scholarly journals Theoretical Analysis of Thin Curved Rod Displacements V. P. Lugovoi1)

2021 ◽  
Vol 20 (5) ◽  
pp. 399-404
Author(s):  
V. P. Lugovoi
Keyword(s):  
Theoretical Analysis ◽  
External Force ◽  
Ultrasonic Method ◽  
Small Diameter ◽  
Elastic Displacement ◽  
Radius Of Curvature ◽  
Circular Arc ◽  
Oscillatory Systems ◽  
Curved Rods ◽  
Traditional Processing

The paper presents a comparative theoretical analysis of the movements of the curved rods of various curvature forms, which can be applied as tools for ultrasonic treatment of holes in fragile materials. It has been shown that the traditional processing of holes by an ultrasonic method is based on the use of straight rods, in which the amplitudes of displacements on the working – free end corresponds to the value of displacements at the point of its attachment to the ultrasonic oscillation concentrator. Supplementing the configuration of a straight rod with a curvilinear shape in the form of a circular arc or a spiral twisted by one turn will allow obtaining additional displacements caused by the elastic properties of a section with a curved shape. The paper considers several calculated schemes of a curvilinear rod bounded by angles j equal to p/2, p and 2p, fferent direction of the external force action. The obtained results have shown that an increase in the circular arc angle leads to a corresponding increase in the elastic displacement index of the rod free end. In this case, the total displacements of the rod free end will be made from displacements caused by vibrations of the acoustic system and the displacements of a curved thin rod from an external force. Calculations have established that the magnitude of the elastic displacements of curved rods is influenced by the shape and magnitude of the angle, the direction of the external force, the radius of curvature, the rigidity of the cross section. The considered schemes of thin rods with curvilinear sections can find practical application in ultrasonic oscillatory systems for processing small-diameter holes in fragile materials. This increases the intensity of tool oscillations and improves the process performance.

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Improving the Characteristics of Gear Pumps: Part A — Discharge

2003 ◽  
Author(s):  
Ahmed M. M. El-Bahloul ◽  
Yasser Z. R. Ali
Keyword(s):  
Correction Factor ◽  
Helix Angle ◽  
Tooth Profile ◽  
Radius Of Curvature ◽  
Circular Arc ◽  
Pressure Angle ◽  
Face Width ◽  
Angle Change ◽  
Number Of Teeth ◽  
Gear Pumps

The main objective of this paper is to study the effect of gear geometry on the discharge of gear pumps. We have used gears of circular-arc tooth profile as gear pumps and have compared between these types of gearing and spur, helical gear pumps according to discharge. The chosen module change from 2 to 16 mm, number of teeth change from 8 to 20 teeth, pressure angle change from 10 to 30 deg, face width change from 20 to 120 mm, correction factor change from −1 to 1, helix angle change from 5 to 30 deg, and radii of curvature equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius of curvature equal 2.5, 2.75, 3m for all addendum circular arc tooth and convex-concave tooth profile, and derived equations representing the tooth profile, and calculated the points of intersections between curves of tooth profile. We drive the formulas for the volume of oil between adjacent teeth. Computer program has been prepared to calculate the discharge from the derived formulae with all variables for different types of gear pumps. Curves showing the change of discharge with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) The discharge increases with increasing module, number of teeth, positive correction factor, face width and radius of curvature of the tooth. 2) The discharge increases with increasing pressure angle to a certain value and then decreases with increasing pressure angle. 3) The discharge decreases with increasing helix angle. 4) The convex-concave circular-arc gears gives discharge higher than that of alla ddendum circular arc, spur, and helical gear pumps respectively. 5) A curve fitting of the results are done and the following formulae derived for the discharge of involute and circular arc gear pumps respectively: Q=A1bm2z0.895e0.065xe0.0033αe−0.0079βQ=A2bm2z0.91ρ10.669e−0.0047β

Thermal Elastohydrodynamic Lubrication Analysis for Point Contact Transmission

2009 ◽  
Author(s):  
Hai-zhou Huang ◽  
Xi-chuan Niu ◽  
Xiao-yang Yuan
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Surface Velocity ◽  
Squeeze Film ◽  
Elastic Displacement ◽  
Circular Arc ◽  
Tooth Width ◽  
Contact Transmission

To investigate the thermal EHL (elastohydrodynamic lubrication) in point contact transmission, a model considering the two-dimensional surface velocity of tooth face and the running-in is proposed. The numerical solutions for pressure, temperature and film thickness distribution in the contact zone are obtained by solving equations including the Reynolds, Energy and the elastic displacement with variable dimension meshing method. The model was used to study the point contact transmission of the circular arc gear in a windlass. The main results show that it is pure rolling along the direction of tooth width, and the rolling speed plays a leading role in improving the lubricating performance and transmission efficiency of circular arc gear. The squeeze film effect makes the pressure peak tend to be gentle and the film thickness increase slightly.

