Root Sum Squares Tolerance Analysis with Nonlinear Problems

1990 ◽  
Vol 112 (4) ◽  
pp. 382-384 ◽  
Author(s):  
W. H. Greenwood ◽  
K. W. Chase
Keyword(s):  
Statistical Analysis ◽  
Design Method ◽  
Design Procedure ◽  
Nonlinear Problems ◽  
Tolerance Analysis ◽  
Iterative Design ◽  
Independent Variables

Elementary tolerance analysis with nonlinear assembly equations or functions can lead to significant errors when either Worst Limits or Root Sum Squares are applied. A previous paper [1] presented the errors and a corrective design method for Worst Limit elementary tolerance analysis. In this paper, Root Sum Squares tolerance analysis is applied to a nonlinear assembly equation, which gives significant errors in the assembly acceptance fraction. Advanced statistical analysis can be used in an iterative design procedure to specify the independent variables which meet the specified assembly in spite of the nonlinearities.

scholarly journals Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Fanwei Meng ◽  
Dini Wang ◽  
Penghui Yang ◽  
Guanzhou Xie
Keyword(s):  
Design Method ◽  
Polynomial System ◽  
Nonlinear Problems ◽  
Sum Of Squares ◽  
Basic Relation ◽  
Analysis And Design ◽  
Iterative Design ◽  
Satellite Attitude ◽  
Dominant Design ◽  
Large Satellite

The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is firstly derived to solve the problem of nonconvex optimization. Then, the problems of SOS in nonlinear H∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H∞ control is presented. The first step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. The second step is to solve the L2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. The nonlinear H∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to find a broad range of applications in the analysis and design of nonlinear systems.

Generic design of ram pumps

1998 ◽  
Vol 212 (2) ◽  
pp. 117-124 ◽  
Author(s):  
B W Young
Keyword(s):  
Rational Design ◽  
Design Space ◽  
Design Method ◽  
Beat Frequency ◽  
Design Procedure ◽  
Upper And Lower Bounds ◽  
Drive Pipe ◽  
Independent Variables ◽  
Dependent Variables ◽  
Generic Design

The hydraulic ram pump was invented over 200 years ago but became obsolete with the general availability of mains water. It is used for pumping surface water and is powered by the potential energy of the supply. Ram pumps are particularly appropriate for use in remote regions of the developing world as their construction is basic and robust and they are inexpensive and easy to install and maintain. A rational design procedure applicable to any ram pump is described in this paper. The method is based on the three non-dimensional relationships that have been found to govern ram pump behaviour. The relationships express beat frequency, quantity delivered and source capacity in terms of the independent variables. By assigning upper and lower bounds to the critical velocity in the drive pipe, it is possible to derive three characteristic pump parameters from which the dependent variables may be determined directly. These parameters all take the same numerical values within a feasible design space. The design method has been confirmed using the results of existing experiments. A number of examples are given which illustrate the ease and rapidity of the procedure.

Integrated Design on Structural Shape and Controller of Spin Stand for High-Speed Positioning

2005 ◽  
Author(s):  
H. Ando ◽  
T. Sakai ◽  
G. Obinata
Keyword(s):  
High Speed ◽  
Design Method ◽  
Integrated Design ◽  
Design Procedure ◽  
Optimization Procedure ◽  
Shape Design ◽  
Performance Indices ◽  
Closed Loop System ◽  
Structural Shape ◽  
Iterative Design

This paper discusses the integrated design on structural shape and controller of positioning actuators for spin stands. To allow highly flexible shape design of the mechanism for the positioning actuator and to improve the calculation efficiency in the shape optimization, this paper proposes an integrated design method in which a structural shape is defined like as a skeleton and meats and a genetic algorithm (GA) is used to search the combination of the skeleton and meats for obtaining better performance of the closed-loop system in iterative design procedure. The iterative optimization procedure includes the shape and the controller updates. It is shown in design examples that the proposed integrated design method can improve the performance of the positioning actuator according to the performance indices. Therefore, the proposed method is effective to such active mechanisms that harder specifications are assigned to the design.

