Sensitivity Analysis of the Conical-Shaped Equivalent Model of a Bolted Joint

2003 ◽  
Author(s):  
Noah D. Manring
Keyword(s):  
Sensitivity Analysis ◽  
Cone Angle ◽  
Equivalent Model ◽  
Design Parameters ◽  
Relative Importance ◽  
Bolted Joint ◽  
Governing Equations ◽  
Spring Rate ◽  
Rate Calculation ◽  
Proper Estimation

In this paper, the conical-shaped equivalent model for a bolted joint is considered. In particular, the governing equations for this model are made non-dimensional for the purposes of conducting sensitivity analysis. From this work, a plot of the dimensionless spring-rate of the clamped material is generated for all reasonable designs for which the conicalshaped equivalent model applies. The sensitivity analysis is then used to discuss the relative importance of estimating the proper model and design parameters and a maximum percent of uncertainty in the spring-rate calculation is also presented. It is shown in this discussion that the calculations are quite sensitive to a proper estimation of the cone angle (a model parameter) and that uncertainty within this calculation can range from 5 to 20%.

Sensitivity Analysis of the Conical-Shaped Equivalent Model of a Bolted Joint

2003 ◽  
Vol 125 (3) ◽  
pp. 642-646 ◽  
Author(s):  
Noah D. Manring
Keyword(s):  
Sensitivity Analysis ◽  
Cone Angle ◽  
Equivalent Model ◽  
Design Parameters ◽  
Relative Importance ◽  
Bolted Joint ◽  
Governing Equations ◽  
Spring Rate ◽  
Rate Calculation ◽  
Proper Estimation

In this paper, the conical-shaped equivalent model for a bolted joint is considered. In particular, the governing equations for this model are made non-dimensional for the purposes of conducting sensitivity analysis. From this work, a plot of the dimensionless spring-rate of the clamped material is generated for all reasonable designs for which the conical-shaped equivalent model applies. The sensitivity analysis is then used to discuss the relative importance of estimating the proper model and design parameters and a maximum percent of uncertainty in the spring-rate calculation is also presented. It is shown in this discussion that the calculations are quite sensitive to a proper estimation of the cone angle (a model parameter) and that uncertainty within this calculation can range from 5 to 20%.

scholarly journals A Shock Mitigation of Pedestrian-Vehicle Impact Using Active Hood Lift System: Deploying Time Investigation

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Tae-Hoon Lee ◽  
Gun-Ha Yoon ◽  
Seung-Bok Choi
Keyword(s):  
Response Time ◽  
Design Parameters ◽  
Passenger Vehicle ◽  
Governing Equations ◽  
Total Response Time ◽  
Shock Mitigation ◽  
Vehicle Impact ◽  
Driving Speed ◽  
Working Principle ◽  
Principal Design

This paper investigates the deploying time (or response time) of an active hood lift system (AHLS) of a passenger vehicle activated by gunpowder actuator. In this work, this is accomplished by changing principal design parameters of the latch part mechanism of the hood system. After briefly introducing the working principle of the AHLS operated by the gunpowder actuator, the governing equations of the AHLS are formulated for each different deploying motion. Subsequently, using the governing equations, the response time for deploying the hold lift system is determined by changing several geometric distances such as the distance from the rotational center of the pop-up guide to the point of the latch in the axial and vertical directions. Then, a comparison is made of the total response time to completely deploy the hood lift system with the existing conventional AHLS and proposed AHLS. In addition, the workable driving speed of the proposed AHLS is compared with the conventional one by changing the powder volume of the actuator.

scholarly journals CONCEPTUAL DESIGN FOR ASSEMBLY IN AEROSPACE INDUSTRY: SENSITIVITY ANALYSIS OF MATHEMATICAL FRAMEWORK AND DESIGN PARAMETERS

2021 ◽  
Vol 1 ◽  
pp. 731-740
Author(s):  
Giovanni Formentini ◽  
Claudio Favi ◽  
Claude Cuiller ◽  
Pierre-Eric Dereux ◽  
Francois Bouissiere ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Conceptual Design ◽  
Design Parameters ◽  
Design For Assembly ◽  
Mathematical Framework ◽  
Commercial Aircraft ◽  
System Architectures ◽  
Complex Engineering ◽  
Aircraft System ◽  
Definition Of

