Indirect Evaluation of the Torque of Engines

Eduardo G. de Souza, Luiz F. Milanez

ABSTRACT proposed device when compared with two other methods HE torque of diesel engines is evaluated indirectly by considered in their work, namely the direct measurement Tthree methods proposed from data obtained in of the fuel consumption and the fuel pump rack position. performance tests in the power take-off of tractors: Measurement of exhaust gas temperature was also used measurement of the fuel consumption, measurement of by Pang et al. (1985) to describe an indirect method of exhaust gas temperature and measurement of the engine indicating tractor fuel consumption. governor control lever position. A statistical analysis of The objective of this study was to evaluate indirectly the results indicated that in the mathematical the torque of the diesel engine of a particular tractor, correlation, for all methods, the engine speed should be and three methods were analyzed: continuous included as an additional independent variable. measurement of the fuel consumption, measurement of Considerations were made regarding the utilization of the exhaust gas temperature and measurement of the each method as function of accuracy, costs and engine governor control lever position. Correlations for adaptability. the three methods are proposed. Based on statistical analysis the engine speed is included in the correlations INTRODUCTION as an additional independent variable for the sake of generality of the equations. Recent oscillations of fuel prices have stimulated utilization of fuel consumption as an important METHODS AND EQUIPMENT parameter in characterizing the performance of a tractor. One of the alternatives to reduce fuel Three tractors equipped with Bosch individual consumption is the utilization of the engine close to its injection pump system were used in the experiments. The maximum economy range by controlling both the engine main specifications of these tractors are given in Table 1. speed and the torque. The engine speed can be easily Each tractor was tested on a PTO Foucault current measured but the direct measurement of the torque is dynamometer equipped with a strain-gauge torque meter more complicated requiring expensive equipment. and digital readout for measuring PTO torque. Therefore it is extremely convenient if the torque of the Fuel consumption was determined by a Seppeler SVU diesel engine of a particular tractor can be evaluated 3-100/500 volume flow transducer. Bypass fuel from the indirectly with some accuracy. injectors was returned through a cooling coil to the Sumner et al. (1986) utilizing data from power take-off injector pump inlet line downstream of the transducer (PTO) dynamometer tests developed equations to predict and therefore all fuel passing through the transducer was PTO power output from engine fuel consumed by two consumed by the tractor engine. Given the volume of fuel tractors. For each particular engine speed a second order consumed and elapsed time, the rate of fuel consumption polynomial regression equation was obtained to predict can be evaluated. The temperature of the fuel leaving the PTO power output from fuel consumption in the transducer is registered in order to estimate the fuel density. dynamometer test. Correlation coefficients were above 0.99 for all equations. The exhaust has temperature was measured by an iron Kirste et al. (1985) designed a measurement system in which the torque and the engine speed were displayed as TABLE 1. MAIN CHARACTERISTICS OF TEST TRACTORS a luminous point on a screen in the tractor panel. The screen has a family of curves showing the dependence of Tractor 1 Tractor 2 Tractor 3 one parameter (fuel consumption) on two varying Tractor Valmet Valmet Valmet parameters shown on the coordinate axes (rpm and 980 4x4 Turbo 118-4 148 4x4 Turbo torque). The exhaust gas temperature, measured by a Engine MWM MWM MWM thermocouple inserted in the manifold near the exhaust TD 229-4 TS D 229-6 VS TD 229-6 TV valve, was used as an indirect indicator of the torque. This method was chosen as most appropriate for the Cylinders 4 6 6 Displacement, L 3.922 5.883 5.883

Compression Article was submitted for publication in October, 1987; reviewed and ratio 15.9:1 16.6:1 15.9:1 approved for publication by the Power and Machinery Div. of ASAE in May, 1988. Presented as ASAE Paper No. 87-1505. Air intake Turbo- Naturally Turbo- The authors are: EDUARDO G. SOUZA, Head of test laboratory, Charged Aspirated Charged Centro Nacional de Engenharia Agricola, CENEA, Sorocaba, SP, Power and 70 kWat 90kWat 107 kWat Brazil; and LUIZ F. MILANEZ, Associate Professor, Departamento rated speed 2300 min-1 2300 min'l 2300 min'^ de Engenharia Mecanica, UNICAMP, Campinas, SP, Brazil.

