Controlling the Frequency Content of Inertia Forces in Dwelling Cam-Follower Systems

2006 ◽  
Vol 129 (5) ◽  
pp. 546-552 ◽  
Author(s):  
Forrest W. Flocker
Keyword(s):  
Lagrange Multiplier ◽  
Natural Frequencies ◽  
Inertia Force ◽  
Frequency Content ◽  
Lagrange Multiplier Technique ◽  
Cam Follower ◽  
Inertia Forces

Background. Cam-driven machines are frequently manufactured with the intent that they be installed in many different end applications, each with its own natural frequencies. A cam-driven component that performs well in one end application can excite obnoxious or damaging vibrations in another. Method of Approach. A Lagrange multiplier technique is presented that optimally modifies follower motion such that unwanted inertia force frequencies are suppressed. Results. An example problem illustrates the method and presents results. Conclusions. The technique provides a robust customization procedure, permitting the use of a cam-driven component in a wider variety of end applications.

Surface Deformation and Convection in Electrostatically-Positioned Droplets of Immiscible Liquids Under Microgravity

2005 ◽  
Vol 128 (6) ◽  
pp. 520-529 ◽  
Author(s):  
Y. Huo ◽  
B. Q. Li
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Free Surface ◽  
Electric Field ◽  
Outer Layer ◽  
Thermal Gradient ◽  
Surface Deformation ◽  
Inertia Force ◽  
Weighted Residuals ◽  
Inertia Forces

A numerical study is presented of the free surface deformation and Marangoni convection in immiscible droplets positioned by an electrostatic field and heated by laser beams under microgravity. The boundary element and the weighted residuals methods are applied to iteratively solve for the electric field distribution and for the unknown free surface shapes, while the Galerkin finite element method for the thermal and fluid flow field in both the transient and steady states. Results show that the inner interface demarking the two immiscible fluids in an electrically conducting droplet maintains its sphericity in microgravity. The free surface of the droplet, however, deforms into an oval shape in an electric field, owing to the pulling action of the normal component of the Maxwell stress. The thermal and fluid flow distributions are rather complex in an immiscible droplet, with conduction being the main mechanism for the thermal transport. The non-uniform temperature along the free surface induces the flow in the outer layer, whereas the competition between the interfacial surface tension gradient and the inertia force in the outer layer is responsible for the flows in the inner core and near the immiscible interface. As the droplet cools into an undercooled state, surface radiation causes a reversal of the surface temperature gradients along the free surface, which in turn reverses the surface tension driven flow in the outer layer. The flow near the interfacial region, on the other hand, is driven by a complimentary mechanism between the interfacial and the inertia forces during the time when the thermal gradient on the free surface has been reversed while that on the interface has not yet. After the completion of the interfacial thermal gradient reversal, however, the interfacial flows are largely driven by the inertia forces of the outer layer fluid.

Optimal Design for Partial Inertia Force Cancellation in Ultra High Speed Pressing Machine

2011 ◽  
Vol 291-294 ◽  
pp. 1909-1916 ◽  
Author(s):  
Jian Yu Bai ◽  
Zaihe Yu ◽  
Sen Lin Tong ◽  
Di Zheng
Keyword(s):  
Optimal Design ◽  
High Speed ◽  
Design Method ◽  
Inertia Force ◽  
Driving Mechanism ◽  
Kinematics Analysis ◽  
Ultra High Speed ◽  
Optimal Design Method ◽  
Inertia Forces ◽  
Manufacturing Machine

The severe vibration and noise caused by inertia forces within a manufacturing machine are often the bottleneck in increasing the manufacturing speed. Based on kinematics analysis of the applied driving mechanism, this paper proposes an optimal design method for partially canceling the inertia force in pressing machine by using limited number of weight-balancing blocks. The proposed method has been validated by simulations.

scholarly journals A XFEM Lagrange Multiplier Technique for Stefan Problems

2016 ◽  
Vol 7 ◽  
Author(s):  
Dave Martin ◽  
Hicham Chaouki ◽  
Jean-Loup Robert ◽  
Mario Fafard ◽  
Donald Ziegler
Keyword(s):  
Lagrange Multiplier ◽  
Stefan Problems ◽  
Lagrange Multiplier Technique

