Circular-arc Profile Research Articles

Design and Testing of a New Type of Planetary Traction Drive Bearing-Type Reducer

This paper presents the design and development of a new type of planetary traction drive bearing-type reducer. In this design, the transmission outer ring is replaced with an elastic ring. The design constructs a circular arc at the axial end of the rolling body’s contour line. This ensures that the contact point of this arc with the reducer’s outer ring and the inner ring’s axial end face is maintained on the radial traction contact line. As a result, it can replace the thrust bearing and provide an axial support function. It has the advantages of simple structure, easy processing, smooth transmission, and low noise. This paper first introduces the design and development process of this bearing-type reducer and presents systematic research on its transmission principle and dynamics. Subsequently, in response to the edge effect phenomenon of the outer ring contact line, the contour line of the outer ring is refined by adopting the shaping method used for bearing rollers, establishing a full circular arc profile shaping method, which significantly improves its edge effect. Finally, in our investigations, combined with experimental tests, a prototype of the bearing-type reducer was fabricated, and the speed ratio, torque, and transmission efficiency of the reducer were studied. The results demonstrate that the bearing-type reducer can achieve high transmission accuracy and efficiency. The transmission performance varies significantly under different lubrication conditions, with the peak efficiency reaching as high as 99.97% when using Santotrac 50 traction oil. The results verify the feasibility of the proposed design method and have the potential to be applied in wheel hub motors and robot joints.

Evaluating surface roughness of curved surface with circular profile based on arithmetic circular arc fitting

A procedure based on Kåsa fit for evaluating the surface roughness of a curved surface with a circular arc profile was suggested in this paper. To investigate the effectiveness of the method, some curved surface profiles with preset surface roughness were numerically generated, and their surface roughness was evaluated by the procedure based on Kåsa fit. And the surface roughness of two experimental surface profiles evaluated by the method based on Kåsa fit was compared with those evaluated by linear fitting and quadratic polynomial fitting to demonstrate both the effectiveness and the preservation of Kåsa fit-based procedure. Results show that the evaluated value of surface roughness by Kåsa fit-based procedure only deviated from the actual value by less than 10%, even in the case of considerable fitting parameters’ error (>30%). Also, the Kåsa fit can report a reasonable value of surface roughness with better preservation of shift and rotation motion of the surface profile compared to both linear fit and quadratic polynomial fitting, especially for the curved surface with a short radius. This procedure based on Kåsa fit can be used in evaluating surface roughness of curved surface with circular arc profile no matter what pose of the object under observed.

Effect of Different Types of External Guide Vanes on the Performance of High-Pressure Centrifugal Compressor

In order to reduce exit swirl and obtain the desired Mach number, axial exit guide vanes (EGV) are often employed in a centrifugal compressor. NASA CC3 compressor, with wedge vane diffuser and without EGV, is considered as the base model for the analysis and validation. An axial flow domain with exit guide vane is added to this base model after the diffuser outlet to study the effect on the compressor performance. The performance of exit guide vane with different profiles: flat plate, symmetric wedge, circular arc, and airfoil vane profiles by maintaining the same chord, number of vanes, and flow angle of the vanes are studied. Numerical simulations are carried out with 60 number of exit guide vanes for all four types of vanes. Among several combinations, when the centrifugal compressor is equipped with 60 circular arc vanes as EGV, the efficiency and pressure recovery values at the design point have increased by 6.5% and 8.9%, respectively.

A running-in strategy based on an efficient wear simulation model for double circular-arc spiral bevel gears

A proper running-in process is necessary for double circular-arc spiral bevel gears to achieve desirable meshing performance. However, this type of gear transmission lacks a suitable running-in wear model, which brings great difficulties to the design of appropriate running-in strategies. To address this problem, the present study establishes an efficient numerical wear model to reveal the wear behavior of double circular-arc spiral bevel gear pairs, based on which a step-wise load running-in strategy is proposed. The established Archard's wear model considers the meshing characteristics of double circular-arc spiral bevel gears and sets a small threshold value, which can reflect the wear behavior of this gear in the running-in stage. To improve the computation efficiency, a two-step parameter updating strategy is proposed to enhance the iteration of p and s. The wear simulation reveals the quantitative relationship contact pressure and running-in cycle during the running-in process. Based on the reveal relationship, a step-wise load running-in strategy is proposed to sharpen the running-in period. The developed wear model and the proposed running-in strategy can be extended to other types of gears with circular-arc profiles.

