2.1. Experimental Method
2.1.1. Experimental Apparatus
According to the turbocharger test method of Mechanical Industry Standard JB-T9752.2-2005 of the People’s Republic of China, the overall structure of the test bench was determined as shown in
Figure 1.
This test bench is a multi-purpose test platform suitable for a turbocharger which can also be used for gas turbine test. The main components include an electric regulating valve, air compressor, pipeline system, fuel supply system, combustion chamber, supercharger, sensor, etc. As shown in
Figure 2, a JK45 turbocharger (JK45, Hunan Tyen Machinery Co., Ltd, Hengyang, China, 2015) is employed to carry out the experiment, the highest speed of which is 230,000 r/min and the volume of which ranges from 0.8 to 2.5 L. Six Kistler pressure sensors (9136B, Kistler, Winterthur, Switzerland, 2020) are employed to measure the pressure. In addition, a corresponding speed sensor, five temperature sensors (WRTK-112, Senxte, Tianjin, China, 2020) and two flow mass sensors (CMF010, Emerson, St. Louis, Missouri, US, 2019) are employed to measure the speed, temperature and flow mass, respectively. An FCMM-2 fuel flowmeter is employed to measure the fuel flow mass. More specifically, the measurement range and error of each instrument are shown in
Table 1.
In the experimental process, regulating valve 1 is closed. External air can enter through regulating valve 3 when the turbine is started and accelerated. After the turbine speed reaches a certain value, fuel is injected into the combustion chamber and burnt, resulting in high-temperature gas. Meanwhile, the turbine drives the compressor impeller to rotate through the turbine shaft. In this test bench, regulating valve 2 is connected to the atmosphere through an exhaust device, and the outlet flow of the compressor can be controlled by adjusting its opening ratio to realize different working conditions. In addition, the air flow into the combustion chamber can be regulated by controlling regulating valve 3. There are oil pressure test points, oil gauges and oil quantity regulating devices which can control the injection quantity between the oil pump and the combustion chamber. By adjusting the air flow and fuel quantity, parameters such as intake temperature and turbine speed can be controlled. Moreover, the cooling water enters from the high-temperature end and passes through the entire turbine bearing with the water jacket; it then outflows from the low-temperature end, finally flowing into the engine-cooling system through a hosepipe for temperature reduction, resulting in cooling water’s constant circulation in the water jacket and bearing cooling.
2.1.2. Data Acquisition and Processing
In the actual experimental environment, the accuracy of the data acquisition system will be affected by the noise, electromagnetic radiation, ground ring and common-mode voltage. Thus, a data acquisition card with a current signal of 4~20 mA is used for measurement, considering these factors in the experimental process. The isolation can isolate the common-mode voltage from the earth ring and prevent the signal attenuation caused by the resistance of the wire during long-distance transmission. At this time, the range of current signals output by the temperature and pressure sensors is also 4~20 mA, and there is the same current signal range for the frequency converters. In addition, the sensors of the PCI-6238 data acquisition device produced by NI are selected to measure the temperature and pressure. The rotational speed is measured by a JC3A rotational speed sensor produced by the Xiangyi Power Testing Instrument Co., Ltd. The Siemens PLC is adopted to control the switching value.
The measurement and control system of the turbocharger test bench is shown in
Figure 3, where an electric control cabinet in the figure is used to control various electrical systems, such as the manual adjustment of valves, the cooling-water and lubrication system, and the total stopping of the air compressor and whole test system. In the experimental process, the signals from various sensors are collected and analyzed by the computer through the instrument interface and data acquisition card, and the control signals are sent to various actuators after processing the data. Similarly, the driver software DAQx and Labview produced by NI were used to develop the program of the measurement and control system, which makes the program complete many functions such as information collection, processing, control, result display and printing [
40].
2.1.3. Temperature Measurement of Water-Cooled Bearing Casing in the Turbocharger
Boiling heat transfer is very important for the turbocharger when it works. In order to obtain the actual temperature distribution of a turbocharger water-cooled bearing, it is necessary to conduct temperature testing for the turbocharger. The turbocharger turbine is affected by the high-temperature exhaust gas, which makes the bearing casing gather a large amount of heat load near the turbine end. Thus, the temperature distribution of the turbine varies with the heat load. Due to the limitation of measurement conditions, it is difficult to directly measure the actual temperature of the bearing casing at the turbine end and the compressor end in the experimental process. Thus, an indirect measurement method (non-contact measurement) is used to test the temperature of the bearing casing at the turbine end and the compressor end. For the indirect measurement method, non-contact thermometry mostly uses advanced optical technology or infrared technology to measure the surface temperature by data conversion. The pixel count of the thermal imaging camera in the test is 640 × 480, the frame frequency is 8.5 Hz, the spectral response is 8–14 μm, and the heat sensitivity is 0.02 °C.
