Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multibeam Parallelogram Mechanisms

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Guangbo Hao ◽  
Haiyang Li
Keyword(s):  
Experimental Testing ◽  
Slenderness Ratio ◽  
Analytical Models ◽  
Stiffness Ratio ◽  
Motion Model ◽  
Characteristic Analysis ◽  
Diagram Method ◽  
Primary Motion ◽  
Parasitic Motion ◽  
Fea Model

This paper deals with nonlinear analytical models of a class of compound multibeam parallelogram mechanisms (CMPMs) along with the static characteristic analysis. The CMPM is composed of multiple compound basic parallelogram mechanisms (CBPMs) in an embedded parallel arrangement. First, nonlinear analytical models for the CBPM are derived using the free-body diagram method through appropriate approximation strategies. The nonlinear analytical models of the CMPM are then derived based on the modeling results of the CBPM. Nonlinear finite element analysis (FEA) comparisons, experimental testing, and detailed stiffness analysis for the CBPM are finally carried out. It is shown that the analytical primary motion model agrees with both the FEA model and the testing result very well but the analytical parasitic motion model deviates from the FEA model over the large primary motion/force. It is also shown from the analytical characteristic analysis that the primary translational stiffness increases with the primary motion but the parasitic motion stiffness decreases with the primary motion, and the stiffness ratio of the parasitic motion stiffness to the primary translation stiffness also decreases with the primary motion. It is found that the larger the beam slenderness ratio is, the larger the stiffness or stiffness ratio is, and the more apparent the change of the stiffness or stiffness ratio is. The varied stiffness ratio indicates the mobility change of the CBPM.

Design of 3-legged XYZ compliant parallel manipulators with minimised parasitic rotations

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 787-806 ◽  
Author(s):  
Guangbo Hao ◽  
Haiyang Li
Keyword(s):  
Finite Element Analysis ◽  
Large Range ◽  
Experimental Testing ◽  
Parallel Manipulators ◽  
Analytical Models ◽  
Parallel Mechanisms ◽  
Characteristic Analysis ◽  
Electric Discharge Machining ◽  
Element Analysis ◽  
Manufacturing Technologies

SUMMARYThis paper deals with the design of 3-legged distributed-compliance XYZ compliant parallel manipulators (CPMs) with minimised parasitic rotations, based on the kinematically decoupled 3-PPPRR (P: prismatic joint, and R: revolute joint) and 3-PPPR translational parallel mechanisms (TPMs). The designs are firstly proposed using the kinematic substitution approach, with the help of the stiffness center (SC) overlapping based approach. This is done by an appropriate embedded arrangement so that all of the SCs associated with the passive compliant modules overlap at the point where all of the input forces applied at the input stages intersect. Kinematostatic modelling and characteristic analysis are then carried out for the proposed large-range 3-PPPRR XYZ CPM with overlapping SCs. The results from finite element analysis (FEA) are compared to the characteristics found for the developed analytical models, as are experimental testing results (primary motion) from the prototyped 3-PPPRR XYZ CPM with overlapping SCs. Finally, issues on large-range motion and dynamics of such designs are discussed, as are possible improvements of the actuated compliant P joint. It is shown that the potential merits of the designs presented here include a) minimised parasitic rotations by only using three identical compliant legs; b) compact configurations and small size due to the use of embedded designs; c) approximately kinematostatically decoupled designs capable of easy controls; and d) monolithic fabrication for each leg using existing planar manufacturing technologies such as electric discharge machining (EDM).

scholarly journals Evaluation of Damage Indices for Rectangular Concrete-filled Steel Tube Structures

2019 ◽  
Vol 19 (4) ◽  
pp. 170-184
Author(s):  
Minsheng Guan ◽  
Siying Lin ◽  
Hongbiao Du ◽  
Jie Cui ◽  
Taizhou Yan
Keyword(s):  
Comprehensive Evaluation ◽  
Selection Process ◽  
Slenderness Ratio ◽  
Damage Index ◽  
Steel Tube ◽  
Stiffness Ratio ◽  
Concrete Filled Steel Tube ◽  
Damage Indices ◽  
Drift Ratio ◽  
Secant Stiffness

