Dinel Popa

Synthesis and kinematic and dynamic analysis of a variable valve lift mechanism with general contact curve

In this paper, a new type of continuously variable valve lift (VVL) system is presented. The mechanism comprises a standard roller finger follower, the camshaft, and an intermediate rocker arm used between them. When the adjustment shaft rotates, the intermediate rocker arm is repositioned with respect to the cam and the roller of the rocker finger. This means that, when the rotation angle of the adjustment shaft is controlled, the valve lift height is also controlled. The intermediate rocker arm is equipped with a special developed contact surface, which is one of the novelties of this paper. The profile of the contact surface is analytically determined using the theory of the envelope curves. Using a certain cam profile, the kinematic analysis of the mechanism proceeds, resulting in the family of the valve lift laws. This paper also establishes the general conditions to design a variable valve timing (VVT) mechanism with continuous VVL and mechanical actuation. Numerical simulation shows that the mechanism continuously varies valve lift height and timing phases, while the valve’s opening time remains constant. The last parts of the paper are dedicated to different aspects concerning the elastohydrodynamic lubrication and valve train dynamics. The study is performed by comparing the optimized cam and a standard harmonic one which achieves the same maximum displacement of the valve. The optimized cam ensures better safety in functioning, a smaller preload, leading to a greater oil film thickness, and not causing excessive deformations in the engine. The calculation model is a general one, and it may be applied to other mechanisms with similar configuration.

Stability of the equilibrium positions of an engine with nonlinear quadratic springs

Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.

The Vibrations of the Engine with Neo-Hookean Suspension

Our paper realizes a study of the vibrations of an engine excited by a harmonic force and sustained by four identical neo-Hookean springs of negligible masses. The considered model is one with three degrees of freedom (one translation and two rotations) and we obtain for it the equations of motion. Using these equations, we determine for the unexcited system the equilibrium positions and their stability. We also study the small oscillations about the stable equilibrium positions and we find the fundamental eigenpulsations of the system. For the case of the excited system we perform a numerical study considering the situation when the pulsation of the excitation is far away from the eigenpulsations and the situation when the pulsation of the excitation is closed to one eigenpulsation, highlighting the beat phenomenon.

Aspects in the Synthesis of a Variable Compression Ratio Mechanism

The mechanism considered in this paper is a VCR one consisting in a crank, a shaft, an intermediate triangular element and a control lever and it was described in previous papers of the authors. The authors start from a classical crank-shaft mechanism for which the extreme positions are known. The first stage of the synthesis consists in determination of the constraint function which has to be fulfilled by the new mechanism so that the extreme position remain unchanged. The new step consists in imposing new conditions for the mechanism so that some new positions have to be obtained. The main hypothesis is that the positions of different characteristic points of the mechanism may be written as continuous functions of the certain input data. Due to aspect, the synthesis of the mechanism implies continuous variations of the output data and, consequently, there exists at least one solution for the synthesis process. In each case the authors determine the extreme positions of the piston. These extreme positions are also continuous functions of the input data. Two main approaches are discussed in the paper. One approach consists in the exact determination of the solution using a numerical procedure. The second one is an approximate one and consists in the determination of an approximate solution of the synthesis and verifying the deviation of this solution. For the new mechanism obtained by synthesis the authors determined the reduced velocities and accelerations of different characteristic elements. Some aspects of the wear are discussed with the aid of the reduced relative velocities.

Nonlinear Oscillations of a Mass with Cubic Stiffness, Harmonic Excitation and Dry Friction

In this paper we study the motion of a mass acted by a harmonic impulse through the end of a nonlinear cubic spring. The mass moves on a horizontal plan and between the mass and the plan there exists a dry friction of known constant value. The motion is described by nonlinear equation with discontinuities given by signature and Heaviside step functions. We also obtained the stop conditions, when the mass does not move at all. Finally the study is completed by numerical simulation.

Constructive Optimization of a Mechanism of Variable Valve Control

The mechanisms of variable valve control are frequently used on thermal engines which equip usual automobiles. In our paper we present such a solution consisting in a cam in rotational motion, a triad and a follower in plane-parallel motion. For this solution we perform the synthesis of cam and the kinematic analysis of the mechanism. The used methods are classical analytical ones of analysis and synthesis of cam, as well as CAD methods. The synthesis of cam by a CAD method assumes: the positioning of the raw material that materializes the cam, construction with solids of the follower as well as its positioning, extraction of the follower from the raw material, rotation by one degree of the obtained solid and the repeating of the procedure for the new angle. These operations are realized with an AutoLisp function which is not influenced by the complexity of the mechanism. The principle of the method of positional analysis by a CAD method consists in the modeling of the cam and follower with solids, variation of the rotational angle of the cam with the aid of an AutoLisp function until the follower is in contact with the cam and, finally, determination of the displacement of the valve of mechanism. In the end of the paper we present the constructive optimization of the cam mechanism by heuristic methods. The used algorithm has four steps, resulting finally the shape of the follower and the optimized cam.

Numerical Simulation of the Mechanical Models Used for the Coupling of the Power Sources

Mechanical systems used for the coupling of the thermal and electric power sources are a solution used by the constructors in the mechanical structure of the hybrid auto-vehicles. The mechanical systems used in this paper are planetary mechanisms with two degrees of mobility. On a virtual automobile one uses more solutions for the coupling of the power sources for which one performs numerical simulations.

Numerical Results Obtained on Models of Dynamical Systems Used in the Study of Active Suspensions

The semi-active and active suspensions are more and more often used in the construction of medium price automotive. The models used by the specialists in the study of the dynamical response of such suspensions are diverse and start from simple models arriving to complex ones. In this paper we perform an analysis of them and of the numerical results obtained by simulation on many models of semi-active and active suspensions. The results are presented as diagrams obtained by using some performance criteria.

Elements of Cam’s Synthesis for a Distribution Mechanism for the Miller-Atkinson Cycle

In this paper we present the synthesis of the cam for a distribution mechanism used for Miller-Atkinson cycle and described in previous works. The input data contain the angles at which the valve opens and closes, respectively, the dimensions of the main parts, the maximum displacement of the valve. and the law of motion of the valve. The authors consider that the law of motion of the valve is described by numerical values, even if in the simulation process they use analytical formulae for this displacement. The head of the valve is considered to be circular. A particular case of flat head of the valve is also described. The relative displacement of the lever and the valve is discussed in two hypotheses: symmetric position and asymmetric position of the contact point with respect to the axis of the valve. The contact between the head of the valve is assured by a cylindrical roller. The contact between the cam and the lever is considered in two main cases: roller tappet and flat tappet. In all cases the cam is obtained by numerical synthesis using a convenient angular degree. A great attention is paid to the convexity of the cam. The resulted cam is transformed in a convex one using the Jarvis March. The authors also perform a comparison between the theoretical profile of the cam and the profile of the convex cam, and between the imposed law of motion of the valve and the real law of motion of the valve using the convex cam. The reduced velocity and acceleration are obtained in all cases. Some aspects of the wear are discussed using the relative linear and angular velocities. The inertia of the mechanism is discussed with the aid of linear and angular accelerations of the elements. The most important resulted tables and diagrams are also presented. The paper closes with a paragraph of conclusions.

A comparative study of planetary mechanisms usable for power sources coupling

In the first part of the paper, a comparative study of the planetary mechanisms solutions which can be used in the coupling of power sources is made, this coming in addition to the previous works of the authors. It is analyzed the functioning mode of two planetary mechanisms used in different configurations and optimal variants are set.