In the temperature measurement process, except for the bearing casing at the turbine end and the compressor end, contact temperature measurement with thermocouples can meet the temperature measurement requirements of the parts of the turbocharger. Therefore, six industrial armored thermocouples (type: WRTK-112, measuring range: −40~1100 °C, diameter: 0.25 mm, reaction time: 0.5 s) are located in six measuring points in
Figure 4 to collect the corresponding heat loads. The full turbocharger’s section can be seen in [
41]. In order to ensure measurement accuracy, the position of the thermocouple hole should be accurate, which can be drilled from the outside to the inside. When a measuring hole is drilled in the wall near the floating bearing of the bearing casing [
42], its radius should be 0.5 mm, and the distance between the bottom of the measuring point and the sealing ring and the floating bearing wall should be less than 1.0 mm.
2.2. Evaluation Method
The increased temperature caused by the unit volume loss in the operation process is the main factor that limits the design capacity of the turbocharger bearing casing [
43,
44]. However, good water-cooling performance can effectively reduce the heat load and improve the operating reliability and power density of the turbocharger bearing casing [
45]. Therefore, it is very important to conduct a reasonable and effective comprehensive evaluation of the design performance of the water-cooling system for a turbocharger [
46,
47].
The analytic hierarchy process [
48] is considered as a good option for a reasonable and effective comprehensive evaluation. It can achieve a qualitative and quantitative analysis of the water-cooling performance for the turbocharger bearing casing. However, the analytic hierarchy process is subjective and non-fuzzy. In this paper, a triangular membership function is used to construct the fuzzy consistency judgment matrix of a turbocharger bearing water-cooling system performance index. Then, the AHP is used to calculate the weight index of water-cooling system performance, and an improved fuzzy analytic hierarchy process is constructed. Thus, a fuzzy analytic hierarchy process evaluation method for the design of a turbocharger bearing water-cooling system is proposed, which can provide strong support for the effective evaluation of the designed turbocharger bearing’s reliability and other performance indexes. The improved FAHP is used to evaluate the water-cooling system performance, and its main steps are as follows:
(1) Firstly, determine the performance evaluation indexes of the water-cooling system. (2) Design a questionnaire for the water-cooling system’s performance. (3) Carry out the fuzzy evaluation of the performance evaluation index of the water-cooling system. (4) Calculate the fuzzy evaluation average value of the water-cooling system performance index. (5) Calculate the correlation of fuzzy evaluation values of the water-cooling system performance. (6) Obtain the performance evaluation value of the water-cooling system.
2.2.1. Performance Evaluation Index System
The performance evaluation of the water-cooling system of the turbocharger bearing casing mainly includes three aspects: structural design evaluation of the water-cooling pipeline, resistance design evaluation of the water-cooling pipeline and heat transfer design evaluation of the turbocharger bearing.
The evaluation value of the water-cooled pipeline structure design S1 includes water pump loss S11, cooling-water flow S12, cross-sectional area of the water-cooled pipeline S13, absorbed heat of cooling water S14, radiating area of the water-cooled pipeline S15, length of the water-cooled pipeline S16, channel number of the water-cooled pipeline S17 and width of the water isolation platform S18. Evaluation value of the water-cooling pipeline resistance design S2 includes: resistance along the way S21, local resistance S22 and water pump loss S23. The evaluation value of the bearing heat transfer design S3 includes: bearing casing temperature drop S31, bearing casing lower temperature drop S32, bearing casing upper temperature drop S33, bearing casing and water jacket assembly gap temperature drop S34, water jacket temperature drop S35, bearing casing total temperature drop S36, engine oil temperature drop S37, water jacket total temperature drop S38 and water jacket surface average temperature S39.
Thus, the performance evaluation index system parameters of the turbocharger bearing water-cooling system can be expressed as: S = (S1, S2, S3), S1 = (S11, S12, S13, S14, S15, S16, S17, S18), S2 = (S21, S22, S23), S3 = (S31, S32, S33, S34, S35, S36, S37, S38, S39).