Determination of Undercutting Avoidance for Designing the Production Technology of Worm Gear Drives with a Curved Profile

One of the most difficult production geometry tasks arising in the machining process of the elements of a drive pair is to avoid undercuts. It is a serious technological challenge to determine the production of the elements of worm gear drives avoiding the phenomenon undercut, especially in the case of a pair consisting of a curved profile worm and its mating wheel. The technology of forming the tooth surface requires a separate examination in each case, running the simulation procedure of the tool geometry and the movement conditions when forming different teeth. This article proposes a new concept for determining and then avoiding the positions of undercutting by examining the patented worm with a circular arc profile in axial section, due to its extremely advantageous aspect in terms of production technology. The cutting edge of the hob, formed from the substitutional worm, moves on the tooth surface of the worm, and produces the tooth surface of the conjugate wheel. The gear tooth surface has been determined based on the main law of gearing with the lines consisting of the contact points of the conjugated surfaces. The conditions for the disappearance of the common normal or the relative velocity fitting to the common tangent plane of the contacting points are defined in this paper.

Geometry design, meshing analysis and error influences of face-hobbed cycloidal bevel gears with double circular-arc profile for a nutation drive

As the core components of nutation drive, the internal meshing pair of bevel gear must be delicately designed to achieve desirable operational performances for the transmission device. For this purpose, this paper designs a face-hobbed internal meshing pair of cycloidal bevel gears with double circular-arc profile (DCAP). First, a cutter head with DCAP cutting edges is designed to generate the tooth surface of internal gear pair. Then, the tooth geometry of the external and internal bevel gears are derived according to the meshing theory. Finally, a finite element model is developed to simulate the meshing characteristics of the gear pair. The simulation results reveal that the proposed face-hobbed cycloidal bevel gear pair with DCAP has higher contact/bending strength, better load sharing and smaller transmission error compared with the logarithmic spiral bevel gear pair with DCAP. The effects of four typical manufacturing errors on meshing characteristics of the proposed bevel gear pair are investigated to provide fundamental references for the tolerance design of cycloidal bevel gears.

Computerized design, simulation of meshing and stress analysis of non-generated double circular-arc helical gear drives with different combinations of transverse pressure angle

The computerized design of non-generated double circular-arc helical gear drives with different combinations of transverse pressure angle based on the active design of the meshing line function is presented. The application of different transverse pressure angles for the double circular-arc tooth profiles is discussed and the parametric equations for the driving and driven gear tooth surfaces are derived. The meshing performance and mechanical behavior are studied in terms of the achieved contact patterns and the evolution of the contact and bending stresses for nine cases of design. The results show that one of the cases of design of double circular-arc helical gear drives considering a combination of transverse pressure angles of 25 and 15 degrees for the convex and concave circular-arc profiles of the pinion shows better mechanical performance with respect to the other combinations of different transverse pressure angles. The proposed geometry of non-generated gears is appropriate for manufacturing by injection molding or additive manufacturing for plastic, ceramic, metal as well as nanocomposite gears.

Estimating the Catenary Parameter for Catenary Shape Using the Newton Raphson Iterative Method as a Tool for Extended Reach Well Buildup Section Design

The catenary well profile was first used to design extended reach well buildup section in 1985, ever since then a number of wells have been constructed using this profile. It towers over the constant build (circular arc) profile in terms of advantages. Prominent of which is the reduction of torque and drag. This advantage was restrained by the catenary parameter “a”, as “a” determines the shape or trajectory of a catenary shape in any given circumstance. We proffered a solution to estimating the catenary parameter “a” using the Newton-Raphson iteration method for linear equations. This method makes it easy to calculate “a” for almost every desired catenary shape. Also after estimating the values for “a” we went ahead to calculate tensions that will produce that calculated catenary parameter “a” as the parameter is the product of tension at the end of the string and inverse of unit weight. This method of catenary parameter prediction has been used to design overhead electrical cables and predict the extent of sagging of this cables. We used it here to design the path or trajectory of an extended reach well with satisfactory success. Results from the study shows that the use of the Newton-Raphson iterative method for the estimation of catenary parameter “a” for buildup section design of extended reach wells makes it easy for engineers to plan catenary trajectories with available materials and also removes the uncertainties that are inherent in predicting the shape of the trajectory. Keywords : Caternary, String, well, Newton-Raphson, Extended Reach well DOI: 10.7176/JETP/11-5-04 Publication date: October 31 st 2021

