A Substructure Technique for Dynamics of Flexible Mechanical Systems With Contact-Impact

1990 ◽  
Vol 112 (3) ◽  
pp. 390-398 ◽  
Author(s):  
S.-C. Wu ◽  
E. J. Haug
Keyword(s):  
Lagrange Multipliers ◽  
Synthesis Method ◽  
Mechanical Systems ◽  
Normal Modes ◽  
Local Deformation ◽  
Contact Forces ◽  
Transverse Impact ◽  
Contact Impact ◽  
Fixed Interface ◽  
Deformation Modes

A substructure synthesis method is proposed to account for contact-impact effects in flexible components of mechanical systems. Components that may come into contact are divided into substructures, on each of which local deformation modes are defined to describe deformation fields of components. Constraint modes and fixed interface normal modes are used to account for elastic deformation within each substructure. A constraint addition-deletion technqiue is used to determine when contact occurs, account for the effect of contact constraints during the period of contact, and delete constraints after the completion of the contact event. Lagrange multipliers associated with the contact constraints, which represent contact forces, are used to determine the time of separation of contacting nodes. Use of the method is illustrated for longitudinal and transverse impact of elastic bars.

A Substructure Technique for Dynamics of Flexible Mechanical Systems With Contact-Impact

1987 ◽  
Author(s):  
S.-C. Wu ◽  
E. J. Haug
Keyword(s):  
Lagrange Multipliers ◽  
Synthesis Method ◽  
Mechanical Systems ◽  
Normal Modes ◽  
Local Deformation ◽  
Constraint Forces ◽  
Transverse Impact ◽  
Contact Impact ◽  
Fixed Interface ◽  
Deformation Modes

Abstract A substructure synthesis method is proposed to account for contact-impact effects in flexible components of mechanical systems. Components that may come into contact is divided into substructures, on each of which local deformation modes are defined to described deformation fields of components. Constraint modes and fixed interface normal modes are used to account for elastic deformation within each substructure. A constraint addition-deletion technique is used to account for contact between impacting bodies. Lagrange multipliers associated with the constraints, which represent constraint forces, are used to determine separation of contacting nodes. Use of the method is illustrated on problems of longitudinal and transverse impact of bodies.

Component Mode Synthesis Method Using Partial Interface Modes: Application to Tuned and Mistuned Bladed Disk With Local Non-Linearity

2009 ◽  
Author(s):  
Duc-Minh Tran
Keyword(s):  
Synthesis Method ◽  
Normal Modes ◽  
Component Mode Synthesis ◽  
New Method ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Generalized Coordinates ◽  
Bladed Disk ◽  
Static Condensation ◽  
Fixed Interface

A new fixed interface component mode synthesis method using partial interface modes is presented. Partial interface modes are the structure normal modes which result from the static condensation of the structure to the interface between the substructures and which are clamped at a part of this interface. This method is the generalization of the classical component mode synthesis method which keeps all the interface physical displacements in the assembled reduced system and the method using interface modes which eliminates all of them. It allows one to reduce the number of the interface generalized coordinates and at the same time to keep some of the physical displacements at the interface. This latter capability is very useful to build reduced order models in which the presence of physical displacements are essential, for example in order to impose prescribed motions or to take into account local non-linearities. The new method is applied to a bladed disk in both tuned and mistuned cases.

scholarly journals Design and Calibration of Robot Base Force/Torque Sensors and Their Application to Non-Collocated Admittance Control for Automated Tool Changing

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 2895
Author(s):  
Hubert Gattringer ◽  
Andreas Müller ◽  
Philip Hoermandinger
Keyword(s):  
Steel Plate ◽  
Robotic Manipulators ◽  
Indirect Measurement ◽  
Local Deformation ◽  
Contact Forces ◽  
The Novel ◽  
Admittance Control ◽  
Load Cells ◽  
Series Elastic Actuators ◽  
Automated Tool

Robotic manipulators physically interacting with their environment must be able to measure contact forces/torques. The standard approach to this end is attaching force/torque sensors directly at the end-effector (EE). This provides accurate measurements, but at a significant cost. Indirect measurement of the EE-loads by means of torque sensors at the actuated joint of a robot is an alternative, in particular for series-elastic actuators, but requires dedicated robot designs and significantly increases costs. In this paper, two alternative sensor concept for indirect measurement of EE-loads are presented. Both sensors are located at the robot base. The first sensor design involves three load cells on which the robot is mounted. The second concept consists of a steel plate with four spokes, at which it is suspended. At each spoke, strain gauges are attached to measure the local deformation, which is related to the load at the sensor plate (resembling the main principle of a force/torque sensor). Inferring the EE-load from the so determined base wrench necessitates a dynamic model of the robot, which accounts for the static as well as dynamic loads. A prototype implementation of both concepts is reported. Special attention is given to the model-based calibration, which is crucial for these indirect measurement concepts. Experimental results are shown when the novel sensors are employed for a tool changing task, which to some extend resembles the well-known peg-in-the-hole problem.

