Algebraic Method for Exact Synthesis of 1-DOF Linkages With Arbitrarily Prescribed Constant Velocity Ratios

2021 ◽  
pp. 1-18
Author(s):  
Kai Liu ◽  
Jingjun Yu
Keyword(s):  
Constant Velocity ◽  
High Speed ◽  
Characteristic Curve ◽  
Velocity Ratio ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Angular Motion ◽  
Open Chain ◽  
Pure Rolling ◽  
Spherical Linkages

Abstract This paper addresses the synthesis of 1-DOF linkages that can exactly transmit angular motion between coplanar axes (i.e. parallel axes or intersectant axes) with arbitrarily prescribed constant velocity ratios. According to motion polynomials over dual quaternions and pure rolling models between two circles, an algebraic approach is presented to precisely synthesize new 1-DOF linkages with arbitrarily prescribed constant velocity ratios. The approach includes four steps: (a) formulate a characteristic curve occurred by the pure rolling, (b) compute the motion polynomial of the minimal degree that can generate the curve, (c) deal with the factorization of the motion polynomial to construct an open chain, (d) convert the open chain to a 1-DOF linkage. Using this approach, several 1-DOF planar, spherical, and spatial linkages for angular motion transmission between parallel axes or intersectant ones are constructed by designating various velocity ratios. Taking the planar and spherical linkages with a constant 1:2 velocity ratio as examples, kinematics analysis is implemented to prove their motion characteristics. The result shows that the generated linkages indeed can transmit angular motion between two coplanar axes with constant velocity ratios. Meanwhile, 3D-printed prototypes of these linkages also demonstrate such a conclusion. This work provides a framework for synthesizing linkages that have great application potential to transmit motion in robotic systems that require low inertia to achieve reciprocating motion with high speed and accuracy.

Inertial Effects in a Multiple-Ball Transmission

1960 ◽  
Vol 82 (4) ◽  
pp. 399-406
Author(s):  
W. S. Rouverol
Keyword(s):  
High Speed ◽  
Velocity Ratio ◽  
Multiple Point ◽  
Inertial Effects ◽  
Power Capacity ◽  
Wear Life ◽  
Pure Rolling ◽  
Ball Diameter ◽  
New Type ◽  
Steel Balls

A new type of mechanical variable-speed transmission, which owes its improved efficiency and wear-life to the utilization of multiple point contacts in pure rolling, has a power capacity in proportion to the maximum tractive forces and rolling velocities developed by a large number of small steel balls. Designing for maximum power capacity depends on finding the point at which the components of tractive force arising from inertial effects at high speed become so large as to interfere with the proper kinematic action of the balls. Consideration is given to the influence of a number of design and operating parameters, such as ball diameter, cage diameter, cage velocities, and velocity ratio.

Grease soap particles passing through an elastohydrodynamic contact under side slip conditions

2000 ◽  
Vol 214 (4) ◽  
pp. 317-325 ◽  
Author(s):  
P Eriksson ◽  
V Wikström ◽  
R Larsson
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Previous Investigation ◽  
Video Camera ◽  
Slip Conditions ◽  
High Speed Video ◽  
Elastohydrodynamic Contact ◽  
High Speed Video Camera ◽  
Pure Rolling ◽  
Minimum Film Thickness

In a previous investigation, grease thickener fibres were tracked as they passed through an elastohydrodynamic (EHD) contact in pure rolling using interferometry in a standard ball-and-disc apparatus. In order to capture single thickener fibres, a high-speed video camera was used. Here, the experiments have been repeated introducing different amounts of side slip for different rolling speeds and a faster video camera capable of capturing 4500 frames/s. The contact was lubricated with a continuous supply of grease. Two greases, based on the same synthetic poly(α-olefin) but thickened with Li-12-OH and lithium complex soap respectively, were studied. It was observed that the thickener fibres were stretched both before entering the contact and as they passed through it. Fibres seem to avoid the minimum film thickness regions and, if they enter, the film is restored immediately after passage.

scholarly journals Numerical Research on Performance of High-Speed Partial Emission Pump