As shown in
Table 2, the performance evaluation data of the water-cooling system are sent to selected experts in the thermal control field of turbocharger bearings. Then, the questions are answered anonymously by them. Half of these experts come from academia, and the other half come from industry. After the test, the questionnaire on performance evaluation of the turbocharger bearing water-cooling system is collected.
Table 3 is used to score the performance index parameters of the turbocharger bearing water-cooling system, and the scoring interval is (0.5~0.9).
2.2.2. Fuzzy Judgment Matrix for Performance Evaluation
The fuzzy judgment matrix construction of the water-cooling system performance evaluation was conducted as follows:
Step 1: If the evaluation value of the performance index parameters is not given by any evaluation experts, the evaluation value is considered to be 0.
Step 2: If the evaluation value of the performance index parameters is only given by one evaluation expert, the evaluation value will be recognized.
Step 3: If the evaluation value of the performance index parameter of the turbocharger bearing water-cooling system is given by
K evaluation experts. The membership degree of the evaluation value
xijk is determined by Formula (1):
where 1 ≤
k ≤
K ≤
n,
uij is the average value of the evaluation values of performance index factors in item
j of class
i,
mij is the fuzzy subset boundary of performance index factor evaluation, and
mij = 2
σij;
σij is the standard deviation of the evaluation values, which is determined by Formula (2):
If the number of evaluation experts excluded in Formula (1) is
k0, then the membership degree calculation formula of the evaluation value
xij of the performance index factor of the turbocharger bearing casing water-cooling system in item
j of category
i is determined by Formula (3):
According to the above method, the fuzzy judgment matrix of the performance index is shown as follows:
where 0 ≤
i ≤
m, and 0 ≤
j ≤
n.
2.2.3. Weight Determination of Performance Index Factors
If there are t evaluation index factors u1, u2, …, ut in a certain layer of the performance evaluation system of the turbocharger bearing water-cooling system, the analytic hierarchy process can be used to construct the judgment matrix C = (cij)t×t, so as to determine the weight of the performance index factors of the turbocharger bearing water-cooling system. Professionals compare the relative importance of each element in pairs and judge the scale values 1–9 and their reciprocal of the elements in the matrix C = (cij)t×t, and they select the values according to the following methods:
Step 1: If ui meets the following requirements compared with uj: {equally important, slightly important, obviously important, especially important, absolutely important}, then cij = {1, 3, 5, 7, 9};
Step 2: If the importance of ui and uj is between their levels, it can be scaled by 2, 4, 6, 8, 1/2, 1/4, 1/6 or 1/8;
Step 3: The element cij in the judgment matrix C = (cij)t×t also has the following properties: (1) cij > 0, (2) cij = 1/cji, (3) ci=j = 1.
The weight
Wi of that performance index factor of the water-cooling system of the turbocharger bearing casing can be expressed as:
By applying the analytic hierarchy process twice, the weights W1, W2 and W3 of some index factors in the performance evaluation system of the turbocharger bearing water-cooling system can be finally obtained, and ∑Wi = 1. The weight set W = (W1, W2, W3). For example, the weight of the water-cooled pipeline structure design evaluation is W1, W1 = (W11, W12, W13, W14, W15, W16, W17, W18). The weight of the water-cooling resistance design evaluation is W2, W2 = (W21, W22, W23). The evaluation weight of the turbocharger bearing heat transfer design is W3, W3 = (W31, W32, W33, W34, W35, W36, W37, W38, W39).
2.2.4. Performance Evaluation Steps of Water-Cooling System
The performance evaluation steps of water-cooling system can be expressed as follows:
Step 1: Find the evaluation matrix bi = wij ri (0 ≤ I ≤ m) of each factor of the performance index, and normalize it.
Step 2: Establish the target price matrix B = (B1T, B2T, …, BiT)T of the performance index, where “T” means matrix transposition.
Step 3: The fuzzy comprehensive evaluation of the performance index is carried out to obtain the fuzzy comprehensive evaluation result set of the water-cooling system performance index, that is, the fuzzy subset
F obtained by combining the weight vector
W and the fuzzy matrix
B is as follows:
The performance evaluation value of the water-cooling system can be obtained from Equation (6), and thus the performance evaluation value of the water-cooling system can be determined.
Step 4: The performance evaluation value of the water-cooling system of the turbocharger bearing casing can be expressed as follows:
where
y is the corresponding score vector in the performance evaluation set of the turbocharger bearing water-cooling system, and its score table is shown in
Table 4.