Procedia Engineering 106 ( 2015 ) 183 – 191

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1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)doi: 10.1016/j.proeng.2015.06.023

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Dynamics and Vibroacoustics of Machines (DVM2014)

Study of the Dynamic Characteristics of a Two-Cylinder Internal Combustion Engine Using Vector Models

Boris B. Kosenok, Valeriy B. Balyakin* Samara State Aerospace University, Moskovskoe shosse, 34, Samara, 443123, Russian Federation

Abstract

It is known that there is the influence of mass and geometric parameters such as the ratio of the lengths of crankshaft and connecting rod of the main mechanism of ICE on the dynamic characteristics of the engine. At the same time the effect of the mutual disposition of crankshafts in multi-cylinder engines on the dynamic characteristics that depend on the location of the cylinders themselves (in-line, v-shaped, horizontally-opposed engine) is not analyzed. The goal of the research is to evaluate the impact of changes in the angle between the crankshafts depending on the position of the cylinders, on improvement of the dynamic characteristics of ICE. For the solution of the matter in question was used the software package KDAM developed on the basis of the method of vector space model, which is capable of modeling different linkages, as well as the indicator diagrams of ICE. The results of numerical experiment show that parameters under consideration do not significantly effect on the amount of torque, but at the same time, their optimization reduces the load on the crankshaft and the vibration of the motor housing. It is important to understand that the obtained results are optimal only for the selected weight dimension characteristics of units and their locations. At the same time, it can be concluded that for the different types of ICE, due to their structural optimization can be obtained less dynamically loaded constructions. © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014).

Keywords: vector; contour; model; modules; slider-crank mechanism; an internal combustion engine; indicator positioning diagram.

* Corresponding author. Tel.: +7-905-018-2468; E-mail address:029-029@mail.ru.

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of organizing committee of the Dynamics and Vibroacoustics of Machines (DVM2014)

184 Boris B. Kosenok and Valeriy B. Balyakin / Procedia Engineering 106 ( 2015 ) 183 – 191

1. Introduction

Currently drones are used in a wide range of applications in the world. The usual power plant of such flying objects are internal combustion engines (ICE) which must have optimum dynamic characteristics at minimum weight. The most commonly used engines are V-shaped and opposite two-cylinder ICE.

Practically all works during design and research of ICE are directed to increasing the engines' effectiveness. Researches in which increase of effectiveness of ICE is studied can be sited as follows: increase of effectiveness by modeling of thermodynamic processes of ICE [1-4], improvement of cooling [5], and optimization of fuel effectiveness [6, 7]. In the works [8, 9] attention is drawn to improving dynamic, strength and vibration characteristics of ICE whereas there are few works [10, 11] in which research is carried out on the influence of kinematic parameters on dynamic and vibration characteristics of ICE. Existing methods of balancing calculations if ICE [12, 13] based on the principle of mirror placement of cranks, which balances first order inertia forces, at the same time, do not answer the question of how effective this layout is in obtaining optimal dynamic and strength characteristics.

This research aims to analyze the dynamics of the existing layouts of engine cylinders and finding relative positions of elements in the basic mechanism of ICE for optimal dynamic and strength characteristics.

2. Problem definition and assumptions

A two-cylinder scheme of ICE with a two-stroke working cycle was chosen for the study model. An assessment is made of the influence of variation of the angle between the axis of engine cylinders (αcyl) and the angle between the cranks of cylinders (αcr) on the balancing moment and useful resistance obtained during mathematical modeling.

In order to obtain a preliminary assessment of the ICE characteristics, the following assumptions were taken: the mechanism consist of ideal elements with ideal links, friction is not considered, the indicator diagram does not depend on the rotating speed of output shaft, the moment of inertia of crank is zero (counterweight is installed), all characteristics are studied for one and the same number of rotations of the engine crankshaft.

3. Method of solution and discussion of results

The study of the dynamics of the slider-crank mechanism of a classical ICE was carried with the by method of vector modeling [14] in the software program "Kinematic and Dynamic Analysis of Mechanisms" (KDAM).