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Qingjiao Shui ◽  
Ting Jiang ◽  
Binghui Pan ◽  
Tianxing Yang ◽  
Wei Pan
Keyword(s):  
Liquid Phase ◽  
High Speed ◽  
Phase Particle ◽  
Characteristic Curve ◽  
Particle Diameter ◽  
Two Phase ◽  
Factors Affecting ◽  
External Characteristic ◽  
Numerical Simulation Methods ◽  
Small Flow

The high-speed partial emission pump is a small flow and high-head pump, which has been widely used. To study the main factors affecting the performance of high-speed partial emission pumps, numerical simulation methods were used to calculate the performance parameters of high-speed partial emission pumps with and without inducers, and the external characteristic parameters were verified through comparison test values. The results show that the head of the high-speed partial emission pump with inducer is nearly 15 m higher than that of the high-speed partial emission pump without inducer. Considering the influence of air in the high-speed partial emission pump on the working performance, the two-phase flow with different flow rates, different particle sizes, and different concentrations was calculated, and the different liquid phase distributions, liquid phase velocity vector diagrams, and external characteristic curve were compared. The results show that under the same flow condition, the gas-phase particle diameter has the most severe influence on the external characteristic.

Effect of velocity ratio on the interaction between plasma synthetic jets and turbulent cross-flow

2019 ◽  
Vol 865 ◽  
pp. 928-962 ◽  
Author(s):  
Haohua Zong ◽  
Marios Kotsonis
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Velocity Ratio ◽  
Vortex Pair ◽  
Synthetic Jets ◽  
Low Energy ◽  
Vortex Rings ◽  
Wall Region ◽  
Mean Velocity ◽  
Counter Rotating Vortex Pair

Plasma synthetic jet actuators (PSJAs) are particularly suited for high-Reynolds-number, high-speed flow control due to their unique capability of generating supersonic pulsed jets at high frequency (${>}5$  kHz). Different from conventional synthetic jets driven by oscillating piezoelectric diaphragms, the exit-velocity variation of plasma synthetic jets (PSJs) within one period is significantly asymmetric, with ingestion being relatively weaker (less than $20~\text{m}~\text{s}^{-1}$) and longer than ejection. In this study, high-speed phase-locked particle image velocimetry is employed to investigate the interaction between PSJAs (round exit orifice, diameter 2 mm) and a turbulent boundary layer at constant Strouhal number (0.02) and increasing mean velocity ratio ($r$, defined as the ratio of the time-mean velocity over the ejection phase to the free-stream velocity). Two distinct operational regimes are identified for all the tested cases, separated by a transition velocity ratio, lying between $r=0.7$ and $r=1.0$. At large velocity and stroke ratios (first regime, representative case $r=1.6$), vortex rings are followed by a trailing jet column and tilt downstream initially. This downstream tilting is transformed into upstream tilting after the pinch-off of the trailing jet column. The moment of this transformation relative to the discharge advances with decreasing velocity ratio. Shear-layer vortices (SVs) and a hanging vortex pair (HVP) are identified in the windward and leeward sides of the jet body, respectively. The HVP is initially erect and evolves into an inclined primary counter-rotating vortex pair ($p$-CVP) which branches from the middle of the front vortex ring and extends to the near-wall region. The two legs of the $p$-CVP are bridged by SVs, and a secondary counter-rotating vortex pair ($s$-CVP) is induced underneath these two legs. At low velocity and stroke ratios (second regime, representative case $r=0.7$), the trailing jet column and $p$-CVP are absent. Vortex rings always tilt upstream, and the pitching angle increases monotonically with time. An $s$-CVP in the near-wall region is induced directly by the two longitudinal edges of the ring. Inspection of spanwise planes ($yz$-plane) reveals that boundary-layer energization is realized by the downwash effect of either vortex rings or $p$-CVP. In addition, in the streamwise symmetry plane, the increasing wall shear stress is attributed to the removal of low-energy flow by ingestion. The downwash effect of the $s$-CVP does not benefit boundary-layer energization, as the flow swept to the wall is of low energy.

