“Dynamics of machinery” unifies the classic fields “Theory of mechanisms and machines” and “Theory of vibration”

1 Introduction

In every university the professors have to decide which elements and to what extent the subject of Machine dynamics shall be taught. There exist several books about Dynamics of machinery and Machine dynamics from the standpoint of theoretical mechanics, dynamics of mechanism, vibration isolation, rotor dynamics or theory of vibrations, in which above all torsional and bending vibrations are being considered. Typically they deal with four-link mechanism, flywheels, cam mechanisms, gear mechanisms, balancing, drive shafts, vehicles, reciprocating engines or robots. These books are mostly for courses consisting of 60 hours of lectures, i.e. 4 hours/week.

In the education of the future engineer, the tendencies in the technical development of machines have to be considered. For what problems in the field of machine dynamics does the future engineer have to be prepared?
- The working speeds of many machines are going to be increased to raise productivity. This will also increase the dynamical load.
- A minimal material consumption is aspired. Due to light weight construction, the risk of becoming disturbing vibrations is increasing. The vibrational load is increasing.
- Vibrations strain working people. Protection of people against sound and vibrations through design actions is going to be increasingly important.
- The simulation of interactions between electrical and mechanical quantities for the control of engines, active mass damper systems and mechatronic systems are getting more significant.
- Through increasingly better numerical models in the numerical simulation, it's possible to reduce the number of prototypes and thereby reducing development time and cost.
- Operational safety and reliability is getting increasingly critical to avoid interferences and failure, which often depend on the dynamical behaviour of the machine.

These tendencies in the development of machines are independent of specific machine types and are treated in the book “Dynamics of Machinery”. The content of this subject matter emerges from the book “Maschinendynamik” (9th edition), which appeared in 2009 in German ^[9] and is available in several other languages (Vietnamese, English, Chinese) as well ^{[10], [11] and [12]}. Also exists an unauthorized (illegal) translation in Arab language of the 3rd edition.
This textbook discusses disciplines that in any countries in classical form are presented separately in lectures titled “Theory of Mechanisms and Machines” (TMM) (e.g. textbooks as [1], [2], [3], [4]) and “Vibrations” or “Theory of Vibrations” (e.g. textbooks as [5], [6], [7], [8]).

The basic idea was to combine these disciplines into “Machine Dynamics”. We worked out this concept relying on our experience gained in our collaborations with engineers in Germany.

2 Content of the book

This textbook is based on the four-semester lecture series on “Engineering Mechanics” and confronts students directly with dynamic problems of their field. In the book Machine Dynamics it is presumed that the reader already has a basic knowledge of kinetics and dynamics from basic studies in the field of technical mechanics, i.e. Newton's laws, free-body diagrams, 2nd order Lagrange equations and the basic principles in the theory of vibrations, free and forced damped vibration.

Machine dynamics is viewed both as a typical field for the mathematical modeling of technological processes and as a branch of mechanical engineering that addresses dynamic problems of power machines (reciprocating engines and turbo machines), processing machines (printing machines, textile machines, packaging machines), hoists and conveyors, agricultural machines and vehicles, as well as industrial plants. It is widely extended to high-speed processing machinery. “Dynamics of machinery” treats dynamic problems of these different machines and vehicles under uniform aspects.

The book comprises relatively independent chapters that discuss typical issues of machine dynamics from the point of view of mechanical engineers.

