Optimal Design of Rack-and-Pinion Steering Linkages

1983 ◽  
Vol 105 (2) ◽  
pp. 220-226 ◽  
Author(s):  
C. E. Zarak ◽  
M. A. Townsend
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Objective Function ◽  
Full Range ◽  
Mathematical Representation ◽  
Optimal Solutions ◽  
Steering Angle ◽  
Design Synthesis ◽  
Constraint Set ◽  
The Difference

A mathematical model is developed for the design synthesis of rack-and-pinion steering linkages. The general objective is to minimize the difference between the steering centers over the full range of steering angle inputs while fitting into a reasonable space. Because there is a substantial amount of design art in these systems and the mathematical representation is not clear, the model, constraints, and objective actually “evolve” to the eventual desired form. The problem has multiple optima, and practical and heuristic considerations are used to choose suboptimal but more realistic solutions, once satisfactory optimal solutions are identified. These involve manipulation of the objective function, constraint set, and intitial guesses. Both leading and trailing link designs are considered, the former being slightly better. Limitations of the model are also presented.

scholarly journals FEATURES OF FINDING OPTIMAL SOLUTIONS IN NETWORK PLANNING

2020 ◽  
pp. 82-96
Author(s):  
Olena Domina
Keyword(s):  
Objective Function ◽  
Response Surface ◽  
Canonical Transformation ◽  
Network Planning ◽  
Experiment Planning ◽  
Optimal Solutions ◽  
Network Diagram ◽  
The Difference ◽  
Input Variables ◽  
Network Diagrams

The object of research is a test network diagram, in relation to which the task of minimizing the objective function qmax/qmin→min is posed, which requires maximizing the uniformity of the workload of personnel when implementing an arbitrary project using network planning. The formulation of the optimization problem, therefore, assumed finding such times of the beginning of the execution of operations, taken as input variables, in order to ensure the minimum value of the ratio of the peak workload of personnel to the minimum workload. The procedure for studying the response surface proposed in the framework of RSM is described in relation to the problem of optimizing network diagrams. A feature of this procedure is the study of the response surface by a combination of two methods – canonical transformation and ridge analysis. This combination of methods for studying the response surface allows to see the difference between optimal solutions in the sense of "extreme" and in the sense of "best". For the considered test network diagram, the results of the canonical transformation showed the position on the response surface of the extrema in the form of maxima, which is unacceptable for the chosen criterion for minimizing the objective function qmax/qmin→min. It is shown that the direction of movement towards the best solutions with respect to minimizing the value of the objective function is determined on the basis of a parametric description of the objective function and the restrictions imposed by the experiment planning area. A procedure for constructing nomograms of optimal solutions is proposed, which allows, after its implementation, to purposefully choose the best solutions based on the real network diagrams of your project

Single Spur Gear Reducer Optimization Design Mathematical Modeling

2013 ◽  
Vol 273 ◽  
pp. 198-202
Author(s):  
Yu Xia Wang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Optimal Design ◽  
Objective Function ◽  
Optimization Design ◽  
Spur Gear ◽  
Design Parameters ◽  
Constraint Function ◽  
Design Variables ◽  
The Mathematical Model

In a given power P, number of teeth than u, input speed and other technical conditions and requirements, find out a set of used a economic and technical indexes reach the optimal design parameters, realize the optimization design of the reducer, This paper determined unipolar standard spur gear reducer design optimization of the design variables, and then determine the objective function, determining constraint function, so as to establish the mathematical model.

The Equivalent Variation and Optimization Design of the Operating Mechanism of the Harvester

2013 ◽  
Vol 373-375 ◽  
pp. 7-11
Author(s):  
Lei Lu ◽  
Kang Luo ◽  
Qiang Wang ◽  
Hua Chen
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Optimization Design ◽  
Engineering Problem ◽  
Operating Mechanism ◽  
Brake Pedal ◽  
Optimal Solutions ◽  
The Operating Mechanism ◽  
The Mathematical Model ◽  
Equivalent Mechanism

In this paper, an equivalent mechanism is obtained by means of optimal design to overcome the drawbacks of an existing brake pedal operating mechanism in a harvester. After establishing the mathematical model, we obtain the optimal design model, including the objective and constraint functions. Consequently the local optimal solutions are worked out, resulting in a solution for the applied engineering problem.

