`Advances in Mechanical EngineeringVolume 2012 (2012), Article ID 763171, 7 pageshttp://dx.doi.org/10.1155/2012/763171`
Research Article

## Fuzzy-Based Evaluation of a Specific Drive Train

Budapest University of Technology and Economics, Bertalan Lajos u. 3. MG, 1111 Budapest, Hungary

Received 22 April 2012; Accepted 11 August 2012

Copyright © 2012 Attila Piros and Zsolt Farkas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper introduces a fuzzy-based evaluation method of a specific portion of the power train. In this case study was evaluated a specific combination of a commercial high-performance tractor engine and power split hydrostatic infinitely variable transmission (IVT). The first part of the study describes the field test of the power train, then the mathematical model of this power train is introduced. The objective of this study was the evaluation of the power train in some specific phases. The tractor is one of the most important machines in the agricultural mechanization and the mostly used tractor speed ranges were generated by different engine speed and transmission ratio combinations. In each case the engine consumption and the transmission efficiency were calculated based on this mathematical model. These results were evaluated with the method of corrected fuzzy mean (CFM). All of these calculations were performed in MATLAB. This study gives a design guide for the future processes of the engine-transmission matching as a result.

#### 1. Introduction

This paper introduces a fuzzy-based evaluation of an engine-transmission combination. The evaluation is based on the investigation of a four-valve, turbocharged, intercoolered, low-emission diesel engine and a Steyr S-Matic infinitely variable transmission (IVT) unit [1, 2]. These components were integrated in Case IH 195 Puma tractor. A modern tractor is one of the most important machines in the agricultural mechanization and its transmission system is a key component representing about 30% of the total tractor first cost. The IVT unit in the transmission of these power machines is not included directly in the power flow, but in one of the power branches after a split. By modifying the ratio gear of a properly selected IVT unit, the transmission can be geared natural and the direction of progress of the vehicle can be changed. Infinitely variable drives with automatic controls is a new area of power train design. This fuzzy-based evaluation helps the design of the automatic control by highlighting the best areas of the parameters’ ranges. The evaluation is based on field test. This test was a mobile PTO (Power Take-Off) brake-test provided the engine characteristics of vehicle (Figure 1).

Figure 1: Case IH 195 Puma tractor in mobile PTO brake test.

We used Sigma 5 Dynamometer (Serial no. 022346). During the test there were four parameters recorded: engine speed [1/min], loading torque [Nm], specific fuel consumption of the engine [g/kWh], and the throttle position [%] (Figure 2). These measurement data were integrated in the mathematical model of the evaluation.

Figure 2: Engine characteristic.

The transmission efficiency is a highly important factor in the evaluation procedure therefore it is necessary to include in the mathematical model. The measuring of a efficiency of the transmission unit can be done a specific test generally but in this tractor brake test was no opportunity to do it. Therefore the concerning data were referenced to the direct measurement of the transmission (Figure 3) [3]. The transmission efficiency is the function of vehicle speed. The influence of the hydrostatic unit to the efficiency graph is significant at the middle of every gear range, where the hydrostatic power portion transferred is zero. At these operating points, the power is transferred purely mechanically.

Figure 3: S-Matic transmission efficiency as a function of vehicle speed [3].

#### 2. Developed Mathematical Model

There are several mathematical models in the field of CVT-IVT-based drive train calculations. Some models cover some specific components of the drive train [4] (Figure 4) [7], other models describe larger portions of the system [5]. These models try to optimize the drive train concerning different goals like fuel consumption [8] or exhaust (NOx) emission (Figure 5) [5].

Figure 4: Modelling a CVT tractor transmission in KISSsys [4].
Figure 5: Derivation of optimum engine operating line [5].

Our evaluation of the engine-IVT system is based on a mathematical model which generates data of engine speed and transmission ratio pairs. Using these input data the model calculates the vehicle speed, transmission efficiency, and the specific fuel consumption of the engine. In the current state of evaluation there are some limitations. A general purpose tractor can operate with a relative wide speed range. In the practice this speed range in forward direction is between 0.5 km/h and 40 km/h. Concerning the distribution of the speed values on agricultural operations the evaluated vehicle speed was set to 8 km/h in the procedure [6] (Figure 6).

Figure 6: Vehicle speed distribution on agricultural operations [6].

The power train control system tries to maintain the desired speed of the vehicle using the sophisticated servo control of the hydraulic transmission in the IVT unit [9]. This speed control provides the required parameters to reach the desired vehicle speed (Figure 7).

Figure 7: High-level view of speed control in a tractor [9].

During the evaluation all of the possible engine speed and transmission ratio pairs were generated with the given resolution. The range of the speed and ratio values was determined with specific limits. These limits are calculated to cover the vehicle speed range between 4 km/h and 14 km/h.

The transmission efficiency calculation is based on the extension of the efficiency measurement data with a specific engine speed (2300 rpm) into a broader range of the engine speeds. The limits of this extension were synchronized with the previous boundary condition of the vehicle speed. The interpolation was executed in two steps to decrease the effect of the mechanical gear shifts (Figure 8). The specific fuel consumption of the engine was calculated with a selected load case (300 Nm loading torque).

Figure 8: Interpolated efficiency of the transmission.