Performance improvement of the axial self-rectifying impulse air-turbine for wave energy conversion by multi-row guide vanes: Design and experimental results

Self-rectifying impulse turbines are a popular alternative to the Wells turbine for oscillating-water-column wave energy converters. Self-rectifying impulse turbines have two sets of guide-vanes placed symmetrically on each side of the rotor, instead of a single set as in unidirectional turbines. The efficiency of self-rectifying turbines with fixed guide-vanes is severely affected by the significant aerodynamic losses due to the inherent misalignment between the outflow from the rotor and the downstream guide-vane system. The paper presents a new design method for high-deflection guide-vane systems arranged into multiple, rather than single, rows. The design method aims to increase the turbine efficiency by reducing the losses caused by aerodynamic outflow stalling at the exit guide-vane system while ensuring the required inlet guide-vane system inflow deflection. The new design method was validated by testing and comparing detailed experimental results for a pair of single-row guide-vane stators, with conventional camber line and thickness distribution vane sections, and a five-row guide-vane stator, with constant thickness circular-arc profiles, on each side of the rotor. A Reynolds number effect correction methodology is presented to estimate the performance of a full-scale self-rectifying turbine from model testing results.

A new solution for sharpening helical flute hobs

• A complete model of a hob sharpener to sharpen helical flute hobs is established. • The model of circular arc wheel profile to sharpen helical flute hobs is established. • The model of machine settings for form grinding machine to sharpen helical flute hobs is established. • Using a circular arc profile CBN wheel and a form grinding machine, the result exceeds DIN AA. Sharpening helical hobs with a hob sharpener is relatively easy and efficient, but the hob sharpener has poor versatility due to its tilted spindle for sharpening helical flutes. In this paper, we propose a new solution for sharpening helical flute hobs. Geometrically, we simplified the wheel profile to a circular arc, which made it easy to obtain the wheel profile through the circular arc NC (numerical control) function G02 or G03. With the simplified wheel profile, it is much easier to obtain the profile of the wheel made with CBN (cubic boron nitride), even with the use of an ordinary CNC (computer-aided numerical control) contour dressing machine. We also calculated the machine settings for a 5-axis form grinding machine, in which the machine settings of a hob sharpener were transformed into through coordinate transformation. With such new machine settings, the helical flute hob can be sharpened by the form grinding machine. Finally, our numerical examples evaluate the variations between the proposed simplified circular arc wheel profile and the theoretical one. Moreover, the results of our experiment using the form grinding machine with the simplified circular arc profile wheel are illustrated in the plots of the measuring machine.

Surface Capacity of Gears of Circular-Arc Tooth-Profile.(Dept.M)

The paper embodies results and analysis of an experimental investigation carried out to study the effect of case depth, case hardness and tooth load on the surface capacity or a relatively new type of gearing having teeth of circular arc profiles. These gears were manufactured from 16 MnCr5. Carburizing. quenching and tempering techniques were used with 0.5, 1.2 and 2 mm case depth and 46, 52 and 58 HRC case hardness. also applied tooth loads 5, 75 and 10 KN were used. These tiny pairs of gears were run to 6.7x107 revolutions at speed 1460rpm In a power circulating gear test rig using forced lubrication technique. Test gears were weighed at interval of times, the accumulated weight of removed metal were drawn with the number of revolutions, Wear rate was calculated and drawn with the applied tooth load, case depth and case hardness. A curve fitting was made for these experimental results using Grapher software. Results show that an optimum case depth of the case hardened gears of circular arc tooth profile equal to 1.1 m and also optimum case hardness of the case equal to 53.5 KRC. Wear rate increases with increasing the applied tooth load. Wear rate for unhardened gears increases by 4 to 192 times than that of the case hardened gears. An empirical formulae for the accumulated weight of removed metal with number of revolution, wear rate with tooth load, case depth and case hardness were derived, also presented on the curves and discussed.

