平面四桿機(jī)構(gòu)的運(yùn)動分析(VB源代碼),平面,機(jī)構(gòu),運(yùn)動,分析,vb,源代碼 Proceedings of the 7th ICFDM2006 International Conference on Frontiers of Design and Manufacturing June 19-22, 2006, Guangzhou, China Pages 25-30 25 STUDY OF THE INFLUENCE THE INFLUENCE OF LOW ENVIRONMENT PRESSURE ON THE BEARING In ICE Feng Kai, Zhang Youyun and Xin Hao Theory of Lubrication and Bearing Institute, Xi’an Jiaotong University, Xi’an 710049, China Abstract: The influence of low environment pressure on the main bearing and big end bearing of I.C. engine was investigated based on a one-cylinder diesel engine. Firstly, a model of one-cylinder engine was set up, by the use of the commercial software EXCITE Designer from AVL company. Then, a series of experiments were done to gain the gas pressure in cylinder under different environment pressure. When the model of the engine considered the gas pressure as load, the applied load, eccentricity ratio and friction loss of the main bearing and the big end one were calculated, with the results validated by the experiments. The calculation results show that, with the decrease in environment pressure, the applied load of main bearing and big end one change, and the eccentricity ratio vary regularly, while their friction loss decrease a little. KeyWords: I.C. Engine; Low Environment Pressure; Bearing Load; Eccentricity Ratio; Friction Loss 1. Introduction Most of western China is high altitude plateau. As the increase of altitude, the air pressure and air density decrease, the air draw into the engine reduces and the combustible mixed gas becomes too dense ， so the combustion process becomes worse and dynamic behavior of the engine deteriorate significantly [1] . Under this working condition, the performance of both the main bearing and concord bearing will be affected by the drop of air pressure. So the research on the working condition of engine main bearing and concord bearing under western low pressure environment has important guiding significance for the design, manufacture and maintenance of engines working under western environment. At present, research documents on engine combustion process and dynamics influence at different altitude are usual at home and abroad [2][3] , but no systematic research work on the influence of low air pressure to the engine bearing appears. In this paper, single cylinder engine model considered the influence of air pressure is constructed. Using the combustion gas pressure measured through experiment under different environment pressure and different rotate speed as the input loading condition of the model, the change of the working condition of main bearing and concord bearing along with the environment air pressure under different rotate speed is calculated with business software EXCITE Designer of AVL Company, and the result is compared and validated with the experimental locus of journal center. 2. The Processing Method of low Air Pressure The influence of plateau low air pressure to the performance of engine bearing mainly comes from the deterioration of the engine dynamic behavior. In this paper, a western environment simulation engine test rig is used to simulate plateau low air pressure and measure the influence of low air pressure to the engine. The key technology of simulating low air pressure environment is how to simulate and adjust the intake pressure of the engine [4] . The exhaust pressure and the pressure in the crank shaft case are not simulated in this test system, and these works will be done later on. In the experiment, the influence of different intake pressure on the pressure in the cylinder is measured and the pressure value is loaded to the model constructed below, and then the influence of low pressure on the performance of engine bearing is worked out. The structure of the test rig is showed in fig. 1. Through the control of engine intake pressure, the simulation case can simulate the working condition of the engine under different environment air pressure. Then the pressure in the cylinder of the engine is measured by the high pressure and high temperature pressure sensor implemented in the cylinder. Due to the restriction of experimental condition, the eccentricity of the main bearing can not be measured directly, so the locus of journal center of the flywheel is measured with vortex sensor, and its eccentricity is worked out to replace that of the main bearing to validate the computational model. There are various factors which affect the combustion gas pressure in the cylinder, among which environment air pressure, rotate speed and load are especially important. Consider to run the engine with no load (the engine mainly do work to overcome friction) and measure Fig. 1 View of the Simulation Test Rig * Sponsored by National Natural Science foundation of China 26 the pressure in the cylinder under different rotate speed and different environment pressure. Fig.2 shows the pressure in the cylinder under different environment air pressure at 1000r/m. 3． The Influence of low Air Pressure on the Load of Engine Bearings 3.1 Force analysis of the piston-shafting system In order to simplify the model, it is assumed that the piston pin and rotate axis of the crank shaft are all on the central line of the piston. Then the force analysis of the engine piston-shafting is showed in fig.3. The gas pressure in the cylinder F Z is disassembled to the bearing. Fig.3 Piston-Shafting Force Analysis and Inertial Force Analysis 22 11 cos 1sin SS Z Z FF F F β λ ψ ′ ==? =? ? (1) 22 sin tan 1sin NN Z Z FF F F λψ β λ ψ ? ′ == =? ?? (2) () 2 22 sincos cos cos 1sin RZ Z FF F λψψβ ψ β λψ ?