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Contents >> Engineering Mathematics >> Hydro Mechanical Drives and Transmissions >> Dynamic Analysis >> Introduction

Dynamic analysis of mechanical transmissions - Introduction

Introduction

The dynamic analysis is the important design stage of mechanical and hydro mechanical drives and transmissions of various machines and mechanisms (cars, self-propelled chassis, tractors, rollers, tractors, loaders, excavators, scrapers, machine tools, etc.) and allows to simulate working processes and to obtain necessary data about dynamic properties of transmission and features of course of working processes long before creation of a pre-production model, to pay attention to presence of  bottlenecks in a drive, and before carrying out of tests to choose the optimum design decision on the basis of results of mathematical simulation and alternative analysis.

Mathematical simulation of various modern technical systems of the certain class (mechanical,  hydraulic, electric, etc.) is connected with construction of the models providing the formalized description of any such system of arbitrary structure.

For construction of formal dynamic model of a hydro mechanical drive as a whole the method based on representation of system in the form of final element-node structure is used. In a basis of such approach the idea of a method of finite elements when the complex system on a configuration can be divided conditionally into separate functional elements which mathematical description is known and for which it is possible to define unequivocally conditions of communications of these elements with each other (an input – an output) within the limits of considered system. Then for description of the system as a whole it is enough to specify a name (the identifier of type) of element, to number its nodes in input and in output, to give necessary physical, geometrical and design data (constants) and to write down the equations, transforming variables in input of element to variables in output.

As such base elements in hydro mechanical drives can be: a diesel engine with a centrifugal regulator, a gear (a box of change of transfers), frictional and hydro dynamical clutches, a hydraulic torque converter, an elastic shaft, a flywheel (the concentrated rotating mass), a differential and a wheel carrier.

Then the structure of any arbitrary transfer can be described by means of identification of elements, numbering of nodes (points of connection of elements in the scheme by a principle an input – an output) and forming on a basis of it matrixes of communications describing the scheme structure (topology).

Feature of simulation of such transfers is presence of two basic modes of movement:

1) the unblocked rotation of masses when a slipping between leading and driven parts of frictional clutch, hydraulic torque converter (called in the further for brevity «clutches») takes place;

2) the blocked rotation when leading and driven parts of clutch rotate with identical angular speed.

For each of these modes of movement the moment realized by clutch, is defined differently, and in the time moment of blocking a jump of acceleration takes place and clutch blocking conditions depend on the scheme structure, distribution of external moments and reduced moments of inertia, and also a mode of rotation of others clutches rigid connected with given clutch. All this in a whole represents the certain difficulties for analysis of similar transfers as constant checking of blocking conditions during their simulation is required with respective alteration of the realized by clutches.

Thus, for simulation of dynamic processes in mechanical and hydro mechanical transfers of arbitrary structure the following instruments are necessary:

 – an algorithm of the structural description of the drive arbitrary schemes;

 – a library of base elements and their mathematical models;

 – an ordering of input data, and a way of their forming and preparation;

 – an algorithm of automatic forming of the system of equations describing mechanical or hydro mechanical drive of arbitrary structure as a whole;

 – a method of solution of the generated system of equations;

 – a program realization of dynamic calculation for arbitrary schemes;

 – a way of representation and analysis of received results.

The program analyzes the input information and depending on set of elements and structures of investigated transfer chooses from library of base elements and their mathematical models the necessary equations, forming the general mathematical model of system and solving it at the given external influences.

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Last updated: April 30, 2015.