Messmer, had been an instructor at of the German Confederation), in what is now Germany. Karlsruhe Institute of Technology.[3] Daimler performed He was a pioneer of internal-combustion engines and well, and when Rollé und Schwilque began making rail- automobile development. He invented the high-speed way locomotives in 1856, Daimler, then 22, was named petrol engine. foreman.[3] Daimler and his lifelong business partner Wilhelm May- Instead of staying, Daimler took two years at Stuttgart’s bach were two inventors whose goal was to create small, Polytechnic Institute to hone his skills, gaining in-depth high-speed engines to be mounted in any kind of loco- grasp of steam locomotives, as well as “a profound con- motion device. In 1885 they designed a precursor of viction” steam was destined to be superseded.[3] He con- the modern petrol (gasoline) engine which they subse- ceived small, cheap, simple engines for light industrial quently fitted to a two-wheeler, the first internal combus- use, possibly inspired by the newly developed gas engines tion motorcycle and, in the next year, to a stagecoach, and of that era.[3] a boat. Daimler called it the grandfather clock engine In 1861, he resigned from R&S, visiting Paris, then went (Standuhr) because of its resemblance to a large pendu- on to England, working with the country’s top engineer- lum clock.