Applied & Engineering Mathematics
Contents
Tools
Volumetric Hydraulic Drive: Dynamic Analysis
Volumetric Hydraulic Drive: Static Calculation
Hydro-Mechanical Drive: Dynamic Analysis
Hydro-Mechanical Drive: Traction Calculation
About
Contents
Applied Mathematics
Numerical Methods
Algebraic and Transcendental Equations
Introduction
Method of iterations
Method of tangents
Method of halving
Method of chords
Examples
References
Interpolation of Functions
Introduction
Newton’s first interpolation formula
Newton’s second interpolation formula
Stirling’s interpolation formula
The spline interpolation
Example
References
Numerical Differentiaon
Introduction
Formulas of numerical differentiaon
Example
References
Numerical Integration
Introduction
The trapezoid rule
Simpson’s rule
Examples
References
Ordinary Differential Equations
Introduction
Euler’s method
Runge-Kutta method
Examples
References
Partial Differential Equations
Introduction
Method of finite differences / Method of grids
Example: solution of the elliptic equation
Method of characteristics
Example: solution of the hyperbolic equation
References
Mathematical Statistics
Elements of Mathematical Statistics
Subject and problems of mathematical statistics
Random variables and distribution laws
Numerical characteristics of random variables
Distributions of discrete random variables
Distributions of continuous random variables
Systems of random variables
Examples
References
Treatment of Experiment Results
Alignment of statistical distributions. Pearson’s curves
Agreement criteria
Regression analysis. The least squares smoothing
Example
References
Software
Matrix Algebra
Principles of Matrix Calculation
Introduction
The basic definitions
Operations with matrices
The transposed matrix
The inverse matrix
Powers of matrices
Rank of matrix
Cellular matrices
Triangular matrices
Elementary transformations of matrices
Example
References
Engineering Mathematics
Mobile Machines
Traction Analysis
Introduction
One engine transmission
Scheme and elements of one engine transmission
System of equations
Method of solution
Example
Two engines transmission
Scheme and elements of two engines transmission
System of equations
Method of solution
Example
References
Software for traction analysis of hydro mechanical transmissions
Hydraulic Systems
Dynamic Analysis
Introduction
Structure description of hydraulic circuits
Library of hydraulic elements and mathematical models
Forming and solving algorithms of hydraulic circuit mathematical model
Form of the analysis results presentation
Examples
References
Software for dynamic analysis of arbitrary structure hydraulic systems
Static Analysis
Introduction
Structure description of hydraulic circuits
Library of hydraulic elements and mathematical models
General scheme of solution
Form of the analysis results presentation
Example
References
Software for static analysis of arbitrary structure hydraulic systems
Dynamic Express Analysis
Introduction
Typical structures of hydraulic circuits and their description
Library of mathematical models of functional blocks
Forming of hydraulic circuit mathematical model and algorithm of solution
Example: dynamics of hydraulic drive of asphalt spreader
References
Software for dynamic express analysis of arbitrary structure hydraulic systems
Synthesis of Hydraulic Circuits
Introduction
Library of standard graphical symbols of hydraulic elements
Forming of principal hydraulic circuits
Forming of simplified hydraulic circuits
References
Software for synthesis of hydraulic circuits
Dynamic Synthesis of Hydraulic Devices
Dynamic synthesis of throttle braking devices of hydraulic cylinders. Introduction
Planning of the piston braking law
Algorithm of dynamic synthesis
Examples of dynamic synthesis
References
Software for dynamic synthesis of hydraulic devices
Control Systems
Dynamic Analysis of Control System of Hydraulic Drive
Introduction
Structure description of arbitrary control systems
Library of mathematical models of typical dynamic links
Algorithms of forming and solving of mathematical model
Examples
References
Software for dynamic analysis of arbitrary structure control systems
Dynamic Synthesis of Control System of Hydraulic Drive
Introduction
Problem statement
Synthesis of control by a power hydraulic drive of volumetric regulation
Method of multiple periods of natural vibrations
Algorithm
Example
Method of the movement law planning
Algorithm
Example
Synthesis of control by a power hydraulic drive of throttle regulation
About control by a power hydraulic drive of throttle regulation
Conclusion
Appendix: Assessment of influence of variable elasticity, losses of pressure and leakages on natural frequency of hydraulic system
References
Control of Flow-Transport System of Concrete Mixing Plants
Introduction
Structural analysis of the transport scheme
Control of the flow-transport system
References
Hydro Mechanical Drives and Transmissions
Dynamic Analysis
Introduction
Structure description of arbitrary hydro mechanical circuits
Classification of drive base elements and their nodes
Structure analysis of hydro mechanical drives
Reduction of inertia moments and transfer attitudes
Library of base elements and mathematical models
Modeling of blocking mode
Blocking of friction clutches and hydraulic torque converters
General case of blocking of arbitrary number of clutches
Algorithms of forming and solving of drive mathematical model
Form of the analysis results presentation
Example: simulation of dynamics of hydraulic transmission of self-propelled chassis
References
Software for dynamic analysis of arbitrary structure hydro mechanical drives and transmissions
Analysis and Design
Introduction
Systems of Hydraulic Drives
Hydraulic Transmissions of Single Bucket Excavators
Traction-dynamic analysis of hydraulic transmissions of wheel single bucket excavators of III-IV dimension groups
Hydraulic Drives of Building Self-propelled Cranes
Dynamics of hydraulic drives of main winch and mechanism of lifting-lowering of boom of the building self-propelled cranes capacity 25 and 100 tons
Hydraulic Drives of Auto Concrete Pumps
Dynamics of the main hydraulic drive of the auto concrete pump SB-126
Dynamics of breaking processes in the main hydraulic drive of the auto concrete pump SB-126A
Dynamics of hydraulic drives of turn mechanism of the auto concrete pump BR-14
Hydraulic Drives of Loaders
Traction analysis of hydraulic transmission of the small-sized loader ТО-31
The analysis of dynamic loads in hydraulic drive of loader ТО-24
Systems of Hydro Mechanical Drives
Hydro Mechanical Transmission of Loader
Traction-dynamic analysis of hydro mechanical transmission of the loader ТО-21-1
Hydro Mechanical Transmissions of the Jib Self-Propelled Cranes
Traction-dynamic analysis of hydro mechanical transmissions of the jib self-propelled cranes KS-63 and KS-100
References