scholarly journals A PC-Based Inverse Design Method Applied to Radial Inflow Turbines

1992 ◽  
Author(s):  
Ivar Helge Skoe
Keyword(s):  
Design Method ◽  
Design Procedure ◽  
Inverse Design ◽  
Solid Model ◽  
The Novel ◽  
Gas Generator ◽  
Iterative Design ◽  
Inverse Design Method ◽  
Inverse Design Problem ◽  
Novel Design

The method described herewith is an ‘engineering’ approach to the inverse design problem where both aerodynamic and mechanical criteria are imposed. A novel exducer configuration, with slanted trailing edge, evloves during the iterative design procedure based on the introduction of: - a realistic loss distribution - a prescribed rotor exit spanwise total pressure distribution - and with the imposed geometric restrictions. For a Gas Generator Turbine, ‘back-to-back’ traverse results show reduced loss for the novel design as compared with a conventionally designed Radial Inflow Turbine. Through extensive use of ‘Bezier Curves’ for the aerodynamically defined 3-D geometry, the same ‘solid model’ is used to prepare the input files for the structural analysis (’meshing’ for the FEM) as well as the geometry definition for production.

PENGARUH PELATIHAN DAN MOTIVASI KERJA TERHADAP KINERJA KARYAWAN PT. BAKRIE PIPE INDUSTRIES BEKASI

2016 ◽  
Vol 4 (2) ◽  
Author(s):  
Imam Wibowo, M.Si ◽  
Rusma Patriansyah
Keyword(s):  
Statistical Analysis ◽  
Employee Performance ◽  
Positive Influence ◽  
Independent Variables ◽  
Operating Division ◽  
Independent Variable

The purpose of this research is to know the information about relationship between independent variables which are training (X1) and motivation (X2) with dependent variable which is employee performance (Y) of PT. Bakrie Pipe Industries Bekasi, both simultaneously and partially. Data collected from 78 employee of PT. Bakrie Pipe Industries Operating Division randomly using Slovin formula. Then all data was analyzed by using regression and statistical analysis using F-statistic to know the influence of independent variable simultaneously and t-statistic to know the influence of independent variable partially with using SPSS Ver. 22 software. The results of this research shown that: 1). Simultaneously, training and motivation have positive influence and significant to employee performance of PT. Bakrie Pipe Industries Bekasi. 2). Partially, training has positive influence and significant to employee performance of PT. Bakrie Pipe Industries Bekasi. 3). Partially, motivation has positive influence and significant to employee performance of PT. Bakrie Pipe Industries Bekasi.

scholarly journals A Two-Round Optimization Design Method for Aerostatic Spindles Considering the Fluid–Structure Interaction Effect

2021 ◽  
Vol 11 (7) ◽  
pp. 3017
Author(s):  
Qiang Gao ◽  
Siyu Gao ◽  
Lihua Lu ◽  
Min Zhu ◽  
Feihu Zhang
Keyword(s):  
Optimal Design ◽  
Optimization Design ◽  
Design Method ◽  
Fluid Structure Interaction ◽  
Design Procedure ◽  
Design Parameters ◽  
Geometrical Parameters ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Aerostatic Spindle

The fluid–structure interaction (FSI) effect has a significant impact on the static and dynamic performance of aerostatic spindles, which should be fully considered when developing a new product. To enhance the overall performance of aerostatic spindles, a two-round optimization design method for aerostatic spindles considering the FSI effect is proposed in this article. An aerostatic spindle is optimized to elaborate the design procedure of the proposed method. In the first-round design, the geometrical parameters of the aerostatic bearing were optimized to improve its stiffness. Then, the key structural dimension of the aerostatic spindle is optimized in the second-round design to improve the natural frequency of the spindle. Finally, optimal design parameters are acquired and experimentally verified. This research guides the optimal design of aerostatic spindles considering the FSI effect.

