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Australian Journal of Basic and Applied Sciences, 5(12): 3112-3121, 2011 ISSN 1991-8178

Cinematic and Kinetic Analyses of the Slider- in of MF-285 Tractor

1Mohammad Reza Asadi, 1Heidar Abdollahian and 1Behnam Nilforooshan Dardashti

1Department of Mechanical , Islamic Azad University, Buinzahra branch, Qazwin, Iran.

Abstract: MF-285 tractor has devoted the highest production level in Iran among the other tractors. According to the literature, malfunction of the internal components of engine of this tractor is high; consequently research about it is necessary. In this regard, this paper presents the cinematic and kinetic analyses of the . Besides crank mechanism cinematic analysis, kinetic analysis of the connecting rod was done with regard to the forces resulting from ignition pressure, mass distribution in the crank mechanism as well as inertia forces. At the end, the graphs of displacement, speed and acceleration of , and also the graphs of ignition pressure, forces on piston, forces on connecting rod and forces on bears in one complete cycle according to the crank angle were drown by mathematica software. The maximum of piston speed equal with 13.5 m/s, the maximum of piston acceleration equal 3550 m/s2, the maximum of ignition pressure equal 2950 KPa, the maximum expansion force on connecting rod equal 10288 N, the maximum of compression force on connecting rod equal 19730 N and the maximum force on bears equal 30000 N were calculated. By the result of this paper there is possibility stress, fatigue, modal, harmonic and etc analyses of rotational part of engine of this tractor and suggest for improvisation of this part.

Key word: Tractor; Crank mechanism; Analyses; Cinematic; Kinetic.

INTRODUCTION

Tractor, as the most important agricultural machinery, has main share in planting, retaining and harvesting operations and then in mechanization sector. Hence, in order to reach sustainable agricultural and to increase mechanization level quality and manufacturing technology of this agricultural machinery and also its quantity must be reached to optimum level. Tractor MF-285 is main production of Iran Manufacturing Tractor Co. Researches show that engine inner parts’ faults of MF-285 are more than other ingredients of this tractor (Anonymous, 2008). Above statements show the importance of optimization of rotating parts of tractor MF-285 engine. The base of engine dynamic mechanism operation is slider-crank mechanism which consist , connecting rod and piston. Pressure due combustion, transferred from piston (the part merely has ) to the connecting rod (the part has both linear and rotation motion) and finally to the crankshaft (the part has merely rotation motion). As investigation of phenomena like vibration, resonance, fatigue, noise . . . , and optimization of these parts, kinematics and kinetic of slider-crank mechanism must be known. Optimization of mechanical instruments has been one of engineer goals. Below paragraphs are some examples: Cveticanin and Maretic have summarized dynamic analysis of a cutting mechanism which is a special type of the crank shaper mechanism (Cveticanin L, 2000). The influence of the cutting force on the motion of the mechanism was Considered. The Lagrange equation was used and boundary values of the cutting force were obtained analytically and numerically. Ha et al. (2006) have derived the dynamic equations of a slider-crank mechanism. They, for this purpose, used Hamilton’s principle, Lagrange multiplier, geometric constraints and partitioning method (Ha JL, 2006). Their formulation was expressed by only one independent variable. Finally to obtain the best dynamic modeling, they compared obtained results and numerical simulations. Also, a new identification method based on the genetic algorithm was presented to identify the parameters of a slider-crank mechanism. Koser (2004) investigated on kinematic performance analysis of a slider-crank mechanism based on robot arm performance and dynamics (Koser K., 2004). He analyzed kinematic performance of the robot arm using generalized Jacobian matrix. It was obtained that the slider-crank mechanism based robot arm had almost full isotropic kinematic performance characteristics and its performance was much better than the best 2R robot arm. He used complex algebra to solve that classical problem and he obtained solution as the root of a cubic equation within a defined range.

Corresponding Author: Mohammad Reza Asadi, Department of , Islamic Azad University, Buinzahra branch, Qazwin, Iran. E-mail: [email protected] 3112

Aust. J. Basic & Appl. Sci., 5(12): 3112-3121, 2011

Another research about angle was carried by Shrinivas and Satish (2002). They have summarized importance of the transmission angle for most effective force transmission. In this regard, they investigated 4-, 5-, 6- and 7-bar linkages, spatial linkages and slider-crank mechanisms (Shrinivas SB, 2002).