#### 3. Evaluation of the Calculated Properties

The evaluation procedure can be separated into three stages (Figure 9). In the first stage the input data field was generated with a given resolution. The engine speed values were generated between 1800 rpm and 2600 rpm by 40 rpm steps. The transmission ratio values located between 2 and 4 by 0.08 resolutions. The resolution can be specified in any fine step values and it is limited only the available computational capacity. The second stage of the evaluation includes the calculation of the vehicle parameters. These parameters are the vehicle speed, the efficiency of the transmission, and the fuel consumption of the engine. In the last stage the fuzzy-based evaluation and the visualization of the results can be found.

Figure 9: The 3 steps of the evaluation.

The evaluation is based on the fuzzy logic. Fuzzy logic handles the ambiguous cases of parameter evaluation. This way is close to human thinking because by answering some simple questions the concerning fuzzy membership functions can be set up [10]. A typical fuzzy membership function (U(HA)) results on its output a number between 0 and 1. Zero means that the studied value (Ey) is totally outside the set or range. 1 marks that the value (Ex) is totally inside the range. Any other value (Ez) between 0 and 1 shows the ratio of the membership. The conventional Boolean logic of the sets is displayed in Figure 10. The fuzzy implementation is displayed in Figure 11.

Figure 10: The conventional boolean logic of the sets.
Figure 11: The fuzzy logic of the sets.

The fuzzy evaluation of the vehicle speed is based on the following fuzzy-membership function (Figure 12). The evaluated seed value is rated to optimal if it is equal to 8 km/h. The deviance from this optimal value is rated with lower fuzzy values up to zero. If the calculated speed is less than 4 km/h or more than 12 km/h the concerning fuzzy value becomes to zero therefore these speed ranges are not acceptable for agricultural operation.

Figure 12: The fuzzy evaluation of the vehicle speed.

The efficiency of the transmission is the function of the engine speed and the vehicle speed. It means that the efficiency is not only dependent on the engine speed also the acceptable efficiency level is varied by the vehicle speed. Renius determined an objective function for the value of total efficiency [11]. The efficiency limit is calculated based on this diagram and the concerning fuzzy membership function is set up with this value (Figure 13).

Figure 13: The fuzzy evaluation of the transmission efficiency [8].

The specific consumption of the tested diesel engine is between 340 g/kWh and 420 g/kWh. Thus the membership function for the evaluation of the consumption is accommodated to these limits (Figure 14).

Figure 14: The fuzzy evaluation of the specific consumption.

In the last stage of evaluation procedure there are three parameters to rate. These are the calculated vehicle speed, the transmission efficiency, and the specific consumption. The concerning fuzzy-membership functions provide three different fuzzy values which have to be transformed back into a single value. This is the defuzzyfication stage of the evaluation and this single value characterize the overall quality of the evaluated state of the power train. There are many methods to perform this defuzzyfication, but in this paper the Corrected Fuzzy Mean (CFM) was used [12]. The fuzzy values are defined with the concerning fuzzy membership function:

Introducing the corrected fuzzy mean () there is a good opportunity to summarize as many results of the fuzzy membership function as it is required to evaluate the specific state. This value is much simpler to calculate than the traditional results of the fuzzy inference systems:

These CFM values indicate well the quality of a given state of the power train specified by the engine speed and transmission ratio value pair. With calculation of the CFM values the different states can be comparable.

Reviewing the results of the evaluation, some important consequences can be drawn. As Figure 15 shows at the engine speed-transmission ratio plane, the best vehicle speed values are concentrated around the 8 km/h value.

Figure 15: Velocity distribution: the best (around 8 km/h) values are highlighted.

Concerning the transmission efficiency the higher the values the better (Figure 16).

Figure 16: Efficiency distribution: the best (higher) values are highlighted.

In case of the engine consumption the lower the values the better (Figure 17).

Figure 17: Consumption distribution: the best (lower) values are highlighted.

Analysing the quality values calculated with the Corrected Fuzzy Mean (CFM) method it is quite aconspicuous that the best quality values are not only distributed on the common best value area of the previous diagrams but also there are outlying values highlighted at the engine speed-transmission ratio plane. It means that a good and acceptable power train state can be combined with many kinds of engine speed-transmission ratio value pairs (Figure 18).

Figure 18: Quality distribution: the best (higher) values are highlighted.

#### 4. Conclusions

This paper introduced a mathematical model of the high-performance tractor power train. The two main components of this power train are the common rail diesel engine and the connected infinitely variable transmission (IVT). This model is based on test measurements and other referenced results concerning the the IVT efficiency. The computed power train parameters were evaluated with fuzzy evaluation. The final results were performed by the method of the Corrected Fuzzy Mean (CFM). The results highlighted that the desired vehicle speed can be combined with many engine speed and transmission ratio pairs with different parameter values. The qualities of these solutions are very variable and the maximization of the quality requires careful selection the engine speed and transmission ratio. This mathematical simulation enables us to determine the optimal values for the integrated engine and transmission electric control. The maximization of the efficiency of the engine-transmission collaboration depends on the good control values. This mathematical model can handle not any engine-transmission combinations but also has more improvement opportunities. One possible improvement can be the handling of other operation speeds, like transport speed, not only one specific speed. Another improvement would be the extension of the input parameters from the engine speed and transmission ratio pairs. Taking into consideration that the change of load torque will increase the accuracy of the mathematical model, therefore the efficiency of the transmission and the specific consumption of the engine are also depending on the load torque.

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