Fig. 1 shows the scheme of the slider-crank mechanism, and Fig. 2 shows its vector model drawn in KDAM. This kind of model describes the kinematic parameters of the chosen scheme of mechanism and allows us to obtain the solution to the problems of positioning, velocities, and accelerations of kinematic elements. By completing the given vector with the mass and moment of inertia of each element, with coordinates of centers of masses, as well as with the values of and coordinates exertion of active loads, we obtain a generalized dynamic model. The results of kinematic and dynamic studies of various mechanisms with the use of the given program were compared with the results obtained from the software program "ADAMS" with less that 3% disparity [15].

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Fig. 1. Kinematic scheme of V- shaped ICE: 1- crankshaft, 2 and 4- couplers, 3 and 5 – pistons.

KDAM has a multi-window working mode, which makes it possible to change any parameter and immediately assess its influence on dynamic characteristics of interest.

The advantages of this method are its simplicity and universality because any kinematic scheme of a linear, V-shaped or opposite-cylinder engine can be represented in a module of vector models.

Indicator diagrams were calculated and converted into loads acting on both cylinders with the use of KDAM. A study was carried out of the work of the main mechanism of ICE for 36 different positions of the angle between

the axis of the cylinders from 0° to 360° in which for each angle, a calculation was made with the changed angle between the cranks of the left and right cylinders from 0° to 360°.

Fig. 2. Vector Model of V- Shaped ICE: 1, 2, 3, 4, 5, 6 –vectors modeling the motion of elements.

Reduced loads and moments of inertia of the reduction link were chosen as characteristics to be analyzed. Link 1 was chosen as the reduction link (see Fig.1).

Fig. 3 shows the variation reduced moments, balancing moments and moment of inertia for the V-shaped ICE with respect to rotation angle of the crankshaft from 0° to 360° (for one work cycle).

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Fig. 3. Graph of reduced МR and balancing МBAL moments, reduced moment of inertia JR

with respect to rotation angle of crankshaft α: - МR; - МBAL; - JR.

Based on these graphs, a search was carried out for the values angles αcyl and αcr that correspond to the minimum value of the maximum balancing moment МBAL (reduced loads from active loads plus forces of inertia and gravity), amplitudes of the reduced moment of inertia ΔJR and of coefficient of mechanical losses (the ratio of negative work to positive work) КML = [A(-)/A(+)] 100%.

The obtained results well collected to common tables and graphs were drawn based on them (Fig. 4 - 6). Fig. 4 shows the graph for obtained maximum balancing moments; the x-axis represent the angle between axis of cylinders αcyl from 0° to 360° while the y-axis represents the maximum balancing moment. Each curve is a function of angle between cranks αcr from 0° to 180°. From 180° to 360°, the obtained values are similar and that is why they are not shown on the graphs.

It is seen that the minimum value of the maximum balancing moment is obtained geometrical parameters of links of mechanism when the angle between the cranks is equal to the angle between the axis of the cylinders minus 180°, i.e. the optimum value of angles from the view point of obtaining maximum amplitude will be the value of angles obtained according to the equation: αcr= αcyl ±180°.

Hence, for a linear ICE, the most optimal angle will be the angle between the cranks plus or minus 180°, for V-shaped ICE - the angle between the crank must be equal to the angle between the axis of cylinders plus or minus 180°, and for opposite cylinder layout - the angle between the cranks must be equal to 0°.

Similarly, the moments of useful resistance were also analyzed. The obtained data show that the value of the moment of useful resistance for various angles between the cranks and the axis of cylinders vary within the range of 1...3% and does not provide a significant advantage.

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Fig. 4. Graph of maximum balancing moments with respect to angle αcyl for various αcr: - 0°, - 60°, - 120°, - 180°.

Fig. 5 shows the graph of the amplitude of moments of inertia ΔJR for each value of αcyl and αcr; x-axis represents the angle between the axis of cylinders αcyl from 0° to 360°, y-axis – the maximum balancing moment, each curve shows the relation with respect to the angle between the cranks αcr from 0° to 180°. From 180° to 360°, the obtained values are the same and are not shown on the graph.