Computational Fluid Dynamics Study of Oil Behavior in a Scoop, and Factors Affecting Scoop Capture Efficiency

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Evgenia Korsukova ◽  
Hervé Morvan
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Gas Turbines ◽  
High Speed ◽  
Velocity Ratio ◽  
Capture Efficiency ◽  
Parameter Analysis ◽  
Parameter Study ◽  
3D Simulations ◽  
Engine Components

Abstract Due to the continuous reduction of engine sizes, efficient under-race lubrication becomes ever more crucial in order to provide sufficient amount of oil to various engine components. An oil scoop is a rotating component that captures oil from a jet, and axially redirects it to the bearing, providing under-race lubrication. Given the importance of lubrication in high-speed engine components, the efficiency study of under-race lubrication appliances receives rapidly growing demands from manufacturers and therefore is of great interest. This work provides description of computational fluid dynamics (CFD) methods that were found to be most accurate and efficient for a large parameter analysis of the scoop capture efficiencies. One of the main purposes of this paper is to demonstrate an optimal and validated computational approach to modeling under-race lubrication with a focus on oil capture efficiency. Second, to show which factors most influence the scoop capture efficiency. Additionally, simulations allow for the fluid behavior inside the scoop to be observed that cannot be visualized experimentally due to high speeds. An improved method of efficiency calculation is also presented and compared to existing methods (Cageao, P. P., Simmons, K., Prabhakar, A., and Chandra, B., 2019, “Assessment of the Oil Scoop Capture Efficiency in High Speed Rotors,” ASME J. Eng. Gas Turbines Power, 141(1), p. 012401; Korsukova, E., Kruisbrink, A., Morvan, H., Paleo Cageao, P., and Simmons, K., 2016, “Oil Scoop Simulation and Analysis Using CFD and SPH,” ASME Paper No. GT2016-57554.). Results of both two-dimensional (2D) and semi-three-dimensional (3D) simulations are provided. Both qualitative comparison of 2D with semi-3D simulations and quantitative comparison of 2D simulations with experiments (Cageao, P. P., Simmons, K., Prabhakar, A., and Chandra, B., 2019, “Assessment of the Oil Scoop Capture Efficiency in High Speed Rotors,” ASME J. Eng. Gas Turbines Power, 141(1), p. 012401) show consistency. Parameter study using 2D simulations is shown with variation of rotational scoop speed, jet angles, velocity ratio. Key results show that changes of the jet angle and velocity ratio can improve the scoop efficiency.

Characteristics of a co-flowing jet with varying lip thickness and constant velocity ratio

2020 ◽  
Vol 92 (4) ◽  
pp. 633-644
Author(s):  
Naren Shankar R. ◽  
Kevin Bennett S. ◽  
Dilip Raja N. ◽  
Sathish Kumar K.
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Critical Limit ◽  
Potential Core ◽  
Content Type ◽  
Free Jet ◽  
Current Scenario ◽  
Wake Zone ◽  
Bypass Ratio ◽  
Practical Implications

Purpose This study aims to analyze co-flowing jets (CFJs) with constant velocity ratio (VR) and varying primary nozzle lip thickness (LT) to find a critical LT in CFJs below which mixing enhances and beyond which mixing inhibits. Design/methodology/approach CFJs were characterized with a constant VR and varying LTs. A single free jet with a diameter equal to that of a primary nozzle of the CFJ was used for characteristic comparison. Numerical simulation is carried out and is validated with the experimental results. Findings The results show that within a critical limit, the mixing enhanced with an increase in LT. This was signified by a reduction in potential core length (PCL). Beyond this limit, mixing inhibited leading to the elongation of PCL. This limit was controlled by parameters such as LT and constant VR. A new region termed as influential wake zone is identified. Practical implications In this study, the VR is maintained constant and bypass ratio (BR) was varied from low value to very high values. Presently, subsonic commercial turbo fan operates under low to ultra-high BR. Hence the present study becomes vital to the current scenario. Originality/value To the best of the authors’ knowledge, this is the first effort to find the critical value of LT for a constant VR for compressible co-flow jets. The CFJs with constant VR and varying LT have not been studied in the past. The present study focuses on finding a critical LT below which mixing enhances and above which mixing inhibits.

scholarly journals Experiment on the Breakup of Liquid Jets in Different Cross-Airflows