Abstract The paper aims to select a simple and effective damage index for estimating the extent of damage of rectangular concrete-filled steel tube (RCFT) structures subjected to ground motions. Two experimental databases of cyclic tests conducted on RCFT columns and frames are compiled. Test results from the database are then used to evaluate six different damage indices, including the ductility ratio (μ), drift ratio, initial-to-secant stiffness ratio (DKJ), modified initial-to-secant stiffness ratio (Dms), energy coefficient (E), and the combined damage index (DPA) as a benchmark indicator. Selection criteria including correlation, efficiency, and proficiency are utilized in the selection process. The optimal alternative for DPA is identified on the basis of a comprehensive evaluation. The evaluations indicate that Dms previously proposed by some of the authors is the most appropriate substitution of DPA, followed by the drift ratio. For the case of the slenderness ratio less than or equal to 30, the same grades of relation between the investigated damage indices and the benchmark are observed. However, in the case of the slenderness ratio larger than 30, the drift ratio tends to be the optimal alternative. In most cases, μ is proved to be an inadequate replacement of DPA.

Characterization and Modeling of Elastomeric Joints in Miniature Compliant Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Dana E. Vogtmann ◽  
Satyandra K. Gupta ◽  
Sarah Bergbreiter
Keyword(s):  
Analytical Model ◽  
Compliant Mechanisms ◽  
Analytical Models ◽  
Accurate Analysis ◽  
Element Analysis ◽  
Fea Model ◽  
Torsional Spring ◽  
Tension Tests ◽  
In Series ◽  
Efficient Exploration

Accurate analysis models are critical for effectively utilizing elastomeric joints in miniature compliant mechanisms. This paper presents work toward the characterization and modeling of miniature elastomeric hinges. Characterization was carried out in the form of several experimental bending tests and tension tests on representative hinges in five different configurations. The modeling portion is achieved using a planar pseudo rigid body (PRB) analytical model for these hinges. A simplified planar 3-spring PRB analytical model was developed, consisting of a torsional spring, an axial spring, and another torsional spring in series. These analytical models enable the efficient exploration of large design spaces. The analytical model has been verified to within an accuracy of 3% error in pure bending, and 7% in pure tension, when compared to finite element analysis (FEA) models. Using this analytical model, a complete mechanism—a robotic leg consisting of four rigid links and four compliant hinges—has been analyzed and compared to a corresponding FEA model and a fabricated mechanism.

scholarly journals A review of friction damping modeling and testing

2019 ◽  
Vol 90 (1) ◽  
pp. 107-126 ◽  
Author(s):  
Louis Gagnon ◽  
Marco Morandini ◽  
Gian Luca Ghiringhelli
Keyword(s):  
Internal State ◽  
Experimental Testing ◽  
Analytical Models ◽  
Friction Damper ◽  
Friction Damping ◽  
Friction Dampers ◽  
Modeling Approaches ◽  
Planar Surfaces ◽  
Wide Range ◽  
Friction Models

Abstract This survey provides an insight into the modeling and testing of uniaxial friction dampers. The focus is on attenuating the linear relative movement along planar surfaces for frequencies between 10 Hz and 1 kHz. An overview of the different approaches seen in the literature concerning friction damping is provided. Examples and evaluation of such dampers excited over a wide range of frequencies are presented. The information required to develop models of friction dampers is covered. To that end, different modeling approaches are presented for dry friction. Dynamic friction models with an internal state are covered, and their advantages are described. Other modeling approaches are reported for complete systems with friction dampers. Both numerical and analytical models are covered. Experimental configurations from a selection of authors are also included. Finally, a series of suggestions for the numerical modeling and experimental testing of a friction damper are given.

Bearing capacity of spread footings on aggregate pier–reinforced clay: updates and stress concentration

2020 ◽  
Vol 57 (5) ◽  
pp. 717-727 ◽  
Author(s):  
Taeho Bong ◽  
Armin W. Stuedlein ◽  
John Martin ◽  
Byoung-Il Kim
Keyword(s):  
Stress Concentration ◽  
Bearing Capacity ◽  
Cross Validation ◽  
Slenderness Ratio ◽  
Ground Improvement ◽  
Analytical Models ◽  
Loading Test ◽  
Replacement Ratio ◽  
Area Replacement Ratio ◽  
Reinforced Clay