Optimal Design of Steering Geometry Using Genetic Algorithm Based on Binomial Weight Function

2013 ◽  
Vol 850-851 ◽  
pp. 363-367
Author(s):  
Jin Hai Wang ◽  
Jian Wei Yang ◽  
Wan He Zhu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Optimal Design ◽  
Weight Function ◽  
Target Function ◽  
Absolute Error ◽  
Function Model ◽  
Steering Angle ◽  
Design Variables ◽  
Angle Of Rotation

For integral steering geometry, its spatial structure rationally is simplified. Based on it, mathematical model of integral front steering geometry that is similar with the reality of elastic tires is built. For ensuring design variables, the target function model is established by the inner wheel steering angle of rotation absolute error and binomial weight function. And the problem is optimized using the Genetic Algorithm in MATLAB. Finally, optimization algorithm is verified by a real example of optimization of econopower car.

Optimization Design of Large-Scale Cross-Roller Slewing Bearing Used in Special Propeller

2011 ◽  
Vol 48-49 ◽  
pp. 787-792 ◽  
Author(s):  
Gang Zhang ◽  
Xue Zhang ◽  
Kai Feng Zhou ◽  
Juan Ruan ◽  
De De Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Objective Function ◽  
Design Process ◽  
Optimization Design ◽  
Large Scale ◽  
Function Optimization ◽  
Design Model ◽  
Slewing Bearing ◽  
The Mathematical Model

According to the working requirement of large-scale cross roller slewing bearing used in special propeller, an optimal design model which includes objective function, optimization variables and constraints is established, and uses genetic toolbox of the Matlab software to solve the mathematical model. An example shows that the bearing’s life is improved significantly by the optimization. It indicates that the optimization design has some guidance significance in the design process of the slewing bearing.

scholarly journals FEATURES OF FINDING OPTIMAL SOLUTIONS IN NETWORK PLANNING

2020 ◽  
pp. 82-96
Author(s):  
Olena Domina
Keyword(s):  
Objective Function ◽  
Response Surface ◽  
Canonical Transformation ◽  
Network Planning ◽  
Experiment Planning ◽  
Optimal Solutions ◽  
Network Diagram ◽  
The Difference ◽  
Input Variables ◽  
Network Diagrams

The object of research is a test network diagram, in relation to which the task of minimizing the objective function qmax/qmin→min is posed, which requires maximizing the uniformity of the workload of personnel when implementing an arbitrary project using network planning. The formulation of the optimization problem, therefore, assumed finding such times of the beginning of the execution of operations, taken as input variables, in order to ensure the minimum value of the ratio of the peak workload of personnel to the minimum workload. The procedure for studying the response surface proposed in the framework of RSM is described in relation to the problem of optimizing network diagrams. A feature of this procedure is the study of the response surface by a combination of two methods – canonical transformation and ridge analysis. This combination of methods for studying the response surface allows to see the difference between optimal solutions in the sense of "extreme" and in the sense of "best". For the considered test network diagram, the results of the canonical transformation showed the position on the response surface of the extrema in the form of maxima, which is unacceptable for the chosen criterion for minimizing the objective function qmax/qmin→min. It is shown that the direction of movement towards the best solutions with respect to minimizing the value of the objective function is determined on the basis of a parametric description of the objective function and the restrictions imposed by the experiment planning area. A procedure for constructing nomograms of optimal solutions is proposed, which allows, after its implementation, to purposefully choose the best solutions based on the real network diagrams of your project

