Mechanical parts and system optimization design modeling and application

Author: Zhou Tingmei Lan Yueming
Publisher:
Publishing Date: 2005-01-01
Features: This book systematically introduces common methods and new research findings in mechanical optimization design, including multi-objective optimization, sensitivity analysis of nonlinear programming, fuzzy optimization, reliability optimization, engineering random variable optimization, and intelligent optimization, among others. It also provides a comprehensive and detailed discussion on the modeling and application of optimization design for mechanical parts and systems, with a focus on engineering applications. This book enables readers to understand the applicable conditions and application methods of various optimization methods. Most of the models in the book have practical engineering backgrounds and can be conveniently applied. It is suitable for reference by mechanical design engineering, research, and development technicians, as well as serving as a textbook for undergraduate and graduate students in relevant fields at colleges and universities.
Introduction: This book systematically introduces common methods and new research findings in mechanical optimization design, including multi-objective optimization, sensitivity analysis of nonlinear programming, fuzzy optimization, reliability optimization, engineering random variable optimization, and intelligent optimization, among others. It also provides a comprehensive and detailed discussion on the modeling and application of optimization design for mechanical parts and systems, with a focus on engineering applications. This book enables readers to understand the applicable conditions and application methods of various optimization methods. Most of the models in the book have practical engineering backgrounds and can be conveniently applied. It is suitable for reference by mechanical design engineering, research, and development technicians, as well as serving as a textbook for undergraduate and graduate students in relevant fields at colleges and universities.
Table of Contents:
Chapter 1 Optimization Design Methods
1.1 Overview of Optimization Design
1.1.1 Mathematical Model of Optimization Design
1.1.1.1 Optimization Design of a Constant-Section Shaft Transmitting Torque and Bending Moment
1.1.1.2 Mathematical Model of Optimization Design
1.1.2 Geometric Description of Optimization Process
1.1.3 Iteration Termination Criteria
1.2 Unconstrained Optimization Methods
1.2.1 Common One-Dimensional Search Methods
1.2.1.1 Determination of Search Interval
1.2.1.2 0.618 Method
1.2.1.3 Other One-Dimensional Search Methods
1.2.2 Gradient Method ( Descent Method)
1.2.2.1 Basic Idea of Gradient Method
1.2.2.2 Example
1.2.2.3 Discussion on Gradient Method
1.2.3 Newton-Type Methods
1.2.3.1 Basic Idea
1.2.3.2 Example
1.2.3.3 Discussion on Newton Method
1.2.4 Conjugate Gradient Method
1.2.5 Variable Metric Method
1.2.5.1 DFP Variable Metric Method
1.2.5.2 Computational Steps of DFP Variable Metric Method
1.2.5.3 BFGS Variable Metric Method
1.2.6 Coordinate Rotation Method
1.2.6.1 Basic Idea of Coordinate Rotation Method
1.2.6.2 Discussion on Coordinate Rotation Method
1.2.7 Powell Method
1.2.7.1 Basic Algorithm of Powell
1.2.7.2 Improved Powell Algorithm
1.2.8 Comparison of Various Unconstrained Optimization Methods
1.2.8.1 Iterative Formula
1.2.8.2 Comparison of Various Methods
1.3 Constrained Optimization
1.3.1 Penalty Function Method
1.3.1.1 Interior Penalty Function Method
1.3.1.2 Exterior Penalty Function Method
1.3.1.3 Discussion on SUMT Method
1.3.1.4 Hybrid Penalty Function Method
1.3.1.5 Computational Process and Flowchart of Penalty Function Method
1.3.2 Complex Shape Method
1.3.2.1 Generation of Initial Complex Shape
1.3.2.2 Search Strategy
1.3.2.3 Discussion on Complex Shape Method
1.3.3 Reduced Gradient Method and Generalized Reduced Gradient Method
