Innovative Automobile Technology
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Innovative Automotive Technology - IAT'01, Ljubljana, April 5-6, 2001
Mechanical Efficiency of Reciprocating Internal Combustion Engines
Ivan Mahalec, Zoran Lulić, Klaudio Skok
Keywords: internal combustion engine, efficiency
Abstract This paper considers the analysis of mechanical losses in the piston engine. The influence of operating parameters and design parameters on the frictional losses is described, and the values of friction work and mechanical efficiency with various engines are stated. Methods of measurement are also briefly stated, and approximate calculations of mechanical losses are given. Special attention is given to the calculation of these losses with Willians, i.e. Schweitzer-line. Results are shown on a selected example.
1 Introduction
First, mechanical losses Wm are satisfied out of the indicated work Wi produced in the engine cylinder, and the rest of it is used on the crankshaft as effective work We. The total work of mechanical losses Wm consists of friction work WR and charge cycle work WLW. The relation is the same for corresponding mean pressures as well. If the work loss due to the charge cycle is expressed as a decrease of efficiency LW, the total mechanical efficiency m will be:
m We /Wi R LW We WLW /W WLW /Wi . (1) Frictional losses depend on operating parameters and design parameters. This paper discusses frictional losses of vehicle engines. The first part shows the developments in the field so far, and the second part gives an analysis of the results of approximation methods.
2 Survey of the field Influence of operating parameters. Numerous papers have shown that mechanical losses depend mostly on mean piston speed, figure 1. In warm engine, most of mechanical losses are caused by friction of the piston set (Derndinger [2], Maass-Klier [9], Thiele [15]). That friction increases together with the increase of mean piston speed, i.e. engine rotational speed, and with the increase of oil viscosity (in the cold engine, for example), and with the prestrained force of piston rings in the cylinder, and also with the increase of engine load but to a lesser degree. Influence of design parameters. Mechanical losses can be reduced by improving almost all parts and sets of the engine. However, any significant reduction of mechanical losses, with unaltered functionality, durability and producebility, is always a common result of a number of improvements (Gruden [3]). Ricardo [12] showed how difficult it is to improve mechanical efficiency. He tested two spark-ignition engines of similar design and power, at full load and the same rotational speed. Only the level of compression ratio was different: 4.2 for 1924 engine and 6.0 for 1948 engine. The mechanical efficiency was (1924/1948): 88.2% and 87.8%, at maximum power and 67.7 % and 67.2 % at maximum torque. In that period of 25 years, almost no improvements were made in the field. 1 12 60 pR, bar = 12,5 Wm, Nm TOTAL 0.9 10 50 auxiliaries 6 0.8 pe = 8 0.8 40 pumping 8 bar intake + exhaust system pe, 0.7 losses 0.7 6 30 bar 4 0.6 4 20 piston rings 2 0.5 piston and 0.5 2 10 connecting rod valve train crankshaft m = 0.3 gears 0.4 0 0 radial packing strips 0 1000 2000 3000 4000 5000 0 2000 4000 6000 0 2000 4000 6000 n, min-1 n, min-1 n , min-1
Figure 1: Left: Influence of load on frictional losses (Schrick [13]). Middle: Mechanical efficiency in the engine operating range (Gruden [3]). Right: Distribution of frictional losses in the engine at full load (Gruden [3]).
Number of cylinders and swept volume. Pischinger and Esch [10] carried out a research (1981) on the influence of the number of cylinders on frictional losses, as well as on the fuel economy. As a starting point two engines were chosen, but due to different design they were not directly comparable. Because of that, for the purpose of a broad calculation analysis, they were modified in such a way that at the same power, the corresponding parts in both engines were subjected to equal stresses. Calculation results (fig. 2, left) showed that in the 6-cylinder engine mechanical losses were even smaller than in the 4-cylinder engine of the same size and power. Since a smaller cylinder diameter the compression ratio can be higher, which results in a higher ideal as well as a higher actual indicated thermal efficiency, it follows that the 6-cylinder engine has an advantage over the 4-cylinder one. 6-cylinder engines also run more smoothly and therefore make less noise. However, they are designed for bigger loads, so they may have bigger mechanical losses than the 6-cylinder engine observed here. Even then, thermodynamic advantages of a 6-cylinder engine enable lower fuel consumption at the same power.