Aggregate piers represent an economical ground improvement technique used to increase bearing capacity and reduce settlements of weak soils. Several approaches have been developed to estimate the bearing capacity of aggregate pier–reinforced clay, but these models exhibit large prediction bias and uncertainty. This study uses newly developed footing loading test data to investigate the relationship between the bearing capacity and the area replacement and slenderness ratios. The bearing capacity of a single aggregate pier, whether isolated or in groups, below a loaded footing increases as the area replacement ratio decreases due to increase in extent of confined soil surrounding the pier. The length and diameter of an aggregate pier is also shown to result in significantly increased bearing capacity, an effect that diminishes with increasing slenderness. New modifications are proposed to existing simplified and cavity expansion models to account for the effect of confinement, area replacement ratio, and slenderness ratio using a leave-one-out cross-validation technique. The cross-validation analysis resulted in robust bearing capacity models that are more accurate than existing analytical models. Additionally, the stress concentration ratio for shallow foundations supported by aggregate pier–reinforced plastic soils at failure was estimated and compared with the available data, indicating its sensitivity to design variables and showing that this critical design parameter may be predicted using the updated models.

On the comprehensive static characteristic analysis of a translational bistable mechanism

2016 ◽  
Vol 230 (20) ◽  
pp. 3803-3817 ◽  
Author(s):  
Guangbo Hao ◽  
John Mullins
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Negative Stiffness ◽  
Beam Length ◽  
Rotational Stiffness ◽  
Characteristic Analysis ◽  
Element Analysis ◽  
Primary Motion ◽  
Bistable Mechanism ◽  
Inclined Angle

Bistable mechanisms have two stable positions and their characteristic analysis is much harder than the traditional spring system due to their postbuckling behaviour. As the strong nonlinearity induced by the postbuckling, it is difficult to establish a correct model to reveal the comprehensive nonlinear characteristics. This paper deals with the in-plane comprehensive static analysis of a translational bistable mechanism using nonlinear finite element analysis. The bistable mechanism consists of a pair of fixed-clamped inclined beams in symmetrical arrangement, which is a monolithic design and works within the elastic deformation domain. The displacement-controlled finite element analysis method using Strand7 is first discussed. Then the force–displacement relation of the bistable mechanism along the primary motion direction is described followed by the detailed primary translational analysis for different parameters. A simple analytical (empirical) equation for estimating the negative stiffness is obtained, and experimental testing is performed for a case study. It is concluded that (a) the negative stiffness magnitude has no influence from the inclined angle, but is proportional to the product of the Young’s modulus, beam depth, and cubic ratio for in-plane thickness to the beam length; (b) the unstable position is proportional to the product of the beam length and the Sine function of the inclined angle, and is not affected by the in-plane thickness and the material (or the out-of-plane thickness). The in-plane off-axis (translational and rotational) stiffness is further analysed to show the stiffness changes over the primary motion and the off-axis motion, and a negative rotational stiffness domain has been obtained.

Experimental Testing and Validation of Tangential Steering Wheel Vibrations Due to Tire Nonuniformity

2005 ◽  
Author(s):  
Virgile Ayglon ◽  
Vinod Cherian ◽  
Nader Jalili
Keyword(s):  
Dynamic Testing ◽  
Experimental Testing ◽  
System Modeling ◽  
Companion Paper ◽  
Steering System ◽  
Analytical Models ◽  
Shop Floor ◽  
Steering Wheel ◽  
Vehicle Speed ◽  
Road Testing

This paper describes the experimental testing and validation of the analytical models developed in our companion paper (IMECE2005-81581) for the nonlinear kinematics and dynamics of the suspension linked to a nonlinear rack and pinion steering system model. More specifically, the experimental results are used to cross verify the numerical simulations of the nibble using custom built analytical and ADAMS models, described in the companion paper. For this, shop floor based quasi-static Kinematic and Compliance (K&C) and dynamic testing results along with track testing on special purpose track at Michelin are presented. Other results include impulse testing of the steering system, as mounted on the vehicle, as well as shaker testing to verify the results. Road testing is also carried out at speeds close to the vehicle critical speed in order to compare and validate the suspension models using the quasi-static K&C testing. The road testing results demonstrate the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear effects in the vehicle system modeling as well as the variation of the shimmy phenomenon with vehicle speed and tire imbalance.