1350 © 1988 American Society of Agricultural Engineers 0001-2351/88/3105-1350$02.00 TRANSACTIONS of the ASAE - constantan thermocouple inserted in the exhaust Method 1 - Measurement of the Fuel Consumption manifold. The temperature read by the thermocouple is The corrected engine torque can be related to the slightly lower than the gas temperature because of heat amount of fuel delivered in one injection by (Khovakh, losses by radiation to the walls and by conduction 1979): through the thermocouple rod. However no corrections in the thermocouple readings were attempted because Te = B-r?- .[2] the complexities introduced in the correlations would not improve the accuracy of the results significantly. where Furthermore the objective of this method is not to B = a constant for the specific engine, N/m^ evaluate the exhaust gas temperature precisely, but to Y]^ = brake thermal efficiency have a parameter that could be correlated to the engine Q = fuel delivery per cycle, m^ torque. The engine torque is proportional to the product fuel The position of the engine governor control lever was delivery times the effective efficiency, the latter being a determined by the engine idle speed because for each function of the engine speed. Therefore it was decided to position of the lever only one idle speed is associated. correlate the engine torque to the mass of fuel delivered Two types of dynamometer tests were carried out: test and engine speed. Knowing the fuel density pf (kg/m^), with the engine speed held constant and test at a fixed the mass amount of fuel delivered to the cylinder per position of the engine governor control lever. cycle G(mg) can be obtained from Measurements were taken after the stabilization of pressure and temperature of the engine coolant and the OS'Pf lubricant oil. 10^ [3] 120 N-d In the test with the engine speed held constant the engine governor control lever position was varied in order where to record data from minimum to maximum torque loads. = rate of fuel consumption, m^/h Engine speeds were 100, 95, 85, 75, 65, 55 and 45% of number of engine strokes rated speed. Data were recorded at each of 10 equal s = engine speed, min~^ intervals between 100 and 10% of maximum torque for N = number of cylinders each speed. This type of test was used to obtain tractor d = performance data to evaluate the torque indirectly by the Method 2 - Measurement of Exhaust Gas Temperature method of continuous measurement of the fuel For a given engine speed of a diesel engine a higher consumption and by the method of measurement of the torque corresponds to a higher exhaust gas temperature. exhaust gas temperature. This is due to the fact that this type of engine operates In the test with the engine governor control lever essentially with a constant volume of air and therefore an maintained at a fixed position, from maximum speed to increase in the mass amount of fuel delivered results in 45% of rated speed, the engine was loaded by the temperature and pressure rise in the cylinder and dynamometer. Table 2 shows the engine idle speed for consequently higher torque and exhaust gas each lever position. This type of test was used to obtain temperature. However, for a given torque, the exhaust performance data to evaluate the torque indirectly by the gas temperature varies with the engine speed. method of measurement of the engine governor control Furthermore the exhaust gas temperature is a function of lever position. the admission air temperature. Therefore the torque was As the engine performance is affected by ambient correlated to the temperature difference AT between conditions (pressure, temperature and air humidity), the exhaust and admission air and to the engine speed. reduction factor of ISO 2288 Standard was used to calculate the corrected engine torque Te: Method 3 - Measurement of Engine Governor Control Lever Position Te = T(K/I) [1] According to Khovakh (1979) for a diesel engine equipped with a variable-speed governor to each position where of the governor control lever corresponds only one engine Te — corrected engine torque, N.m idle speed Nm. T = PTO torque, N.m In Fig. 1 for example, torque Te^ is defined by the K = reduction factor from ISO 2288 engine speed N^ and by the engine idle speed Nm4. In I = transmission ratio PTO/engine conformity with the engine load, the governor automatically changes the torque from maximum (curve TABLE 2. ENGINE GOVERNOR CONTROL LEVER AB in Fig. 1) to (idle speed). The torque was then POSITION AND ASSOCIATED ENGINE IDLE SPEED correlated to the engine idle speed and engine speed, but in this case two correlations were needed: one for the Engine idle speed, Nm (min'l) Lever maximum torque curve and another after the governor position Tractor 1 Tractor 2 Tractor 3 reduces the torque to zero.

