Machine Motion Equations at the Internal Combustion Heat Engines

Article history Received: 05-03-2015 Revised: 09-03-2015 Accepted: 06-04-2015 Abstract: This paper presents an algorithm for setting the dynamic parameters of the classic main mechanism of the internal combustion engines. One presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed) is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic (generated by the forces out of mechanism). Kinetic energy conservation shows angular speed variation (from the main shaft) with inertial masses, while the dynamic coefficient introduces the variation of ω with forces acting in the mechanism. Deriving the first equation of motion of the machine it obtains the second equation of motion dynamics. From the second equation of motion of the machine one determines the angular acceleration of the motor shaft. It shows the distribution of the forces (on the main mechanism of the engine) to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. The method is applied separately for two distinct situations: When the engine is working on a compressor and into the motor system. For the two separate cases, two independent formulas are obtained for the engine dynamic cinematic (forces speeds). Calculations should be made for an engine with a single cylinder.


Introduction
In conditions which started to magnetic motors, oil fuel is decreasing, energy which was obtained by burning oil is replaced with nuclear energy, hydropower, solar energy, wind and other types of unconventional energy, in the conditions in which electric motors have been instead of internal combustion in public transport, but more recently they have entered in the cars world (Honda has produced a vehicle that uses a compact electric motor and electricity consumed by the battery is restored by a system that uses an electric generator with hydrogen combustion in cells, so we have a car that burns hydrogen, but has an electric motor), which is the role and prospects which have internal combustion engines type Otto, Diesel or Wankel (Amoresano et al., 2013;De Falco et al., 2013a;2013b;Ferguson and Kirkpatrick, 2001;Gunston, 1999;Gupta, 2006;Guzzella, 2004;Heywood, 1988;Karikalan et al., 2013;Lee, 2005;Liu, 1995;Mahalingam and Ramesh Bapu, 2013;Naima and Liazid, 2013;Narasiman et al., 2013;Piltan et al., 2012;Rahmani et al., 2013;Ravi and Subramanian, 2013;Ronney et al., 1994;Sapate and Tikekar, 2013;Sethusundaram et al., 2013;Zahari et al., 2013;Zhu et al., 2007).
Magnetic motors (combined with the electromagnetic) are just in the beginning, but they offer us a good perspective, especially in the aeronautics industry (Gunston, 1999). Probably at the beginning they will not be used to act as a direct transmission, but will generate electricity that will fill the battery that will actually feed the engine (probably an electric motor).
The Otto engines or those with internal combustion in general, will have to adapt to hydrogen fuel . Hydrogen can be extracted industrially, practically from any item (or combination) through nuclear, chemical, by radiation, by burning, etc... (Most easily hydrogen can be extracted from water by breaking up into constituent elements, hydrogen and oxygen; by burning hydrogen one obtains water again that restores a circuit in nature, with no losses and no pollution) . Hydrogen must be stored in reservoirs cell (a honeycomb) for there is no danger of explosion; the best would be if we could breaking up water directly on the vehicle, in which case the reservoir would feed water (and there were announced a few successes) . Now and the life of the jet engine begin to end (only in these forms). Even in these conditions internal combustion engines will be maintained in land vehicles (at least), for power, reliability and especially their dynamics.
Old gasoline engines carry us every day for nearly 150 years. "Old Otto engine" (and his brother, Diesel) is today: Younger, more robust, more dynamic, more powerful, more economical, more independent, more reliable, quieter, cleaner, more compact, more sophisticated, more stylish, more secure and more especially necessary and wanted. At the global level we can manage to remove annually about 60,000 cars. But annually appear other million cars (Table 1). In full energy crisis since 1970 until today, production and sale of cars equipped with internal combustion heat engines has skyrocketed, from some millions yearly to over sixty millions yearly now and the world fleet started from tens of millions reached today the billion. As long as we produce electricity and heat by burning fossil fuels is pointless to try to replace all thermal engines with electric motors, as loss of energy and pollution will be even larger. However, it is well to continuously improve the thermal engines, to reduce thus fuel consumption. Planet supports now about one billion motor vehicles in circulation. Even if we stop totally production of heat engines, would still need 10,000 years to eliminate total the existing car park in the current rate. Electric current is still produced in majority by combustion of hydrocarbons, making the hydrocarbon losses to be higher when we use electric motors. When we will have electric current obtained only from green energy or nuclear, sustainable and renewable energy sources, it is only then that we'll be able to enter gradually and electric motors Rahmani et al., 2013;Ravi and Subramanian, 2013;Ronney et al., 1994;Sapate and Tikekar, 2013;Sethusundaram et al., 2013;Zahari et al., 2013;Zhu et al., 2007).
Otto and diesel engines are today the best solution for the transport of our day-to-day work, together and with electric motors and those with reaction.
For these reasons it is imperative as we can calculate exactly the engine efficiency, in order to can increase it permanently.

