Complete Balancing of Multicylinder Engines Without Requiring Harmonic Balancers

1995 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
New Method ◽  
Harmonic Force ◽  
Vector Method ◽  
Numerical Examples ◽  
Single Cylinder ◽  
Linearly Independent ◽  
Phase Angles ◽  
Shaking Moment

Abstract Presently used balancing methods for multicylinder engines and pumps are for partial balancing. As a result the complete shaking force, shaking torque, and shaking moment balancings of engines require the use of harmonic force and harmonic torque and moment balancers. This article presents a new method for complete shaking force and shaking moment balancing of multicylinder engines that requires no harmonic balancers. This is achieved by keeping the total center of mass of each slider crank loop stationary, where the design equations are developed using a linearly independent mass vector method. Balancing the shaking force also balances the shaking moment. Shaking torque is balanced by eliminating the angular momentum of each mechanism loop and by arranging the phase angles of the crank throws. Four-, six-, and eight-cylinder engines are balanced in the numerical examples given. Two methods of completely balancing single-cylinder engines are also given.

Momentum Balancing of Four-Bar Linkages

1976 ◽  
Vol 98 (4) ◽  
pp. 1289-1295 ◽  
Author(s):  
J. L. Wiederrich ◽  
B. Roth
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
Primary Objective ◽  
Simple Design ◽  
Numerical Examples ◽  
Mass Distributions ◽  
Computer Based ◽  
Four Bar Linkage ◽  
Shaking Moment

The primary objective in this work is the determination of conditions for reducing the angular momentum fluctuations (i.e., vibration) transmitted to the frame of a completely force balanced four-bar linkage. This approach leads to relatively simple design equations for determining the inertial properties of the links for good momentum balancing. The essence of this procedure is that it yields analytical results as opposed to the computer-based search techniques required by most previously published methods, which are based on reducing the shaking forces and moments rather than the momentum fluctuations. Furthermore, this method allows for off-line mass distributions (i.e., the center of mass of the link is not on the line of pivots) and, as we show in the paper, this can result in better momentum balancing than the in-line case to which most previous works have been restricted. Some numerical examples are given and the results are compared to similar results obtained by minimizing the RMS shaking moment.

Complete Shaking-Force, -Moment, and, -Torque Balancing of Multi-Cylinder Engines Without Requiring Harmonic Balancers

1996 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Center Of Mass ◽  
Connecting Rod ◽  
Mass System ◽  
Vector Method ◽  
Output Torque ◽  
Axis Parallel ◽  
Force Moment ◽  
Balanced Designs ◽  
Phase Angles ◽  
Shaking Moment

Abstract Conventional engine balancing process truncates the piston acceleration to form harmonics form for the shaking force; then using dynamically equivalent two-particle mass system for the connecting rod, the shaking force is balanced by arranging the phase angles of the crank throws. During this process, the shaking torque balancing (about the crank shaft axis) is ignored. Shaking force due to truncated portion of piston acceleration is left unbalanced; and that some phase angle arrangements cannot balance the harmonics of the shaking force. This requires force harmonic balancers. Unbalanced inertial forces generate shaking moment about the transverse axis (normal to crankshaft axis) that remains unbalanced. Shaking moment due to force harmonics for some phase angles also remain unbalanced. They require moment harmonic balancers. This article presents a complete balancing method by which shaking force in each slider-crank loop is completely balanced. This also means that shaking moment is also completely balanced, thus eliminating the need for both force-, and moment-harmonic balancers. Article uses linearly independent mass vector method to retain the total center of mass of each slider-crank loop stationary. Shaking torque (sum of the inertial torques about the axis parallel to the crankshaft axis) causes variation in the output torque generated. This variation may be considered when designing the flywheel. However, the shaking torque is also balanced (or minimized) retaining the total angular momentum of each loop constant by arranging the phase angles of the crank throws. Several multi-cylinder engines are completely balanced for shaking force, shaking moment and shaking torque in the application examples, including balanced designs of connecting rod and throw sides.

