OPTIMAL DESIGN OF CYLINDRICAL GEARS WITH CONVEX-CONCAVE CONTACT: OBJECTIVE FUNCTION AND VARIABLES PLANNING

Reducing the mass and dimensions of gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with a convex-concave contact of the teeth. Therefore, the study is devoted to the development of methods for the optimal design of cylindrical gears with convex-concave contact of the working surfaces. Optimality criteria: minimum contact stresses and (or) minimum relative sliding velocities, taking into account design, geometrical and technological constraints. C-C gearing was chosen as the object of research. It was proposed by the Slovak scientists M. Boshanski and M. Veresh. An objective function is constructed for the case of minimizing contact stresses. The optimality criterion is formulated as follows: contact stresses σH in the mesh must take the minimum possible value when all constraints are met. An objective function is also constructed for the case of minimizing the relative sliding velocities of profiles. The optimality criterion is formulated as follows: the relative sliding s velocities of profiles λ at the extreme points of mesh must take the minimum possible value when all the constraints are met. Variables planning are defined. These are pressure angle at the pole αС, the curvature radius at the upper part of contact path rkh, and the curvature radius at the lower part of contact path rkd. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned to form a system of constraints on variables planning, to develop methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results. Keywords: gear, convex-concave contact, optimal design, objective function, variables planning

An application of Newton-like algorithm for H∞ proportional–integral–derivative controller synthesis of seesaw-cart system

This paper is concerned with the synthesis of proportional–integral–derivative (PID) controller according to the [Formula: see text] optimality criterion for seesaw-cart system. The equations of dynamics are obtained through modelling a seesaw-cart system actuated by direct-current motor via rack and pinion mechanism using the Euler–Lagrange approach. The obtained model is linearised and synthesis of the PID controller for linear model is performed. An algorithm based on the sub-gradient method, the Newton method, the self-adapting backpropagation algorithm and the Adams method is proposed to calculate the PID controller gains. The proposed control strategy is tested and compared with standard linear matrix inequality (LMI)-based method on computer simulations and experimentally on a laboratory model.

A Pathfinding Problem for Fork-Join Directed Acyclic Graphs with Unknown Edge Length

In a previous paper by the author, a pathfinding problem for directed trees is studied under the following situation: each edge has a nonnegative integer length, but the length is unknown in advance and should be found by a procedure whose computational cost becomes exponentially larger as the length increases. In this paper, the same problem is studied for a more general class of graphs called fork-join directed acyclic graphs. The problem for the new class of graphs contains the previous one. In addition, the optimality criterion used in this paper is stronger than that in the previous paper and is more appropriate for real applications.

Facing sampling techniques as an optimal design problem

Summary The aim of this paper is to investigate and discuss the common points shared, in their line of development, by both Sampling Theory and Design of Experiments. In fact, Sampling Theory adopts the main optimality criterion of the Optimal Design of Experiments, the minimization of variance, i.e. D-optimality. There is also an approach based on c-optimality, as far as ratio estimates are concerned, in Design of Experiments, and the A-optimality involved in a proposed Sampling technique. It is pointed out that the L2 norm is mainly applied as a distance measure.

Optimization of automatic control of the speed of rotation of a marine diesel engine

Annotation – The well-established method of tuning the speed governors (SG) of diesel engines during their operation under conditions of step disturbances, which are characteristic of diesel-generators, cannot be used for the main marine engines, the dynamic modes of which are associated, first of all, with heavy seas, because disturbances cannot change stepwise both along the channel for setting the rotational speed and along the load channel. In this regard, the practical need for the development of a method for tuning the SG of the main engines, which takes into account the peculiarities of their operation in heavy seas, has been determined. The study simulates the automatic speed control system (ASC) of the main marine engine HYUNDAI – MAN B&W 6G70ME-C9.2 of the large crude carrier "GOLDWAY" with the AutoChief 600 electronic SG. The minimum of instability of the controlled parameter was used as an optimality criterion, i.e. the amplitude of the oscillations of the rotational speed of the diesel engine shaft, with the most probable values of the amplitude and period of oscillations (rolling) of the disturbing effect. The study has established that changing the tuning parameters of the governor may lead to local extrema of the optimality criterion when using an electronic governor in the ACS in the factor space of disturbances on a diesel engine, which are typical for heavy seas. It means that the task, requiring finding local extrema using specialized methods, can be set when using an electronic governor in the ACS. However, a significant decrease in the instability of the rotational speed was achieved by carrying out a simple enumeration of the tuning parameters of the SG. It was also found that with a "heavy" propeller, the rotational speed stability can be increased by decreasing the proportional gain, as well as increasing the integrator time.

DC MOTOR FUZZY MODEL BASED OPTIMAL CONTROLLER

This paper presents a method for the design of optimal fuzzy controller of a DC motor using a fuzzy model based approach with emphasis on minimal knowledge on the controlled system. In the first part of the paper we describe the method of the black-box fuzzy model design based only on the system´s measured input/output data without the necessity of preliminary knowledge of its internal structure and parameters. This fuzzy model is in the second part used in the design of optimal fuzzy controller based on finding the sequence of input signal values that will transfer the controlled system into the desired state in accordance with the selected optimality criterion. The realized simulation and experimental measurements performed on HIL platform have confirmed the correctness and effectiveness of the proposed design method and also its applicability to others dynamic systems with as little previous knowledge as possible.

Research of Kinematic Stepping Mechanism

In this paper, a kinematic analysis of Theo Jansen’s stepping mechanism has been carried out and an algorithm for finding the output link trajectory from the given dimensions of the stepping mechanism elements, implemented by Mathcad program, has been developed. It is possible to output characterising parameters of all intermediate links with any number of intermediate links of a step cycle of the mechanism. The dimensions of the mechanism elements have been selected so that they provide the optimal smooth trajectory of the stepping point, minimising the mechanism oscillations in the vertical plane. A comparison of the trajectories of the foot in this study with the classical trajectory of Theo Jansen and the trajectory from article [7] has been provided. A minimum swing of the oscillation of the centre of mechanism masses in the vertical plane has been selected as an optimality criterion, combined with the maximum smoothness of the trajectory, provided that maximization of the step height is not required.

ON THE OPTIMAL LAW OF THE FOOT TRANSFER OF THE WALKING PROPULSION DEVICES WHEN OVERCOMING AN OBSTACLE

The problem of walking machine leg transfer is being solved. Optimal laws of transfer are determined with regards to geometrical features of ground underwater. Complex optimality criterion is introduced as sum of indexes of quality of the movement multiplied each by weight coefficients.

Three-Bar structure optimality criterion using the linear resizing rule

The static analysis of the indeterminate three-bar structure is developed using the Castigliano's first theorem, taking the lengths and inclination angles as variables. Some reductions are applied in the resulting set of equations to approximate them to the references models. From now on, the minimum mass optimization model with restrictions is established. Then, the Optimality Criterion linear resizing optimization rule algorithm for the unbounded and bounded design variables is applied in two numerical cases. The analytical and Matlab Optimization Toolbox results are also obtained and they demonstrate the Optimality Criterion linear resizing rule effectiveness in structural optimization with a minimum mass objective and size restrictions.