1 2490 2440 2495 CORRELATION AND ANALYSIS OF VARIANCE 2 2190 2190 2175 3 1940 1940 1865 A statistical analysis of test results confirmed that in 4 1690 1690 1570 the correlation to evaluate the engine torque indirectly, 5 1440 1440 1260 for all methods, the engine speed should be included as 6 1190 1190 - an additional independent variable and indicated that

Vol. 31(5):September-October, 1988 1351 with RJ., = coefficient of multiple determination with n-1 variables R^ = coefficient of multiple determination with n variables

RESULTS AND DISCUSSION Method 1 - Measurement of the Fuel Consumption Table 3 presents coefficients for equation [4] obtained 900 1200 Nx N,n4 2100 2400 2700 by stepwise regression entered by order of significance ENGINE SPEED ( min. ") according to the F-test used in statistics. It can be seen that for tractor 1 a correlation including only the variable Fig. 1—Performance of tractor 1 for different positions (1 to 6) of the engine governor control lever. mass amount of fuel G has a coefficient of multiple determination R2 = 0.977. When a second variable in order of significance (N^) is included R^^ 0.991, and so the first, second and third powers of the independent on. variables could be significant. Therefore the following For tractors 2 and 3 the results are formally quite correlation to evaluate the engine torque was proposed: similar except that C^ is more significant than C,. This fact, however, does not affect the overall result because Te = CQ + Ci Y + C2Y2 + C3X + C4XY + C5XY2 by considering the first four significant variables (G, N^, N and G^) the coefficient of multiple determination R^ is equal to 0.998, 0.999 and 0.999 for tractors 1, 2 and 3, + C^X2 + CyX^Y + C8X2Y2 + C9Y3 + C^ QX^ respectively. Therefore the proposed correlation to evaluate the corrected engine torque Te by method 1 with .[4] an average coefficient of multiple determination of 0.999 is where X = independent variable 1; G, AT or Nm Te = ao + a^ G + a2G2 + a3N + a4N2 .[6] Y = independent variable 2, N Q,..,Cio = constants where a^ to 3,4 are constants to be determined from Several regression equations with increasing number performance tests of a given tractor. of group of variables were obtained by the method of For all tractors the inclusion of the engine speed and stepwise regression. To evaluate the increase in accuracy its square as variables in the correlation was F-test when going from an expression with n-1 variables to an significant at 0.1% level of probability. Therefore the expression with n the percentual increase in the non-dependence of the torque on the engine speed coefficient of multiple determination AR^ was used mentioned by Kirste et al. (1985) was not confirmed. Furthermore the inclusion of the mass amount of fuel and its square as variables was observed to be F-test AR2 = " ^ "-^ . 100% [5] significant at 0.1% level of probability, thus confirming R^-1 the conclusions of Sumner et al. (1986).

TABLE 3. REGRESSION EQUATION COEFFICIENTS FOR METHOD 1 AND TRACTOR 1

C3 C2XIO6 Cixl02 C6xl02 C7XIO6 CgxloS R2 AR2

52.52 5.779* 0.977 32.55 5.786* - 7.18* 0.991 1.4% 132.2 5.796* -44.61* 12.63* 0.994 0.3% 164.6 7.738* -45.72* 12.83* -2.46* 0.998 0.4% 151.5 7.691* -45.05* 11.93* -3.03* 4.01* 0.998 0.0% 73.06 7.591* -15.22* 2.01* -7.41* 62.44* -1.76* 1.000 0.2%

^F-test significant at 0.1% level of probability

TABLE 4. REGRESSION EQUATION COEFFICIENTS FOR METHOD 2 AND TRACTOR 1

Co C3XIO2 C2xl05 C4xl04 C6xlo4 C5XI08 R2 AR2

-125.60 76.38* 0.949 - 98.64 77.38* -1.094* 0.980 3.2% - 39.28 45.30* -3.577* 2.138* 0.993 1.3% - 2.29 22.22* -3.384* 2.036* 3.276* 0.995 0.2% - 10.31 2.02t -2.904* 4.687* 3.605* -9.064* 0.998 0.3% - 8.05 -2.905* 4.776* 3.775* -9.313* 0.998 0.0%

*F-test significant at 0.1% level of probability t F-test non-significant at 10% level of probability

1352 TRANSACTIONS of the ASAE TABLE 5. REGRESSION EQUATION COEFFICIENTS TABLE 6. REGRESSION EQUATION COEFFICIENTS FOR METHOD 3 AND FOR METHOD 3 AND TRACTOR 1 TRACTOR 1 AFTER THE GOVERNOR REDUCES THE TORQUE FOR THE MAXIMUM TORQUE CURVE Co Ci C3 C6xl05 C5XI08 R2 AR2 Co Cixl02 C2xl05 C9xl( R2 AR2 14.8 -1.872* 1.866* 0.948 -267.9 -1.898* 2.215* -8.799* 0.968 2.1% 396.6 -3.839* 0.585 -498.8 -2.144* 2.825* -28.480t 3.655$ 0.972 0.4% 166.5 22.56* -7.96* 58.6% 0.928 *F-test significant at 0.1% level of probability -140.1 84.39* -47.62* 8.12* 0.973 4.8% tF-test significant at 1% level of probability :j:F-test significant at 5% level of probability *F-test significant at 0.1% level of probability

