Assembly Variation Analysis of Incompletely Positioned Macpherson Suspension Systems Considering Vehicle Load Change

2020 ◽  
Vol 143 (5) ◽  
Author(s):  
Zhihua Niu ◽  
Sun Jin ◽  
Zhimin Li
Keyword(s):  
Compliant Mechanisms ◽  
Error Rates ◽  
Variation Analysis ◽  
Equilibrium Equations ◽  
Suspension Systems ◽  
Assembly Shop ◽  
Automobile Factory ◽  
Adams Simulation ◽  
Wheel Alignment ◽  
Process Strategy

Abstract The assembly precision of wheel alignment parameters is vital to vehicle handling stability. Due to the vertical wheel displacement and compliant components in suspension systems, it is difficult to assemble qualified vehicles with proper wheel alignment parameters. In the assembly shop of the automobile factory, the adjustment of wheel alignment parameters is the most time-consuming process because it relies on trial and error. In order to provide a theoretical guidance to the precision control of wheel alignment parameters, this paper extends the theory of equilibrium equations of incremental forces (EEIF) to 3D compliant mechanisms. Constraint equations of kinematic joints are adopted to express the spatial relationships of different parts. A couple of fixed and floating joint coordinate systems (CSs) are used together to represent deviations of compliant components. The impacts of suspension part deviations on vertical wheel displacement and assembly deformations are well illustrated by such approach. Accuracy of the proposed method is verified by comparing with ADAMS simulation. The results show that the error rates of the 3D EEIF method are less than 5%. Furthermore, statistical assembly variation analysis of a Macpherson suspension is accomplished by using the proposed method and an optimized process strategy is put forward.

Equilibrium Equations of Incremental Forces and its Application in Assembly Variation Analysis of Compliant Structures

2019 ◽  
Author(s):  
Zhihua Niu ◽  
Zhimin Li ◽  
Sun Jin ◽  
Xinxin Li
Keyword(s):  
Compliant Mechanisms ◽  
Theory Development ◽  
Coefficient Matrix ◽  
Sensitivity Coefficient ◽  
Manufacturing Cost ◽  
Variation Analysis ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Compliant Joints ◽  
Internal Relationships

Abstract Assembly variation analysis is used to handle the tradeoff between product performance and manufacturing cost. Traditionally, the assembly variation analysis of compliant structures is achieved by combining finite element analysis (FEA) and Monte Carlo simulation. Although the distribution of assembly dimensions can be obtained by such a process, the internal relationships between component deviations and assembly precisions are hidden in the reduplicative computational process. This study aims to shed light on the internal relationships between component deviations and assembly deformations of compliant mechanisms by Equilibrium Equations of Incremental Forces (EEIF). Dimensional deviation is an additional part to theoretical dimension, so does incremental force is to theoretical assembly load. EEIF is the bridge between dimensional deviations and incremental forces. This paper extends the application area of EEIF from compliant joints to compliant beams. The beginning of this paper reviews mainstream assembly variation analysis methods and the application of compliant mechanisms. Following is the basic conceptions about Equilibrium Equations of Incremental Forces. In the theory development part, compliant joints and compliant beams are discussed respectively. Precision of the method is verified by comparing it with an ADAMS/Flex model. Then, the output sensitivity coefficient matrix is used to conduct statistical assembly variation analysis for compliant mechanisms.

Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

2005 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Design Requirements ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.

Assembly variation analysis of compliant mechanisms by combining direct linearization method and Lagrange’s equations

2019 ◽  
Vol 39 (4) ◽  
pp. 740-751 ◽  
Author(s):  
Zhihua Niu ◽  
Zhimin Li ◽  
Sun Jin ◽  
Tao Liu
Keyword(s):  
Compliant Mechanisms ◽  
Linearization Method ◽  
Application Area ◽  
Variation Analysis ◽  
Content Type ◽  
Compliant Joints ◽  
Lagrange’S Equations ◽  
Element Simulation ◽  
Direct Linearization ◽  
Lagrange's Equations

Purpose This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis procedure extends the application area of direct linearization method (DLM) to compliant mechanisms and also illustrates the dimensional interaction within multi-loop compliant structures. Design/methodology/approach By applying DLM to both geometrical equations and Lagrange’s equations of the second kind, an analytical deviation modeling method for mechanisms with compliant joints are proposed and further used for statistical assembly variation analysis. The precision of this method is verified by comparing it with finite element simulation and traditional DLM. Findings A new modeling method is proposed to represent kinematic relationships between joint deformations and parts/components deviations. Based on a case evaluation, the computational efficiency is improved greatly while the modeling accuracy is maintained at more than 94% rate comparing with the benchmark finite element simulation. Originality/value The Equilibrium Equations of Incremental Forces derived from Lagrange’s equations are proposed to quantitatively represent the relationships between manufactured deviations and assembly deformations. The present method extends the application area of DLM to compliant structures, such as automobile suspension systems and some Micro-Electro-Mechanical-Systems.

Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Takayuki Yamada ◽  
Shintaro Yamasaki ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Structural Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Equilibrium Equations ◽  
Thermal Actuators ◽  
Level Set Function ◽  
Initialization Scheme ◽  
Set Function

Compliant mechanisms are designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in micro-electromechanical systems by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated or are subjected to an electric potential. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the finite element method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

Design of Three New Cam-Based Constant-Force Mechanisms

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Javier López-Martínez ◽  
Daniel García-Vallejo ◽  
Francisco Manuel Arrabal-Campos ◽  
Jose Manuel Garcia-Manrique
Keyword(s):  
Compliant Mechanisms ◽  
Rolling Friction ◽  
Design Guidelines ◽  
Design Parameters ◽  
Constant Force ◽  
Equilibrium Equations ◽  
Constant Input ◽  
Friction Forces ◽  
Input Force ◽  
Cam Profile

Constant-force mechanisms are designed to keep a constant or nearly constant input force along a prescribed stroke of the mechanism. The implementation of this kind of mechanisms has been approached in literature using compliant mechanisms or through a certain combination of springs and nonlinear transmissions. In this work, three new constant-force mechanisms based on the use of springs, rollers, and cams are presented and analyzed. The rolling friction forces between the rollers and the cam are included in the force equilibrium equations and considered in the integration of the cam profile. The influence of the friction force on the input force as well as the design parameters involved is studied based on numerical techniques and simulations. In fact, the results evidence that to obtain a precise constant-force mechanism, rolling friction forces must be considered in the cam profile definition. The main design guidelines for the three constant-force mechanisms proposed are described.

Constraint-Force-Based (CFB) Modeling of Compliant Mechanisms

2015 ◽  
Author(s):  
Haiyang Li ◽  
Guangbo Hao
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Modeling Method ◽  
Static Equilibrium ◽  
Constraint Forces ◽  
Equilibrium Equations ◽  
Constraint Force ◽  
Element Analysis ◽  
External Forces ◽  
Force Equilibrium

Numerous works have been done on modeling compliant modules or joints, and the closed-form models of many widely-used compliant modules have been developed. However, the modeling of complex compliant mechanisms with considering external forces is still a challenging work. This paper introduces a constraint-force-based method to model compliant mechanisms. A compliant mechanism can be regarded as the combination of rigid stages and compliant modules. If a compliant mechanism is at static equilibrium under the influence of a series of external forces, all the rigid stages are also at static equilibrium. The rigid stages are restricted by the constraint forces of the compliant modules and the exerted external forces. This paper defines the constraint forces of the compliant modules to be variable constraint forces since the constraint forces vary with the deformation of the compliant modules, and defines the external forces as constant constraint forces due to the fact that the external forces are specific forces exerted which do not change with the deformation of the compliant mechanism. Therefore, the force equilibrium equations for all rigid stages in a compliant mechanism can be obtained based on the variable constraint forces and the constant constraint forces. Moreover, the model of the compliant mechanism can also be derived through solving all the force equilibrium equations. The constraint-force-based modeling method is finally detailed demonstrated via examples, and validated by the finite element analysis. Using this proposed modeling method, a complex compliant mechanism can be modelled with a particular emphasis on considering the position spaces of the associated compliant modules.

Design of Compliant Thermal Actuators Using Structural Optimization Based on the Level Set Method

2008 ◽  
Author(s):  
Takayuki Yamada ◽  
Shintaro Yamasaki ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Structural Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Compliant Mechanisms ◽  
Optimization Method ◽  
Equilibrium Equations ◽  
Micro Electro Mechanical Systems ◽  
Thermal Actuators ◽  
Level Set Function ◽  
Set Function

Compliant mechanisms are a new type of mechanism, designed to be flexible to achieve a specified motion as a mechanism. Such mechanisms can function as compliant thermal actuators in Micro-Electro Mechanical Systems (MEMS) by intentionally designing configurations that exploit thermal expansion effects in elastic material when appropriate portions of the mechanism structure are heated. This paper presents a new structural optimization method for the design of compliant thermal actuators based on the level set method and the Finite Element Method (FEM). First, an optimization problem is formulated that addresses the design of compliant thermal actuators considering the magnitude of the displacement at the output location. Next, the topological derivatives that are used when introducing holes during the optimization process are derived. Based on the optimization formulation and the level set method, a new structural optimization algorithm is constructed that employs the FEM when solving the equilibrium equations and updating the level set function. The re-initialization of the level set function is performed using a newly developed geometry-based re-initialization scheme. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.

Compliant Mechanism Configurations for Vehicle Suspension Systems

2004 ◽  
Author(s):  
Timothy Allred ◽  
Larry L. Howell ◽  
Spencer P. Magleby ◽  
Alexandre E. Guerinot
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Vehicle Suspension ◽  
Leaf Spring ◽  
Potential Cost ◽  
Flexible Beams ◽  
Suspension Systems ◽  
New Concepts ◽  
Spring Suspension ◽  
Control Forces

This paper explores the use of compliant mechanisms or flexible beams in vehicle suspension systems. An example of a compliant suspension mechanism is the leaf spring suspension commonly found on trucks. New concepts are developed through rigid-body replacement synthesis and other methods with the objective of improving wheel control. The compliant A-arm is discussed and shown to be a promising concept for further research based on FEA results and other comparisons. The A-Arm concept performs well in controlling wheel deflections and has low stress values in response to control forces when compared to other compliant concepts considered and leaf spring configurations. The A-Arm uses less space than than the other compliant concepts considered and the potential cost of manufacture and assembly is potentially equal to current leaf spring congifurations.

A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms

2005 ◽  
Vol 128 (4) ◽  
pp. 776-786 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Potential Energy ◽  
Static Analysis ◽  
Compliant Mechanisms ◽  
Potential Energy Function ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Force Moment ◽  
Four Bar Linkage ◽  
Derivatives Of ◽  
Raphson Iteration

This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.

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