Free Vibration of Plates of Various Shapes with Intermediate Point Supports by the Hp-Cloud Method and Lagrange Multiplier

2016 ◽  
Vol 16 (09) ◽  
pp. 1550055 ◽  
Author(s):  
Sajad Jamshidi ◽  
Mojtaba Azhari ◽  
Hossein Amoushahi
Keyword(s):  
Lagrange Multiplier ◽  
Natural Frequencies ◽  
Cell Structure ◽  
Ritz Method ◽  
Thin Plates ◽  
Plate Boundaries ◽  
Shape Functions ◽  
Intermediate Point ◽  
Simply Supported ◽  
Kronecker Delta

The Hp-Cloud meshless method was developed to study the dynamic analysis of arbitrarily shaped thin plates with intermediate point supports. By proposing a special pattern for the influence radius of nodes and a polynomial type of enrichment function, the Hp-Cloud shape functions with Kronecker delta property were constructed. They can satisfy the zero deflection conditions for the field nodes at the point supports. The results obtained from these shape functions agree well with the previous ones, showing good accuracy and convergence. For plates with sharp corners, it is not possible to construct the Hp-Cloud shape function with Kronecker delta property. To this end, the Lagrange multiplier method was used for enforcing the boundary conditions. The computations were carried out by the Ritz method, and the cell structure method is refined to improve the speed and accuracy of numerical integration on the subscription surface of clouds intersecting with the plate boundaries. Using the algorithm developed, the natural frequencies of plates of various shapes and support patterns were computed. By increasing the number of point supports on the plate edges, the natural frequencies computed of the plate tend to those of the simply supported plate. Appropriate pattern of point supports distribution was presented for modeling the simply supported plates of various shapes by comparing the corresponding natural frequencies.

Minimizing Residual Vibrations in High-Speed Cam-Follower Systems Over a Range of Speeds

1995 ◽  
Vol 117 (1) ◽  
pp. 166-172 ◽  
Author(s):  
M. Chew ◽  
C. H. Chuang
Keyword(s):  
Boundary Conditions ◽  
Lagrange Multiplier ◽  
High Speed ◽  
Displacement Function ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Rules Of Thumb ◽  
Cam Follower

A direct procedure, based on the generalized Lagrange multiplier method, will be presented for designing high-speed cam-follower systems over a range of cam speeds. With this method residual vibrations at the end of the rise of a Dwell-Rise-Dwell (DRD) cam motion are minimized for any specified range of rise times. A minimum of boundary conditions on the cam displacement function will be specified to reduce unnecessary constraints on the cam displacement function. The applicability of rules of thumb generally accepted in designing for minimum vibrations will be discussed and compared to the results from this approach.

Performance Analysis and Optimization of Annular Fin With a Step Change in Thickness

2000 ◽  
Vol 123 (3) ◽  
pp. 601-604 ◽  
Author(s):  
B. Kundu ◽  
P. K. Das
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Performance Analysis ◽  
Optimum Design ◽  
Lagrange Multiplier ◽  
Step Change ◽  
Annular Fin ◽  
Lagrange Multiplier Technique ◽  
Annular Disc ◽  
Fin Length

The temperature distribution in a concentric annular fin with a step change in thickness (AFST) has been obtained analytically. The optimum design of such fins has been performed using Lagrange multiplier technique considering either the fin volume or the rate of heat transfer as the constraint. It has been demonstrated that the optimum AFSTs transfer more heat compared to optimum annular disc fins for a given fin volume as well as for given fin volume and fin length.

On Certain Least-Squares Synthesis Methods Misconceptions

1979 ◽  
Vol 101 (1) ◽  
pp. 47-50 ◽  
Author(s):  
G. H. Sutherland
Keyword(s):  
Least Squares ◽  
Lagrange Multiplier ◽  
Numerical Results ◽  
Synthesis Methods ◽  
Linear Superposition ◽  
Synthesis Techniques ◽  
Lagrange Multiplier Technique ◽  
False Premise

This paper shows a fundamental flaw in previously published linear superposition least-squares synthesis techniques. These techniques have the desirable noniteration characteristic. However, this paper shows, by a reformulation of the method, that they are based on a false premise. Numerical results bear this out. A Lagrange-multiplier technique is suggested as a superior alternative.

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