300 25 2.6 3 Swept volume, dm 2.0 2.0 W k pe = 5 bar WR, ,
Number of cylinders 4 6 s e Nm 20 e s s Stroke / diameter, mm 80 / 89 66 / 80 m o u l
1.6 l
200 l Frictional losses at full and part load o a 4-cyl. 15 1.46 v
n t
( ... means less losses) o p i
t 1,3 e c i Cranshaft, main bearings 0 3 w 6-cyl. r 10 dm s f
l 100 f
Big end bearings 0 a o t
r o e Piston 0 5 T w
Piston rings 0 0 o P Engine 0 0 0 Auxiliaries 0 0 2000 4000 6000 0 2000 4000 6000 -1 -1 TOTAL of frictional losses 0 n, min n, min
3 Figure 2: Left and Middle: Total friction work WR of two spark-ignition engines, 2.0 dm , equal power, 4 and 6 cylinders (Pischinger [10]). Right: Friction power of four vehicle engines of different sizes with different number of cylinders (van Basshuysen [1]).
Van Basshuysen, Schmädeke and Vogt [1] indicated four types of engines, three samples of each type (Audi NSU Auto Union, 1980) and by comparing them confirmed these findings too. Three 4-cylinder engines of different sizes were compared with a 6-cylinder one (fig. 2, right). With all four types of engines a significant dependence of the mean pressure of frictional losses on rotational speed was established, as well as a less significant dependence on load. The mean pressure of frictional losses depends very little on the swept volume of the engine, so that friction power was approximately proportional to the swept volume. If a 4-cylinder engine is replaced by a 6-cylinder one, it does not necessarily mean that the mechanical efficiency is reduced. It was even proven that a bigger 6-cylinder engine, at the same friction power as a smaller 4-cylinder one, but at a lower rotational speed, produces more power by more than 25%.
0.80 0.80 0.80 1 H = 82 m m m m D= 0.78 0.8 Full load 82 90 0.76 0.76 H/D = 0.9 0.76 0.6 Part load 90 98 0.74 0.4 0.72 0.72
98 0.72 0.2
0.68 0.68 0.70 0 0.8 0.9 1 1.1 1.2 1.3 1.4 0.8 0.9 1 1.1 1.2 1.3 1.4 300 400 500 600 700 800 900 4 8 12 16 20 24 3 H/D H/D V H, cm Compression ratio
Figure 3: The influence of the design parameters on mechanical efficiency (Gruden [4,5]).