+ =? =? ? ?? ?? ?? ?? (3) () 22 sin sin cos sin cos 1sin RZ Z FF F ψβ λ ψ ψ ψ β λψ +?? =? =? + ?? ?? ?? ?? (4) F Z is the combustion gas pressure in the cylinder, the input load of the model; F T and F R are the forces applied on the concord big end bearing; FZ and FS are the force applied on the main bearing. 3.2 Inertial force analysis of the piston-shafting In this paper, two kinds of inertial force are considered as shown in fig.3 1) Rotate inertial force along the crank shaft radial direction 2) 1 st and 2nd order reciprocal inertial force along the piston central axis direction Disassemble to coordinate system: ( ) 0 2 01 0 cos cos cos 2 Zr Fr m mA mAωψ ψ ψ=? ? ? ? + ? ? + ? ? +K (5) 2 sin ry Fr mω ψ=? ? ? (6) Through force analysis of piston-shafting of the engine, combustion gas pressure in the cylinder is disassembled to the main bearing and concord big end bearing, at the same time the inertial force caused by the movement of the piston-shafting system. The load force on the main bearing and concord big end bearing can be derived from the combination of these two kinds of force. 3.3 Calculation result and analysis of bearing load Fig.2 Gas Pressure in the Cylinder under Different Environment Pressure at 1000r/m (a) 1000r/m Main Bearing Load (b) 1800r/m Main Bearing Load (d) 1000r/m Concord Big End Bearing Load (c) 2200r/m Main Bearing Load 27 Fig.5 Main Bearing and Concord Big End Bearing under Different Rotate Speed and Different Environment Pressure Fig.5 shows that as the environment air pressure decreases, the load of main bearing and the concord big end bearing significantly reduces during the deflagration stroke, and slightly changes during other strokes. Read in and analysis the load of the main bearing and concord big end bearing during the deflagration stroke, the results are showed in form 1: Form 1 Analysis of the Load of Main Bearing and Concord Big End Bearing during Deflagration Stroke under Different Environment Pressure and Different Rotate Speed Main Bearing Environment Pressure (kPa) 97 80 60 Bearing Load (kN) 16000 13500 110001000 r/m Decrease Percent (relative to 97kPa) 15.6 31.3 Bearing Load (kN) 14000 10000 4500 1800 r/m Decrease Percent 28.6 67.8 Bearing Load (kN) 9000 5000 3000 2200 r/m Decrease Percent 44.4 66.7 Concord Big End Bearing Environment Pressure (kPa) 97 80 60 Bearing Load (kN) 32500 27500 225001000 r/m Decrease Percent 15.4 30.8 Bearing Load (kN) 28000 20000 100001800 r/m Decrease Percent 28.6 64.3 Bearing Load (kN) 20000 11500 8000 2200 r/m Decrease Percent 42.5 60.0 It shows in form 1 that the load of the main bearing and concord big end bearing will decreases along with the reduce of environment air pressure at any speed. The lower the air pressure, the more significant the load decreases. As the rise of engine rotate speed, the decrease of the deflagration load of the main bearing and the concord big end bearing augment becomes more significant. In another word, the higher the engine rotate speed, the more sensitive the deflagration load of the main bearing and concord big end bearing is to the environment air pressure. The reason of this situation is that as the engine rotate speed rises, the decrease of the pressure in the cylinder increases, then the load of the bearing reduces significantly. Further more, as the rotate speed rises, the inertial force augment, but the load of the bearing reduces under the combinational influence. However, when the rotate speed rises to 1800r/m and the air pressure drops to 60kPa, the decrease of the deflagration load of the main bearing and concord big end bearing do not change along with the rise of the engine rotate speed. It means that when the rotate speed rise to a certain extent, and the environment air pressure is low enough, the influence of the environment air pressure to the load of the bearing in deflagration process is almost the same at different rotate speed. This is because when the environment air pressure decrease to a certain extent, and the rotate speed is upper, the influence of the air pressure to the combustion in the cylinder decreases, at the same time the pressure in the cylinder is pretty high, and the effect of the inertial force is minor, so the