Effect of Inner and Outer Wheels Driving Force Control on Small Electric Vehicle

2020 ◽  
Vol 17 (4) ◽  
pp. 8246-8254
Author(s):  
K. Shibazaki ◽  
H. Nozaki
Keyword(s):  
Control System ◽  
Angular Velocity ◽  
Electric Vehicle ◽  
Force Constant ◽  
Force Control ◽  
Driving Force ◽  
Vehicle Control ◽  
Steering Angle ◽  
Force Control System ◽  
The Difference

In this study, in order to improve steering stability during turning, we devised an inner and outer wheel driving force control system that is based on the steering angle and steering angular velocity, and verified its effectiveness via running tests. In the driving force control system based on steering angle, the inner wheel driving force is weakened in proportion to the steering angle during a turn, and the difference in driving force is applied to the inner and outer wheels by strengthening the outer wheel driving force. In the driving force control (based on steering angular velocity), the value obtained by multiplying the driving force constant and the steering angular velocity,  that differentiates the driver steering input during turning output as the driving force of the inner and outer wheels. By controlling the driving force of the inner and outer wheels, it reduces the maximum steering angle by 40 deg and it became possible to improve the cornering marginal performance and improve the steering stability at the J-turn. In the pylon slalom it reduces the maximum steering angle by 45 deg and it became possible to improve the responsiveness of the vehicle. Control by steering angle is effective during steady turning, while control by steering angular velocity is effective during sharp turning. The inner and outer wheel driving force control are expected to further improve steering stability.

Optimization Research on Dynamic Balance of Spatial Engine under Limiting Shaking Moment

2009 ◽  
Vol 626-627 ◽  
pp. 693-698
Author(s):  
Yong Yong Zhu ◽  
S.Y. Gao
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Kinetic Analysis ◽  
Optimization Design ◽  
Design Method ◽  
Dynamic Balance ◽  
Optimized Design ◽  
Design Variables ◽  
The Mathematical Model ◽  
Shaking Moment

Dynamic balance of the spatial engine is researched. By considering the special wobble-plate engine as the model of spatial RRSSC linkages, design variables on the engine structure are confirmed based on the configuration characters and kinetic analysis of wobble-plate engine. In order to control the vibration of the engine frame and to decrease noise caused by the spatial engine, objective function is choosed as the dimensionless combinations of the various shaking forces and moments, the restriction condition of which presents limiting the percent of shaking moment. Then the optimization design is investigated by the mathematical model for dynamic balance. By use of the optimization design method to a type of wobble-plate engine, the optimization process as an example is demonstrated, it shows that the optimized design method benefits to control vibration and noise on the engines and improve the performance practically and theoretically.

Optimal design and mathematical model applied to establish bioassay programs

2006 ◽  
Vol 123 (4) ◽  
pp. 457-463 ◽  
Author(s):  
G. Sánchez ◽  
J. M. Rodríguez-Díaz
Keyword(s):  
Mathematical Model ◽  
Optimal Design

Multi-Object Multi-Discipline Probabilistic Design of High-Pressure Turbine Blade-Tip Radial Running Clearance

2013 ◽  
Vol 572 ◽  
pp. 551-554
Author(s):  
Wen Zhong Tang ◽  
Cheng Wei Fei ◽  
Guang Chen Bai
Keyword(s):  
Mathematical Model ◽  
High Pressure ◽  
Optimal Design ◽  
Mechanical System ◽  
High Accuracy ◽  
Probabilistic Design ◽  
High Pressure Turbine ◽  
Surface Method ◽  
Blade Tip ◽  
The Mathematical Model

For the probabilistic design of high-pressure turbine (HPT) blade-tip radial running clearance (BTRRC), a distributed collaborative response surface method (DCRSM) was proposed, and the mathematical model of DCRSM was established. From the BTRRC probabilistic design based on DCRSM, the static clearance δ=1.865 mm is demonstrated to be optimal for the BTRRC design considering aeroengine reliability and efficiency. Meanwhile, DCRSM is proved to be of high accuracy and efficiency in the BTRRC probabilistic design. The present study offers an effective way for HPT BTRRC dynamic probabilistic design and provides also a promising method for the further probabilistic optimal design of complex mechanical system.

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