AN INDEPENDENT ACTIVE BALANCER FOR PLANAR MECHANISMS

2007 ◽  
Vol 31 (2) ◽  
pp. 167-190 ◽  
Author(s):  
Zhang Ying ◽  
Yao Yan-An ◽  
Cha Jian-Zhong
Keyword(s):  
Working Conditions ◽  
Design Method ◽  
Design Procedure ◽  
Vibration Absorber ◽  
Planar Mechanisms ◽  
Dynamic Balancing ◽  
Joint Coupling ◽  
Design Requirements ◽  
Novel Concept ◽  
Two Degree Of Freedom

This paper proposed a novel concept of active balancer for dynamic balancing of planar mechanisms. Somewhat similar to a vibration absorber, the active balancer is designed as an independent device, which is placed outside of the mechanism to be balanced and can be installed easily. It consists of a two degree-of-freedom (DOF) linkage with two input shafts, one of which is connected to the output shaft of the mechanism to be balanced by a joint coupling, and the other one is driven by a controllable motor. Flexible dynamic balancing adapted to different working conditions can be achieved by varying speed trajectories of the control motor actively. A design method is developed for selecting suitable speed trajectories and link parameters of the two DOF linkage of the balancer to meet various design requirements and constraints. Numerical examples are given to demonstrate the design procedure and to verify the feasibility of the proposed concept.

scholarly journals Novel Robust Design Method of Multilayer Optical Coatings

ISRN Optics ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Suyong Wu ◽  
Xingwu Long ◽  
Kaiyong Yang
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Design Method ◽  
Analytical Calculation ◽  
Design Procedure ◽  
Deposition Process ◽  
Practical Significance ◽  
Optical Coatings ◽  
Optical Films ◽  
Robust Design Method

We present a novel fast robust design method of multilayer optical coatings. The sensitivity of optical films to production errors is controlled in the whole optimization design procedure. We derive an analytical calculation model for fast robust design of multilayer optical coatings. We demonstrate its effectiveness by successful application of the robust design method to a neutral beam splitter. It is showed that the novel robust design method owns an inherent fast computation characteristic and the designed film is insensitive to the monitoring thickness errors in deposition process. This method is especially of practical significance to improve the mass production yields and repetitive production of high-quality optical coatings.

Multi Mode Vibration Control and Broder Band Motion Control of Three Dimensional Shaking Table

2005 ◽  
Author(s):  
Tsunehiro Wakasugi ◽  
Toru Watanabe ◽  
Kazuto Seto
Keyword(s):  
Vibration Control ◽  
Controller Design ◽  
Design Method ◽  
Three Dimensional ◽  
Design Procedure ◽  
Equation System ◽  
State Equation ◽  
Shaking Table ◽  
Mode Vibration ◽  
And Control

This paper deals with a new system design method for motion and vibration control of a three-dimensional flexible shaking table. An integrated modeling and controller design procedure for flexible shaking table system is presented. An experimental three-dimensional shaking table is built. “Reduced-Order Physical Model” procedure is adopted. A state equation system model is composed and a feedback controller is designed by applying LQI control law to achieve simultaneous motion and vibration control. Adding a feedforward, two-degree-of-freedom control system is designed. Computer simulations and control experiments are carried out and the effectiveness of the presented procedure is investigated. The robustness of the system is also investigated.

scholarly journals Semi-Inverse Design of Compressor Cascades, Including Supersonic Inflow

1990 ◽  
Author(s):  
A. Kirschner ◽  
H. Stoff
Keyword(s):  
Flow Field ◽  
Design Method ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Design Procedure ◽  
Meridional Plane ◽  
Simple Method ◽  
Blade Loading ◽  
Through Flow ◽  
Blade Element

A cascade design-method is presented which complements the meridional through-flow design procedure of turbomachines. Starting from an axisymmetric flow field and the streamline geometry in the meridional plane this simple method produces a solution for the quasi three-dimensional flow field and the blade-element geometry on corresponding stream surfaces. In addition, it provides intra-blade data on loss and turning required for a consistent design and a convenient means of optimizing blade loading. The purpose of this paper is to describe the theoretical basis of the method and to illustrate its application in the design of transonic compressors.

Sign in / Sign up

Export Citation Format

Share Document