Response Surface Algorithms for Engine Mount Optimization in Motorcycles

2009 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra
Keyword(s):  
Response Surface ◽  
Optimization Problem ◽  
Vibration Isolation ◽  
Design Space ◽  
Substantial Reduction ◽  
Response Surface Model ◽  
Fractional Factorial ◽  
Surface Model ◽  
Design Variables ◽  
Engine Mount

This paper presents a Response Surface Modeling (RSM) approach for solving the engine mount optimization problem for a motorcycle application. A theoretical model that captures the structural dynamics of a motorcycle engine mount system is first used to build the response surface model. The response surface model is then used to solve the engine mount optimization problem for enhanced vibration isolation. Design of Experiments (DOE), full factorial and fractional factorial formulations, are used to construct the governing experiments. Normal probability plots are used to determine the statistical significance of the variables and the significant variables are then used to build the response surface. The design variables for the engine mount optimization problem include mount stiffness, position vectors and orientation vectors. It is seen that RSM leads to a substantial reduction in computational effort and yields a simplified input-output relationship between the variables of interest. However, as the number of design variables increases and as the response becomes irregular, conventional use of RSM is not viable. Two algorithms are proposed in this paper to overcome the issues associated with the size of the governing experiments and problems associated with modeling of the orientation variables. The proposed algorithms divide the design space into sub-regions in order to manage the size of the governing experiments without significant confounding of variables. An iterative procedure is used to overcome high response irregularity in the design space, particularly due to orientation variables.

Response Surface Methodology Models for Engine Mount Optimization in Motorcycles

2006 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra ◽  
Timothy G. Hunter
Keyword(s):  
Response Surface Methodology ◽  
Theoretical Model ◽  
Response Surface ◽  
Optimization Problem ◽  
Vibration Isolation ◽  
Statistical Significance ◽  
Substantial Reduction ◽  
Fractional Factorial ◽  
Engine Mount ◽  
Rsm Model

This paper presents Response Surface Methodology (RSM) modeling techniques to solve the engine mount optimization problem for motorcycle applications. A theoretical model that represents the structural dynamics of the engine mount system in motorcycles is first used to build the RSM model. The RSM model is then used to solve the engine mount optimization problem to enhance vibration isolation. This leads to a substantial reduction in computational effort and simplifies the governing model, yielding an input-output relationship between the variables of interest. Design of Experiments (DOE) techniques are used to build the RSM model from the theoretical model. Full factorial and fractional factorial formulations are used to construct the governing experiments. Normal probability plots are used to determine the statistical significance of the resulting coefficients. The statistically significant variables are then used to build the response surface. The design variables for the engine mount optimization problem include mount stiffness, position and orientation vectors. The influence of the orientation variables is highly non-linear and is difficult to model by using a response surface consisting of lower order terms only. Two separate algorithms are proposed to overcome this problem and the results from the RSM models are compared to those from the theoretical model.

Kriging Modeling for Engine Mount Optimization in Motorcycles

2009 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra
Keyword(s):  
Correlation Function ◽  
Theoretical Model ◽  
Optimization Problem ◽  
Design Space ◽  
Substantial Reduction ◽  
Kriging Model ◽  
Surrogate Models ◽  
Fractional Factorial ◽  
Engine Mount ◽  
Selection Of

This paper addresses two critical aspects associated with the successful use of a Kriging model for solving the engine mount optimization problem. The two aspects are the selection of an appropriate correlation function and the use of a suitable governing design for sampling within the design space. The selection of a correlation function is critical in building a Kriging model since the function should accurately represent the behavior of the response over the entire design space. Whereas the Gaussian correlation function is most commonly used for building Kriging models, it is generally suitable for only those processes or systems which have a relatively smooth response within the entire design space. The correlation functions that have been evaluated in this paper for building the Kriging models for solving the engine mount optimization problem are as follows: Exponential, Linear Spline, Matern’s 3/2, Matern’s 5/2 and Gaussian. Three types of experimental designs – Fractional Factorial, D-optimal and Latin Hypercube, have been used to select the sampling points for making simulation runs in order to build the Kriging models. A theoretical model that represents the dynamics of the engine mount system in a motorcycle application has been used to build all the surrogate models. The Kriging models are then used to solve the engine mount optimization problem for enhanced vibration isolation with mount stiffness, mount orientation and mount location as the design variables. The optimization results of the Kriging models are compared to the results of the theoretical model. It is found that the D-optimal design in conjunction with Matern’s 3/2 correlation function provides the best results. This can be attributed to the high irregularity of the response function in the design space, especially due to the influence of orientation variables. The use of the surrogate Kriging model simplifies the governing model and leads to a substantial reduction in computational effort for solving the optimization problem. Based on the results, it can be concluded that the Kriging modeling technique can be successfully used to build surrogate models for the engine mount problem for design iterations as well as for design optimization if the correlation function and the governing design are judiciously chosen.