The advantages of a larger number of smaller cylinders for the increase of power and rotational speed have been known for a long time in the field of racing engines. However, the size and the number of cylinders do not depend so mach on mechanical losses, but rather on the total behaviour of the engine while running, as shown by Fritz Indra [7] in his excellent analysis of the Formula 1 engines. In 1997 he anticipated a 10-cylinder Vee-engine which, twelve years later, became a key to success in Formula 1 (first used in 1989: Renault RS1 and Honda R109E). 100
4 100 90 10 5 bar %
8 , 7 80 y 3 c 6 n 80 11 -1 e
i 3.0 l DTM, 298 kW / 8800 min c i f
f 60 e 9
l 70 a
c -1
i 1 3.0 l Serie, 150 kW / 6000 min n 40 a
h 2 c
e 60 M 20
50 4 6 8 10 12 14 16 18 20 22 0 Mean piston speed, m/s 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Figure 4: Left: Mechanical efficiency of spark-ignition engines running at maximum output, if not marked otherwise (Hütten [6]). 1 - US-V8-engines, 1975; 2 - NSU 250 cm3, racing 1-cylinder 4-stroke engine, 1953; 3 - Porsche-911, 6-cylinder engine, 1970 (friction power was measured with the ignition off); 4 - BMW-2000 tii, 4-cylinder engine, 2.0 dm3, 96kW; 5 - MZ Re-125, racing 2-stroke 1-cylinder engine, 125cm3 (5454), 19kW at 11,000 min-1; 6 - MZ Re-125-III, racing 2-stroke 3-cylinder engine, 125cm3, 22kW at 14,500 min-1; 7 - Yamaha 125 cm3 (3532,4), racing 2-stroke 4-cylinder double-twin engine, 1968, 32kW at 17,600 min-1; 8 - Yamaha 125 cm3 (4441), racing 2-stroke 2-cylinder engine, 1966, 26kW at 15,000 min-1; 9 - Honda 125 cm3, racing 4-stroke engines with 2, 4 and 5 cylinders, stroke: 41, -1 -1 32 mm and 27.4 mm, 5-cylinder engine: m = 85% (at 12,500 min ) and 70% (at 19,500 min ); 10 - Opel 3.0 dm3, 4-valve 6-cylinder in-line engine, 50kW/dm3 at 6,000 min-1; 11 - its racing version for DTM-racing, 100 kW/dm3 at 8,800 min-1. Right: Indicated cylinder pressure diagrams for Opel 6-cylinder engines (points 10 and 11 in left diagram) (Indra and Tholl [8]). Compression ratio and cylinder dimensions. As early as the end of the 19th century Rudolf Diesel discovered that the increase of compression ratio was the basic means for the increase of engine efficiency. While the optimum of compression ratio in diesel engine is determined by the criteria of cold start in winter, in spark-ignition engine it depends on fuel quality, combustion chamber design, cylinder diameter, safety distance to combustion knock, and production possibilities. With the present intensive development, it would be unfair to state any number as an optimum for compression ratio. Twenty-year-old measurement results shown in fig. 3, serve only as an illustration of this problem.
3 Measurement and calculation of mechanical losses For measurement of frictional losses the following methods are applied:
Indicating. By recording (p,V)-diagram the total friction in the engine is measured: pm = pi - pe. Advantages: the work of charge cycle can be singled out, operating parameters are considered (load, temperature, rotational speed, etc.). Disadvantages: the procedure is expensive and complicated (a pressure sensor has to be installed in the combustion chamber), a large number of factors influences the accuracy of measurement (determining of top dead centre (TDC), influence of temperature on measurement sensors, etc.), pressure sensors have to be calibrated. Towing. The engine with the ignition off is towed (rotated) by an external source of energy and the power needed is measured on the test bench. Advantages: the share of individual components in total engine friction can be singled out. Disadvantages: load, temperatures and thermal losses do not correspond to the actual engine running. Stopping experiment. After turning off the ignition or cutting the fuel supply, the time needed for the engine to stop running is measured. Friction torque is MR = J·(d/dt), where: J - total inertia moment of all rotating masses in the engine, - angular velocity, t - time. Disadvantages: engine load is not considered, charge cycle losses are included, it is difficult to determine the exact amount of inertia moment J.
WILLIANS-Line. At constant rotational speed n fuel flow is measured for different values of mean effective pressure pe. The flow line is extended to the intersection with the negative part of the axis pe, and the distance from the intersection to the origin of the co-ordinate system equals to the mean pressure of frictional losses. Disadvantages: engine load is not considered, uncertainty regarding extrapolation of the line has as its consequence unreliable results, losses of charge cycle are included in total losses. Advantages: a fuel consumption map is sufficient for the calculation. Approximation equations according to Maass-Klier [9]. Mean pressure of mechanical losses of diesel trunk-piston engines equals:
pm pR,0 ΔpR, j j , (2) where: pR,0 – basic value of pressure of frictional losses of the engine, running under small load, with a valve mechanism and a fuel injection pump without any other auxiliaries; pR,j – components of pressure of frictional losses dependant on load and auxiliaries.