bearing load keeps unchanged to a large extent. Fig.5(c) (f) shows the change of the load of the main bearing and concord big end bearing in relation to the crank angle at the rotate speed of 2200r/m. It shows in the figure that the decrease or increase of the load of the two bearing is not congruously along with the diminishment of the environment air pressure in the whole working process of the engine, but differ in different strokes. This phenomenon can be explained as follows: In the whole working process of the engine, the air pressure in the cylinder (F Z in formula (1)-(4)) especially the combustion gas pressure in the deflagration process decreases along with the decrease of the environment air pressure, so the load of the main bearing and concord big end bearing decreases as a whole. The increase of bearing load when the crank angle is between 300～ 360 and -360～ -300 is because the piston is in the latter half of exhaust stroke and the first half of air intake stroke at that time, and the cylinder is exchanging air with the environment; here the inertial force along the negative direction of z axis F Z is smaller than that along the positive direction of z axis, it means that the resultant force is along the positive direction of z axis, as F Z diminish, the resultant force will augment on the contrary, so the bearing load will increase. 4． The influence of low Air Pressure to the Eccentricity of the Engine Bearing 4.1 The establish of Reynolds' equation and the solving of the eccentricity The Reynolds’ equation of the engine bearing can be expressed as [5] : () () () () () 2 33 ** 1 cos 1 cos 22 6sin sin cos D BR z dd dt dz ππ εφ εφ φφφ εδ ε ε φδ φδ φδ ωω ?????? ?? +++ ???? ???? =? ? + ? ? ? (7) In which D is the diameter of the bearing bush, BR is the width of the bearing bush, ε is the eccentricity, η (e) 1800r/m Concord Big End Bearing Load (f) 2200r/m Concord Big End Bearing Load 28 is the dynamic viscosity of the engine oil, δ is the minimum gap angular velocity, ω is the rotate speed of the journal. π is the oil film pressure, t is the time coordinate, φ and z are dimensional coordinate. Analyze the increase and decrease process of the bearing eccentricity respectively, the relation of the differential coefficient of eccentricity and the journal rotate speed can be expressed as below: () 2 Psin cos tan / , V B B So BR D BR D ψ ε ηβε ? ? ?? ?? ?? null null nullnullnull ＝ (8) () 2 * sin sin / , D PB So BR D BR D ψ ω η βε = ?? ?? ?? null null nullnullnull (9) In which B=δ S －γ S 0≤︱ B︱≤ 90° In the calculation Butenschoen method is used, and Sommerfeld number S OD and S OV can be find in reference [5], then Runge-Kutta method is used to solve the eccentricity through loop iteration. 4.2 Computing result and analysis of the bearing eccentricity Fig.6 Eccentricity of the Main Bearing and Concord Big End Bearing under Different Environment Air Pressure. Fig.6 (a) (d) show that when the engine rotate speed is under 1000r/m, both of the eccentricity shape of the two bearing shrink; fig.6 (b) (e) show that when the speed is 1800r/m, both of the eccentricity shape expand, and the deviation direction of the main bearing changed; and fig.6 (c) (f) show that when the rotate speed is 2200r/m, both of the eccentricity of the two bearing expand. We can conclude from the above figures that when the engine rotate speed is lower, the eccentricity shape of the main bearing and concord big end bearing shrink as the decrease of the environment air pressure, the lubrication condition of the bearing is improved and the bearing works more stable; when the rotate speed is higher, the eccentricity shape of the two bearing expand on the (a) 1000r/m Main Bearing Eccentricity (b) 1800r/m Main Bearing Eccentricity (c) 2200r/m Main Bearing Eccentricity (d) 1000r/m Concord Big End Bearing Eccentricity (e) 1800r/m Concord Big End Bearing Eccentricity (f) 2200r/m Concord Big End Bearing Eccentricity 29 contrary, the lubrication condition deteriorate and the bearing works unstable. At specific rotate speed, the deviation of the eccentricity may also change as the environment air pressure decreases. The load of the bearing is determined by the resultant force of the combustion gas pressure and the reciprocating inertial force of the shafting. When the rotate speed is lower, the reciprocator inertial force is lesser, and the main load of the engine bearing is caused by the combustion gas pressure in the cylinder (this is also the reason why the bearing eccentricity deflect to one side of the axis center). For this reason, the decrease of the environment air pressure causes the decrease of the pressure in the cylinder, thus the bearing eccentricity shrink. But when the engine rotate speed is higher, the reciprocating inertial force of the shafting increases and may at specific crank angle exceeds the combustion gas pressure in the cylinder if rotate speed is high enough. This makes the shape of the bearing eccentricity deflect to another side of the shaft center. At this time, when the decrease of environment air pressure causes the decrease of the pressure in the cylinder, the deflection of the bearing eccentricity also changes. As the engine rotate speed keeps on increasing, the reciprocating inertial force of the shafting exceeds the pressure in the cylinder in a bigger range of the crank angle. As a result, the bearing load is the result of the reciprocating inertial force minus the combustion gas pressure in the cylinder. When the decrease of the environment air pressure causes the decrease of the pressure in the cylinder, the load of the bearing increases and the eccentricity augments. 