Engine Mount Optimization for Vibration Isolation in Motorcycles

2006 ◽  
Author(s):  
Sudhir Kaul ◽  
Anoop K. Dhingra ◽  
Timothy G. Hunter
Keyword(s):  
Optimization Problem ◽  
Vibration Isolation ◽  
Total Force ◽  
Engine Mounts ◽  
The Road ◽  
Design Variables ◽  
Swing Arm ◽  
Engine Mount ◽  
Six Degree Of Freedom

This paper presents a comprehensive model to capture the dynamics of a motorcycle system in order to evaluate the quality of vibration isolation. The two main structural components in the motorcycle assembly - the frame and the swing-arm - are modeled using reduced order finite element models; the power-train assembly is modeled as a six degree-of-freedom (DOF) rigid body connected to the frame through the engine mounts and to the swing-arm through a shaft assembly. The engine mounts are modeled as tri-axial spring-damper systems. Models of the front-end assembly as well as front and rear tires are also included in the overall model. The complete vehicle model is used to solve the engine mount optimization problem so as to minimize the total force transmitted to the frame while meeting packaging and other side constraints. The mount system parameters - stiffness, position and orientation vectors - are used as design variables for the optimization problem. The imposed loads include forces and moments due to engine imbalance as well as loads transmitted due to irregularities in the road surface through the tire patch.

Optimization Design of Pressure Shell in Underwater Vehicle Based on Response Surface Model

2009 ◽  
Vol 419-420 ◽  
pp. 89-92
Author(s):  
Zhuo Yi Yang ◽  
Yong Jie Pang ◽  
Zai Bai Qin
Keyword(s):  
Finite Element ◽  
Response Surface ◽  
Optimization Design ◽  
Engineering Application ◽  
Element Model ◽  
Response Surface Model ◽  
Design Stage ◽  
Surface Model ◽  
Design Variables ◽  
Structure Strength

Cylinder shell stiffened by rings is used commonly in submersibles, and structure strength should be verified in the initial design stage considering the thickness of the shell, the number of rings, the shape of ring section and so on. Based on the statistical techniques, a strategy for optimization design of pressure hull is proposed in this paper. Its central idea is that: firstly the design variables are chosen by referring criterion for structure strength, then the samples for analysis are created in the design space; secondly finite element models corresponding to the samples are built and analyzed; thirdly the approximations of these analysis are constructed using these samples and responses obtained by finite element model; finally optimization design result is obtained using response surface model. The result shows that this method that can improve the efficiency and achieve optimal intention has valuable reference information for engineering application.

Thermal Optimization of a Microchannel Heat Sink With Trapezoidal Cross Section

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Shape Optimization ◽  
Thermal Resistance ◽  
Objective Function ◽  
Response Surface ◽  
Heat Sink ◽  
Fractional Factorial ◽  
Surface Model ◽  
Microchannel Heat Sink ◽  
Reference Shape ◽  
Design Variables

A microchannel heat sink shape optimization has been performed using response surface approximation. Three design variables related to microchannel width, depth, and fin width are selected for optimization, and thermal resistance has been taken as objective function. Design points are chosen through a three-level fractional factorial design of sampling methods. Navier–Stokes and energy equations for steady, incompressible, and laminar flow and conjugate heat transfer are solved at these design points using a finite volume solver. Solutions are carefully validated with the analytical and experimental results and the values of objective function are calculated at the specified design points. Using the numerically evaluated objective-function values, a polynomial response surface model is constructed and the optimum point is searched by sequential quadratic programming. The process of shape optimization greatly improves the thermal performance of the microchannel heat sink by decreasing thermal resistance of about 12% of the reference shape. Sensitivity of objective function to design variables has been studied to utilize the substrate material efficiently.

