Large Helix Angle Research Articles

Computerized generation, deviation correction and rapid tooth contact analysis of helical face gear

This paper delves into the generation of helical face gears using a grinding worm. It investigates the computerized generation process and explores the inherent geometric constraints associated with the application of a grinding worm for helical face gears. An approximate grinding method, tailored for helical face gears featuring large helix angles, is proposed, with an evaluation of the resulting theoretical deviations. Furthermore, a novel rapid computational approach for determining the bearing contact of helical face gear pairs is introduced and validated through Finite Element Analysis (FEA). The subsequent analysis comprehensively examines the effects of the machine tool positioning errors on tooth flank deviations, bearing contact, and transmission errors. A sensitivity matrix is developed to elucidate the relationship between machine tool positioning errors and the tooth flank deviations, leading to the proposition of a correction method for theoretical generating deviations. Finally, the paper introduces a tooth flank modification method for helical face gears and the meshing performance is highly improved.

Effects of process parameters on cutting forces, material removal rate, and specific energy in trochoidal milling

Trochoidal milling has been developed to enhance tool life during slot machining. It is characterized by reduced cutting forces, cutting temperature, and tool wear as compared to conventional milling processes. It is effective in machining difficult-to-cut materials, high-speed machining, and groove corners. However, this process has not been deeply investigated enough to discover its advantages and optimize its parameters. A full factorial design of 144 experiments has been applied in this paper to investigate extensively the effects of axial depth of cut, feed rate, and trochoidal step on material removal rate, cutting forces, and specific energy in trochoidal milling. Trochoidal step and axial depth of cut almost have the same contributions on cutting forces by 32% and 31% respectively, followed by feed rate by 25%. Feed rate, trochoidal step, and axial depth of cut influence the material removal rate by 37%, 30%, and by 19% respectively. The contributions of feed rate, trochoidal step, and axial depth of cut on relative specific energy are 57%, 24%, and 8% respectively. The increase of axial depth of cut increases the maximum resultant force till a threshold value, then it stabilizes. This behavior occurred due to the increase of the maximum engagement angle to a certain limit, then it does not increase any more. Both feed rate and trochoidal step linear affect maximum resultant force and material removal rate, while the relationships are non-linear for specific energy. It is recommended to machine slots in full depth with the highest possible trochoidal step and feed rate, considering the increase of tool wear and surface roughness. It is preferred to use a cutting tool of a large helix angle and small diameter to reduce the threshold axial depth of cut. Overall, this study is significant in characterizing, designing, and optimizing of trochoidal milling through experimental work.

Dynamic Analysis of the Helical Gear Transmission System in Electric Vehicles with a Large Helix Angle

Sliding friction is an important excitation for the vibration and noise of a transmission system. However, in cases where the helix angle of the helical gear is large, the dynamic characteristics of the transmission system in an electric vehicle caused by friction excitation have not been explored explicitly. In this study, the helix angle of helical gears is 30.5 degrees. A mesh stiffness calculation algorithm is derived. A dynamic model of a Motor Two-Stage helical gear transmission system in an electric vehicle at a constant speed is established. A bench test is carried out to verify the model. A friction model is employed. The dynamic characteristics are analysed after considering the friction and the axial stiffness component. The friction makes the vibration in the x direction increase. The vibration in the y direction is suppressed by friction. The vibration in the z direction has a small change. The components in the frequency domain also change. The axial stiffness components only make the vibration and the meshing force increase in the time domain. This indicates that friction needs to be considered when dynamic characteristics are analysed. The study is good for the reduction of vibration and noise. This may provide a theoretical base for the condition monitoring of the gear system in electric vehicles.

