Nicolae-Doru Stănescu

Numerical Analysis with Applications in Mechanics and Engineering: Teodorescu/Numerical Analysis with Applications in Mechanics and Engineering

A much-needed guide on how to use numerical methods to solve practical engineering problemsBridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results.Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes:How to deal with errors in numerical analysisApproaches for solving problems in linear and nonlinear systemsMethods of interpolation and approximation of functionsFormulas and calculations for numerical differentiation and integrationIntegration of ordinary and partial differential equationsOptimization methods and solutions for programming problemsNumerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.

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.

Analytical synthesis and computer-aided kinematic analysis of a continuously variable valve lift mechanism

This paper presents an original continuously variable intake valve lift mechanism designed for the automotive spark ignition engines. The paper first presents the analytical kinematic synthesis of the variable intake valve lift mechanism, which consists in finding out the required intake cam profile starting from an imposed intake valve lift law. Then, by using the obtained cam profile, a computer-aided kinematic analysis of the variable intake valve lift mechanism is performed using commercial CAD software. The accuracy of the motion conversion performed with CAD software is validated by checking the degree of correlation between the resulted intake valve lift law and the imposed law used when performing the analytical synthesis. The goals of the kinematic analysis are first to find the partial laws of the intake valve lift, corresponding to the engine part loads and second, to find the transfer functions of the elements used to command the mechanism, i.e. the dependency between these elements and the intake valve lift law. The designed variable intake valve lift mechanism is successfully operated on an engine prototype and proved its energetic improvement potential.

A new approach in the study of frictionless collisions using inertances

This paper presents a complete study on the collision without friction of two rigid bodies with and without bilateral constraints. Our goal is to obtain the same formulae for the impulse, the energy of the lost velocities, and the loss of kinetic energy as in the case of the collision of two particles. The study is performed with the aid of the notion of inertance. The dependence on the constraints is given by the inertances. The calculations are realized using the results from the theory of screws (plückerian coordinates). The obtained formulae are general, written in matrix form, and they may be easily used in any practical problem. We give the general algorithms for the collision of two rigid bodies with and without bilateral constraints. The equality of the coefficients of restitution in the Newton, Poisson, and energetic models is also proved. The numerical examples highlight the theory.

Determination of the Tool’s Trajectory for the Manufacturing of the Profile of a Cam

This paper discusses the determination of the position of the cutting tool in the manufacturing process of a cam. The input data are the coordinates of certain points of cam’s profile and the radius of the cutting tool. Using these coordinates, the authors calculate approximates for the coordinates of the center of the osculating circle of the profile of cam at certain positions. The position of the manufacturing tool is determined considering that the tool is tangent at the osculating circle at the contact point. Two variants are selected for the cam: one variant considers the cam as it results in the synthesis process; the second variant considers the cam obtained by applying the Jarvis March in order to be a convex one. For both variants the trajectory of the cutting tool is determined and the obtained numerical results are compared.

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.

Kinematic Analysis of a Variable Compression Ratio Mechanism

In our previous papers [13, 14] we presented a variable compression mechanism. In this paper we study the kinematic analysis of this mechanism. Two cases are considered: there is no motion for the control lever, and the second one is characterized by the existence of a known motion for one edge of the control lever. The kinematic analysis is performed firstly in a classical way by determining the positions of some characteristic geometric parameters and by derivation of these parameters with respect to time. The second way is by use of the multibody approach to determine the matrix of constraints for the mechanism. In the last situation we can not determine all the linear and angular velocities for the mechanism. Usually, a number of new equations (this number is equal to the degree of mobility of the mechanism) must be added in order to determine all kinematic parameters. A numerical example concludes this study.

A new approach in the study of the collisions with friction using inertances

This paper presents a complete study on the collision with friction of one or two rigid bodies without constraints. The differential formula between the velocities and impulse uses the notion of inertance resulting from the theory of screws (Plückerian coordinates). One thus may calculate the kinematic and dynamic parameters, the velocities and the kinetic energies of the two rigid solids after the collision, and the variation of the kinetic energy. The calculation is detailed for the Newton, Poisson, and energetic variants of the coefficient of restitution. The variation of the kinematic and dynamic parameters in relation to the coefficient of restitution and coefficient of friction for all the three variants are presented and discussed. A numerical example highlights the theory.