Contact Modeling Technique of a Flexible Piston and Cylinder Using Modal Synthesis Method

2005 ◽  
Author(s):  
W. K. Kim ◽  
S. H. Sohn ◽  
H. J. Cho ◽  
D. S. Bae ◽  
J. H. Choi
Keyword(s):  
Contact Force ◽  
Synthesis Method ◽  
Normal Modes ◽  
Modeling Technique ◽  
Mode Shapes ◽  
Dynamics Analysis ◽  
Contact Modeling ◽  
Static Correction ◽  
Modal Synthesis ◽  
Contact Surfaces

In this paper, contact modeling technique and dynamics analysis of piston and cylinder system are presented by using modal synthesis method. It is very important to select mode shapes representing a global or local behavior of a flexible body due to a specified loading condition. This paper proposes a technique to generate the static correction modes which are nicely representing a motion by a contact force between a piston and cylinder. First normal modes of piston and cylinder under a boundary condition are computed, and then static correction modes due to a contact force applied at contacted nodes are added to the normal modes. Also, this paper proposes an efficient dynamics analysis process while changing the shape of the piston and cylinder. In optimization process or design study, their geometric data can be changed a bit. The slight changes of their contact surfaces make a high variation of the magnitude of a contact force, and it can yield the different dynamic behavior of an engine system. But, since the variations of the normal and correction modes are very small, the re-computation of their normal and correction modes due to the change of contact surfaces can be useless. Until now, whenever their contact surfaces are changed at a design cycle, the modes have been recomputed. Thus, most engineers in industries have been spent many times in very tedious and inefficient design process. In this paper, the normal and correction modes from the basic geometry of the piston and cylinder are computed. If the geometry shape is changed, nodal positions of the original modal model are newly calculated from an interpolation method and changed geometry data. And then the updated nodes are used to compute a precise contact force. The proposed methods illustrated in this investigation have good agreement with results of a nodal synthesis technique and proved that it is very efficient design method.

Impact on Beams

1936 ◽  
Vol 3 (2) ◽  
pp. A55-A61
Author(s):  
H. L. Mason
Keyword(s):  
Historical Development ◽  
Contact Region ◽  
Local Deformation ◽  
Lateral Vibration ◽  
Transverse Impact ◽  
Concentrated Mass ◽  
Impact Theory ◽  
Inelastic Impact ◽  
Maximum Contact

Abstract This paper deals with transverse impact on beams the mass of which is of importance. Experimental results are presented for comparison with theory. Impacts which appear single to the eye are shown to consist in reality of several blows in quick succession. Section 1 of the paper traces the historical development of this subject by discussing the investigations of Young, Hodgkinson, Cox, Saint Venant, and Timoshenko. Section 2 treats a simplified system in which a concentrated mass strikes a smaller concentrated mass having a “soft” spring restraint. For elastic impact, theory predicts for the struck mass a path composed of sinusoidal elements separated by instantaneous blows. For inelastic impact it predicts a joint harmonic motion. Records of the paths of both masses were obtained experimentally. Section 3 of the paper uses Timoshenko’s method of combining local deformation of the contact region with lateral vibration of the beam. An experimental investigation of maximum contact pressure and of blow duration gives what is believed to be the first confirmation of this theory. Section 4 describes an experimental determination of flexural stresses in elastic and inelastic impact on a 3-in. I-beam by the use of a Westinghouse magnetic strain gage. The indication is that stresses may be higher than those calculated by the usual approximations.

Modeling of Flexible Bodies for Dynamic Analysis of Multi-Body Dynamic Systems Using Ritz Vectors

1991 ◽  
Author(s):  
Henry T. Wu ◽  
Neel K. Mani
Keyword(s):  
Dynamic Analysis ◽  
Mechanical Systems ◽  
Normal Modes ◽  
Flexible Bodies ◽  
Static Correction ◽  
Ritz Vectors ◽  
Regeneration Procedure ◽  
Efficient Vector ◽  
Multi Body ◽  
Body Dynamic

Abstract Vibration normal modes and static correction modes have been previously used to model flexible bodies for dynamic analysis of mechanical systems. The efficiency and accuracy of using these modes to model a system depends on both the flexibility of each body and the applied loads. This paper develops a generalized method for the generation of a set of Ritz vectors to model flexible bodies for dynamic analysis of multi-body mechanical systems. The Ritz vectors are generated using the distribution of dynamic loading on a flexible body. Therefore they form the most efficient vector basis for the spatial distribution of the loadings. The Ritz vectors can be re-generated when the system undergoes significant changes of its configuration and the regeneration procedure is inexpensive. The combinations of vibration normal modes and the proposed Ritz vectors thus form more efficient and accurate vector bases for the modeling of flexible bodies for dynamic analysis.