Chapter 1 “Model Generation and Parameter Identification” contents characteristic values of springs, dampers and excitations. Examples: Gear mechanism, Crane, Machine elements, Coil springs and rubber springs, Empirical damping values

Chapter 2 “Dynamics of machine consisting of rigid bodies” includes kinematics of mechanisms and gears, kinetics of one rigid body, kinetics of planar mechanisms, balancing of mechanisms and rotors. Examples: Kinematics of the gimbal-mounted gyroscope, Kinetics of edge mills, Flywheel, Planetary gear mechanism, Press drive, Counterbalancing of rigid rotors, Mass balancing of planar mechanisms, Crankshaft of a four-cylinder machine

Chapter 3 “Foundation of machines and isolation of vibrations” treats periodical excitation, impacting loads, optimal vibration isolation. Examples: Vibrations of foundation, Vibration isolation, Optimal vibration absorber, Hammer

Chapter 4 “Torsional and longitudinal vibrations” explained free and forced vibrations of discrete oscillators with chain- structure, absorbers and dampers in driving systems, time-depending coefficients. Examples: Drive shaft, Six-cylinder machine, Printing machine, Gear mechanism, Application of software, Clutch, Parameter-excited vibration,

Chapter 5 “Bending vibrations” discusses models of discrete oscillators, gyroscopic effect, beams with continuously distributed mass. Examples: Timoshenko-beam, Jeffcott-rotor, Gyroscopic effect, Startup, Centrifuge, Textile mandril,

Chapter 6 gives a general overview of linear oscillators and includes methods discussed in chapters 3, 4 and 5. We were fully aware and accepted some overlap and repetitions, making many cross-references among sections. Application of matrix calculus. Modal analysis. Examples: Model generation and model validation, Vibration of frames, Impulse excitation and response, Belt-drive,

Chapter 7 discusses nonlinear and self-excited oscillators, for which calculations are becoming more and more relevant to practical application. Examples: Influence of nonlinear springs, Subharmonic vibrations, Oscillating conveyor, Self-synchronization of rotors, Chatter of a machine tool, Flutter of a plate.

Chapter 8 still does not contain any equations, but the rules compiled there are important for engineering practice.

Examples: Selection of the mechanical structure, Influence of changes of the parameters on the natural frequencies, Constructional measures for the avoidance of resonances, Rules for the reduction of oscillations. Rules for the reduction of oscillations

Chapter 9 “On interrelations with system dynamics and mechatronics” to enhance the understanding of these adjacent disciplines. This chapter prepares the readers for a more general approach to solving problems of machine dynamics by including sensors and actuators. Example: Application of a Controller

The 60 exercises and solutions are meant to help in grasping and consolidating the subjects taught. A new feature of this edition is the enclosed CD-ROM, which does not only contain the student version of the SimulationX® software, but also program parts that were used for solving the examples given in the book so that the readers can work with them themselves.

3 Highlights of the book

The book ^{([9], [10], [11],[12])} includes a comprehensive material, in which it's possible to pick out the interesting themes. If one wants to use the whole book, it would take about 120 to 150 hours of lectures, which is more than one single term.

The book is not only written for students, but also for practicing engineers. The examples from many fields of mechanical engineering and the specification of parameter values, as well as references to guidelines and regulations, underline this. We have considered the way in which engineers think by discussing estimation methods, rough calculations and minimal models, and by explaining many instructive dynamic effects (gyroscopic effect, resonance, absorption, self-synchronization, ) that are relevant for the design of machines that operate under a high dynamic load.

The fast development of hardware and software entailed that nowadays there is software available for almost every problem in machine dynamics. While computers always provide some numbers and diagrams, the engineer is still responsible for the results. It remains the engineer’s job to provide the respective calculation models, to assess the applicability of a software product, to check the result of a simulation, and to have some idea of the result to be expected before the calculation starts.

Since the current development shows a trend towards refined modelling, we pointed out three aspects: the training of physical understanding, the utilization of modal analysis including sensitivity analysis, and the application of computer-aided methods. We stress the fact that the goal of calculations is not only to arrive at a numerical result, but to achieve a better understanding of the dynamic behaviour of real objects and to be able to take design measures that are based on physical theory.