1.3.3.1 Reduced Gradient Method
1.3.3.2 Generalized Reduced Gradient Method
1.4 Application Examples
1.4.1 Optimization Design of Planetary Gear Train
1.4.2 Optimization Design of Key Connection
1.4.2.1 Failure Modes and Mathematical Models of Flat Key, Wedge Key, and Tangential Key
1.4.2.2 Optimization Results
1.4.3 Optimization Design of Sliding Block Universal Joint
1.4.3.1 Establishment of Optimization Model
1.4.3.2 Selection of Optimization Method
1.4.3.3 Computational Results and Processing
1.4.4 Optimization Design of Variable-Section Steel Plate Spring for Automobile
1.4.4.1 Establishment of Mathematical Model
1.4.4.2 Optimization Design Calculation
1.4.4.3 Analysis of Computational Results
References
Chapter 2 Modeling and Evaluation of Optimization Methods in Mechanical Optimization Design
2.1 General Process of Mechanical Optimization Design
2.2 Basic Principles of Mechanical Optimization Design Modeling
2.2.1 Determination of System Boundary
2.2.2 Selection of Design Variables
2.2.3 Determination of Objective Function
2.2.4 Establishment of Constraint Function
2.3 Analysis and Transformation of Mathematical Models in Mechanical Optimization Design
2.3.1 Concept and Role of Model Transformation
2.3.2 Concept of Scale Transformation
2.3.3 Linearization of Model
2.3.4 Transformation of Algebraic Model into Geometric Programming
2.4 Evaluation of Optimization Methods
2.4.1 Selection of Test Cases
2.4.2 Evaluation Indicators for Optimization Methods and Programs
2.4.3 Evaluation Results
2.4.4 Selection Method for Optimization Method Programs
References
Chapter 3 Modeling and Application of Multi-Objective Optimization Design
3.1 Mathematical Model of Multi-Objective Optimization Design
3.2 Solving Methods of Multi-Objective Optimization Design
3.2.1 Unified Objective Method
3.2.1.1 Linear Weighting Method
3.2.1.2 Ideal Point Method
3.2.1.3 Goal Programming Method
3.2.1.4 Multiplication and Division Method
3.2.1.5 Efficiency Coefficient Method
3.2.2 Main Objective Method
3.2.3 Hierarchical Sequential Method
3.2.4 Max-Min Method
3.3 Application Examples
3.3.1 Multi-Objective Optimization Design of Cycloidal Pinwheel Planetary Reducer
3.3.1.1 Geometric Calculation of Basic Dimensions
3.3.1.2 Establishment of Mathematical Model for Optimization Design
3.3.1.3 Selection of Multi-Objective Optimization Design Method
3.3.1.4 Computational Example
3.3.2 Multi-Objective Optimization Design of Four-Bar Variable Amplitude Mechanism
3.3.2.1 Analysis of Four-Bar Variable Amplitude Mechanism
3.3.2.2 Mathematical Model of Multi-Objective Optimization Design of Four-Bar Variable Amplitude Mechanism
3.3.2.3 Optimization Results of Four-Bar Variable Amplitude Mechanism
References
Chapter 4 Sensitivity Analysis in Nonlinear Programming
4.1 Overview
4.2 Principles and Methods of Using Geometric Programming for Sensitivity Analysis
4.2.1 Basic Principles of Positive Definite Geometric Programming and Geometric Programming with Negative Numbers for Sensitivity Analysis
4.2.1.1 Introduction to Geometric Programming
4.2.1.2 Basic Principles of Using Geometric Programming for Sensitivity Analysis
4.2.2 Algorithm for Using Geometric Programming for Sensitivity Analysis
4.2.3 Sensitivity Analysis in Structural Optimization Design Using Geometric Programming
4.2.3.1 Establishment of Mathematical Model for Optimization Design of Hollow Beam
4.2.3.2 Sensitivity Analysis Using Geometric Programming
4.2.3.3 Points to Note
4.3 Principles and Methods of Using Penalty Function Method for Sensitivity Analysis
4.3.1 General Parameter Nonlinear Programming
4.3.2 Basic Principles of Sensitivity Analysis
4.3.3 Basic Principles of Using Penalty Function Method for Sensitivity Analysis
4.4 Sensitivity Analysis in Structural Optimization Design of Crane Using Penalty Function Method
4.4.1 Optimization Problem of Box-Shaped Main Beam of Crane