Single and multi-objective optimization for cutting force and surface roughness in peripheral milling of Ti6Al4V using fixed and variable helix angle tools

Ti6Al4V titanium (Ti) alloy is a frequently used engineering material in industrial applications due to its superior properties. In this work, single-objective and multi-objective methods were used to optimize control factors (cutting speed, feed rate, and cutting tool helix angle) for minimal cutting force (Fc) and surface roughness (Ra) in peripheral milling of Ti6Al4V. Machinability experiments were performed using carbide end mill cutting tools with fixed and variable helix angles. Following the machinability tests performed using the L18 orthogonal array, the Taguchi technique was used as a single-objective optimization for each of the cutting forces and surface roughness. The Entropy-weighted TOPSIS approach was used in the second step to provide the optimum levels of the control factor, which minimizes both cutting force and surface roughness. The effects of control factors and interactions on thrust force and surface roughness were determined by Analysis of Variance (ANOVA) and contour plots. As a result of this study, it was determined that the helix angle of the cutting tool (84.91 % contribution) was the most effective parameter on the cutting force and the feed rate (22.71 % contribution) on the surface roughness. The cutting force and surface roughness values decreased in peripheral milling at high cutting speed, whereas the cutting forces increased, and the surface quality of the workpiece deteriorated in machining at high feed rates. The helix angle of the cutting tool has a favorable influence on the cutting force and surface roughness when milling with fixed helix tools. Cutting forces are minimized, and workpiece surface quality is improved using cutting tools with a larger helix angle. Variable helix tools with a large helix angle performed best in cutting force and surface roughness. Variable helix end mills with large helix angle (HA = 35°/38°), high cutting speed (Vc:108 m/min), and a low feed rate (f:0.04 mm/tooth) should be used in peripheral milling of Ti6Al4V Ti alloy to achieve both minimum cutting force and best surface quality. The mean cutting force and surface roughness values were obtained as 628.69 N and 0.363 μm, respectively, in the peripheral milling process performed at different levels of control factors. The cutting force was reduced to 227.52 N (34.71 % improvement) and the surface roughness value to 0.237 μm (276.32 % improvement) using the Entropy-weighted TOPSIS multi-objective optimization approach.

Experimental research on refrigerant condensation heat transfer and pressure drop characteristics in the horizontal microfin tubes

The condensation heat transfer characteristics and pressure drop for R410A were investigated in the horizontal smooth and microfin tubes. The 6.35-mm-OD, 7-mm-OD and 8-mm-OD tubes with active length 2 m were selected for condensation test cooled by the heat transfer fluid (water) circulated in a surrounding annulus. A refrigerant superheating 2–3 °C was set at the test section inlet and the mass flux range was 300–1100 kg·m−2·s−1. The heat transfer coefficient (HTC) of the microfin tube was about 1.63–2.29 times of that of the smooth one. The microfin one yields ~28.9% higher pressure drop than the smooth one. Large helix angle and fin height were beneficial to enhance heat transfer due to the centrifugal force and surface tension, but increased the pressure drop. 6.35-mm-OD tube produced both the higher HTC and pressure drop than the 7-mm-OD and 8-mm-OD tubes due to the increased effect of the surface tension and the sheer stress at the gas-liquid interface. It was necessary to optimize finned structure to enhance heat transfer. Experimental data were also compared with previous correlations proposed for smooth and microfin tube. It was necessary to collect more data source and make a generally-accepted and accurate correlation in future.

Non-Hertzian Elastohydrodynamic Contact Stress Calculation of High-Speed Ball Screws

In order to eliminate the calculation error of the Hertzian elastohydrodynamic contact stress due to the asymmetry of the contact region of the helix raceway, a non-Hertzian elastohydrodynamic contact stress calculation method based on the minimum excess principle was proposed. Firstly, the normal contact stresses of the screw raceway and the nut raceway were calculated by the Hertzian contact theory and the minimum excess principle, respectively. Subsequently, the Hertzian solution and the non-Hertzian solution of the elastohydrodynamic contact stress could be determined by the Reynolds equation under different helix angles and screw speeds. Finally, the friction torque test of the double-nut ball screws was designed and implemented on a self-designed bed for validation of the proposed method. The comparison showed that the experimental friction torque was the good agreement with the simulated friction torque, which verified the effectiveness and correctness of the non-Hertzian elastohydrodynamic contact stress calculation method. Under the large helix angle, the calculation accuracy of asperity contact stress for the non-Hertzian solution was more accurate than that of the Hertzian solution at the contact region of ball screws. Therefore, the non-Hertzian elastohydrodynamic contact stress considering the asymmetry of the raceway contact region could more accurately analyze the wear depth of the high-speed ball screws.