AbstractOne of the most challenging activity in the engineering design process is the definition of a framework (model and parameters) for the characterization of specific processes such as installation and assembly. Aircraft system architectures are complex structures used to understand relation among elements (modules) inside an aircraft and its evaluation is one of the first activity since the conceptual design. The assessment of aircraft architectures, from the assembly perspective, requires parameter identification as well as the definition of the overall analysis framework (i.e., mathematical models, equations).The paper aims at the analysis of a mathematical framework (structure, equations and parameters) developed to assess the fit for assembly performances of aircraft system architectures by the mean of sensitivity analysis (One-Factor-At-Time method). The sensitivity analysis was performed on a complex engineering framework, i.e. the Conceptual Design for Assembly (CDfA) methodology, which is characterized by level, domains and attributes (parameters). A commercial aircraft cabin system was used as a case study to understand the use of different mathematical operators as well as the way to cluster attributes.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Daniel Dopico
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Automatic Differentiation ◽  
Time Integration ◽  
General Purpose ◽  
Contact Forces ◽  
Design Parameters ◽  
Computational Techniques ◽  
Computationally Efficient ◽  
Integration Algorithm

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

2007 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
The State ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
State Variables ◽  
Sensitivity Coefficients ◽  
Design Variables

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

Analytical Derivatives Technology for Parametric Shape Design and Analysis in Structural Applications

2006 ◽  
Author(s):  
Srikanth Akkaram ◽  
Jean-Daniel Beley ◽  
Bob Maffeo ◽  
Gene Wiggs
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Automatic Differentiation ◽  
Thermal Response ◽  
Aircraft Engine ◽  
Design Parameters ◽  
Shape Design ◽  
Computer Simulation Model ◽  
Structural Applications ◽  
Analytical Derivatives

The ability to perform and evaluate the effect of shape changes on the stress, modal and thermal response of components is an important ingredient in the ‘design’ of aircraft engine components. The classical design of experiments (DOE) based approach that is motivated from statistics (for physical experiments) is one of the possible approaches for the evaluation of the component response with respect to design parameters [1]. Since the underlying physical model used for the component response is deterministic and understood through a computer simulation model, one needs to re-think the use of the classical DOE techniques for this class of problems. In this paper, we explore an alternate sensitivity analysis based technique where a deterministic parametric response is constructed using exact derivatives of the complex finite-element (FE) based computer models to design parameters. The method is based on a discrete sensitivity analysis formulation using semi-automatic differentiation [2,3] to compute the Taylor series or its Pade equivalent for finite element based responses. Shape design or optimization in the context of finite element modeling is challenging because the evaluation of the response for different shape requires the need for a meshing consistent with the new geometry. This paper examines the differences in the nature and performance (accuracy and efficiency) of the analytical derivatives approach against other existing approaches with validation on several benchmark structural applications. The use of analytical derivatives for parametric analysis is demonstrated to have accuracy benefits on certain classes of shape applications.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

scholarly journals Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Dynamics ◽  
Multibody Systems ◽  
Real Life ◽  
Design Parameters ◽  
Vehicle Model ◽  
Adjoint Sensitivity ◽  
Penalty Formulation ◽  
Sensitivity Approach ◽  
Dynamic Performance Analysis

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline makes it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization for multibody systems. In this paper, we focus on gradient-based optimization in order to find local minima. Gradients are calculated efficiently via adjoint sensitivity analysis techniques. Current approaches have limitations in terms of efficiently performing sensitivity analysis for complex systems with respect to multiple design parameters. To improve the state of the art, the adjoint sensitivity approach of multibody systems in the context of the penalty formulation is developed in this study. The new theory developed is then demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14 degree of freedom (DOF) vehicle model. The five-bar mechanism is used to validate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and optimization for large and complex multibody systems with respect to multiple design parameters with high efficiency.

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