4.4.2 Sensitivity Analysis
4.5 Sensitivity Analysis in Multi-Objective Optimization Design of Four-Bar Variable Amplitude Mechanism Using Penalty Function Method
4.5.1 Sensitivity Analysis with Constraint Right-Hand Side Interference
4.5.2 Sensitivity Analysis with Parameter Interference
4.5.3 Results of Sensitivity Analysis of Four-Bar Variable Amplitude Mechanism
References
Chapter 5 Modeling and Application of Fuzzy Optimization Design
5.1 Conventional Mechanical Optimization Design and Fuzzy Optimization Design
5.2 Mathematical Model of Fuzzy Optimization Design
5.2.1 Design Variables in Fuzzy Optimization
5.2.2 Objective Function in Fuzzy Optimization Design
5.2.3 Constraints in Fuzzy Optimization Design
5.2.4 Mathematical Model of Fuzzy Optimization
5.3 Basic Meaning and Classification of Fuzzy Optimization Design
5.3.1 Basic Meaning of Fuzzy Optimization Design
5.3.2 Classification of Fuzzy Optimization Design
5.4 Symmetric Fuzzy Optimization Design and Its Solution Methods
5.4.1 Symmetric Fuzzy Optimization Model
5.4.2 Other Forms of Fuzzy Dominance Set
5.4.3 Methods for Solving Non-Fuzzy Objective Function Extremes
5.5 Basic Solution Methods for Fuzzy Optimization Iteration
5.5.1 Basic Principles of Fuzzy Optimization Iteration
5.5.2 Steps of Symmetric Fuzzy Optimization Iteration
5.6 Mathematical Model of Non-Symmetric Optimization Design
5.6.1 Mathematical Model of Non-Symmetric Fuzzy Optimization Design
5.6.2 Determination of Tolerance
5.6.3 Level Cuts of Non-Symmetric Fuzzy Optimization Model
5.7 Multi-Objective Fuzzy Optimization
5.7.1 Fuzzy Solution Method for Conventional Multi-Objective Optimization Design
5.7.2 Solving Symmetric Multi-Objective Fuzzy Optimization Model
5.7.3 Solving General Multi-Objective Fuzzy Optimization Model
5.7.4 Multi-Objective Optimization Solution Using Fuzzy Comprehensive Evaluation
5.7.5 Ideal Point Method for Multi-Objective Fuzzy Optimization Design
5.8 Application Examples
5.8.1 Research on Fuzzy Reliability Optimization Design of Plunger Hydraulic Pump System
5.8.1.1 Establishment of Reliability Model of Plunger Pump System
5.8.1.2 Fuzzy Reliability Allocation of Plunger Pump System
5.8.1.3 Computational Results and Conclusions
5.8.2 Fuzzy Multi-Objective Optimization Design of Cylindrical Helical Compression Spring
5.8.2.1 Establishment of Multi-Objective Fuzzy Optimization Model
5.8.2.2 Treatment of Fuzzy Constraints
5.8.2.3 Solution of Optimization Model
References
Chapter 6 Modeling and Application of Reliability Optimization Design
6.1 Mechanical Reliability Calculation Models
6.1.1 Stress-Intensity "Interference" Model of Mechanical Parts
6.1.2 Reliability Model with Both Stress and Strength Normally Distributed
6.1.3 Reliability Calculation When Stress and Strength Are Other Distributions
6.1.4 Approximate Calculation Models for Strength Reliability of Mechanical Components
6.1.4.1 Graphical Approximate Calculation Model
6.1.4.2 Approximate Calculation Model Based on Edgeworth Series of Probability Distribution
6.1.4.3 Monte Carlo Approximate Calculation Model
6.1.4.4 -Failure Probability Method
6.1.4.5 Reliability Calculation Using Other Approximate Calculation Methods
6.1.5 Reliability Calculation of Mechanical Systems
6.1.5.1 Reliability of Series Systems
6.1.5.2 Pure Parallel Systems
6.1.5.3 Voting Systems
6.1.5.4 Waiting Systems
6.1.5.5 Complex Mechanical Systems
6.2 Mechanical System Reliability Allocation Models
6.2.1 Equal Allocation Model
6.2.2 Relative Failure Rate Model
6.2.3 AGREE Allocation Model
6.3 Mechanical Reliability Optimization Design
6.3.1 Mathematical Programming Model of Mechanical Reliability Optimization Design
6.3.1.1 Mathematical Programming Model of Reliability Optimization Design of Unit Components
6.3.1.2 Mathematical Programming Model of System Reliability Allocation
6.3.1.3 Overall Mathematical Programming Model of System Reliability Optimization Design