Vibration Analysis and Health Monitoring of Cracks in Composite Disk Rotor Systems

2005 ◽  
Author(s):  
Xin Hai ◽  
George Flowers ◽  
Roland Horvath ◽  
Jerry Fausz
Keyword(s):  
Health Monitoring ◽  
Natural Frequencies ◽  
Experimental Testing ◽  
Vibration Characteristics ◽  
Rotor Systems ◽  
Plane Vibration ◽  
Fea Model ◽  
Rotating Systems ◽  
Out Of Plane ◽  
Composite Disk

Cracks and voids are common defects in rotating systems and are a precursor to fatigue-induced failure. Identifying the presence and growth of cracks is a critical concept for the health monitoring and diagnostics of such systems. A combined computational and experimental study of the vibration characteristics of a composite hub flywheel rotor system with a cracked hub disk is presented. First, experimental testing of both in-plane and out-of-plane vibration characteristics using a rotor with a composite disk hub supporting a relatively massive rim was conducted. A crack was deliberately introduced into the hub disk during fabrication. Based upon these results, a finite element (FEA) model was developed to further explore the relationship between natural frequencies and crack properties. Finally, a simplified theoretical model for the primary in-plane vibration mode was developed and used in a series of parametric studies. Good agreement was found between the model predictions and the experimental results. It was observed that the presence of a crack tends to affect both the magnitudes and distribution of the rotor natural frequencies. Certain primary frequencies for rotors with a crack are smaller than for those without a crack. In addition, the frequency values of associated with the “in-crack” direction are generally smaller than those associated with the “off-crack” direction, introducing a non-symmetry into the rotordynamics which can serve as an indicator for rotor health monitoring.

Modeling of a Cartwheel Flexural Pivot

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Bi Shusheng ◽  
Zhao Hongzhe ◽  
Yu Jingjun
Keyword(s):  
Parametric Design ◽  
Bending Moment ◽  
Equivalent Model ◽  
Vertical Force ◽  
Element Analysis ◽  
Rotational Angle ◽  
Single Beam ◽  
Primary Motion ◽  
Center Shift ◽  
Parasitic Motion

A cartwheel flexural pivot has a small center shift as a function of loading and ease of manufacturing. This paper addresses an accurate model that includes the loading cases of a bending moment combined with both a horizontal force and a vertical force. First, a triangle flexural pivot is modeled as a single beam. Then, the model of cartwheel flexural pivot based on an equivalent model is developed by utilizing the results of the triangle pivot. The expressions for rotational displacement and center shift are derived to evaluate the primary motion and the parasitic motion; the maximum rotational angle is simply formulated to predicate the range of motion. Finally, the model is verified by finite element analysis. The relative error of the primary motion is less than 1.1% for various loading cases even if the rotational angle reaches ±20 deg, and the predicted errors for the two center shift components are less than 15.4% and 7.1%. The result shows that the model is accurate enough for designers to use for initial parametric design studies, such as for conceptual design.

A Case and Elastomer Annulus Under Lateral Impulse

1989 ◽  
Vol 42 (11S) ◽  
pp. S142-S149 ◽  
Author(s):  
Herbert E. Lindberg ◽  
Yvonne D. Murray
Keyword(s):  
Finite Element ◽  
Fourier Series ◽  
Early Time ◽  
Typical Case ◽  
Analytical Models ◽  
Motion Model ◽  
Series Solutions ◽  
Elastomeric Material ◽  
Boundary Model ◽  
Radiation Boundary

Fourier series and finite element solutions are given for stresses in a cylindrical case filled with an annulus of elastomeric material. The Fourier series solutions are for membrane stresses, which dominate at early time, and are given for three case-elastomer models: (1) a slide boundary model in which the case wall moves as a unit with the elastomer in radial motion but, with a weak bond between the case and elastomer, is free to slide relative to the elastomer in tangential motion, (2) a unit motion model for a well-bonded elastomer in which the case wall and elastomer are assumed to move together as a unit in both radial and tangential motion, and (3) a radiation boundary model in which tangential motion of the case wall radiates energy into a well-bonded elastomer. For typical case, elastomer and bond mechanical properties, the radiation boundary model gives the most appropriate solution, which differs substantially from the other solutions even for very soft elastomers. Finite element solutions agree closely with and support the validity of all three analytical models, which were used to guide the finite element “experiments” and interpret and generalize their results.

Sign in / Sign up

Export Citation Format

Share Document