Circular-Arc Radial Cams with One Connection Arc

This paper deals with the geometric and kinematic analysis of the circular-arc profile cams with one connection arc. If the maximum lift of the follower is required, it is shown that it is possible to connect two circular-arcs – that are defined by center of curvature and radius – through a single circular-arc, and the connection points result. But, if the connection points of two given circular-arcs of the cam profile are required, at least two circular-arcs are needed to connect them. The specific equations for the geometric analysis for one circular-arc profile are described. Also, for two mechanisms, one with straight-line profile and another with one circular-arc connection profile, the geometric and kinematic analysis and simulations of the movements using SolidWorks and ADAMS programs are presented

Numerical Investigation of Heat Transfer and Fluid Flow Characteristics in Circular Wavy Microchannels with Sidewall Rib

AbstractPurpose: Numerical investigation was carried out to study the hydro-thermal characteristics in circular wavy microchannels (CWMCs) with sidewall rib. Thermal resistance and pressure drop penalty were compared with sinusoidal wavy microchannels (SWMCs) design. Parametric study on sidewall rib was also carried to minimize the pressure drop penalty and to achieve lower thermal resistance. Introducing sidewall rib in the CWMCs leads to the formation of more Deans vortices. This leads to an effective fluid mixing and augments the convective heat transfer. Design methodology/approach: A computational solid domain was created in SOLIDWORKS and the fluid domain was produced by circular arc profile for the entire length of heat sink. 3-D numerical investigation was carried out using ANSYS FLUENT software. Created computational domain was imported into ANSYS WORKBENCH. Meshing was executed in ANSYS mesh module. The computational domains were meshed using hexahedral elements adopting match control on both sides of microchannel (MC). The numerical investigation was carried out in the Re range from 100 to 300 with constant heat flux (50 W/cm2) applied at the bottom of the channel. Heat transfer and fluid flow characteristics were explained with velocity vectors, velocity contours and temperature contours. Findings: From numerical studies, it is concluded that CWMC with sidewall rib width (0.15 mm) leads to 33.6 % lower thermal resistance than SWMC with pressure drop penalty. Originality/Value: Present study is useful to identify the optimum deign to augment the heat dissipation performance of microchannel heat sink.

Efficient Low-Reynolds-Number Airfoils

A low speed wind tunnel investigation is presented characterizing the effect of leading and trailing edge flaps on thin flat plate airfoils at low Reynolds numbers. Flap size and setting angle were varied. Tests were conducted at Reynolds numbers of 40,000, 60,000, and 80,000, consistent with the operational regime of micro aerial vehicles. Performance was contrasted against a circular arc profile and three conventional airfoils. Testing encompassed force balance and surface pressure measurement. The numeric data were complemented by on and off surface flow visualization as well as the development of an analytic prediction model. The results indicate that the deployment of leading and trailing edge flaps can significantly improve the airfoil’s efficiency—not just compared with a flat plate but also a 5% camber circular arc profile. For the tested geometries, a leading and trailing edge flap angle of 15 deg was optimal. Conventional airfoil performance degraded significantly at low Reynolds numbers, yielding efficiencies far below any of the flat plate airfoils for and 60,000. Increasing the Reynolds number to 80,000 showed a dramatic improvement in the performance of the conventional airfoils.

Mathematical Validation for Maximum Heat Transfer in the Optimal Straight Fin with Circular Arc Profile Constrained by Material Volume

The central objective of the theoretical study is to analyze mathematically the straight fin with circular arc profile proposed inquisitively by Isachenko et al. back in 1969. The importance of this kind of optimal straight fin with circular arc profile stems from the fact that it maximizes heat transfer for a fixed volume of material. The mathematical analysis will be pursued with a quasi one-dimensional heat equation, constant thermal conductivity and mean convection coefficient where the controlling thermo-geometric parameter is the Biot number. Owing to the irregular shape of the circular arc, the solution of the quasi one-dimensional heat conduction equation with variable coefficients cannot be carried out analytically, and forcibly has to be carried out numerically with the finite difference method. After post-processing the computed numerical temperatures for selected Biot numbers, the veracity of maximum heat transfer could be assessed or ignored. The main finding of the present work is to incorporate to the Isachenko’s theory the limiting factor of the Biot number constraint, which must be equal to one.