When the first three significant variables N, Nm and Nm2 are included R2 is 0.968, 0.920 and 0.974 for Method 2 - Measurement of Exhaust Gas Temperature tractors 1, 2 and 3, respectively. However, inclusion of Table 4 presents stepwise regression coefficients for Nm^ was not significant for the naturally aspirated equation [4] with exhaust gas temperature and engine engine (tractor 2) and in this case only N and Nm should speed as independent variables to evaluate the engine be considered. Therefore when the governor is reducing torque of tractor 1. the torque the correlation for the torque is, for Variable AT was the first to be introduced in the turbocharged engine correlation corresponding to a coefficient of multiple determination R2 equal to 0.949, 0.865 and 0.957 for Te = ho + h^N + h2Nm + h3Nm2 [9a] tractors 1, 2 and 3 respectively. When the first four significant variables (AT, N.AT, N^ and AT^) are and for naturally aspirated engine considered R2 is equal to 0.995, 0.997 and 0.990 for regression equation of tractors 1, 2 and 3, respectively. Te • ho + h^N + h2Nm [9b] Thus, the proposed correlation to evaluate Te by method 2 with an average coefficient of multiple determination of where h^ to h-^ are constants to be determined from 0.994 is performance tests. The average coefficient R^ for these correlations is 0.954. Te = bo + bi AT + b2AT2 + b3 N- AT + b4N2 .... [7] When using method 3 to evaluate the engine torque care must be taken because two correlations are where b^ to h^ are constants to be determined from provided: equation [8] for the maximum torque zone tractor performance tests. (curve AB in Fig. 1) and equation [9] for when the governor is reducing the torque (curves like 1 to 6 in Fig. Method 3 - Measurement of the Engine Governor 1). Therefore to evaluate the engine torque Te for a given Control Lever engine speed N and engine idle speed Nm: a. Correlation for the Maximum Torque Zone: Table 5 shows stepwise regression coefficients for equation [4], Te = min ( Te (equation [8]), Te (equation [9]) j obtained from tractor 1, with the engine speed as the independent variable. .[10] Inclusion of N^ was F-test significant at 0.1% level of probability for turbo-charged engines (tractors 1 and 3) but not significant at 10% level of probability for that is, Te is the minimum value given by equation [8] or naturally aspirated engine (tractor 2). When N, N^ and equation [9]. N^ are considered in the correlation R^ is 0.973, 0.993 and 0.976 for tractors 1, 2 and 3, respectively. For tractor 2, R^ is the same if only N and N^ are considered. CONCLUSIONS The proposed correlation for the torque, for a turbo- The objective of this study was to investigate methods charged engine is of evaluating the torque of diesel engines indirectly. Three methods were proposed: measurement of the fuel Te = do + d^N + d2N2 + d3N^ [8a] consumption, measurement of exhaust gas temperature and measurement of engine governor control lever and for naturally aspirated engine. position. Three tractors were used in performance tests in order to consider 4 and 6 cylinders, turbo-charging Te = do + diN+d2N2 [8b] and naturally aspirated engines. The results were not significantly influenced by the type of tractors and where d^, to d3 are constants to be determined from therefore the proposed correlations can be taken as valid performance tests. These correlations have an average for any tractor. coefficient of multiple determination of 0.981. In the average, method 1 is the most accurate, b. Correlation After the Governor Reduces the followed by methods 2 and 3, respectively. Method 3 Torque: Stepwise regression was used to obtain requires the least cost, followed by methods 2 and 1. coefficient for equation [4] with engine speed and engine Finally, regarding the adaptability of measuring systems, idle speed as independent variables. Table 6 presents method 3 is the most appropriate because it requires only performance results for tractor 1. an engine speed meter.

Vol. 31(5):September-October, 1988 1353 References 1. Khovakh, M. 1979. Motor vehicle engines. Mir Publishers, based on indirect fuel measurement. TRANSACTIONS of the ASAE Moscow. 28(4):994-998. 2. Kirste, T., W. Grunbeck and M. Feller. 1985. Kennfeldmonitor 4. Sumner, H. R., R. E. Hellwig and G. E. Monroe. 1986. fuer Dieselmotoren. LANDTECHNICK 40(10):426-30. Measuring implement power requirements from tractor fuel 3. Pang, S. N., G. C. Zoerb and G. Wang. 1985. Tractor monitor consumption. TRANSACTIONS of the ASAE 29(l):85-89.

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