Both mathematical-physical basics and questions that arise in the design-engineering processes are treated. The book communicates knowledge and skills, independent of a specific art of machinery, which can be used on any machine (even not yet existing machines). Besides the physical knowledge arising from the presented theory, things important from the engineering sciences are pointed out: attention to engineering standards and guidelines, methods of modelling, methods of measurement and test engineering, parameter identification and determination, balancing, vibration isolation, software application and result interpretation.

By selecting material for the book it was taken into account what kind of problems the engineers have to solve in the field of dynamics. Only a small part of the alumni will be concerned with solving dynamical problems in their working life. From experience we know that in a design department for general machine construction with 20 to 40 engineers, only one single person is specialized in dynamics. The non-specialists shall recognize the dynamic problems in the machines and give the problem solving over to the specialists. Every engineer working in the design-construction has to have an overview of the field of dynamics. The specialized engineers and mathematics working in large numerical simulation departments (e.g. in the aerospace industry, shipbuilding, vehicle construction, train manufacturing, turbine manufacturing and energy engineering) will learn important basics in the Machine Dynamics. In their continuing education they can improve on these basics with topics as structural dynamics, non-linear vibrations, modal analysis, measurement engineering, numerical methods and specific software.

What are the book’s substantial benefits for the target group?

-The combination of practical application and theory of machines and vibration theory.

-The illustration by successfully solved industrial problems and experiences.

-The overview about different typical tasks in dynamics of machines.

-The low-degree of freedom modelling, ad-hoc-modelling, mathematical description, analytical solutions and numerical solutions with software (CD included).

-The physical interpretation, to view things “physically”.

-The suggestion, evaluation and discussion of possibilities, to improve vibrational behaviour of machines.

-The constructors point of view.

-The application of analytical methods and modern software to solve exercises.

4 Conclusions

It will be shown how to master the (historical considered) ever increasing content: emphasis on fundamental knowledge, treatment of common appearing practical problems, some special mathematical methods, usage of software (e.g. eigenvalues, integration of differential equations, FFT, …), checking of plausibility, result interpretation.

The lecture motivates and explains the highlights of this book in detail. It is argued that the book presents a concept that is important for the future education of engineers.

References

[1] Artobolewski, I.I.: Mechanisms in Modern Engineering

Design (transl. from Russian), Mir Publishers, Moscow,

1975

[2] Burton Paul: Kinematics and dynamics of planar

machinery, Prentice Hall, Inc. Englewood Cliffs, 1979

[3] Waldron: Kinematics & Design of Machinery.1998

[4] Norton, R.L.: Design of Machinery, 4 ed, McGraw Hill

Book Company, 2007

[5] Magnus, K.: [Schwingungen.] Vibrations (transl. from

German by L. Macquisten-Wallace). Blackie & Son:

London, Glasgow, 1965.

[6] Den Hartog, J.P.: Mechanical Vibrations, Dover

Publications Inc., 1985

[7] Timoshenko, S.P.; Young, D.H.; Weaver, W.: Vibration

Problems in Engineering. Chichester: John Wiley & Sons,

5th.Edition, 1990

[8] Dimarogonas, A.: Vibration for Engineers. Prentice Hall,

1998

[9] Dresig, H.; Holzweißig, F.: Maschinendynamik.(in

German) 9th edition, with software-CD, Springer- Verlag, Berlin Heidelberg, 2009, ISBN: 978-3-540-87693-9

[10] Holzweißig, F.; Dresig, H.: Giao trinh. Dong Luc Hoc

May (in Vietnamese)(transl .from Nguyen Van Khang), Publisher Nha Xuat Ban Khoa Hoc Va Ky Thuat, Hanoi/Vietnam ,2001

[11] Dresig, H., Holzweißig, F.: Dynamics of Machinery.

Theory and Applications, Springer- Verlag, Berlin-Heidelberg, 2009, ISBN: 978-3-540-89939-6;

[12] Dresig, H., Holzweißig, F.: Dynamics of Machinery.

Theory and Applications, (in Chinese) (transl. from Zhu

Sihong and Gao Xingliang), Science Press 2009