Geometry and parameter design of novel circular arc helical gears for parallel-axis transmission

Based on the space curve meshing equation, in this article, a geometry design of a novel circular arc helical gear mechanism with pure rolling for parallel transmission was presented. Different from conventional circular arc gears, the meshing points of circular arc helical gears were limited at the instantaneous centre of rotation. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equation, and parameter equations of the concave–convex circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was presented, and the impact factors influencing the contact ratio were discussed. Then, the parameter design was presented for the geometry parameters of tooth profiles, such as normal pitch, tooth height and tooth thickness. Using the deduced equations, several numerical examples were then considered, and prototype samples were produced to experimentally validate the contact ratio equation and the theoretical kinematic performance. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance such as a pure rolling meshing, a high contact ratio and a large comprehensive strength, when considering engineering applications.

Development of Combined Trochoidal Profile of a Gerotor Pump

Gerotor pumps are a kind of internal gear pump, widely used in applications of lubricating system of on-road or off-road engines. Normally their outer rotors are the circular arc profile while their inner rotor profile is the conjugate curve of the outer rotor. This research focuses on how to derive the combined trochoidal profile of a gerotor pump. The hypocycloidal and epicycloidal profile of the inner rotor is generated at first. And then the profile of the outer rotor, based on the inner rotor profile, is obtained by analytical approach and computationally graphical approach. The paper provides feasibility to develop the unconventional profile of a gerotor pump.

The Resulting Toolpath of Turning a Special Surface on CNC Lathe

The surface of workpiece in NC turning process, often encounter the workpiece surface cross quadrant arc, if the use of the same processing methods and ordinary arc, often leads to the emergence of cross quadrant arc machining shape error, through the research of the NC machining of workpiece surface cross quadrant arc, CNC turning reasonable go knife and tool path in NC turning, solve cross quadrant arc, some defects in the surface of the workpiece processing, ensure the machining with circular arc profile theory demands, so as to improve the machining quality and the machining accuracy requirements.

초음파 피로시험시 시험편의 유한요소 동적 해석

An accelerated ultrasonic fatigue test (UFT) was used for analyzing very high cycle fatigue (VHCF, Nf > 10 ) behaviors of a specimen with a test resonance of 20 kHz. Using the finite element method (FEM), the dynamic behaviors of the specimen was studied by calculating the stresses along its gauge portion, with displacement. The shape of gauge portion profile was assumed to be a hyperbolic according to the stress equation of the UFT. However, as the specimen used in the test had a circular arc profile, the FEM was used for studying the local stresses for two cases of the gauge profile. The results were compared with those obtain from the stress equation of the UFT. The dynamic behavior of the gauge portion could be understood for further comparison with the actual results.

Effect of diffuser vane shape on the performance of a centrifugal compressor stage

The present paper reports the results of experimental investigations on the effect of diffuser vane shape on the performance of a centrifugal compressor stage. These studies were conducted on the chosen stage having a backward curved impeller of 500 mm tip diameter and 24.5 mm width and its design flow coefficient is ϕd=0.0535. Three different low solidity diffuser vane shapes namely uncambered aerofoil, constant thickness flat plate and circular arc cambered constant thickness plate were chosen as the variants for diffuser vane shape and all the three shapes have the same thickness to chord ratio (t/c=0.1). Flow coefficient, polytropic efficiency, total head coefficient, power coefficient and static pressure recovery coefficient were chosen as the parameters for evaluating the effect of diffuser vane shape on the stage performance. The results show that there is reasonable improvement in stage efficiency and total head coefficient with the use of the chosen diffuser vane shapes as compared to conventional vaneless diffuser. It is also noticed that the aero foil shaped LSD has shown better performance when compared to flat plate and circular arc profiles. The aerofoil vane shape of the diffuser blade is seen to be tolerant over a considerable range of incidence.