An Optimal Shaft Balance Solution Using Integer Programming

2003 ◽  
Author(s):  
Eric Bechhoefer ◽  
Shawn Tayloe
Keyword(s):  
Integer Programming ◽  
Residual Vibration ◽  
Single Plane ◽  
Mathematical Solution ◽  
Vibration Data ◽  
Optimal Balance ◽  
Influence Coefficients ◽  
Balance Solution ◽  
Minimum Residual ◽  
Minimum Number

A mathematical solution for optimal balance weights is presented for single-plane, discrete weight and discrete adjustment point balance. The algorithm uses influence coefficients, either given or derived, and measured synchronous complex vibration data to determine the best adjustment. The solution has a user selected objective: minimum residual vibration or minimum number of adjustments to reach a given vibration. The algorithm is part of Goodrich’s Integrated Mechanical Diagnostics Health Usage Monitoring System (IMD HUMS), currently installed on a number of helicopter platforms.

scholarly journals An Optimum Balance Weight Search Algorithm

1993 ◽  
Author(s):  
James C. Austrow
Keyword(s):  
Search Algorithm ◽  
Least Square ◽  
Test Case ◽  
Influence Coefficient ◽  
Residual Vibration ◽  
Single Plane ◽  
Vibration Data ◽  
Influence Coefficients ◽  
Balance Weight ◽  
Optimum Balance

A mathematical description for an optimum balance weight search algorithm for single plane multipoint balance is presented. The algorithm uses influence coefficients, either measured or known beforehand, and measured complex vibration data to determine an optimum balance correction weight. The solution minimizes the maximum residual vibration. The algorithm allows user defined balance weights to be analyzed and evaluated. A test case is presented showing actual results and comparison with a least square solution algorithm. An efficient multiplane influence coefficient calculation scheme is also presented.

An Optimum Balance Weight Search Algorithm

1994 ◽  
Vol 116 (3) ◽  
pp. 678-681 ◽  
Author(s):  
J. C. Austrow
Keyword(s):  
Search Algorithm ◽  
Solution Algorithm ◽  
Test Case ◽  
Influence Coefficient ◽  
Residual Vibration ◽  
Single Plane ◽  
Vibration Data ◽  
Influence Coefficients ◽  
Balance Weight ◽  
Optimum Balance

A mathematical description for an optimum balance weight search algorithm for single-plane multipoint balance is presented. The algorithm uses influence coefficients, either measured or known beforehand, and measured complex vibration data to determine an optimum balance correction weight. The solution minimizes the maximum residual vibration. The algorithm allows user-defined balance weights to be analyzed and evaluated. A test case is presented showing actual results and comparison with a least-squares solution algorithm. An efficient multiplane influence coefficient calculation scheme is also presented.

Fourier-based optimal design of a flexible manipulator path to reduce residual vibration of the endpoint

Robotica ◽  
1993 ◽  
Vol 11 (3) ◽  
pp. 263-272 ◽  
Author(s):  
Kyung-Jo Park ◽  
Youn-Sik Park
Keyword(s):  
Equations Of Motion ◽  
Optimal Path ◽  
Correlation Coefficients ◽  
Considerable Effect ◽  
Flexible Manipulator ◽  
Residual Vibration ◽  
Matching Problems ◽  
Design Variables ◽  
Minimum Residual ◽  
Minimum Number

SUMMARYA method is presented for generating the path which significantly reduces residual vibration. The desired path is optimally designed so that the system completes the required move with minimum residual vibration. The dynamic model and optimal path are effectively formulated and computed by using special moving coordinates, called virtual rigid link coordinates, to represent the link flexibilities. Also joint compliances are included in the model. Characteristics of residual vibration are identified from the linearized equations of motion. From these results, the performance index is selected to reduce residual vibration effectively. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path.

Path design of redundant flexible robot manipulators to reduce residual vibration in the presence of obstacles

Robotica ◽  
2003 ◽  
Vol 21 (3) ◽  
pp. 335-340 ◽  
Author(s):  
Kyung-Jo Park
Keyword(s):  
Robot Manipulator ◽  
Optimal Path ◽  
Correlation Coefficients ◽  
Flexible Robot ◽  
Residual Vibration ◽  
Matching Problems ◽  
Design Variables ◽  
Minimum Residual ◽  
Minimum Number ◽  
Link Flexibility

A method is presented for generating the path that significantly reduces residual vibration of the redundant, flexible robot manipulator in the presence of obstacles. The desired path is optimally designed so that the system completes the required move with minimum residual vibration, avoiding obstacles. The dynamic model and optimal path are effectively formulated and computed by using a special moving coordinate, called VLCS, to represent the link flexibility. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables. A planar three-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate path, in the presence of obstacles.