The basic value pR,0 (bar) is determined by cylinder diameter D (m) and mean piston speed vm (m/s). For the engine warmed up to the running temperature, the following is valid:
2 pR,0 A0 A1 vm A2 vm (3) A0 0.609 0.026 D
A1 0.0453 D 0.02143 D (4a) 2 A2 0.00835 0.00024 D 0.00017 D
vm 2Hn, m/s (4b) where: H, m – stroke; n, s-1 – engine rotational speed.
Component pR,1 depends on engine load (pe) and the combustion chamber design: engines with direct injection (naturally aspirated engines):
2 ΔpR,1 0.01375 pe 0.00282 pe (5a) naturally aspirated engines chamber engines (prechamber and swirl-chamber):
2 3 ΔpR,1 0.02748 pe 0.00263 pe 0.0019 pe (5b) pressure charged engines, vm 14m/s : p L ΔpR,1 1 0.5 0.035 vm (5c) pa where: pL –boost pressure, pa – ambient air pressure pressure charged engines, vm 14m/s :
ΔpR,1 0 (5d)
Other components pR,2, ..., pR,5 include devices needed for the engine running and they are calculated according to the engine maximum output Pe,max as follows: Δp 0.1 0.15 bar lubricating pump + wet sump R,2 (6) 0.15 0.25 bar lubricating pump + dry sump fresh water cooling pump in closed ΔpR,3 0.1 0.3 bar (7) circuit of the engine cooling sea water cooling pump in open ΔpR,4 0.2 0.4 bar (8) cooling circuit of marine engine fan in an air-cooled engine, at Δp (0.25 0.40) (1), bar R,5 maximum output engine speed (9) (0.25 0.35) (1), bar fan in a water-cooled engine with cellular radiator P P e,A e,S (10) Pe,S where: – boost factor; Pe,S – effective engine output of naturally aspirated engine; Pe,A – effective engine output of pressure charged engine.
4 Evaluation of approximation methods What kind of an insight into mechanical losses of the engine do approximation methods give? Considering the complexity and high costs of measurement, the answer to this question definitely deserves attention. For that purpose, the equations presented above were examined, as well as the Willians-line in its modified form suggested by Schweitzer [14], fig. 5. Instead of observing fuel flow in dependence on mean effective pressure, Schweitzer introduced mean fuel pressure pB as an independent variable. By means of that variable he expresses mean effective pressure pe and draws its line. In that way the axes of the observed co-ordinate system become universal values (pB, pe) so that the lines of engines different in size can be compared, which is an important advantage of this method. The characteristic of the line is that it is rectilinear in the area of lower loads, which enables an easy extrapolation to the intersection with the ordinate. In addition, all inaccuracies in measurements are noted at first glance as irregularities (bumps), much clearer than on the Willians-line (see fig. Error: Reference source not found).
r 10 a g/kWh 250 300 b
, 180 e e r p 7.5 u 400 s s e r
p 5
. f f e
.
c 2.5 pe pi i d n i
n 0 a
e 0 5 10 15 20 25 30 35 pm M -2.5
-5 Mean fuel pressure pB, bar
Figure 5: Left: Analysed map of fuel consumption. Right: Schweitzer-line of mean effective pressure pe as a function of fuel pressure pB.
Mean fuel pressure pB is equal to the content of added heat Q1 per one swept volume VH, and it is calculated on the basis of the definition of mean indicated pressure pi:
Wi Q1 i pi pB i (11) VH VH where: i – actual indicated thermal efficiency.