Nomenclature
Is the moment of inertia (mass or mechanical) reduced to the motor shaft .

Din m C
a : Is the dynamic acceleration of the point C (in motor system) ϕ 1 = ϕ: Is the position angle of the crank ω m = ω n : Is the constant (nominal) angular rotation speed of the crank (the motor shaft) ω: Is the variable (dynamic) angular rotation speed of the crank (the motor shaft) ε: Is the angular rotation acceleration of the motor shaft; Appears only in dynamic schemes ϕ 2' = ψ: Is the position angle of the rod (element 2), if the rod is considered from the point C ψɺ : Is the angular rotation speed of the rod (element 2) ϕ 2 = θ: Is the position angle of the rod, if the rod is considered from the point B l 1 : Is the length of the crank l 2 : Is the length of the rod (the connecting rod) λ: Is the raport between l 1 and l 2

Determining the First Machine Equation
One presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed) is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic (generated by the forces out of mechanism).
Kinetic energy conservation shows angular speed variation (from the main shaft) with inertial masses, while the dynamic coefficient introduces the variation of ω with forces acting in the mechanism 2013a;2013b;Petrescu and Petrescu, 2014;.
In system (1) The first movement equation of the machine takes the initial forms (system 2) (were selected from system 1 just the two final relations): Since J* is a function of the angle ϕ and ω n is a function of n, it follows that ω is a function of angle ϕ and angular rotation speed n=>ω=ω(ϕ,n).
An additional variation of angular speed is added by multiplying by the coefficient dynamic (generated by the forces out of mechanism). The final forms of the first movement equation of the machine can be seen in the system (3).
where, the dynamic coefficient D takes the values of the system (4) or (5); (4) when the engine works in compressor system and (5) when the mechanism works in motor system: Method is applied separately for two distinct situations: When the engine is working on a compressor and into the motor system. Calculations should be made for an engine with a single cylinder 2013a;2013b;Petrescu and Petrescu, 2014;.

Determining the Second Machine Equation
One keeps just the final relations (7): Observation If one compares the presented equation of motion of the machine (6-7) with the fever (Lagrange), it can identify the reduced (rotation) force, (the reduced load: 8):

Application to the Otto Engine
To determine dynamics at an Otto engine must (first at all) to set the formula of reduced moment of inertia (9); Fig. 1 (it takes a 1 = 0 One determines: How to work: With * *' , J J and * m J it determines the variable ω and ε with relations (3, 7), or (11): Then one calculates the dynamic cinematic with the relations from the system (12):

Dynamic Kinematics Analysis for the Otto Engine in Compressor System
Now, one can see the engine main mechanism in compressor system (when the motor mechanism is acting from the crank) 2013a;2013b;Petrescu and Petrescu, 2014;. It is determining now, the velocities and the accelerations of the piston and motor shaft, normal and dynamic (Fig. 2-5).

Dynamic Kinematics Analysis for the Otto Engine in Motor System
Now, one can see the engine main mechanism in motor system (when the motor mechanism is acting from the piston) 2013a;2013b;Petrescu and Petrescu, 2014;. It is determining now, the velocities and the accelerations of the piston and motor shaft, normal and dynamic ( Fig. 6-9).

Dynamic Kinematics Analysis for an Otto Engine, Mono-cylinder
Now, one can see the engine main mechanism in motor and compressor system (when the motor mechanism is acting from the piston and from the crank). It is determining now, the velocities and the accelerations of the piston and motor shaft, normal and dynamic ( Fig. 10-14).

Discussion
In full energy crisis since 1970 until today, production and sale of cars equipped with internal combustion heat engines has skyrocketed, from some millions yearly to over sixty millions yearly now and the world fleet started from tens of millions reached today the billion. As long as we produce electricity and heat by burning fossil fuels is pointless to try to replace all thermal engines with electric motors, as loss of energy and pollution will be even larger. However, it is well to continuously improve the thermal engines, to reduce thus fuel consumption.
Planet supports now about one billion motor vehicles in circulation. Even if we stop totally production of heat engines, would still need 10,000 years to eliminate total the existing car park in the current rate. Otto and diesel engines are today the best solution for the transport of our day-to-day work, together and with electric motors and those with reaction. For these reasons it is imperative as we can calculate exactly the engine efficiency, in order to can increase it permanently. However, it is well to continuously improve the thermal engines, to reduce thus fuel consumption.

Conclusion
To the internal combustion heat engines the real velocities and accelerations (in dynamic regimes) are different that the cinematic (classic) velocities and accelerations. In this study one can see the engine main mechanism in motor and compressor system (when the motor mechanism is acting from the piston and from the crank). It is determining now, the velocities and the accelerations of the piston and motor shaft, normal and dynamic.
The first movement equation of the machine takes the initial forms (see the relations 2).
The second machine equation is determined by the derivation of the first machine equation in function of the time (see the relations from the system 6).