Mathematical Model For Optimal Design Research Articles

Optimization and Test of Structural Parameters of Flat Hob Chopper

In order to reduce the chopping power consumption of a flat hob chopper (referred to herein as chopper) on the premise of ensuring the chopping effect of the chopper, the mathematical model of optimal design of chopper is established in this paper with the minimum chopping power as the objective. With the help of MATLAB software, the mathematical model is solved. The chopping power curves of each point on the chopper blade edge line before and after the optimization of structural parameters are generated. The results indicate that when the coordinate value of point A on the blade edge line on the Z axis is 0.7 m; the included angle between the bottom surface of the blade and the axis of the cutter roll is 6°. When the radius of the chopper is 0.11 m, the chopper can obtain the theoretical minimum chopping power. The analysis result of chopping power curve is the chopping power after structural parameter optimization is reduced by about 25.50% compared with that before optimization. The choppers before and after the optimization of structural parameters was trial manufactured and sequentially mounted on the performance test bench of the chopping system of the forage ramie harvester. The test results show the standard-length rate of ramie stalk chopped by the choppers before and after the optimization of structural parameters were 92.96% and 92.84%, respectively, which were extremely close to each other, indicating that the optimization of structural parameters has no influence on the chopping effect of the chopper. The chopping power of the chopper is reduced by 22.25% after optimization, which is close to the software analysis value (25.50%), indicating that the optimization result is accurate and reliable. This study can provide parameter foundation and an optimization method for lowering chopping power consumption of the chopper.

Minimum Cost for Reinforced Concrete Rectangular Beams with Parabolic Haunches

El objetivo de esta investigacion es presentar un modelo matematico para el diseno optimo de trabes de seccion transversal rectangular con cartelas parabolicas bajo el criterio de costo minimo tomando en cuenta el costo del concreto y costo de acero de refuerzo, y considerando las ecuaciones del reglamento (ACI 318S-19). Este modelo presenta las ecuaciones para dos tipos de cargas: Carga uniformemente distribuida y Carga concentrada localizada en cualquier parte de la trabe. Dos ejemplos han sido desarrollados por el modelo propuesto para ambos casos. Los resultados muestran que las trabes prismaticas para los dos casos tienen un costo total, un volumen total y un peso total mayor con respecto a las trabes no prismaticas. Por lo tanto, las trabes no prismaticas son mas economicas, tienen menos volumen y tambien tienen menos peso con respecto a las trabes prismaticas.

Optimal design of reinforced concrete beams for rectangular sections with straight haunches

Objective of this research is to present a mathematical model for optimal design of rectangular cross-section beams with straight haunches under the criterion of minimum cost considering the concrete cost and reinforcing steel cost, and taking into account the equations of the regulation (ACI 318S-14). This model presents the equations for a uniformly distributed load and a concentrated load located anywhere on the beam. Two examples are developed by the proposed model, one for uniformly distributed load and another for concentrated load showing the best solution for each case. The results show the following: a) The prismatic beams for uniformly distributed load have a total cost of the 8% greater, a total volume and a total weight of the 9% greater with respect to the non-prismatic beams; b) The prismatic beams for concentrated load have a total cost, a total volume and a total weight of the 6% greater with respect to the non-prismatic beams. The main conclusions are: For a smaller b width the optimal design for both models is presented. The non-prismatic beams are more economical, also these have less volume and less weight with respect to prismatic beams.

Optimal Design of Shafting System for Wind Turbine in Multi-cases

Based on a typical structure of the main shafting of wind turbine, a novel mathematical model for optimal design of the shafting system is presented for wind fields with different characteristics, in which the multi-objective functions are taken into account with the volume, weight and strength of the shafting. The constraint functions, including the geometric constraints and the performance constraints, are established by means of the ISO standards. The several cases for the wind turbine to work in the typical wind fields are mentioned, and the corresponding load spectrum of the shafting of the wind turbine and the corresponding multi-objective functions are discussed. Finally, a numerical example of optimal design of a shafting system is required, which indicates the validity of the optimization model and the algorithm.