Complete Shaking Force and Shaking Moment Balancing of Link Mechanisms Using Balancing Idler Loops

1982 ◽  
Vol 104 (2) ◽  
pp. 482-493 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Center Of Mass ◽  
Numerical Example ◽  
Shaking Moment

A method for completely balancing the shaking forces and shaking moments in mechanisms is presented. The method introduces shaking moment balancing idler parallelogram loop (or loops) which transfers the motion of a coupler link to a shaft on the frame of the mechanism, where the rotary balancers balance the shaking moment. The complete balancing of a mechanism is accomplished by maintaining the total center of mass of the mechanism stationary meanwhile achieving that the total angular momentum of the moving links of the mechanism vanishes. Positioning of the idler loops is illustrated for a series of multiloop mechanisms. Theorems on the complete balancing of shaking forces and shaking moments in mechanisms are established. Design equations for completely balancing some single and multiloop mechanisms are given. A numerical example is included.

A New Method for Completely Force Balancing Simple Linkages

1969 ◽  
Vol 91 (1) ◽  
pp. 21-26 ◽  
Author(s):  
R. S. Berkof ◽  
G. G. Lowen
Keyword(s):  
Center Of Mass ◽  
Time Dependent ◽  
New Method ◽  
Practical Applications ◽  
Mass Distributions ◽  
Linearly Independent ◽  
Planar Linkages

A new method, herein referred to as the “Method of Linearly Independent Vectors,” is shown to permit the complete force balancing of certain planar linkages. This method consists of writing the equation describing the position of the total mechanism center of mass in such a way that the coefficients of the time-dependent terms may be set equal to zero. In this way, the total center of mass can be made stationary, and the shaking force vanishes. Derivations as well as practical applications are shown for four-bar and six-bar linkages with arbitrary link mass distributions.

Shaking Moment Optimum Balancing of Planar Mechanisms

2011 ◽  
Vol 314-316 ◽  
pp. 2348-2352
Author(s):  
Er Bao ◽  
Xue Ye Ang ◽  
De Yong Liu
Keyword(s):  
Angular Momentum ◽  
New Method ◽  
Planar Mechanisms ◽  
Shaking Moment

A new method of shaking moment balancing of force balanced linkages is presented in this paper. The shaking moment balancing is gained based on the angular momentum principle. The method of synthesizing a dyad to balance the shaking moments is given, two kinds of structure types are calculated, all the maximum absolute values of the shaking moments are decreased by more than 75 % and the f1uctuation values of those are reduced by more than 68 %.

scholarly journals Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

THE STEREODYNAMICS STUDY OF THE C(3P) + OH (X2 Π) → CO(X1Σ+) + H(2S) REACTION

2010 ◽  
Vol 09 (05) ◽  
pp. 935-943 ◽  
Author(s):  
PENG SONG ◽  
YONG-HUA ZHU ◽  
JIAN-YONG LIU ◽  
FENG-CAI MA
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Title Reaction ◽  
High Collision Energy ◽  
Dependency Relationship ◽  
Energy Dependency ◽  
Mass Frame

The stereodynamics of the title reaction on the ground electronic state X2A' potential energy surface (PES)1 has been studied using the quasiclassical trajectory (QCT) method. The commonly used polarization-dependent differential cross-sections (PDDCSs) of the product and the angular momentum alignment distribution, P(θr) and P(Φr), are generated in the center-of-mass frame using QCT method to gain insight of the alignment and orientation of the product molecules. Influence of collision energy on the stereodynamics is shown and discussed. The results reveal that the distribution of P(θr) and P(Φr) is sensitive to collision energy. The PDDCSs exhibit different collision energy dependency relationship at low and high collision energy ranges.

Complete Balancing of Linkages Using Complete Dynamical Equivalents of Floating Links: CDEL Method

1992 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Moments Of Inertia ◽  
Numerical Examples ◽  
Long Time ◽  
Shaking Moment

Abstract Partially dynamically equivalent link concept has been used for partial shaking force balancing of the slider-crank mechanisms of engines for a long time. The article offers methods of forming complete dynamically equivalent link (CDEL) for floating binary, ternary, and quaternary links by which a mechanism can be completely balanced eliminating shaking force and shaking moment. Developments and applications are simple. Four-bar and slider-crank mechanisms, Walt’s and Stephenson’s type six-bar mechanisms and some eight-bar mechanisms are completely balanced to illustrate different forms of CDEL in different mechanisms. CDEL uses auxiliary masses and mass moments of inertia on a floating link. The use of the auxiliary masses is illustrated in numerical examples. A Watt’s type body guiding six-bar mechanism interacting with a robot is completely balanced in an application example.

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