The Investigation of the Sensitivity and Direction of the Maximum Surface Error in Peripheral Milling

In this paper, we developed a virtual model predicting the tool deflection induced surface error and investigated the sensitivity and direction of the maximum surface error in various tool geometries and cutting conditions. The characteristics of the error were classified into the axial sensitive, radial sensitive, robust, overcut, and overlap zones according to the depth of cut. The maximum surface error was sensitive to the uncertainty of the radial depth of cut and robust to axial depth variation at the finishing process using a small radial depth of cut. The radial sensitivity was reduced by a large helix angle of tool. The sensitivity was decreased by increasing the depth of cut and it arrived at zero in the robust zone where the maximum surface error was not changed by both radial and axial depths of cut. An overcut occurred if axial and radial depths were deep and the overcut zone was enlarged by the helix angle and the number of teeth.

The researches concern the influence of the helix angle on the composite machining process

Magnesium oxide-reinforced wood fiber composites (MgO/WF) are a new type of multifunctional material, which can be used in different occasions, such as shopping malls, hotels, and residential buildings. Referring to the relevant literature, there is no research on the milling performance of MgO/WF. In order to better understand the relevant knowledge of the processability of MgO/WF, three cutters with different helix angles were used in this experiment to carry out the cutting of MgO/WF, and the variation trend of its cutting force, tool wear, and surface roughness was measured. The results are as follows: First, under the same cutting parameters, the resultant force decreases with the increase of helix angle. Second, with the increase of helix angle, the tool wear was slightly improved. Third, the surface roughness (Ra) showed an increasing trend with the decrease of helix angle. In the end, when milling MgO/WF, better machined surface quality and less tool wear can be obtained by selecting the tool with larger helix angle.

Experimental and numerical studies on metrological characteristics of swirlmeters with different swirler helix angles in a gas–solid two-phase flow

Swirlmeters are widely used to measure natural gas because of their simple structure, absence of internal moving parts and high measurement accuracy. However, fine particles in natural gas can affect swirlmeters’ metering accuracy. Hence, this study evaluated the metrological characteristics of swirlmeters measuring gas–solid two-phase flow with fine particles and different swirler helix angles. Experiments and simulations for swirlmeters with different solid–gas mass ratios and helix angles were performed. The results demonstrated that the swirlmeter meter factors decreased and pressure losses increased as the solid–gas mass ratio increased. With different solid–gas mass ratios, the most effective sensor detection position was at the throat outlet a half radius from the centre of the runner. The swirler with a smaller helix angle could significantly increase the meter factor, while the swirler with a larger helix angle could significantly decrease pressure losses. The swirlmeter internal flow losses were mainly derived from the swirler.

Bending stress evaluation of case-carburized helical gears with large helix angles

Bending stress evaluation of case-carburized helical gears with large helix angles