Modeling Expected Wear in Revolute Joints With Clearance in Multibody Mechanical Systems

2007 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Research Work ◽  
Contact Forces ◽  
Joint Surface ◽  
Force Model ◽  
Wear Model ◽  
Continuous Contact ◽  
Revolute Joints ◽  
Sliding Motion ◽  
Impact Forces ◽  
Contact Impact

The main goal of this work is to develop a methodology for studying and quantifying the wear phenomenon in revolute clearance joints. In the process, a simple model for a revolute joint in the framework of multibody systems formulation is presented. The evaluation of the contact forces developed is based on a continuous contact force model that accounts for the geometrical and materials properties of the colliding bodies. The friction effects due to the contact in the joints are also represented. Then, these contact-impact forces are used to compute the pressure field at the contact zone, which ultimately is employed to quantify the wear developed and caused by the relative sliding motion. In this work, the Archard’s wear model is used. A simple planar multibody mechanical system is used to perform numerical simulations, in order to discuss the assumptions and procedures adopted throughout this work. Different results are presented and discussed throughout this research work. From the main results obtained, it can be drawn that the wear phenomenon is not uniformly distributed around the joint surface, owing to the fact that the contact between the joint elements is wider and more frequent is some specific regions.

Haptic Display of Interaction Forces in MEMS Assembly Processes

2000 ◽  
Author(s):  
Daniel J. Evans ◽  
Sankar Jayaram ◽  
John T. Feddema ◽  
Uma Jayaram ◽  
William A. Johnson ◽  
...  
Keyword(s):  
Boundary Element ◽  
Force Feedback ◽  
Complex Geometry ◽  
Mechanical Systems ◽  
Contact Forces ◽  
Haptic Display ◽  
Electrostatic Forces ◽  
Monolithic Integrated Circuit ◽  
Micro Electro Mechanical Systems ◽  
Human Scale

Abstract In recent years, the world economy has seen expansive market growth in the area of Micro-Electro Mechanical Systems (MEMS). It is predicted that the MEMS market could reach more than $34 billion by the year 2002. Today, commercially available MEMS products include accelerometers for airbags and inkjet printer heads. These products require little or no assembly because a monolithic integrated circuit process is used to develop the devices. However, future MEMS will be more elaborate. Monolithic integration is not feasible when incompatible processes, complex geometry, or different materials are involved. For these cases, new and extremely precise micro-manipulation capabilities will be required for successful product realization. This paper outlines the design and implementation of a computer aided simulation of Micro Electro Mechanical Systems (MEMS) assembly utilizing force feedback devices for display of forces of interaction. The system described in this paper solves boundary element equations for electrostatic forces between MEMS components and then displays this solution in near real time with the help of the PHANToM force feedback device. Issues discussed in this paper include: boundary element solutions of electrostatic forces, interpolation of a six degree of freedom solution grid, scaling up of electrostatic forces to human scale, and use of the PHANToM device for haptic display of electrostatic and contact forces.

Influence of Reference Conditions in the Analysis of the Impact of Flexible Bodies

2001 ◽  
Author(s):  
José L. Escalona ◽  
Juana Mayo ◽  
Jaime Domínguez
Keyword(s):  
Rigid Body ◽  
Reference Conditions ◽  
Normal Modes ◽  
Frame Of Reference ◽  
The Body ◽  
Natural Boundary Condition ◽  
Flexible Bodies ◽  
Free Interface ◽  
Fixed Interface ◽  
The Impact

Abstract In this paper, the floating frame of reference approach is applied to the dynamics of the impact of flexible bodies, while component mode synthesis is used to describe deformation. The influence of the reference conditions, that indicate the type of attachment between the body fixed frame of reference and the flexible bodies, is investigated. Rigid and free attachments allow the use of fixed interface and free interface normal modes, respectively. A finite number of fixed interface modes does not fulfil the natural boundary condition at the attachment point. Free interface normal modes cannot describe the compressive forces at the contact surface. However, it is shown that both set of modes are able to describe the impact-induced elastic waves. In the evaluation of the kinematic coefficient of restitution, these two approaches differ significantly. When free attachment is considered, the derivatives of the reference co-ordinates coincide with the equivalent rigid body velocities of the flexible bodies, remaining constant after the impact. However, if the body frame of reference is rigidly attached, the equivalent rigid body velocities of the flexible body have to be evaluated as a linear combination of the derivative of reference and elastic co-ordinates. The axial impact of a rigid body on a flexible rod and the transverse impact of a flexible pendulum with a fixed stop are simulated to illustrate these facts. Hertzian contact forces are assumed to occur during impact.

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