6 10 5000 g/kWh 3000 Fuel Willians -1 Schweitzer 180 min 5 r 5000 kg/h a 7.5 -1
b min
4000 , e p 4 5 P
3000 E M
3 I 2.5 800 g/kWh 2000 4000 2 1000 0 1 p 0 5 10 15 20 25 30 35 1000 m -2.5 Porsche 924 TOP, 1 cylinder
0 Porsche 924 TOP, 1 cylinder -4 -2 0 2 4 6 8 10 -5
pm Indicat. mean eff. pressure pe, bar Mean fuel pressure pB, bar
Figure 6: Willians-line (left) and Schweitzer-line (right) calculated on the basis of a diagram of specific effective fuel consumption of a spark-ignition engine with swept volume of 2.0 dm3. In the area of lower load, errors in measurement of specific fuel consumption be are noted as bumps, which are more expressed on Schweitzer-lines of mean effective pressure pe. On the other hand, based on the quantity of energy that entered the cylinder, mean indicated pressure of the naturally aspirated engine is:
H u pi i L,0 pB i (12) VH where: – volumetric efficiency, L,0 – density of ambient air, Hu – lower heating value of fuel, VH – swept volume.
In an analogue way mean effective pressure pe is obtained as a function of fuel pressure pB, at specific effective fuel consumption be (g/kWh) and heating value Hu (MJ/kg): 3600 pe pB e pB . (13) be H u
This equation enables to draw a line of constant brake specific fuel consumption be (BSFC-line) in the observed co-ordinate system, fig. Error: Reference source not found. Analysis of several published diagrams of specific fuel consumption have shown inaccuracies in measurements with lower loads and smaller rotational speeds, which are seen in the shape of bumps on those parts of the line which should be straight. So, for example in figure Error: -1 Reference source not found, line pe calculated for 1,000 min even turns in the wrong direction.
Figure 7 shows the calculation results of mean pressure of mechanical losses in the pressure charged diesel engine VW 1.9 TDI, maximum output 66 kW (MTZ 11/1996/610). Maass-Klier equations for the empirical calculation of mechanical losses can be applied perfectly to that engine, which enables comparison of these results with those obtained by Schweitzer-line. Unfortunately, the results were not quite correct, and that was manifested through bumps on the lines. Therefore, this additional check was made: 1. based on obtained mechanical losses and mean effective pressure, mechanical efficiency was calculated; 2. out of specific effective fuel consumption, effective efficiency was calculated; 3. finally relative efficiency g was calculated
(g=e/t) and compared to Pischinger's results [11] (in the diagram: mark: (P)). In the calculation, the problem of uncertain extrapolation of the line pe in the area of negative values was solved in two ways: 1. the line was extended by a linear trend-line through all points (mark:
S1); 2. the bumpy part at lower load of the line pe was abandoned, and through the remaining points polynomial trend-line of second order (mark: (S2)) was drawn. Lines (5Error: Reference source not founda), (5Error: Reference source not foundb) and (5Error: Reference source not foundc) represent calculated mean pressure of mechanical losses. Calculation was carried out by using approximation equations marked with corresponding numbers. r
a 5 0.80 100%
b s (S2) , e
m (S2) s (5b) p s 0.75
o 3/4 l
4 90% l
a m
0.70 c
i S1 y (5c) c n g 1/4 load n a S1 y 0.65 c
(5c) e h 80%
3 (P) i c n c i e e f i S1 f
c 0.60 m i e
f
f l f
(5c) i o e 70% 2 n 0.55 e a e r (S2) v h i u c t s e a s 0.50 l e
(5a) M e VW 1.9 TDI 60%
r 1 R p VW 1.9 TDI 0.45
n VW 1.9 TDI a e 0 0.40 50% M 1000 2000 3000 4000 1000 2000 3000 4000 1000 2000 3000 4000 Engine speed n, min-1 Engine speed n, min-1 Engine speed n, min-1
Figure 7: Mean pressure of mechanical losses (left), calculated by the Schweitzer-line and the empirical equation for full load, was additionally checked by calculating relative efficiency (right). (Double lines correspond to minimum and maximum of mean pressures of frictional losses of individual devices. Relative efficiency was calculated for mean value.)