Design on the Main-Axis in Big Power Inverted Umbrella Aeration Machine Based on Genetic Algorithms

Genetic Algorithms is a new method, which has good robustness in optimization design for complex system. In this paper, we make the mathematical model of optimization design for the main-axis in big power inverted umbrella aeration machine by studying Genetic Algorithms. Using coding method, we complete the optimization design of the main-axis in big power inverted umbrella aeration machine.

Study on Mechanical Design Optimization Based on Improved Particle Swarm Optimization Algorithm

In view of local optimization in particle swarm optimization algorithm (PSO algorithm), chaos theory was introduced to PSO algorithm in this paper. Plenty of populations were generated by using the ergodicity of chaotic motion. The uniformly distributed initial particles of the particle swarms were extracted from the populations according to the Euclidean distance between particles, so that the particles could uniformly distribute in the solution space. Local search was carried out on the optimal position of the particles during evolution, so as to improve the development capability of PSO algorithm and prevent its prematurity, thus enhancing its global optimizing capability. Then the improved PSO algorithm was applied to mechanical design optimization. With optimization design for two-stage gear reducer as the study object, objective function and constraint conditions were determined by building a mathematical model of optimization design, thus realizing optimization design. Simulation and comparison between the improved algorithm and unimproved algorithm show that improved PSO algorithm can optimize the optimization results of PSO algorithm at a faster convergence rate.

A Prevalent Error in Optimization Design of Helical Springs

This paper reveals the popular error and problem in optimization design of helical springs. Most of the engineers and researchers regard wire diameter d, mean coil diameter D and number of active coils n as design variables in the mathematical model of optimization design for helical springs. In fact, only two variables are independent variables in the three design variables. The dependent variable in the optimization design model influences the behavior of the systems to be optimized, which is also possible to calculate wrong results. This paper analyses relationship of wire diameter d, mean coil diameter D and number of active coils n. To take number of active coils n as the dependent variable is reasonable. It can lead to wrong results to take n as the independent variable. The right independent variables in optimization design of helical spring are wire diameter d and mean coil diameter D.

Optimization Design of Rectangular Cross-Sectional Wire Race Ball Bearing

Wire race ball bearing with large radial size and small axial size, saves space extremely, and is widely used in rotary devices of large machineries. This paper establishes a mathematical model of optimization design of rectangular cross-sectional wire race ball bearing,and considers minimum friction torque as objective function, and analyses constraints of contact intensity and design specifications of wire race ball bearing, and forges an optical design method that determines the number of balls, the diameter of ball, the contact angle and the diameter of ball center circle as optimal design parameters, to attain the purpose of extending bearings life. Comparing results of Optimization with original sample, the friction torque of ball that bears maximum load reduces by 10.20%. This method provides a reference for conducting further scientific researches on wear of wire race ball bearing.

Sequential Quadratic Programming Design of Gear Transmission

The optimization design of gear transmission based on MATLAB is studied for the purpose of finding a convenient and practical method. A mathematical model of optimization design is established in order to minimize the volume of gear transmission, the sequential quadratic programming method (SQP) is used to solve the nonlinear constrained optimization problems. The method how to solve gear parameter optimization base on optimization toolbox of MATLAB is introduced in detail. An optimization design example is given, the optimization result accords with the standard specifications of mechanical design and can be directly used. The result shows that this method is convenient and effective, and can simplify computer programming, is especially suitable for engineer.

Optimal Design of a Speed Reducer

The mathematical model for optimal design of a speed reducer is a generalized geometric programming problem that is non-convex and not easy be globally solved. This paper applies a deterministic approach including convexification strategies and piecewise linearization techniques to globally solve speed reducer design problems. A practical speed reducer design problem is solved to demonstrate that this study obtains a better solution than other methods.