Study on NC Compliant Bonnet Tool Abrasive Polishing Based on Magnetorheological Torque Servo

2010 ◽  
Vol 443 ◽  
pp. 411-416 ◽  
Author(s):  
Yong Jie Shi ◽  
Di Zheng ◽  
Jian Ming Zhan ◽  
Long Shan Wang ◽  
Xiao Feng Liu ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Contact Pressure ◽  
Applied Load ◽  
Initial Pressure ◽  
Radius Of Curvature ◽  
Hertz Theory ◽  
Factors Affecting ◽  
Polishing Force ◽  
Polishing Tool ◽  
Polishing Efficiency

In this paper, a NC compliant abrasive polishing system was developed based on a magnetorheological torque servo (MRT), using a bonnet as the polishing tool. The MRT was uesd to provide a load acting on bonnet tool to produce the polishing force. In order to find the factors affecting the polishing quality, the models of the applied load, polishing force and contact pressure between the bonnet and the part were established based on Hertz theory, and the factors affecting the contact pressure were analyzed. Theoretical analysis indicated that there was a significant effect of the applied load, the initial pressure of the bonnet and the radius of curvature of the part on contact pressure. Experiments were carried out to verify the validity of the models, and experiment results showed that the roughness of the part was improved greatly and the polishing efficiency could be controlled by changing the initial pressure of the bonnet and applied load.

scholarly journals The effect of surface roughness on the adhesion of elastic solids

1975 ◽  
Vol 345 (1642) ◽  
pp. 327-342 ◽  
Keyword(s):  
Flat Surface ◽  
The Other ◽  
Contact Theory ◽  
Elastic Displacement ◽  
Radius Of Curvature ◽  
Statistical Average ◽  
Elastic Solids ◽  
Maximum Value ◽  
Effect Of Surface ◽  
Adhesive Forces

This paper describes a study of the adhesion between elastic solids and the effect of roughness in reducing the adhesion. The experiments were carried out between optically smooth rubber spheres and a hard smooth flat surface of Perspex which could be roughened to various degrees. The radius of the rubber spheres was varied by a factor of 8, their elastic modulus by a factor of 10, while the centre line average (c.l.a.)of the roughened Perspex surface was varied from 0.12 to 1.5 μm. The results show that c.l.a. roughnesses which are small compared with the overall deformation occurring at the region of the rubber-Perspex contact can produce an extremely large reduction in adhesion. The effect is more marked for rubbers of higher modulus. On the other hand the curvature of the sphere (over the range examined) has little influence. For this reason and because the analytical problem of a sphere on a rough flat is extremely complicated a theoretical analysis has been developed for the simpler case of a smooth flat in contact with a rough flat surface. As in Greenwood & Williamson (1966) the rough surface is modelled by asperities all of the same radius of curvature and with heights following a Gaussian distribution of standard deviation σ. The overall contact force is obtained by applying the contact theory of Johnson, Kendall & Roberts (1971) to each individual asperity. The theory predicts that the adhesion expressed as a fraction of the maximum value depends upon a single parameter, 1/Δ e ,which is the ratio between a and the elastic displacement δ C that the tip of an asperity can sustain before it pulls off from the other surface. The analysis shows that the adhesion parameter may also be regarded as representing the statistical average of a competition between the compressive forces exerted by the higher asperities trying to prize the surfaces apart and the adhesive forces between the lower asperities trying to hold the surfaces together. Although the theory is derived for two nominally plane surfaces it is found to fit the experimental results for a sphere on a flat reasonably well.

Condensation on a Downward-facing Horizontal Rippled Surface

1972 ◽  
Vol 94 (3) ◽  
pp. 315-320 ◽  
Author(s):  
Avram Markowitz ◽  
B. B. Mikic ◽  
A. E. Bergles
Keyword(s):  
Experimental Data ◽  
Small Diameter ◽  
Horizontal Cylinder ◽  
Analytical Investigation ◽  
Film Condensation ◽  
Radius Of Curvature ◽  
Condensation Rate ◽  
Projected Area ◽  
Condensate Film ◽  
Constant Radius

An analytical investigation is presented for film condensation on a downward-facing horizontal doubly rippled surface. Small undulations having constant radius of curvature are combined with larger cylindrical grooves designed to aid condensate runoff. A direct expression for the condensate film thickness at the top of an undulation crest, as well as on a small-diameter horizontal cylinder, is derived. An upper-bound expression for the condensation rate on the rippled surface is then obtained which predicts that the condensation rate will be five times the rate attainable on a flat horizontal surface of the same projected area. This analytical expression is compared with experimental data.

