Modeling and Analysis of a Manipulator Joint Driven Through a Worm Gear Transmission

1989 ◽  
Author(s):  
B. W. Mooring ◽  
D. C. May ◽  
M. S. Schulte
Keyword(s):  
Linear Model ◽  
Nonlinear Model ◽  
High Velocity ◽  
Experimental System ◽  
Worm Gear ◽  
Gear Transmission ◽  
Servo Motor ◽  
Modeling And Analysis ◽  
Excited Vibration ◽  
Unstable Vibration

Abstract Worm gear transmissions are capable of high velocity ratios as well as redirection of rotation. Both of these features are desirable for some robot geometries. A problem has been encountered in several robot designs, however, where a self excited vibration occurs for some configurations of the manipulator in the joint containing the worm gear. In this work, a system which exhibits this type of undesirable motion is examined. The system consists of a DC servo motor which is used to position a flexible cantilever arm through a worm gear transmission. A nonlinear model is developed to describe the motion of the system. The model is then validated by comparing the predicted response to the observed response of an experimental system. It is demonstrated that the model accurately predicts the onset of the unstable vibration. The model is then linearized and it is shown that the linear model will predict the occurrence of the instability as well.

Modeling and Analysis of a Manipulator Joint Driven Through a Worm Gear Transmission

1990 ◽  
Vol 112 (4) ◽  
pp. 551-556 ◽  
Author(s):  
B. W. Mooring ◽  
D. C. May ◽  
M. Schulte
Keyword(s):  
Linear Model ◽  
Nonlinear Model ◽  
High Velocity ◽  
Experimental System ◽  
Worm Gear ◽  
Gear Transmission ◽  
Servo Motor ◽  
Modeling And Analysis ◽  
Excited Vibration ◽  
Unstable Vibration

Worm gear transmissions are capable of high velocity ratios as well as redirection of rotation. Both of these features are desirable for some robot geometries. A problem has been encountered in several robot designs; however, where a self-excited vibration occurs for some configurations of the manipulator in the joint containing the worm gear. In this work, a system which exhibits this type of undesirable motion is examined. The system consists of a DC servo motor which is used to position a flexible cantilever arm through a worm gear transmission. A nonlinear model is developed to describe the motion of the system. The model is then validated by comparing the predicted response to the observed response of an experimental system. It is demonstrated that the model accurately predicts the onset of the unstable vibration. The model is then linearized and it is shown that the linear model will predict the occurrence of the instability as well.

scholarly journals Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall

2021 ◽  
Vol 6 (3) ◽  
pp. 26
Author(s):  
Christoph Brandstetter ◽  
Sina Stapelfeldt
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Structural Vibration ◽  
Experimental Investigations ◽  
Vibration Modes ◽  
Critical Problem ◽  
Safety Critical ◽  
Unstable Vibration ◽  
Aero Engines ◽  
Lock In

Non-synchronous vibrations arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern aero-engines. Recent numerical and experimental investigations have shown that these vibrations are caused by the lock-in of circumferentially convected aerodynamic disturbances and structural vibration modes, and that it is possible to predict unstable vibration modes using coupled linear models. This paper aims to further investigate non-synchronous vibrations by casting a reduced model for NSV in the frequency domain and analysing stability for a range of parameters. It is shown how, and why, under certain conditions linear models are able to capture a phenomenon, which has traditionally been associated with aerodynamic non-linearities. The formulation clearly highlights the differences between convective non-synchronous vibrations and flutter and identifies the modifications necessary to make quantitative predictions.

QUALITATIVE PROPERTIES OF A POPULATION DYNAMICS SYSTEM DESCRIBING PREGNANCY

2005 ◽  
Vol 15 (04) ◽  
pp. 507-554 ◽  
Author(s):  
G. FRAGNELLI ◽  
P. MARTINEZ ◽  
J. VANCOSTENOBLE
Keyword(s):  
Population Dynamics ◽  
Asymptotic Behavior ◽  
Linear Model ◽  
Nonlinear Model ◽  
Total Population ◽  
Type A ◽  
Qualitative Properties

We study a model of population dynamics describing pregnancy: our model is composed by an equation describing the evolution of the total population, and an equation describing the evolution of pregnant individuals. These equations are of course coupled: one coupling expresses that the total population varies with the number of born people, and another coupling says that the number of fecundated individuals depends on the total population. We study three models of that type: a linear model without diffusion, a nonlinear model without diffusion and a linear model with diffusion. For these three models, we study precisely the qualitative properties and the asymptotic behavior of the solutions.

scholarly journals Efficient Market Hypothesis and the RMB-Dollar Rates: A Nonlinear Modeling of the Exchange Rate

2018 ◽  
Vol 10 (2) ◽  
pp. 150
Author(s):  
Hongxing Yao ◽  
Abdul Rashid Abdul Rahaman
Keyword(s):  
Exchange Rate ◽  
Root Mean Square Error ◽  
Linear Model ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Nonlinear Model ◽  
Efficient Market Hypothesis ◽  
Mean Square ◽  
Forecast Performance ◽  
The Exchange Rate

This paper uses a SETAR model to determine threshold(s) in the RMB/US$ exchange rate from 1981 to 2016 using monthly data. Also, it compares the forecast performance of the univariate nonlinear model to a univariate linear model. We further analyze the forecast performance of the SETAR model to a multivariate linear model, e.g., a Reduced-form VAR. In addition, the research assesses the claim by Boero and Marrocu (2002) that the root mean square error masks the superiority of the nonlinear models.We found five significant thresholds in the RMB/US$ exchange rate, and this result reflects five major episodes of policy reforms or structural changes in the renminbi exchange rates from the period 1981 to 2016. We also found that the univariate nonlinear model out performs both the univariate and multivariate linear models in predicting the exchange rate movements. This finding is consistent with the results in Kyei and Gyamfi (2016), Boero and Marrocu (2002), Krager and Kugler (1993), Peel and Speight (1994) and Chappell et al. (1996). Furthermore, we did not find any evidence of the root mean square error masking the superiority of the nonlinear model.