6.3.1.4 Relationship and Proof Among Three Mathematical Programming Models
6.3.2 Implementation Strategy for Mechanical System Reliability Optimization Design
6.3.2.1 Coupled Optimization Strategy
6.3.2.2 Decentralization and Coordination Optimization Strategy
6.3.2.3 Decentralized Optimization Strategy
6.4 Application Examples
6.4.1 Reliability Optimization Design of Planetary Gear Drive System
6.4.1.1 Optimization Design Model of Planetary Gear Drive System
6.4.1.2 Reliability Optimization Design Process of Planetary Gear Drive System
6.4.1.3 Computational Example and Analysis
6.4.2 Reliability Optimization Design of Loader Differential
6.4.2.1 Reliability Calculation of Bending Strength of Gear Tooth Root of Differential
6.4.2.2 Establishment of Mathematical Model for Reliability Optimization Design of Differential
6.4.2.3 Optimization Method and Analysis of Computational Results
References
Chapter 7 Modeling and Application of Engineering Random Variable Optimization Design
7.1 Mathematical Model of Engineering Random Variable Optimization Design
7.1.1 Uncertainty of Engineering Design Information
7.1.2 Basic Concepts of Engineering Random Optimization Design
7.1.3 Several Basic Models of Engineering Random Optimization Design
7.1.3.1 Statistical Mean Model
7.1.3.2 Probability Constraint Function Model
7.1.3.3 Risk Design Model
7.1.3.4 Tolerance Design Model
7.1.3.5 Compensation Model
7.1.3.6 Unified Form of Engineering Random Optimization Design Models
7.2 Solving Methods for Random Models
7.2.1 Random Quasi-Gradient Method
7.2.2 Random Approximation Method
7.2.3 Random Simulation Search Method
7.3 Application Examples
7.3.1 Probability Optimization Design of Pressure Vessel
7.3.1.1 Mathematical Model of Probability Optimization Design of Pressure Vessel
7.3.1.2 Optimization Design Results
7.3.2 Tolerance -Optimization Design of Pneumatic Reversing Device Output Characteristics
7.3.2.1 Design Conditions
7.3.2.2 Establishment of Tolerance Design Model
7.3.2.3 Computational Results
7.3.3 Reliability Optimization Design of Link with Incomplete Probability Information
7.3.3.1 Mechanical Model of Link
7.3.3.2 Mathematical Model of Link Optimization Design
7.3.3.3 Optimization Solution of Link
7.3.4 Optimization Design of Probability Constraint Function Model of V-Belt Drive
7.3.4.1 Establishment of Probability Constraint Function Model of V-Belt Drive
7.3.4.2 Optimization Solution of V-Belt
References
Chapter 8 Modeling and Application of Intelligent Optimization Design
8.1 Neural Network Optimization Calculation Principles
8.1.1 Principles and Process of Neural Network Optimization Calculation
8.1.2 Several Neural Network Models Used in Mechanical Optimization Design
8.1.2.1 Feedback Neural Network
8.1.2.2 Multi-Layer Forward Neural Network
8.2 Engineering Applications of Neural Network Optimization Calculation
8.2.1 Artificial Neural Network-Assisted Optimization Design of Gear Drive Mechanism
8.2.1.1 BP Neural Network Model Principles
8.2.1.2 Gear Mechanism BP Network-Assisted Optimization Design
8.2.2 Neural Network Method for Multi-Objective Optimization of Disc Brakes
8.2.2.1 Establishment of Mathematical Model for Optimization Design of Disc Brakes
8.2.2.2 Neural Network Optimization
8.2.2.3 Analysis of Computational Results
8.3 Evolutionary Computing Methods Used in Mechanical Optimization Design
8.3.1 Genetic Algorithm
8.3.1.1 Computational Steps of Genetic Algorithm
8.3.1.2 Optimization Design of Dual Universal Joint Based on Genetic Algorithm
8.3.2 Application of Evolutionary Strategy in Mechanical Optimization Design
8.4 Process-Based Optimization Algorithms and Their Application in Machine Tool Spindle
8.4.1 Basic Theory of Process-Based Optimization Algorithms
8.4.2 Process-Based Optimization Design of Machine Tool Spindle
8.4.3 Analysis of Computational Results
8.5 Conclusion
References