Study on Single-Plane Biaxial Balance Monitor System in ULTRA-Precision Grinding

2006 ◽  
Vol 304-305 ◽  
pp. 251-255
Author(s):  
L. Zheng ◽  
Yin Biao Guo ◽  
Z.Z. Wang
Keyword(s):  
Mutual Influence ◽  
Machining Accuracy ◽  
Monitor System ◽  
Machining Parameters ◽  
Precision Grinding ◽  
Single Plane ◽  
Workpiece Surface ◽  
Surface Error ◽  
Vibration Data ◽  
Ultra Precision

This paper puts forward an intelligent single-plane biaxial balance monitor system, which is used in ultra-precision grinding. It adopts the method of single-plane balance correction for the vibration of wheel and workpiece. And this system can also be used for integral balance. For ultra-precision grinding, caused by the mutual influence of the vibration of wheel and workpiece, there will be a ripple on the workpiece surface, which is mainly influenced by the frequency ratio of wheel to workpiece, the feed rate and the vibration of wheel and workpiece. This system can improve the machining accuracy, reduce the surface error of workpiece and appraise the integrated machining result, by analyzing the vibration data of wheel and workpiece and adjusting machining parameters.

scholarly journals Strategy and Technique of High Efficiency Balancing in Field for Turbo-Generator Units with Large Capacity

2021 ◽  
Vol 2101 (1) ◽  
pp. 012011
Author(s):  
Wenfang Cai ◽  
Songyuan Lu ◽  
Zhengfeng Wu ◽  
Guangyao Ying ◽  
Wenjian Wu
Keyword(s):  
High Efficiency ◽  
Large Capacity ◽  
Construction Period ◽  
Vibration Data ◽  
Influence Coefficients ◽  
Turbo Generator ◽  
Accurate Judgment ◽  
Key Techniques ◽  
Selection Of ◽  
Modal Method

Abstract Abstract.This paper aims at the high efficiency of field balancing for turbo-generator with large capacity currently, and introduces the strategies and key techniques of the rotor system balancing with practical cases of power plant in field. The acquisition, analysis and former processing of the original vibration data for balance calculation are included. Furthermore, they involve complete measuring points and conditions, accurate judgment for the types of unbalance exciting force and selection of stable vibration data, all these could reduce the blindness of balancing effectively. The strategies and techniques also contain the determination for axial plane of unbalance by the modal method, then the optimal steps and the plane of adding weight are chosen during the implementation of balancing. Besides, this paper also introduces the analysis and selection of influence coefficients and the phase of trial weight, these can help determine the final correction weight accurately in order to guarantee the balancing process prompt and efficient. Meanwhile, the restriction of practical location for adding weight and construction period of maintenance and production for the units should be considered during the high efficiency balancing in field. These strategies and techniques of high efficiency balancing have practical application value in promoting the technology of field balancing for turbo- generator units with large capacity.

COMPUTING THE REVERSAL DISTANCE BETWEEN GENOMES IN THE PRESENCE OF MULTI-GENE FAMILIES VIA BINARY INTEGER PROGRAMMING

2007 ◽  
Vol 05 (01) ◽  
pp. 117-133 ◽  
Author(s):  
JAKKARIN SUKSAWATCHON ◽  
CHIDCHANOK LURSINSAP ◽  
MIKAEL BODÉN
Keyword(s):  
Integer Programming ◽  
Combinatorial Problem ◽  
Gene Families ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
High Accuracy ◽  
Biological Data ◽  
Binary Integer Programming ◽  
A Genome ◽  
Minimum Number

Hannenhalli and Pevzner developed the first polynomial-time algorithm for the combinatorial problem of sorting signed genomic data. Their algorithm determines the minimum number of reversals required for rearranging a genome to another — but only in the absence of gene duplicates. However, duplicates often account for 40% of a genome. In this paper, we show how to extend Hannenhalli and Pevzner's approach to deal with genomes with multi-gene families. We propose a new heuristic algorithm to compute the nearest reversal distance between two genomes with multi-gene families via binary integer programming. The experimental results on both synthetic and real biological data demonstrate that the proposed algorithm is able to find the reversal distance with high accuracy.

Minimizing Residual Vibration for Point-to-Point Motion

1985 ◽  
Vol 107 (4) ◽  
pp. 378-382 ◽  
Author(s):  
P. H. Meckl ◽  
W. P. Seering
Keyword(s):  
Minimum Energy ◽  
Residual Vibration ◽  
Test Fixture ◽  
Square Wave ◽  
Wave Forcing ◽  
Forcing Function ◽  
Point Motion ◽  
Minimum Residual ◽  
Order Of Magnitude ◽  
Point To Point

This paper describes an appropriately shaped forcing function for moving a dynamic system over an incremental distance with minimum residual vibration. The function is constructed by combining harmonics of a “ramped sinusoid” function so that minimum energy is introduced to the system at its resonant frequencies. A test fixture to evaluate this approach is described and experimental results are given. Residual vibration amplitudes for the ramped sinusoid function are compared with those for a square wave input and a bang-bang function. In practice, the ramped sinusoid achieves nearly an order-of-magnitude reduction in residual vibration amplitude as compared to the square wave forcing function.

scholarly journals Weapon Target Assignment

2021 ◽  
Author(s):  
Mohammad Babul Hasan ◽  
Yaindrila Barua
Keyword(s):  
Integer Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Nonlinear Integer Programming ◽  
Integer Programming Problem ◽  
Combinatorial Optimization Problems ◽  
Target Assignment ◽  
Minimum Number ◽  
Np Complete

This chapter is mainly based on an important sector of operation research-weapon’s assignment (WTA) problem which is a well-known application of optimization techniques. While we discuss about WTA, we need some common terms to be discussed first. In this section, we first introduce WTA problem and then we present some prerequisites such as optimization model, its classification, LP, NLP, SP and their classifications, and applications of SP. We also discuss some relevant software tools we use to optimize the problems. The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research. It consists of finding an optimal assignment of a set of weapons of various types to a set of targets in order to maximize the total expected damage done to the opponent. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There are constraints on weapons available of various types and on the minimum number of weapons by type to be assigned to various targets. The constraints are linear, and the objective function is nonlinear. The objective function is formulated in terms of probability of damage of various targets weighted by their military value.

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