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The piston ring and liner undergoes boundary lubrication with approximate friction coefficient of μ = 0.08 near TDC and BDC owing to the low velocity. As the ring and liner surfaces rubs against each other under boundary conditions, the heat generated corresponds to the product of velocity, pressure and friction coefficient,

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and it has to be dissipated by conduction into both bodies, thus raising their temperature.

If higher friction occurs in a particular spot, due e.g. to a momentary lack of lubrication or a speck of dirt, more heat is produced and the temperature of this spot will rise. It will expand, and a tiny bulge will be formed. This bulge will rub harder, produce more heat, and consequently grow further rubbing still harder, etc. Now, if the rate of wear under such conditions is high enough to wear the bulge off as fast as it grows, conditions remain stationary and, as soon as normal lubricating is reestablished, the spot cools off and shrinks, producing a little scar. But if the rate of growth is faster than the wear rate, the bulge will rub more and harder, and will destroy lubrication completely. The temperature then rises above critical levels for welding, and scoring will result.

3.2.2 Mathematical modeling of thermoelectric method:

The additional heat production is increased by greater values of rubbing speed, ‘Cm’, friction coefficient, ‘µ’ and pressure, ‘p’:

In an one dimensional system, when piston ring is rubbing over the liner, the heat will be absorbed by both rings and liner. Total additional heat contained in the liner and rings is:

∫

and the total elongation of the liner

∫

By elimination we get

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If the boundaries of the system are assumed to be rigid, this thermal elongation must be taken up by wear and elastic compression of the liner.

If the wear rate is sufficiently high, nothing is changed in the system geometry and the ‘wear will prevent scuffing’. But if it is too low, the elastic compressions

generate an additional contact pressure, which will in turn increase the friction heat and thus lead to an exponential growing friction. Assuming in the extreme case the wear to zero, we get the pressure rise

From equation 3.95 and the equality of the quantity of heat generated and the quantity of heat stored follows:

∫ ∫

With equation 3.100, we obtain

∫ Assuming constant friction conditions, the integral solution is:

This rate of pressure rise characterizes the potential scuffing index and is related to Tt, the instantaneous temperature of liner and rings and

where,

f Cross section of rubbing element (m2) lr Length of liner and ring thickness (m)

Cm Sliding speed (mean piston speed) (m/s)

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E Young’s modulus (N/m2)

ρ Density (kg/m3)

csp Specific heat (J/kg. 0C)

ε Coefficient of thermal expansion (m/m.0C)

µ Coefficient of friction (-)

Q Stored energy (J)

Δp/Δt ‘Scuffing index’ (N/m2s)

In order to prevent scuffing, Equation 3.103 can be used with a set amplitude for the maximum rate of pressure rise. Accordingly, a maximum temperature Tt can

also be derived. However, such dependence on the maximum temperature may be too late to prevent the onset of scuffing, as the reflected high temperature simply meant that the scuffing already is in progress. From the previous experience and the recorded temperature analysis of cylinder liners, it was discovered that, a series of fluctuating temperature pattern were always present prior to the onset of scuffing. It was also noted that full blown scuffing could be avoided, if some countermeasures are taken during this fluctuating temperature symptom, such as reducing the engine load and increasing the lubricant flow etc. It is then confirmed that the fluctuating temperature was related to the higher friction heat generated from the adhesive wear breaking of oil film on the liner surface and restoring the oil film with fresh supply of oil. This sporadic oil film breakage and restored film

thickness was responsible for the temperature fluctuation. Hence, this fluctuating temperature pattern could be used as the early warning for scuffing detection. Fluctuating temperatures were not found to be regular. Interval of wave peak, amplitude and mean temperature were also not fixed. Furthermore, when the gap or open end of the piston ring came in line with the temperature sensor, the

temperature measured on the sensor rose. The temperature subsequently dropped when the ring end moved away from the sensor.

Hence, it was necessary to differentiate the fluctuating temperature from the ring- end temperature rise in order to create a mathematical function to assess the detection of scuffing. A Fourier series model was formulated for the analysis of the

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series of fluctuating pattern against a specified period interval as shown in the Figure 3.30.

Figure 3.30 Fourier profile of temperature readings

∫ ∫ ∫ ∫ Integration by parts: ∫ ∫ Taking x = u; du/dx =1; du = dx dv = cosnx; v = (1/n) sinnx ∫ ∫ {[ ] [ ] } cosnπ = 1 (n even) cosnπ = -1 (n odd) π 2π -π X Y Y=2X

119 So, ∑ ∑ { }

The solution of the fourier series for various values of ‘x’ is shown below in Figure