5. The influence of low Air Pressure to the Friction Power loss of Engine Bearing 5.1 The calculation of the friction power loss [5] If there is no direct contact between the bearing journal and bush, most of the friction power loss is caused by the shearing force of the engine oil viscosity. In this paper, only this part of friction power loss is considered. The friction coefficient ()μ α is: () () 4 sin 21 D So μα π ε β ψ ε =+ ?? (10) () () 2 * D D F So BR D αψ α η ω ? = ??? (11) Then the friction power loss is: () () () 2 4 * 0 42 Z FD BR D PSod π ηω μα α ωαα πψ ψ ??? =?? ? ∫ (12) 5.2 Calculation result and analysis of friction power loss of the bearing Fig.7 Friction Power Loss of the Main Bearing and Concord Big End Bearing under Different Environment Air Pressure It is figured out in Fig.7 that the power loss of the main bearing and concord big end bearing caused by the engine oil viscosity minish slightly along with the decrease of the environment air pressure. This is because the bearing load decrease as a whole when environment air pressure decreases, and the oil viscosity also reduces along with the increase of pressure [6] , thus the shearing force caused by the oil viscosity also decrease slightly, so the friction power loss reduces. Furthermore, it is shown in the fig that the influence of environment pressure to the friction power loss is relatively more significant during the deflagration stroke. This is also because the decrease of the bearing load is more severe at that time. 6. Experimental Verification Measure the locus of journal center of the flywheel with vertex displacement sensor on the “Western environment engine test rig” and calculate its eccentric, and then use it instead of the eccentricity of the main bearing to verify the computational model. (a) 2200r/m Main Bearing Friction Power Loss (a) 2200r/m,97kPa Calculated Eccentricity of the Main Bearing (b) 2200r/m,97kPa Eccentricity at the Fly Wheel Measured Through Experiment (b) 2200r/m Concord Big End Bearing Friction Power Loss 30 Fig 8 Eccentricity of Main Bearing Because of the restriction of experimental condition, the eccentricity of the main bearing can not be measured directly, so the eccentricity measured in the experiment is that of the flywheel. Because the crank shaft is flexible and will bend and distort under the stress of the concord and the engine cabinet, the eccentricity of the main bearing and the flywheel, which are at different section of the crank shaft, is apparently different. But there should be some common characteristics between them; the movement condition should be the same, and the locus of journal center should be similar. This is mainly because the main bearing and the flywheel are both on the crank shaft and the distance between them is not long, so the bend and distortion of the crank shaft is limited, thus the eccentricity shape is similar to some extent. Furthermore, because they are both on the crank shaft, and both have the same load, the change trend of the eccentricity should be the same. In this paper, the eccentricity at the flywheel measured through experiment and the calculated eccentricity of the main bearing are compared to verify the computational model. Fig.9 The movement condition of the eccentricity As shown in fig.8, it can be seen from the shape of the two graphics and the order of the marked point that both of them are moving according to the direction in fig.9 from A to B, C …H in turn. Compared to fig.8 (a), point A, G and H in fig.8 (b) deflect a little to the right, and point F deflects slightly up. This is mainly caused by the distortion of the crank shaft. Through the analysis and comparison of the two figure above, we can see that the movement rule of the two eccentricity are consistent, and the shape of them are similar to some extent. So we can come to the conclusion that the computational result is verified correct and credible through experiment. 7. Conclusion In this paper, single cylinder engine model considered the influence of low air pressure to the main bearing and concord big end bearing is constructed and verified through experiment. Generally, the higher the rotate speed of the engine