From the graphs, it can be seen that various positions of the cranks make it possible to obtain amplitude values of reduced moment of inertia that differ by up to 200% which requires damping or balancing mechanisms, and this makes the design of the mechanism more complex. Optimum angles from the view point of obtaining minimum amplitudes of reduced moment of inertia and hence, minimum vibrations, will be values of angles obtained according to the equation αcr= αcyl ±90°.

At values of αcr= αcyl +0° or αcr= αcyl ±180°, we have maximum amplitudes of the moment of inertia. Fig. 6 shows the graph of the coefficient of mechanical losses КML for each value of αcyl and αcr; the x-axis

represents the angle between the axis of cylinders αcyl from 0° to 360°, the y-axis represents the maximum balancing moment , each curve shows variation with respect to the angle between the cranks αcr from 0° to 180°. From 180° to 360°, the obtained values are the same and are not shown on the graph.

For the coefficient of mechanical losses, values of the angles will be obtained according to the equation αcr= αcyl ±180°.

The vector model with αcr= αcyl+0° and its respective indicator diagrams and show on Fig. 7.a. The indicator diagrams obtained using KDAM are transformed into loads acting on the pistons of both cylinders

(Fig. 7.b).

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Fig. 5. Graph of amplitudes of moment of inertia ΔJR with respect to αcyl for αcr at: - 0°, - 60°, - 120°, - 180°.

Fig. 6. Graph of coefficient of mechanical losses КML with respect to angles αcyl for αcr at: - 0°, - 60°, - 120°, - 180°.

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а) b)

Fig. 7. Vector model (а) and its corresponding indicator diagrams (b) (identical for both the right and left pistons) with respect to α– angle of rotation of the crankshaft for a work cycle.

The vector model with αcr= αcyl ±180° (optimum mode) and its corresponding indicator diagram are shown in Fig. 8. Lets graphs of balancing moment and moment of inertia on the same coordinate axis for these given models and also for models with minimum amplitude of JR (min ΔJR) (and αcr= αcyl ±90°). The obtained graphs are shown in Fig. 9 for reduced moments of inertia and in Fig. 10 for balancing moments.

а) b)

Fig. 8. Vector model with MУР (min) and its corresponding indicator diagram, where α– angle of rotation of crankshaft for a work cycle, - F1 force of the right piston, -F2 force of the left piston.

Combined graphs for all three models are shown in Fig. 11.

Fig. 9. Graph of reduced moments МR with respect to α: -MR(max), - MR(min), - MR(min JR).

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Fig. 10. Graph of balancing moments MBAL with respect to α: - MBAL (max), - MBAL (min), - MBAL (min ΔJR).

Fig. 11. Graphs of moments of inertia: - JR (MBAL max), - JR(MBAL min), - JR (min ΔJR).

4. Conclusion

By analyzing the obtained results, it can be concluded that reduced load on constructions for various types of ICE could be achieved using design principles based on dynamic optimization of geometric parameters.

From the view point of minimum mechanical losses and minimum stresses in weak cross-sections of the crankshaft, an optimum two-cylinder ICE could be designed under the fulfilment of the expression αcr= αcyl ±180°. The expression αcr= αcyl ±90° should be used in the case of high-speed engines with the aim of reducing dynamic loads not withstanding high mechanical losses.

A conclusion can also be made that for opposite-cylinder ICE for aviation applications, it is better to arrange the cylinders in a vertical plane than on a horizontal plane in order to reduce horizontal vibrations. In the case where problems arise in using the recommended layout of ICE in aircraft, it is better to use four-cylinder engine for compensation of increased inertia vibrations in such a mechanism.

Generally, during design of a multi-cylinder ICE, it is necessary to carry out similar dynamic analyzes of the kinematic scheme of the main mechanism at the preliminary stages of the design process in order to choose optimum

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geometric parameters which lead to reduction of dynamic loads on elements of the mechanism and increase in strength and fatigue life cycle characteristics.

Acknowledgements

This work was carried out with the support of the Ministry of Education and Science of the Russian Federation under the frame work of implementing programs for enhancing the competiveness of Samara State Aerospace University among the world's leading scientific and educational centers for the years 2013-2020.

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