2. Methods: 2.1 Kinematics Analysis Of Slider-Crank Mechanism: MF-285 engine has 4 cylinders with linear arrangement. and qualifications has been shown in Table 1.

Table 1: Configuration and qualifications of MF-285 engine (Anonymous, 2008). Number of Cylinders 4 Piston Course (mm) 127 diameter (mm) 101 Indicated Revolution (rpm) 2000 Maximum Revolution (rpm) 2200 Indicated Engine Power (Hp) 71 Maximum (N/m2) 278 Revolution in Maximum Torque (rpm) 1300

According to figure (1) distance of piston from center of rotation can be obtained by below equations:

Sp  Rcos  Lcos (1) That: R: Radius of crank shaft L: Length of connecting rod

Fig. 1: Schematics of crank mechanism.

With regard to triangular equations in OAB triangle:

Rsin  Lsin  (2)

By aid of above equation we can delete  from equation 1:

1 S  R(cos  1 2 sin 2  ) (3) p 

By developing above equations we will have:

 1   (4) S P  R  cos  (cos2)  4 

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According to this point that  is function of time (a  t) for calculating speed and acceleration of connecting rod we calculate differential of equation 4 so:  V  R(sin  sin 2) (5) 2

  R 2 (cos   cos2) (6)

2-2 Kinetics Analysis Of Connecting Rod: 2-2-1 Forces Due To Ignition Of Fuel: During a work cycle which is a combination of breathing, congestion, explosion and discharge stages, a lot of interactions occur in the engine which will affect on one another and make the calculation difficult. For example, we can mention the heat transfer during the ignition between gas and the engine partition, the effect of the mixture form on the auto-engine and the effect of transfusion quality in the . So, only by studying the actions and reactions one by one, we can reach to an accurate conclusion. Therefore, it is necessary to study the engine performance under the simple hypotheses, and neglect the unimportant effects. The selected process for designing the diagram of gas pressure in terms of crank angle consists of following hypotheses (Asadi, M., 2008); 1. The mixture of gas and fuel is considered the ideal gas. 2. There is no physical or chemical change in the congested weather in the congestion stage and before the explosion. 3. Immediate alteration of gas and fuel mixture with the hot gas product of combustion. 4. The congestion and explosion stages are adiabatic. 5. The suction and discharge occur in the atmosphere pressure.

The forces produced by combustion, are the factors which make the mechanism move. For dynamic calculations, we substitute the pressure on the piston with a force in the direction of the cylinder. Amount of this force in any moment is calculated from this equation:

Fg  (Pg  P0 ).AP (7)

Pg: the gas pressure at any moment Po: the pressure of the weather outside AP: the area of the piston surface

The only unknown variable in the above equation is Pg which is a function of the angle and is calculated from thermodynamics relationship by the above hypotheses.

A) The Congestion Stage: Considering the adiabatic process of the gas congestion we will have: n P2  V1     (8) P1 V2 

P1 and P2 are respectively the primary and secondary pressure V1 and v2 are respectively the primary and secondary volume

The primary pressure changes, in terms of the movement velocity of piston, the relative size of tubes, the appearance of tubes and other factors. When the engine works at low speed with maximum load, the pressure approaches the atmosphere pressure.

The analysis of indicator diagrams has shown that the "n" value for this engine is about 1.21 (Prvardhans, 2005). The height of cylinder chamber is calculated through this equation: l h  (9) r 1

l: the length of piston r: congestion ratio

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The distance of the to the piston crest, while piston is at the bottom dead center is: l rl l   (10) r 1 r 1

Now we assume the piston is in the distance x from the top dead center. The pressure in this stage will be: 1.21  rl    1.21  r  l   rl  1.21 Pg  Pi  Pi   x (11)  x   r 1    

P1: the gas pressure at the beginning of congestion

B) The Explosion Stage: In this stage, the pressure is constant until the fuel is sprayed, and after the spraying interruption and explosion ending, the pressure decreases with the increase of the volume. So we can define this stage consisting of two kinds of pressures: the constant pressure and the variable pressure. Knowing that the fuel spraying continues up to 30 degrees after the top dead center, so the pressure will be constant from the top dead center to 30 degrees after top dead center, which is calculated by this equation: n P4 V3     (12) P3 V4 