Numerical Study of Customised Mesh for Twin Screw Vacuum Pumps

The market for dry vacuum pumps is expected to increase in the coming years. Improving the efficiency of these machines requires comprehensive understanding of the flow dynamics within the working chambers. For this purpose, Computational Fluid Dynamics (CFD) is used as it offers better insight of the working process of a screw machine. In this study, a twin-screw vacuum pump with a large helix angle was analysed. This is a challenging case for CFD due to the limitations of grid generation in the transverse plane on the mesh quality. Two types of transverse meshes were generated using the software SCORGTM: casing to rotor non-conformal mesh and casing to rotor conformal mesh. The quality of the mesh in terms of aspect ratio and orthogonality were compared. The casing to rotor conformal mesh was used with ANSYS Fluent in order to obtain performance characteristics of the vacuum pump with the moderate helix angle of 62° such as the mass flow rate, rotor torque, and indicated power. The performance prediction results were satisfactory but the grid quality was relatively low with orthogonality reaching 40° and aspect ratio over 250 in some cases. As the helix angle increases the quality of mesh decreases. This paper presents the new development of a grid generation algorithm which uses the normal rack to map the fluid domain in the normal plane instead of the transverse plane. This new mesh generation method is expected to better align the computational grid with the main and leakage flows in order to significantly improve grid quality and reduce the numerical diffusion in case of screw machines with large helix angles.

Bending fatigue strength of case-carburized helical gears with large helix angles up to 40 degrees

Case-carburizing of helical gears with large helix angles may form too large hardened layers near the tooth width end on the acute angle side (ACUTE-END), and adversely affect the bending fatigue strength. We investigated the bending fatigue strength of casecarburized helical gears with large helix angles up to approximately 40° through a bending fatigue test, hardness test, and residual stress measurement. We found that the case-carburizing formed large hardened layers near ACUTE-END, reduced the compressive residual stress near ACUTE-END, and restricted the improvement of the bending fatigue strength in a meshing state where tooth root stress became large near ACUTE-END. Based on the obtained bending fatigue limits, we revealed that ISO 6336-3:2006 overestimated the rate of increase of the permissible circumferential loads for helix angles exceeding approximately 30°, and ISO/DIS 6336-3:2018 underestimated this rate for helix angles near 30°.

Normal Rack Grid Generation Method for Screw Machines with Large Helix Angles

Improving the efficiency of the screw machine is highly significant for industry. Numerical simulation is an important tool in developing these machines. The 3D computational fluid dynamic simulation can give a valuable insight into the flow parameters of screw machines. However, it is currently difficult to generate high quality computational grids required for screw rotors with large helix angle. This is mainly due to the excessively high cell skewness of the rotors with large helix angel, which would introduce errors in numerical simulation. This paper presents a novel grid generation algorithm used for the screw rotors with large helix angel. This method is based on the principles developed for the grid generation in transverse cross-section. Such mesh is generated by SCORGTM using normal rack grid generation method which means numerical meshes are generated in a plane normal to the pitch helix line. The mesh lines are then parallel to the helix line and thus an orthogonal mesh will be produced. The main flow and leakage flow directions are orthogonal to the mesh, potentially reducing numerical diffusion. This developed algorithm could also be employed for single screw machines.

Influence of helix angles on bending fatigue strength of case-carburized helical gears with large helix angles

Influence of helix angles on bending fatigue strength of case-carburized helical gears with large helix angles

Numerical study on screw machines with large helix angles

Modelling and performance calculation of screw machines with large helix angles such as a single and multiphase screw pumps by use of Computational Fluid Dynamics is challenging. The numerical procedures explained in literature are based on the 3D numerical meshes generated by series of 2D transverse cross sections which allows mesh to either follow the helix or be perpendicular to the rotor axis. This allows generating a conformal mesh. However, if the rotor helix angle is large, the cell skewness becomes prohibitively large which introduces errors in numerical simulation. The paper firstly attempts to generalize the generation method of rotor profiles with emphasis on producing a normal rack and rotors profiles. Then it introduces the method which uses series of 2D numerical meshes in the planes normal to each of the rotors and rack in order to decompose the working domain in two sub-domains. By this means it is possible to achieve 3D numerical mesh with extended capability of mesh refinement in clearances and alignment of the mesh to the main and leakage flows. However, special treatment is required to provide conformal interface between two moving meshes and with the casing. It is expected that it will greatly benefit accuracy and ease of performance calculation using a number of CFD solvers. In addition it is expected that it will allow generation of various different screw machine configurations like single screw machines or machines with conical rotors.