Dynamics of a Cleaning Blade Based on a 2DOF Link Model

2009 ◽  
Author(s):  
Yoshinori Inagaki ◽  
Tsuyoshi Nohara ◽  
Go Kono ◽  
Minoru Kasama ◽  
Masatsugu Yoshizawa
Keyword(s):  
Amplitude Equation ◽  
Laser Printer ◽  
Small Disturbance ◽  
Governing Equations ◽  
Supercritical Bifurcation ◽  
Narrow Region ◽  
Hamiltonian Hopf Bifurcation ◽  
Excited Vibration ◽  
Link Model ◽  
Unstable Vibration

To analyze the dynamics of a cleaning blade in a laser printer, observation of the vibration of the cleaning blade and analysis of a 2DOF model have been carried out. First, from the observation of the vibration of the actual cleaning blade, the stationary self-excited vibration has been confirmed. Next, a 2DOF model has been presented and its governing equations have been derived. The bottom of the model is assumed to always contact a floor surface, and the friction coefficient is constant and not dependent on the floor velocity. Third, by solving the equations governing the motion of the 2DOF model, five patterns of static equilibrium states have been obtained. Moreover it has been clarified from linear stability analysis that one of five patterns corresponds to the shape of the cleaning blade and is unstable for a small disturbance in a narrow region. This unstable vibration is a bifurcation classified as Hamiltonian-Hopf bifurcation. Fourth, by keeping up to the 3rd order terms, the nonlinear complex amplitude equation has been obtained, and the steady amplitude can be decided. As a result, the steady amplitude has been determined as the products of the 2nd order terms. Furthermore it has been clarified that such a self-excited vibration is classified as the supercritical bifurcation.

The Modeling of Electrohydraulic Proportional Valves

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Davide Cristofori ◽  
Andrea Vacca
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Nonlinear Model ◽  
3D Model ◽  
Fluid Dynamic ◽  
Body Motion ◽  
General Nature ◽  
Relief Valve ◽  
Real Component ◽  
Electromagnetic Model

The present work describes the modeling of a proportional relief valve actuated by an electromagnet. Two models were developed and compared each other: a detailed nonlinear model and its linearized version. The modeling approach presented has a general nature and can be applied to various types of electrohydraulic proportional valves (EHPV). The comparison between nonlinear and linear model results shows the limits of the linear approximation to study the real component. Substantially, the nonlinear model is composed by three submodels: the fluid-dynamic model (for the evaluation of the main flow features), the mechanical model (which solves the mobile body motion), and the electromagnetic model (which evaluates the magnetic forces and the electric transient). All submodels are based on a lumped parameter (LP) approach and they implement a specific set of nonlinear equations. However, to carefully model the main electromagnetic phenomena that characterize the proportional electromagnet behavior (including: magnetic losses, fringing effects, and magnetic saturation), a finite element analysis (FEA) 3D model was developed by the authors. The LP electromagnetic model is based on a particular use of the FEA 3D model steady state results. A series of transient simulations were performed through the FEA 3D model in order to quantify the effect of the eddy currents and to determine a second order transfer function used in the linear model to describe the electromagnet dynamics. The remaining parts of the linear model are obtained by linearizing the nonlinear model equations. The FEA 3D model was experimentally validated in steady-state conditions, while the results of the overall model of the valve were verified in both steady-state and dynamic conditions.

scholarly journals Flux Reflection Model of the Ferroresonant Circuit

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Kruno Miličević ◽  
Ivan Flegar ◽  
Denis Pelin
Keyword(s):  
Physical Model ◽  
Linear Model ◽  
Nonlinear Model ◽  
Steady States ◽  
Reflection Model ◽  
Proposed Model ◽  
Simulation Results ◽  
Ferroresonant Circuit ◽  
Nonlinear Coil

The paper presents a linear model of ferroresonant circuit with flux reflection. The proposed model—flux reflection model—derives from observations of typical flux waveforms of nonlinear coil during ferroresonant steady states. Simulation results of the flux reflection model are compared with simulation results of the usual nonlinear model as well as with measurements carried out on the physical model of the ferroresonant circuit. The flux reflection model enables a novel comprehension of the ferroresonant circuit behavior and simplifies the modeling of the nonlinear coil in the ferroresonant circuit.

Accurate Prediction of Wall Shear Stress in a Stented Artery: Newtonian Versus Non-Newtonian Models

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Juan Mejia ◽  
Rosaire Mongrain ◽  
Olivier F. Bertrand
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Linear Model ◽  
Newtonian Fluid ◽  
Nonlinear Model ◽  
Numerical Models ◽  
Neointimal Hyperplasia ◽  
Computational Cost ◽  
Arterial Segment ◽  
Wall Shear

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood’s lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.

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