P4: the gas pressure at the end of explosion stage P3: the gas pressure in the fuel spraying stage V4: the volume at the end of explosion stage V3: the volume at the end of fuel spraying stage From the equation above, the pressure at the time of fuel spraying was found 2950 KPa. The second stage of the explosion course begins after fuel spraying ending. The equation for this stage is: n P4 V3     P3 V4 

P4: the gas pressure at the end of explosion stage p3: the gas pressure after the fuel spraying stage v4: the volume at the end of explosion stage (the secondary volume) v3: the volume after the fuel spraying stage

As it was calculated, the distance of the cylinder head with the piston crest while the piston is at the bottom dead center, is found from 10 equation. So the secondary volume in the explosion stage will be: rl V  A (13) 4 r 1 P

AP: The area of piston surface Therefore we will have: 1.21   P  V  4   3  (14) P  rl  3  A   v 1 p 

If the piston would be at the x distance of the top dead center, the pressure in this stage will be: 1.21  rl  1.21 Pg  Pi   x (15)  r 1 Pi: the gas pressure at the end of the explosion cycle

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Aust. J. Basic & Appl. Sci., 5(12): 3112-3121, 2011

In the suction and discharge stages, the chamber pressure is considered equal with the atmosphere pressure on the basis of simplifying hypotheses.

2-2-2 The Masses Distribution In The Crank Mechanism: To avoid the complicated calculations, the masses are divided to two parts in the crank mechanism: 1) The reciprocating masses 2) The rotational masses

As the connecting rod has both transferring and rotating movements, we consider its masses concentrated on two ends (two eyes). So the mass in the small eye performs mere transferring movements and the one in the big eye (crank end) does mere rotational movement. The masses distribution is done by the following estimation (Naderi, H., 1982):

 Lcrc  mcrp  mcr   Lcr    (16) L m  crp m   crc cr   Lcr 

Lcrp: the distance of the center of gravity with the center of the small eye of the connecting rod Lcrc : the distance of the center of gravity with the center of the big eye of the connecting rod Lcr: the distance of the center of the small eye with the big eye of the connecting rod Mcrp: the concentrated mass in the small eye Mcrc: the concentrated mass in the big eye

Figure (2) indicates this mass distribution.

Fig. 2: The mass distribution in the piston eyes.

Usually, the distribution of aforementioned masses, are equal to the following values: mcrp  0.275mcr (17) mcrc  0.725mcr

The total concentrated mass in the small eye of the connecting rod which is characterized by (ma) is equal with:

ma  m p  mcrp (18)

Mp: the mass of the piston and piston pin Mcrp: the concentrated mass of the connecting rod in the small eye

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Fig. 3: The mass distribution to two concentrated masses ma and mR.

And the concentrated mass in the big eye of the connecting rod equals with:

mR  mc  mcrc (19)

mcrc: the concentrated mass of the connecting rod in the big eye mc: the mass of the crankshaft crank

Considering figure (4), mc which is the mass of the crankshaft crank is calculated as following:  m  m  2m  2m (20) c cp cp w R

mcp: pin journal of crankshaft which the connecting rod is locked on it. Mw: the mass of crankshaft blade (arm of the crank) R: radius of the crank  : The main journal radius of the crankshaft

Fig. 4: The cut scheme of the crankshaft.

2-2-3 Inertia Forces: In the previous chapter, we divided all the masses to two parts: the reciprocating and rotational masses. Now we calculate the inertia forces caused by the movement of these masses. The direction of inertia force of ma (in the small eye) is always along the cylinder axis and opposite the acceleration of piston direction and the inertia force direction of mg is along the crank radius. The value of the reciprocating inertia force using the equation 6 is described as following:

2 Fi  ma R cos   cos2  (21)

The value of the rotational inertia force is described by the equation for rotational acceleration as following:

2 FR  mR R  cte (22)

The resultant of the forces in A (figure 5) is:

F  F l  F g (23)

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Aust. J. Basic & Appl. Sci., 5(12): 3112-3121, 2011

Now we study the effect of resultant force (F) on the connecting rod. According to figure (6) and the trigonometric relations we have:

N  F tan  (24)

F S  (25) cos 

F cos   K  (26) cos 

F sin   T  (27) cos 

N force is exerted on the cylinder wall and the rod of connecting rod tolerates S force. S force is divided to two components in the big eye, which T component is responsible for the creation of the torque in the crankshaft. The resultant of K and T and FR forces are the force exerted on bearings.