A New Model for the Single Mesh Stiffness Calculation of Helical Gears Using the Slicing Principle

In this paper, two types of helical gear pairs are defined based on the relationship between the transverse contact ratio and overlap contact ratio. An improved analytical model using the slicing principle is proposed for the calculation of the single mesh stiffness of helical gears. The main improvement in this model against traditional models, that assume no coupling effects between neighbouring sliced tooth pieces, is that a parabola-like weighting factor distribution along the tooth face width is assigned on the sliced tooth pieces for the consideration of the coupling effect. This allows each tooth piece to be associated with a weighting factor and therefore have a different influence on the total mesh stiffness. The calculation results for the single mesh stiffness of two types of helical gear pairs obtained from various methods are compared and discussed. It was found that, compared with the traditional analytical method, the proposed analytical method yields more accurate results in terms of the shape of the single mesh stiffness curve and maximum value of the single mesh stiffness, especially for helical gears with a wide face and large helix angle.

Mass transfer intensification in a novel airlift reactor assembly with helical sieve plates

A novel airlift reactor (ALR) assembly with helical sieve plates (HSPs) in the riser section was developed to intensify gas–liquid mass transfer process. The mass transfer and mixing characterization of the ALR assembly with different HSP structures was analyzed and compared using gas holdup, volumetric mass transfer coefficient, bubble velocity, and mixing time as assessment parameters. With optimized HSP, the gas holdup and volumetric mass transfer coefficient of the reactor were significantly increased by 38–53% and 76–144%, respectively, compared with those of the classical ALR. The empirical equations of gas holdup and volumetric mass transfer coefficient in the new ALR under the experimental condition were proposed. With the increase in the free area ratio in the HSP, a large number of bubbles were broken into small bubbles. Thereafter, the gas–liquid mass transfer efficiency was improved by increasing the gas–liquid interfacial area. Large helix angle caused part of the bubbles to flow helically. As a result, the circumferential mixing of fluid was enhanced whereas the overall mixing time was shortened.

Bending Fatigue Strength of Case-Carburized Helical Gears with Large Helix Angles

Bending Fatigue Strength of Case-Carburized Helical Gears with Large Helix Angles

Bending fatigue strength of case-carburized helical gears (In the case of large helix angles)

Case-carburizing enlarges the depth of the hardened layer at the tooth width end on the acute angle side of helical gears. For the helical gears with large helix angles (Exceeding 25°), this hardened layer may lower their bending fatigue strength. Therefore, we investigated the influence of this hardened layer on their bending fatigue strength through the bending fatigue tests. Our results suggest that this hardened layer might reduce the case-carburizing’s effect to enhance their bending fatigue strength. Thus, using only the maximum tooth root stress would be inadequate for evaluating their bending fatigue strength, and it would be necessary to consider the relationship between the hardened layer and the tooth root stress distribution (Especially, the stress applied at the tooth width end on the acute angle side) from the beginning of meshing to the end.

Numerical Experiment for Flow Characteristics and Cavitation Influence Factors of the External High Pressure Pump

In order to study the influence of flow pulsation coefficient on the internal flow field of the external helical gear high pressure pump, the influence of the helix angle on the flow pulsation coefficient is analyzed by the theoretical formula. Combined with computational fluid dynamics (CFD), the numerical experiment of the flow field in the external gear helical gear is carried out, and the influence of different speed and radial clearance on the pressure pulsation and flow characteristics was analyzed. The results show that when the flow pulsation coefficient is low, the flow field quality is higher and the gear pump leakage is smaller, the larger helix angle will reduce the flow pulsation coefficient and improve the quality of the outlet flow, the influence of speed on flow pulsation coefficient is larger and the average reduction rate is about 2.5%. The greater the rotational speed, the greater the change in pressure in the meshing area.When the sp eed and radial clearance increase,the leakage flow and leakage vortex intensity will be reduced. The study of the motion law and flow pulsation characteristics of the internal flow field of the high pressure pump has some reference value for the design and optimization of the external helical gear.