Optimization Design of Transmission Gears Considering the Noise Factors on the Basis of Weighting Method

According to the traditional methods to design the gears in gearbox, the effect of the volume or noise of gears can not be involved. In order to design better gears, this paper used the simple and effective weighting method and considered the three aspects of minimizing the sum of volume of gears, the bending stress in tooth roots and the working noise to design gears. A mathematical model of optimal design of gears was established, where the contact fatigue strength on tooth surface, bending fatigue strength in tooth roots, tooth number, helix angle, big end modulus, overlap contact ratio, tooth width and so on were set as the constraint conditions and the big end modulus, the tooth width, helix angle of tooth width midpoint, and tooth number of the small bevel gear when transmission ratio is given were chosen as the design variables. Finally an example was solved. The results show that the present method can scheme out the gears of lower noise level.

Optimization design of spar cap layup for wind turbine blade

Based on the aerodynamic shape and structural form of the blade are fixed, a mathematical model of optimization design for wind turbine blade is established. The model is pursued with respect to minimum the blade mass to reduce the cost of wind turbine production. The material layup numbers of the spar cap are chosen as the design variables; while the demands of strength, stiffness and stability of the blade are employed as the constraint conditions. The optimization design for a 1.5MW wind turbine blade is carried out by combing above objective and constraint conditions at the action of ultimate flap wise loads with the finite element software ANSYS. Compared with the original design, the optimization design result achieves a reduction of 7.2% of the blade mass, the stress and strain distribution of the blade is more reasonable, and there is no occurrence of resonance, therefore its effectiveness is verified.

Optimal Design for Prestressed Structures Based on Continuous and Discrete Variables

The mathematical model of optimal design for prestressed structures is established and a two-level algorithm based on hybrid variables is proposed. At the first level, the prestressed forces are chosen to be the design variables and the optimal design for prestressed forces based on continuous variable is carried out. At the second level, the cross-sectional areas are chosen to be the design variables and the discrete sizing optimization is carried out under fixed prestressed forces, the local constrains are satisfied with one-dimensional search algorithm, the integral constrains are satisfied with the relative difference quotient algorithm, and the efficiency of the relative difference quotient algorithm is greatly improved by introducing the assumption of statically determinant structures. The numerical example shows the correctness and effectiveness of the method.

OPTIMAL ECONOMICAL DESIGN OF MAIN IRRIGATION PIPE NETWORK FOR IRRIGATION PROJECTS

Energy is required for pumping water in the irrigation pipe distribution networks. The need for this energy and its cost are continuously increasing due to the on-going expansion of the Arab countries in general and the Gulf countries in particular in using modern irrigation systems in their agricultural irrigation projects. Most pumped pipe-networks designed on hydraulic basis only without paying attention to the cost of power, thus huge loss in energy and capital needed for projects operation occur Sometimes. The design is based on economical basis without taking hydraulic aspects into consideration which results in low performance efficiency of the system or damage to the pipe network and consequently high maintenance costs. The paper presents computerized mathematical model for optimal design of main pipe distribution networks of sprinkler irrigation system using linear programming. The pressure head at the inlet of the pipe distribution network is assumed unknown, thus the objective is to minimize the sum of the initial cost of the pipe network and the cost of energy for pumping. The constraints included the minimum and maximum pressure head at all points along the pipes of the network in addition to the flow rates requirements within the network and at the inlet of each farm . The study revealed that using the proposed model in the design assuming unknown inlet pressure head to system has resulted in 9.32% saving in the total cost of the network compared to the existing design which is based on known inlet pressure head for a selected irrigation sector inside a large planned irrigation project near Mosul city, northern Iraq. Key words: Optimal Economical Design, Irrigation Pipe Network.

Optimum Design of Wheeled Loader's Steering Rubber Buffer Seat Based on ANSYS

Steering rubber buffer seat of loader is one of important methods to enhance the operating comfort of machine. This article detailed identified the design variables, constraint functions and the objective function of the rubber buffer seat's optimal design model. It combined with project experience and based on the analysis of rubber buffer seat's bearing features in the right, and established the correct mathematical model of optimal design in theory. Then, based on ANSYS software's optimized design module "Design Opt", completed set of all calculated parameters by the operations of alternate interface, thus created a rubber buffer seat's finite element model of optimization calculation. Optimized iterative calculations later, got the result of the final optimized design. After the optimized design, rubber buffer seat has been used in the market volume, it's very useful, so this design method is proved correct and reasonable.

