Józef Drewniak

Graph-Based Models of Compound Planetary Gear Boxes

In the paper, graph-based models of planetary gears are presented. Especially, compound planetary gear boxes are analyzed. The rules of assignment of particular graphs are shortly described. Based upon these models, ratios for consecutive drives are calculated. Graph transformations are introduced aiming for presentation of every single drive separately. Kinematic equations are generated in algorithmic way based on the adequate subgraphs as well as their codes. Compatibility of results - obtained by means of different methods - was achieved. The presented method is simple and effective, moreover it can be used for other design tasks as e.g. optimization and further analyzes i.e. evaluation of effectiveness.

Model of Fatigue Damage Accumulation

In this paper, the analytical method of fatigue life estimation of gear teeth is proposed. The computational model of fatigue damage accumulation was built using the adequate NASGRO 2/3 formula, moreover Formans and Paris-Erdogans laws were utilized for comparison. The ranges of stress intensity factor were determined using the boundary element method.

Evaluation of Fatigue Life of Cylindrical Geared Wheels

The main aim of the work is determination of numerical and numerical-analytical methods of evaluation of fatigue strength and life of geared tooth considering tooth breakage phenomenon. The discussed tasks were performed using the following tools: dual boundary element method, BEASY package as well as fracture mechanics

Analysis of Automatic Automotive Gear Boxes by Means of Versatile Graph-Based Methods

Automotive gear boxes are special mechanisms which are created based upon some planetary gears and additionally equipped in control systems. The control system allows for an activation of particular drives. In the present paper, some graph based models of these boxes are considered i.e. contour, bond and mixed graphs. An exemplary automatic gear box is considered. Based upon the introduced models, ratios for some drives have been calculated. Advantages of the proposed method of modeling are: algorithmic approach and simplicity.

Kinetics of Fatigue Crack Propagation at the Tooth Root of a Cylindrical Gear Wheel

The present paper proposes an analytical method for determining the course (path) of crack propagation. A fatigue crack arises at the tooth root of a cylindrical geared wheel due to loading connected with gear work conditions. The cracking model was built using the adequate NASGRO2/3 formula; moreover, for comparison purposes, Forman and Paris-Erdogan’s laws were utilized. The length of an increase (propagation) in the crack was directly calculated by means of the boundary element method.

Modelling Multi-Way Planetary Gears by Means of Contour Graphs

The present paper presents multi-way planetary gears modelled by means of contour graphs. The goals of modelling could be versatile: ratio calculating via algorithmic generation of equations, the analysis of forces and acceleration or optimization and structure analysis. The article describes an exemplary gear. Several drives/gears are consecutively taken into account discussing functional schemes, assigned contour graphs and a generated system of equations and their solutions. The advantages of the method include an algorithmic approach and a general approach where particular drives are the cases of the generally created model. Moreover, the method allows further examination and synthesis tasks, e.g. checking the isomorphism of design solutions.

Synthesis of Planetary Gears by Means of Artificial Intelligence Approach ‒ Graph-Theoretical Modeling

Graph-based modeling of planetary gears was applied in the presented research work for their synthesis. The tailored Hsu and contour graphs were used. Graphs encode the structure (layout) of a planetary gear and upon them - the systems of equations can be generated. These systems enable determination of rotational velocities of planetary gear elements. The method is algorithmic and simple. It allows for an easy comparison of different design solutions and selection of the most appropriate one. The list of the possible modes of operation for an exemplary planetary gear is also provided in the paper.

Charts of Relative and Absolute Velocities of Chosen Parts of Plane Biplanetary Gear

The aim of the present paper consists in presentation of new method of kinematical analysis of biplanetary gear. In particular, the method lies in preparation of chats of relative and absolute tangent velocities of particular gear parts. The algorithm is based on less complicated approach of determination of distribution of relative tangent velocities of wheels and arms of the considered gear. The obtained value of kinematical ratio was additionally achieved via other known analytical method, for comparison.

Kinematics of Biplanetary Epicyclic Gears

In the present paper, the biplanetary gears are analysed. They have complex layouts and their functioning is not too easy to recognize based upon these general schemes. However, it has been proved that two methods i.e. Willis and Kutzbach could be useful for their detailed kinematical analysis, enclosing e.g. directions of rotation of particular geared wheels. The exemplary gears analysed e.g. kinematical ratios have been calculated. The analysis of these gears could be a good training for mechanism understanding by students and researchers.

Kinematical Analysis of Variants of Wind Turbine Drive by Means of Graphs

Variants of a wind turbine drive are discussed in the paper. The drive should be adjustable. The control tools should be reliable and simple. Several variants of drive system based upon a compound planetary gear accompanied by a friction gear are analysed and compared. Graph models had been used for analysis of the gear itself. The analysis of the whole system using graphs is proposed via modification of known approaches. The analysis of results shows their full compatibility.