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Tian Deng ◽  
Wei Chen ◽  
Xing-ming Ren ◽  
Shuai Jiang ◽  
Chao-hua Yuan
Keyword(s):  
Penetration Depth ◽  
High Speed ◽  
Velocity Ratio ◽  
Flux Ratio ◽  
Liquid Jets ◽  
Uniform Shear ◽  
Jet Trajectory ◽  
Uniform Case ◽  
Jet Penetration ◽  
Exponential Relation

The experiment is conducted with a high-speed camera to investigate the breakup processes of liquid jets in uniform, shear-laden, and swirling cross-airflows. The liquid used in the test is water, the nozzle diameter is 2 mm, and the liquid-to-air momentum flux ratio q ranges from 5 to 3408.5. The results indicate that liquid jets break up to form small droplets in the uniform cross-airflow. There is an exponential relation between the broken position and q. In the shear-laden cross-airflow, the penetration depth of the jet is similar to that of the uniform case, both of which increase with the increase of q. When q and the mean Weber number are the same as the uniform case, the penetration depth of the jet increases by 25% when the velocity ratio of the upper and lower inlets is UR=5; the jet penetration depth decreases by 47.2% when the ratio of UR=0.2 and the jet breaks up quickly and the atomization effect will be better. In the swirling cross-airflow, the jet trajectory is similar to the uniform case and also satisfies the exponential property. When the swirl is weak (swirling number SN=0.49), the jet penetration depth increases compared to the uniform case; when the swirl is strong (SN=0.82), the cross-swirling airflow restrains the jet penetration depth.

AN ALGEBRAIC APPROACH TO THE INTERACTION OF A THREE-LEVEL ATOM INTERACTING WITH QUANTIZED RADIATION FIELD

2000 ◽  
Vol 14 (14) ◽  
pp. 1459-1471
Author(s):  
XU-BO ZOU ◽  
JING-BO XU ◽  
XIAO-CHUN GAO ◽  
JIAN FU
Keyword(s):  
Algebraic Structure ◽  
Evolution Operator ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Time Evolution Operator ◽  
Level Atom ◽  
Unitary Transformations ◽  
Quantized Field ◽  
Quantized Radiation Field ◽  
Multiphoton Interaction

The system of a three-level atom in the Ξ configuration coupled to two quantized field modes with arbitrary detuning and density-dependent multiphoton interaction is studied by dynamical algebraic method. With the help of an su(3) algebraic structure, we diagonalize the Hamiltonian by making use of unitary transformations and obtain the eigenvalues, eigenstates and time evolution operator for the system. Based on this su(3) structure, we also show that the system of a three-level atom in the Ξ configuration can be exactly transformed to an effective two-level Hamiltonian by an unitary transformation. Finally, we show that there exist an su (N) algebraic structure in the system of a N-level atom interacting with N-1 field modes.

Normal form method for large/small amplitude instability criterion with application to wheelset lateral stability

2014 ◽  
Vol 14 (03) ◽  
pp. 1350073 ◽  
Author(s):  
H. Dong ◽  
J. Zeng
Keyword(s):  
Normal Form ◽  
Small Amplitude ◽  
High Speed ◽  
Order Approximation ◽  
Algebraic Approach ◽  
Instability Criterion ◽  
Lateral Stability ◽  
Subcritical Bifurcation ◽  
Large Amplitude Oscillation ◽  
The Stability

Subcritical and supercritical bifurcations are two typical behaviors that exist in high speed railway vehicles. In the presence of instability, the former and the latter behaviors may lead to large amplitude oscillation and small amplitude swaying, respectively. The normal form (NF) method of Hopf bifurcation provides a way to study the supercritical and subcritical bifurcation. The wheelset is a key component in the vehicle system and it plays an important role in vehicle lateral stability. To study the lateral stability problems, three wheelset models are considered, which involve the NF theory. This method is an algebraic approach as opposed to the integration approach. Like the sign of Re (λ) that determines the stability of linear system, the sign of Re c1(0) determines the two bifurcation modes, meaning that Re c1(0) > 0 for supercritical bifurcation and Re c1(0) < 0 for subcritical bifurcation. Furthermore, if the ordinary differential equation (ODE) is local linear near the equilibrium position, it leads to the condition of Re c1(0) = 0, resulting in the jumping phenomenon. Besides, the expression of the 1/2-order approximation of limit cycle can be further obtained.

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