Optimization Design of Walking Beam Based on Stiffness Constraint

The excessive deformation of walking beam which is used in automatic packaging line of cathode copperplates is analysed. The mathematical model of optimization design of the walking beam is established, using deflection less than 7mm as a constraint condition. The optimization is completed by COSMOSWorks and the most optimal deflection is 6.95mm, the most optimal mass of the walking beam is decreased 25.2%. The optimization also indicates that strength of the walking beam is surplus and further optimization is feasible.

Structural Optimization Design of Rear Axle Housing Excited by Dynamic Load

In order to obtain structural optimization design of rear banjo axle housing, a seven degree of freedom dynamic model of vehicle was presented. Based on the model, vehicle vibrating equations were presented. Random phase method was used to generate C grade road surface irregularity of time history that applied to vibrating equations to acquire dynamic load imposed on the banjo axle housing. A detailed CAD model of the housing was developed by using of UG software. The finite element model of the housing was built, and the stress and strain of the housing were obtained by using of ANSYS Workbench software. The mathematical model of optimal design was constructed and analyzed based on the result of finite element method. The optimization result shows that the weight of banjo axle housing can be reduced under satisficing the stress and strain condition that excited by dynamic load.

The Optimization Design of the Pressure Foot Mechanism in a Single-Sheet Feeder

Based on the analysis of the working principle of the pressure foot (the cam- linkage compound mechanism) in a single-sheet feeder, using VB to develop the design of cam mechanism, a mathematical model of optimization design is set-up in which the object function is the minimum deviation between the real locus of the pressure foot and the required locus. The resolving method for this model is also studied with one real example. It is practically valuable.

Optimization of a solar-assisted drying system for drying bananas

This paper presents a mathematical model for optimal design of a solar-assisted drying system for drying bananas. The optimization model consists of a simulation model of a solar-assisted drying system combined with an economic model. The simulation model is composed of two systems of differential equations: one for the collector and other for the drying cabinet. These systems of the differential equation were solved using the finite difference method. Values of the model parameters were determined experimentally. A computer program in FORTRAN was developed to simulate the performance of the drying system. The model was validated by comparing the simulation results with the experimental results and they were in good agreement. This simulation model was used for the optimization of the solar-assisted drying system. An economic model was formulated to calculate the annual drying cost. The optimization problem was defined as the optimization of the geometry and operational parameters of the drying system so as to minimize the drying cost per unit of dried product. Currently used collector area and the air recycle factor were considered as the parameters for basic mode of operation of the drying system. The adaptive pattern search technique was adopted to find the optimum values of the solar collector area and the recycle factor. The optimum values of the collector area and the recycle factor were found to be 26 m 2 and 90%, respectively. The computer program developed in this study can be used to optimize similar drying systems.

Analysis of optimality criteria and gradient projection methods for optimal structural design

Abstract A general mathematical model for optimal design of structural and mechanical systems is defined. The finite element techniques for analysis of these systems are incorporated into the model. Optimality conditions for the model are derived. It is shown that an analytical solution of the optimality conditions is impossible except for trivial design problems. Numerical methods for solving these optimality conditions are presented. A direct method based on the gradient projection concept is derived. Numerical aspects for the method are discussed. These include step size selection, calculation of Langrange multipliers, identification of dependent design sensitivity vectors of constraint functions, and convergence criterion. Both direct and indirect approaches require total derivatives of cost and various constraint functions with respect to design variables. This is accomplished by integrating into both the approaches the state space design sensitivity analysis that has proven to be very general and efficient. It is shown that other major calculations of the two approaches are essentially the same. Thus there is potential for continuous transition between various algorithms for structural optimization. Optimal solutions for two design examples are obtained by hybrid methods to show the potential for further development of these methods.