Fig. 5: The foreign forces on the piston handle without displaying the reactions.

Fig. 6: The effect of N force on the big eye.

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Aust. J. Basic & Appl. Sci., 5(12): 3112-3121, 2011

Results: Figures 7,8 and 9 show the diagrams of situation, speed and acceleration of the piston (that have been drown with the help of the Mathematica software) which have been achieved by placing the MF-285 tractor data in relations 4,5 and 6.

0.3

0.28

0.26

0.24 m p 0.22 S

0.2

0.18

0.16

0 2 4 6 8 10 12 14 wt radian Fig. 7: Changes of piston situation at crankshaft angle regarding MF-285 tractor.

15

10

5

0 v m/s

-5

-10

-15 0 2 4 6 8 10 12 14 wt radian Fig. 8: Changes of piston speed at crankshaft angle.

3000

2000

1000 2

0

-1000 acceleration m/s acceleration -2000

-3000

-4000 0 2 4 6 8 10 12 14 wt radian Fig. 9: The changes in the piston acceleration at crankshaft angle regarding MF-285 tractor.

Also, the final relationship for gas pressure gained as following. Figure 10 shows the related diagram (the pressure changes regarding to crankshaft angle during a working cycle).

101.3 0      1.21 7.53x     2 (28)  Pg  2950 2    13 / 6  1.21 29.8x 13 / 6    3 101.3 3    4

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3000

2500

2000

1500

pressure KPa pressure 1000

500

0 0 2 4 6 8 10 12 14 crank angle degree Fig. 10: The diagram of pressure changes regarding to crankshaft angle for MF- 285 tractor.

Figure 11 shows the sum of inertia forces and gas pressure on the head of connecting rod during a working cycle. In figure 12, the sum of forces on the bearings is shown.

Fig. 11: The diagram of the sum of forces on the connecting rod regarding to crankshaft angle for MF-285 tractor.

Fig. 12: The sum of forces on the bearings.

Conclusion: The achieved diagrams in the results part show the place, speed and acceleration of piston, the changing of forces on the connecting rod, , and crank of the crankshaft regarding to crankshaft angle during a working cycle. As the mentioned diagrams show, the maximum amount speed of piston was 13/5 m/s, the maximum amount acceleration of piston was 3550 m/s2, the maximum amount of combustion pressure was 2950 kpa, the maximum amount of pressing force on the connecting rod was 19730 N, the maximum of pulling force on the connecting rod was 10288N, and the maximum of forces on the bearings was 3000N. Using the

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Aust. J. Basic & Appl. Sci., 5(12): 3112-3121, 2011 aforementioned results and diagrams, we can analyze the stress, fatigue, strain, modal, and harmonic of the mentioned components, and study the reasons for their malfunction, and offer the necessary suggestions for optimizing them. Therefore, analysis of stress, fatigue, strain, energy, modal and harmonic of aforementioned components with the help of the present results, can be suggested for future researches.

REFERENCES

Anonymous, 2008. "MF-285 Maintenance and Repayments catalogue," Iran Manufacturing Tractor Co,. Asadi, M., 2008. "Fatigue analyzing in MF-285 tractor connecting rod using finite element method," M.Sc. thesis, Department of Mechanic of agricultural Machinery, University of Mohaghegh Ardabili, Ardabil. Cveticanin, L., R. Maretic, 2000. Dynamic analysis of a cutting mechanism. Mech. Mach. Theory, 35(10): 1391-1411. Ha, J.L., R.F. Fung, K.Y. Chen, S.C. Hsien, 2006. Dynamic modeling and identification of a slider-crank mechanism. J. Sound Vib., 289(4): 1019-1044. Koser, K., 2004. A slider-crank mechanism based robot arm performance and dynamic analysis. Mech. Mach. Theory, 39(2): 169-182. Mahmoodi, A., H. Rezakhah, 2007. "Reviewing fails of MF-285 tractor," Third student conference on Mechanic of Agricultural Machinary Eng., Shiraz. Naderi, H., 1982. Design of Internal Combustion , Mir Publication, Tehran, pp: 437. Prvardhans, shenoy and A. Fatemi, 2005. Connecting Rod Optimization for Weight and Cost Reduction. Journal of Sound and Vibration, 243(3): 389-402. Shrinivas, S.B., C. Satish, 2002. Transmission angle in mechanisms (Triangle in mech) Mach. Theory, 37(2): 175-195.

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