DYNAMIC MODELLING OF PISTON THE MOTION IN COMBUSTION ENGINES

Resume The presented work discusses a methodology for analysis of noise emissions from a diesel engine. A numerical model of the piston motion, analyzing its lateral, reciprocating and rotation motion, has been presented in order to investigate the lateral motion of the piston skirt assembly and resulting vibrations induced as a result of these motions in the engine block. Various parameters of modal analysis were obtained using the mobility analysis. The presented methodology was validated by data obtained from a diesel engine test set up. The predicted results matched well with those of measured data, hence validating the presented scheme.


Piston assembly model
The secondary motion of a skirt for the case of a 240 cc engine was modeled as depicted in Figure 1. The piston was considered as a point mass of 0.363 kg (m p ) and inertia (I P ) of 7.8540X10 −9 kg-m 2 having two degree of freedom in motion (X p ,θ). The cylinder block was considered as a lumped mass of 48.5 kg (m b ) with a single degree of freedom X b , as shown in equation (1).
The nominal clearance of 0.5 mm allows the piston assembly to move in the lateral direction, as well as to rotate about the piston pin. The clearance between the skirt and a liner Xc was modeled as a mechanical stop in lateral direction.
For condition of no impact, (X p -X b =X c ) the motion was governed by Equation (1).

Introduction
In combustion engines a lateral space is present between the skirt and a cylinder liner that gives a motion freedom in lateral direction during the engine operation [1]. The existence of this gap puts a limit on magnitude of piston motion [2]. The piston assembly contributes to about 30-40 % of mechanical losses and hence its design is a major concern for automotive engineers [3][4]. The piston thrusts liner to other side due to changing in direction of side thrust force due to motion of a connecting rod [5][6].
A dynamic model of the crank slider mechanism has been presented by Flores et al. [2]. The existence of lateral gap makes the system nonlinear and chaotic in nature. The reaction force between the liner and a skirt also plays an important role in dynamics of motion. As the coefficient of restitution decreases, the motion transforms from bouncing to a periodic one [7][8].
McFadden and Turnbul analyzed effects of combustion gas pressure on primary motion of a piston [9]. A two degree of freedom system has been analyzed showing a correlation between the piston slap and resulting vibrations [10][11][12][13][14][15][16]. Various parameters affecting B10 N A R A Y A N e t a l .
and a liner can be obtained from the product of elastic tension and the coefficient of frictional force. As the speed of engine increases, the coefficient of friction decreases gradually until reaching the minimum at the mid stroke. The frictional forces between the liner and a skirt (F f ) and piston rings and liner (F fr ) may be expressed in terms of the sliding velocity of a piston (V), nominal clearance (h), lubricating oil viscosity(μ), number of piston rings (n) and the shear area of a contact (A s ) as : where A s1 is the shear contact area between the liner and a skirt and A s2 is the shear contact area between the liner and rings.
3 Piston side thrust force The major issue, affecting this lateral motion of a skirt, is the side thrust force (Fx) imparted to skirt by a connecting rod, as shown in Figure 2.
The frictional forces act between the piston skirt and a cylinder liner (F f ) as well as between the rings and a liner (F fr ). The force exerted by the connecting rod on piston pin was resolved along X (F rodX ), as well as Y axis (F rodY ). The side thrust force (F x ) takes into consideration both inertial forces as well as gas forces (F g ) [21][22][23][24].

Piston frictional force
Various friction forces play a predominant role in the total mechanical loss of an engine [25][26]. According to Zweiri et al. [27], frictional force between the rings per minute)-(2000 rpm and 3000 rpm) and load values (80 % and 100 %) were chosen with an aim to cover complete engine operational conditions. The data recorded during each test was under steady state conditions as seen in Table 4. Figure 3 shows the general layout of the test rig with placement of various sensors. Above the anti resonance frequency, the point mobility can be written as :

Experimental setup
Tests were done on a single cylinder HARTZ engine having specifications as presented in Table 1.
The in-cylinder pressure was monitored by an AVL transducer, having specifications shown in Table  2. Block vibrations were measured by means of an Endveco7240C type Mono axial accelerometer, having features accelerometer are presented in Table 3.
Various engine testing speeds in rpm (Revolutions       changes its direction at both dead centers. In order to visualize the pistons secondary motion during the reciprocating motion, the piston secondary motion is represented in a graphical form and the piston lateral motion and rotating motion are normalized to the piston stroke position, based on the reciprocating motion of a piston, as shown in Figure 13. It is evident from the plot that the piston remains at the lower boundary cylinder liner for a longer time, as compared to the upper boundary of a cylinder wall. In addition, the piston is predicted to slide for a crank angle of 100 º before the TDC along the cylinder liner ( Figure 13). Figure 14 shows the measured vibratory response of the cylinder block in the vibration amplitudes, as captured by accelerometer. The vibration of the cylinder decays after the first impact of the piston on the upper boundary of a liner. The vibration is induced once simulate the piston velocity for given testing conditions, as shown in Figures 6 and 7.
Using Equation (6), the mobility was computed, e as seen in Figures 8 and 9.
Similarly, the Mobility of a r cylinder block was computed using integration of accelerometer data as shown in Figures 10 and ,11.
Using the concept of anti-resonant frequency(ω a ), as discussed in previous section, various dynamic parameters of the liner-piston were computed for the given test conditions (Table 4), as seen in Table 5.
During the motion simulation, the bottom dead center positions (BDC) was taken as a reference point. The initial location of a piston is set at 0 mm as the bottom boundary of liner and the upper boundary of the cylinder liner is set at 0.5 mm, which is a clearance between the skirt and a liner.
As seen from Figure 12, the piston tilting angle   force, acting on the piston, results in the piston bouncing off the cylinder liner more frequently at higher speeds, as seen from Figures 15 and 16.
The induced vibrations of a block also increase with engine speed. The sliding duration also falls with again when the piston impacts lower cylinder liner. The induced vibrations had an amplitude of order of 7 × 10 -3 m. As the engine operating speed increases, the piston side thrust force, which is a function of the engine rotating speed, increases. An increase in the side thrust Values of the first resonance frequencies of both the skirt and a liner were found to be in 100 Hz-160 Hz range and it remains unaffected by variations in the engine operational conditions. Several peaks were found in the simulated block vibrations, which were related to impacts of a skirt with liner. The COMSOL-7 software was then used to analyze the tilting motion of a piston, which showed a good match with that simulated by solving dynamic equations of motion.
Effects of load and speed on lateral motion of piston skirt were also investigated. The piston skirt was also found to slide along a liner a few crank angle degrees before the TDC position. This sliding motion was less dominant during the power stroke as the bouncing motion dominates the dynamic motion of a skirt. The duration of sliding motion of a piston along the liner was observed to decrease with increase in load and speed conditions, which is in agreement with previous available literature.
an increase in velocity as shown in Figures 17 and 18. This is due to the higher impact force and acceleration generated during the piston slap and the reaction impact force from a liner acting on the skirt increases. At the lower engine speeds, the vibration response of the cylinder block induced by the first slap of a piston has a longer duration to decay before the second slap occurs. However, with the speed increase, the vibration response of a block has the shorter duration of decay and response from the second slap is combined with the first one.

Conclusions
A lumped system model was discussed in the present paper. Various dynamic parameters of a system were calculated, using the concept of mobility, which were later used to simulate the lateral motion of a piston, as well as the resulting engine block vibrations.