scholarly journals Central Composite Design for Response Surface Methodology and Its Application in Pharmacy

2021 ◽  
Author(s):  
Sankha Bhattacharya
Keyword(s):  
Central Composite Design ◽  
Response Surface ◽  
Response Surface Model ◽  
Fractional Factorial ◽  
Surface Model ◽  
Experimental Conditions ◽  
Design Models ◽  
Central Composite

The central composite design is the most commonly used fractional factorial design used in the response surface model. In this design, the center points are augmented with a group of axial points called star points. With this design, quickly first-order and second-order terms can be estimated. In this book chapter, different types of central composite design and their significance in various experimental design were clearly explained. Nevertheless, a calculation based on alpha (α) determination and axial points were clearly described. This book chapter also amalgamates recently incepted central composite design models in various experimental conditions. Finally, one case study was also discussed to understand the actual inside of the central composite design.

Optimization of Double Pivot Suspension Kingpin Axis during Steering

2014 ◽  
Vol 551 ◽  
pp. 232-236
Author(s):  
Tian Ze Shi ◽  
Deng Feng Wang ◽  
Shu Ming Chen ◽  
Hong Liang Dong
Keyword(s):  
Response Surface ◽  
Response Surface Model ◽  
Prototype Model ◽  
Surface Model ◽  
Suspension Parameters ◽  
Design Variables ◽  
Kingpin Axis ◽  
Relationship Of ◽  
The Relationship ◽  
Suspension Performance

A double pivot suspension used for in-wheel motor electric vehicle was designed, and the virtual prototype model of the suspension assembly was build. The suspension parameters changed greatly during steering. In order to solve this problem, this paper proposed a non-linear response surface model to fit the relationship of suspension parameters and design variables. An optimization scheme was designed based on the response surface model. The suspension performance was improved significantly using optimized variables.

Multi-Objective Optimization Design of Flexible Risers Based on Bi-Scale Response Surface Models

2018 ◽  
Author(s):  
Zhixun Yang ◽  
Jun Yan ◽  
Svein Sævik ◽  
Luqing Zhen ◽  
Naiquan Ye ◽  
...  
Keyword(s):  
Response Surface ◽  
Response Surface Model ◽  
Surface Model ◽  
Flexible Riser ◽  
Optimization Framework ◽  
Scale Response ◽  
Design Variables ◽  
Global Configuration ◽  
Flexible Risers ◽  
Scale Optimization

An optimized flexible riser design not only requests that the stress of local cross-section shouldn’t exceed the allowable strength, but also can be compliant with the floater to improve the fatigue life. It should be particularly pointed out that the flexible riser is a typical multi-scale system, which consists of the local cross-sectional scale and the global configuration scale, which differentiates each other a lot from their geometrical scales. A bi-scale response surface model is established to perform the optimized design of flexible risers by considering the parameters of local cross-sections and global configurations simultaneously. The response surface model can be an effective surrogate model to integrate the local and global responses into one loop so that the computational efficiency can be increased significantly. In the bi-scale response model, design variables of a flexible riser are extracted and defined at both the local sectional scale and global configuration scale. Sensitivity analyses of the two objectives, ultimate tension and bending strength on the design variables are then deduced to establish the bi-scale optimization framework through the response surface methodology. Finally, the optimization framework is implemented on a flexible riser with lazy-wave configuration which is considered as a case study. The properties of the optimized flexible risers are compared with those without the optimization. It is found that the ultimate load bearing capacity and fatigue life of the optimized flexible riser are improved significantly. Moreover, the feasibility and effectiveness of the bi-scale optimization strategy are verified through numerical simulations, which indicates that the bi-scale response surface optimization methodology provides a new thought and approach to explore the design potential of flexible risers.

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