DYNAMICS MODELING OF A POWER TRANSMISSION MECHANISM WITH LINKAGE AND INERTIAL MASS

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1 FACULTY OF MCHANICS AND TCHNOLOGY SCINTIFIC BULLTIN AUTOMOTIV series, ear XIX, no. B DYNAMICS MODLING OF A POWR TRANSMISSION MCHANISM WITH LINKAG AND INRTIAL MASS Ion ION-GUTA Universit of Pitesti, Romania, ion.ion@upit.ro Article histor: Received: ; Accepted: Abstract: This article describes construction of an model of inertial mechanism with two degrees of freedom. This mechanism is a mechanical application of the theor on the transmission of mechanical power b vibrations. The mechanical power is transmitted from engine to the output shaft through a sstem of oscillating levers, inertial masses end a unidirectional mechanism. This torque converter is analzed b AMSim. Dnamics modeling of an automotive application will demonstrate its high performances characteristics. In the modeling of this power transmission sstem, the stiffness of the shaft and various control logics are included. INTRODUCTION A mechanical linkage is an assembl of bodies connected to manage forces and movement. The movement of a bod, or link, is studied using geometr so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain. Linkages ma be constructed from open chains, closed chains, or a combination of open and closed chains. ach link in a chain is connected b a joint to one or more other links. Thus, a kinematic chain can be modeled as a graph in which the links are paths and the joints are vertices, which is called a linkage graph. Linkages are important components of machines and tools. xamples range from the four-bar linkage used to amplif force in a bolt cutter or to provide independent suspension in an automobile, to complex linkage sstems in robotic arms and walking machines. The internal combustion engine uses a slider-crank four-bar linkage formed from piston, connecting rod and crankshaft to transform power from expanding burning gases into rotar power. Relativel simple linkages are often used to perform complicated tasks. Mechanical linkages are usuall designed to transform a given input force and movement into a desired output force and movement. The ratio of the output force to the input force is known as the mechanical advantage of the linkage, while the ratio of the input speed to the output speed is known as the speed ratio. The speed ratio and mechanical advantage are defined so the ield the same number in an ideal linkage. Figure. Schematic representation of linkage mechanism 65

2 FACULTY OF MCHANICS AND TCHNOLOGY SCINTIFIC BULLTIN AUTOMOTIV series, ear XIX, no. B The mechanism proposed to be analzed in this article is presented in figure. It is composed of a skew-smmetric assembl of bars,, and connected through kinematic couples, A, B and C and a inertial mass located on the toolbar extension of bar. TH QUATIONS OF MOTION On the basis of the notations l 5, can be write relations x A l cos ; A l sin () x C l cos ; C l sin () xb xa l cos xc l cos () B A l sin C l sin () where,,, are the position angles of bars,, and relative to the axis ox. Based on relations and we obtain where Based on the above relations, can be write S S U C arctan (5) C U S S V C arctan (6) C V S l sin l sin (7) C l cos l cos (8) U l l C S l (9) l l C S V (0) l, (), () l5 cos xd, l5 sin D, x D xb () D B () The kinetic energ of this mechanical sstem is xd D J J md (5) where J, J are moments of inertia of the input and output shaft, and d d d d ; ; x D xd ; D D dt dt dt dt (6) The Lagrange equations for this mechanism can be write as form d dt With notations ; ; ;, it is obtained the following relations d dt T sign T (7) 66

3 FACULTY OF MCHANICS AND TCHNOLOGY SCINTIFIC BULLTIN AUTOMOTIV series, ear XIX, no. B with initial conditions SIMULATION SCHM f, g,,,,, (8) t 0; (9) 0 Simulation scheme of mechanical transmission is presented in figure. It is composed from input shaft, oscillating mechanism, unidirectional mechanism and output shaft. Simulation was made b two distinct wa: - b actuating with prime mover with constant speed ; - b actuating with prime mover with constant torque T. Figure. Simulation scheme of mechanical transmission Figure. Time variation of load (output torque T) Figure. Torques variation T and T depending on the output speed 67

4 FACULTY OF MCHANICS AND TCHNOLOGY SCINTIFIC BULLTIN AUTOMOTIV series, ear XIX, no. B Figure 5. Output power P and efficienc variation depending on the output speed The main characteristics of operation b actuating with prime mover with constant speed are presented in figures,5 and 8a. The main characteristics of operation b actuating with prime mover with constant torque are presented in figures 6,7 and 8b. Time variation of load is presented in figure. Simulations was made with the following initial data: 500 rev / min ; T 0 Nm ; l 0mm ; l 70mm ; l 00 mm ; l 00 mm ; l 00 mm m D 5 kg; 5 ; J kgm ; J 0k gm ; Figure 6. Output Torque T and input speed depending on the output speed Figure 7. Output power P and efficienc variation depending on the output speed T CONCLUSIONS a) Figure 8. Output speed variation to square variation of output torque T a) for prime mover with const. ; b) for prime mover with T const. From the analsis of the above charts it is noticed major differences between operation with the loading in ascending sequence and the operation in descending sequence of loads. These differences b) 68

5 FACULTY OF MCHANICS AND TCHNOLOGY SCINTIFIC BULLTIN AUTOMOTIV series, ear XIX, no. B increase with increase of moments of inertia J and J. The maximum power is transmitted to the median speed of the output shaft. RFRNCS [] Guerlet, B., Valéo: Modeling of Complex Sstems with Applications in Automotive Transmissions, uropean AMSim Users' Conference, Paris, Ma 6th 000. [] Lebrun, M., Richards, C., W., Imagine: How to Create Good Models Without Writing a Single Line of Code, Fifth Scandinavian International Conference on Fluid Power, SICFP'97, Linköping Sweden, Ma