Dynamic responses and control of geared transmission system based on multibody modeling methodology

In this study, an innovative modeling approach is put forward to research the effect of eccentricity on the nonlinear dynamical behaviors of geared-bearing system. This refined model contains the rigid body of the rotor-bearing system and separated gear teeth which are considered as individual bodies elastically attached to the gear hub with revolute joints. The internal and external excitations of the proposed model include torsional joint stiffness, roll bearing forces, friction between gear pair, gear eccentricity, and so on. The systematic procedure for the calculation of torsional joint stiffness, bearing forces and friction coefficient considering elastohydrodynamic is also conducted. After that, the influence of eccentricity on nonlinear dynamic characteristics of the geared transmission system is analyzed. To avoid the system moving in the unstable motion state, a dry friction damper controller is designed to control the nonlinear behaviors simulated on the basis of above model. The linear feedback and periodic excitation non-feedback control strategies are, respectively, selected to design the actuator. It is indicated that undesirable behaviors of the geared transmission system can be avoided effectively by applying the proposed control method.

A Hybrid Ale Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

The present work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two dimensional beam finite element is presented, based on the Absolute Nodal Coordinate Formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as the case of (continuously) distributed mass.

Investigation of the Stability of Axially Moving Beams With Discrete Masses

The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.

Preliminary Study on Multibody Modeling and Simulation of an Underactuated Gripper With Differential Transmission

Robotic grippers have represented a challenge for designers and engineers since at least three decades, due to the complexity of grasping and manipulation tasks. Underactuated and soft robotic grippers are a technology that allows good dexterity and manipulating capabilities, by reducing the number of actuators. However, this type of device requires the use of complex mechanical systems to compensate the underactuated implementation limits, such as differential mechanisms. The differential mechanism is necessary to decouple finger closures and distribute forces. The multibody simulation allows to evaluate the main parameters of the elements to understand how the differential system can work. The development and design of complex mechanical systems is simplified by this technique. In particular, this paper presents a multibody simulation analysis which recreates an elementary model of a gripper with two links and a single actuator; the developed model reproduces the grasping of an object using a mechanical differential pulley system, placed beneath the fingers. Some results are presented to study the role of the differential when the fingers grasp an object with different configurations. The aim of this work is to show how an accurate and still manageable multibody model integrated in Matlab environment is able to extend the classical grasp metrics to a more general dynamic setup.

Haptic Devices Based on Real-Time Dynamic Models of Multibody Systems

Multibody modeling of mechanical systems can be applied to various applications. Human-in-the-loop interfaces represent a growing research field, for which increasingly more devices include a dynamic multibody model to emulate the system physics in real-time. In this scope, reliable and highly dynamic sensors, to both validate those models and to measure in real-time the physical system behavior, have become crucial. In this paper, a multibody modeling approach in relative coordinates is proposed, based on symbolic equations of the physical system. The model is running in a ROS environment, which interacts with sensors and actuators. Two real-time applications with haptic feedback are presented: a piano key and a car simulator. In the present work, several sensors are used to characterize and validate the multibody model, but also to measure the system kinematics and dynamics within the human-in-the-loop process, and to ultimately validate the haptic device behavior. Experimental results for both developed devices confirm the interest of an embedded multibody model to enhance the haptic feedback performances. Besides, model parameters variations during the experiments illustrate the infinite possibilities that such model-based configurable haptic devices can offer.

Multibody Modeling Method for UHV Porcelain Arresters Equipped with Lead Alloy Isolation Device

This paper presents a multibody modeling method for seismic analysis of UHV porcelain surge arresters equipped with a kind of seismic isolation device. An UHV arrester is modeled as a planar multibody system whose number of DOF is equal to the number of the arrester units. Joint coordinate method is adopted to construct the governing equations of motion. The seismic isolation device utilizing a number of lead alloy dampers as its core energy dissipation components is also investigated. An analytical model of this device is given by modeling each lead alloy damper as a hysteretic spring and reducing the entire device to a planar system consisting of a range of hysteretic springs. Its mechanical characteristic is derived theoretically, and the obtained moment-angle relationship is expressed as a system of differential algebraic equations. The initial rotational stiffness of the device is formulated in terms of the structural and mechanical parameters of the device. This analytic expression is used in estimating the fundamental frequency of the isolated equipment. By this modeling method, it is easy to construct the governing equations of motion for the isolated system. An UHV arrester specimen is analyzed by this proposed method. The effectiveness of the isolation device in terms of reducing the internal base moment is significant and the influence of system parameters on the effectiveness is also discussed. The proposed method shows its potential usefulness in optimal design of the isolation device.