Alberto Luiz Serpa

Investigation of tooth contact deviations from the plane of action and their effects on gear transmission error

Abstract In this paper tooth contact deviations from the plane of action and their effects on gear transmission error are investigated. Tooth contact deviations come from intentional modification of involute tooth surfaces such as tip and root profile relief; manufacturing errors such as adjacent pitch error, profile errors, misalignment and lead errors; and tooth elastic deflections under load, for example, bending and local contact deflections. Those deviations are usually neglected on gear tooth contact models. A procedure to calculate the static transmission error of spur and helical gears under loading is proposed. In the proposed procedure, contact analysis is carried out on the whole tooth surface, eliminating the usual assumption that tooth contact occurs only on the plane of action. Lead and profile modifications, manufacturing errors and tooth elastic deflections are considered in the calculation procedure. The method of influence coefficients is employed to calculate the tooth elastic deflections. Load distribution on gear meshing is determined using an iterative-incremental method. Results of some numerical examples of spur and helical gears are analysed and discussed. The results indicate that the tooth contact deviations from the plane of action can lead to imprecision on the gear transmission error calculation if they are not take into account. Therefore, the proposed procedure provides a more accurate calculation methodology of gear transmission error, since a global contact analysis is done.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Reduced order ℋ∞ controller design for vibration control using genetic algorithms

The design of vibration controllers for flexible structures requires special attention due to the size of structural models, generally with a high number of degrees of freedom. The implementation of full order controllers for structures with high numbers of degrees of freedom often requires a high computational processing effort and advanced hardware. To avoid this, it is desirable to use reduced order controllers. The design of reduced order H ∞ controllers characterizes a nonconvex optimization problem. In this context, this work presents a direct minimization method to design reduced order H ∞ controllers in the controllable canonical form. An optimization problem is formulated to minimize the H ∞ norm with an additional constraint to consider stability of the closed-loop system. The solution of the optimization problem is obtained using genetic algorithms, exploiting the advantage of this point of view in the solution of nonconvex problems. This formulation is verified in the active vibration control of a cantilever beam. A comparison of the proposed formulation with the formulation that uses linear matrix inequalities and the Augmented Lagrangian method is presented in this work and some numerical aspects of the problem are discussed.

Influence of the main contact parameters in finite element analysis of elastic bodies in contact.

One of the key issues in solving contact problems is the correct choice of the contact parameters. The contact stiffness, the penetration limit and the contact algorithm are some of the parameters that have to be adjusted. There are no methodologies available in the literature for choosing the contact parameters, relying only on the user experience for this important task. In this work we investigate how the contact parameters behave in a commercial finite element analysis software. We will show that while the contact stiffness has great influence on the finite element analysis, other parameters will not affect it significantly. Some contact examples are shown to illustrate the performance of the contact parameters during the solution of a contact problem.

Discrete optimization for actuator and sensor positioning for vibration control using genetic algorithms

Research about actuator and sensor positioning is important to obtain smart structures that can achieve better performance, and studies concerning controller design techniques are also important. In some studies on smart structures, the positioning of sensors and actuators are defined by some physical criteria and, thereafter, the controller is designed to satisfy some requirements of the controlled system. However, the optimal number and placement of sensors and actuators can also be obtained through the solution of an optimization problem, taking into account, for example, the possible positions to allocate the active elements and the available number of these. This paper presents a discrete heuristic optimization technique in order to determine the discrete positions of the active elements in active control systems. Furthermore, a technique that involves the determination of the number of active elements and the positioning is shown. These techniques have been implemented based on the genetic algorithms. Depending on the desired number of the sensors and actuators, and the number of candidate positions, it is impractical to use a combinatorial algorithm, as this is very expensive in terms of computational time due to the number of possible combinations. Thus, the techniques developed here have the aim to obtain good solutions analyzing fewer combinations than the combinatorial method and in reduced computational time. In this paper, the controllers are designed based on the H ∞ control theory. The objective function used to solve the positioning problem of active elements is the H ∞ norm of the closed-loop system.

Vehicle Rollover Avoidance by Application of Gain-Scheduled LQR Controllers Using State Observers

Abstract Many researches have been conducted in the area of control applied to vehicle dynamics, aiming at reducing the possibility of the occurrence of the type of accident known as rollover. In this research, based on a common nonlinear model and its linearisation, a method for properly selecting matrices for solving the Riccati equation considering different speeds was proposed. The method showed in which ways speed really influences the choice of controller gains. By developing the dynamic equations for the yaw- and roll-coupled motions and modelling of controllers and state observers, it is possible to compare the efficacy of this control strategy using both linear and nonlinear simulations using Matlab. Significant results were obtained regarding the reduction of the rollover coefficient for a double-lane change manoeuvre at different speeds, thus indicating advantages of using this controller in practical cases.