Analyzing the Contacting Stresses of Ball in Servo Disc Brake

2013 ◽  
Vol 419 ◽  
pp. 280-285
Author(s):  
Jin Yue Tian ◽  
Zheng Ning Ren ◽  
Jin Wei Wang ◽  
Jin Yu Yao ◽  
Shi Xin Lan ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Theoretical Analysis ◽  
Contact Stress ◽  
Contact Surface ◽  
Optimization Design ◽  
Three Dimensional ◽  
Elastic Displacement ◽  
Disc Brake ◽  
Ball Bearings

The ball's stress distribution in tractor servo disc brake usually is three dimensional in tractor. In this article,the contact theoretical analysis is used to calculate the contact face action distribution between the saddle ball bearings, the elastic displacement, train and stress distributed situation was determined in contact surface. The results show that the method is completely feasible, this method was suitable similarly for the solution contact stress question, the data has provided the important reference for the contact face optimization design.

Improving the Characteristics of Gear Pumps: Part B — Pressure

2003 ◽  
Author(s):  
Ahmed M. M. El-Bahloul ◽  
Yasser Z. R. Ali
Keyword(s):  
Correction Factor ◽  
Helix Angle ◽  
Tooth Profile ◽  
Radius Of Curvature ◽  
Circular Arc ◽  
Pressure Angle ◽  
Face Width ◽  
Angle Change ◽  
Number Of Teeth ◽  
Gear Pumps

The main objective of this paper is to study the effect of gear geometry on the oil pressure of gear pumps. We have used gears of circular-arc tooth profile as gear pumps and have compared between these types of gearing and spur, helical gear pumps according to pressure. The chosen module change from 2 to 16 mm, number of teeth change from 8 to 20 teeth, pressure angle change from 10 to 30 deg, face width change from 20 to 120 mm, correction factor change from −1 to 1, helix angle change from 5 to 30 deg and radii of curvatures equal 1.4, 1.5, 2, 2.5, 2.75, and 3m are considered. The authors deduced that the tooth rack profile with radius or curvature equal 2.5, 2.75, 3m for all- addendum circular arc tooth and convex-concave tooth profile, and derived equations of pressure difference for spur, helical, and circular- are gear pumps. Computer program has been prepared to calculate the pressure from the derived formulae with all variables for different types of gear pumps. Curves showing the change of pressure with module, number of teeth, pressure angle, face width, correction factor, helix angle, and radius of curvature are presented. The results show that: 1) Pressure increases with increasing helix angle. 2) Pressure decreases with increasing face width, number of teeth, positive correction factor, module, pressure angle and radius of curvature of the tooth. 3) The all- addendum circular-arc gears generates pressure higher than helical, convex-concave and spur gear pumps. 4) A curve fitting is done for all variables with pressure and the following formulae derived for the pressure: P=A3b−0.943z−1.175m−2.1β0.175e−0.61xe−0.0048αP=A4b−1z−1.34m−2β0.119ρ1−0.393 These formulae represent simple tool for the designer to calculate the pressure of involute and circular arc gear pumps.

Theoretical Analysis of Gas and Oil Storage Cavern in Bedded Salt Rock Using a Love Function

2012 ◽  
Vol 204-208 ◽  
pp. 1499-1502 ◽  
Author(s):  
Gui Jun Wang ◽  
Peng Xie
Keyword(s):  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Elastic Theory ◽  
Elastic Displacement ◽  
Salt Rock ◽  
Axisymmetric Model ◽  
Rock Formation ◽  
Oil Storage ◽  
Stress Components ◽  
Logarithmic Functions

Based upon the elastic theory, the gas and oil storage cavern in bedded salt rock formation is generalized as a spatially axisymmetric model. A Love function was built from polynomial and logarithmic functions at first, and then solved, considering the gravity, the internal gas and oil pressure of the cavern, the boundary conditions, as well as the continuity conditions at the interface between salt and non-salt media. Finally, the elastic displacement and stress components are achieved which are satisfied to the main boundary and continuity conditions.

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