5 Conclusion Results obtained have shown that in evaluation of mechanical losses in an engine it is always better to use both ways, and subsequently eliminate factors that cause errors by a thorough analysis. With this approach the results obtained by the Schweitzer-line and by the Maass-Klier formulae will correspond relatively well. Dispersion of results obtained by the Schweitzer-line for various methods of extrapolation was unfortunately in the wide range from 1:1.14 to 1:1.53. Considering that only a smaller part of the indicated work is wasted due to mechanical losses at maximum load, dispersion of calculated values of mechanical efficiency in that case was significantly smaller: m = 69 ... 82%. The results of the Maass-Klier equations corresponded best to those of Schweitzer-line, at rotational speed of 2000 min-1, where the Schweitzer-line was most regular.
References
[1] Van BASSHUYSEN, R., SCHMÄDEKE, W., VOGT, R.: Reibungsverluste von Fahrzeugmotoren unter- schiedlicher Größe und Zylinderzahl, MTZ 11/1980, 509-511. [2] DERNDINGER, H.-O.: Konstruktive Mittel zur Leistungssteigerung von Fahrzeugmotoren, ATZ 3/1965, 85-93. [3] GRUDEN, D.: Energiebilanz des Ottomotors – Absenkung mech.anischer Verluste, JUMV, Opatija 1983. [4] GRUDEN, D., HAHN, R., STRIEBICH, H.: Möglichkeiten der Verbrauchsverringerung bei Ottomotoren hoher spezifischer Leistung, ATZ 2/1980, 77 – 82 [5] GRUDEN, D., KÜPER, P.-F., STRIEBICH, H.: Über die Energieausnutzung im Ottomotor, Automobil- Industrie 1/1980, 67-74 [6] HÜTTEN, H.: Schnelle Motoren seziert und frisiert, 6. Aufl., Verlag Richard Carl Schmiddt & Co. Braunschweig, 1977, ISBN 3-87708-060-10. [7] INDRA, F.: Entwicklunsstand heutiger Formel-1-Rennmotoren sowie eine denkbare Alternative, MTZ 9/1977, 359-368. [8] INDRA, F., THOLL, M.: Der 3,0-l-Opel-Rennmotor für die Internationale Deutsche Tourenwagen- meisterschaft, MTZ 9/1991, 454-465. [9] MAASS, H., KLIER, H.: Kräfte, Momente und deren Ausgleich in der Verbrennungskraftmaschine, Springer-Verlag, Wien - New York 1981, ISBN 3-211-81677-1. [10] PISCHINGER, F., ESCH, H.-J.: Einfluß der Zylinderzahl auf die Reibungsverluste von Personenwagenmotoren, MTZ 12/1981, 525-528. [11] PISCHINGER, R., KRASSNIG, G., TAUČAR, G., SAMS, Th.: Thermodynamik der Verbrennungskraft- maschine, Neue Folge Band 5, Springer-Verlag, Wien - New York 1989, ISBN 3-211-82105-8. [12] RICARDO, H.-R.: Der schnellaufende Verbrennungsmotor, Springer-Verlag, Berlin / Göttingen / Heidelberg 1954 [13] SCHRICK: Neue experimentelle Methoden für die schnelle Motorenentwicklung, MTZ 1997, Sonderheft Engineering Partners, 114-117 [14] SCHWEITZER, P., H.: Darstellung von Versuchsergebnissen mit Hilfe des Brennstoffdruckes, MTZ 12/1963, 445-446 [15] THIELE, E.: Ermittlung der Reibungsverluste in Verbrennungsmotoren, MTZ 6/1982, 253-258.
Authors Mahalec Ivan, PhD Assistant Professor at Department of Engines and Vehicles Telephone: + 385 1 6168159, E-mail: [email protected] Lulić Zoran, PhD Senior Assistant at Department of Engines and Vehicles Telephone: + 385 1 6168177, E-mail: [email protected] Klaudio Skok, BSc Assistant at Department of Engines and Vehicles Telephone: + 385 1 6168144, E-mail: [email protected] University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture Croatia , HR - 10000 Zagreb, Ivana Lučića 5