Helix Angle Research Articles

An analytical method for the meshing characteristics of asymmetric helical gears with tooth modifications

This paper establishes a time-varying meshing stiffness (TVMS) analytical method for asymmetric helical gear pairs based on the potential energy principle and slice method. The method considers the adjacent teeth' influence on the deformation of the gear body part. The proposed method is verified the reasonableness by finite element (FE) analysis. The basic parameters of asymmetric helical gear such as helical angle, pressure angle and tooth width are estimated for the meshing characteristics. The results show that the increase of helix angle, pressure angle of the driving side, normal modulus and tooth width will affect the contact ratio and maximum meshing stiffness of helical gears. The variation of these parameters can minimize the fluctuation of the TVMS curve when the overlap contact ratio reaches an integer. The variation trend of the loaded-static transmission error (LSTE) is opposite to that of the TVMS curve. The load share ratio (LSR) on a pair of gear pairs will decrease with the increase of the degree of reattachment. Furthermore, the influence of tooth modifications on TVMS is estimated by using the proposed method. The mean value of stiffness is reduced after the tooth modifications. The TVMS curve changes more gently after the tooth tip modification.

Optimising the Geometric Parameters of a Gear in a Tractor Transmission Under Constraints Using Kisssoft

Abstract We optimise the speed gears in a tractor transmission with KISSsoft software under three constraints: input power torque, transmission system volume and the gear ratio for each speed. This study aimed to optimise the module, face width, gear quality, centre distance, number of teeth, helix angle, addendum modification coefficient and pressure angle for each speed while considering the above constraints based on an optimisation chart. Tooth bending stress, tooth contact stress, contact ratio and specific sliding were considered during optimisation. Additionally, the effects of changes in a module on the gear profiles, overlap ratio, number of teeth and weight of the gear pair were examined. Strength calculations of gear pairs that were optimised and defined for all geometric parameters with KISSsoft were calculated with the mathematical model described in ISO 6336, and results were then compared. Finally, backlash was minimised for all gear pairs as defined with geometric parameters, and all dimensions and tolerances were determined for gear inspection after manufacturing. A concept design was also presented. We conclude that both the KISSsoft results and mathematical model results are within the range of the target value.

Meshing theory of face worm gear drive with hardened cylindrical worm

This article proposes a novel linear contact face worm gear drive. The novel face worm gear drive consists of a face worm gear and a cylindrical worm enveloped by a tapered surface. The meshing theory for the novel face worm gear drive is systematically built up. The meshing theory on the base of the reference point is further developed aimed at the worm pair where the indexing surfaces are planar and cylindrical. The design methods of the rough size for the face worm gear are introduced. The computing method for the worm limit axial mounting distance is presented by employing the meshing limit line function. The asymmetry of the tooth surfaces for the worm pair is evaluated using the helix angle at the midpoint on the line of section for the worm gear tooth surface and the tooth profile angle for the worm axial section. Numerical results show that the geometric characteristics and the meshing properties for the tooth surface on both flanks of the novel face worm gear drive are asymmetrical. However, the meshing properties for the novel face worm gear drive are satisfactory.

Modelling and prediction on the modal and harmonic response of helix tube in large-scale spiral-wound heat exchangers

Spiral-wound heat exchangers (SWHEs) have been widely used in chemical production processes. As the equipment becomes larger, the SWHEs start facing the problem of failure caused by the flow-induced vibration (FIV) phenomenon. To assure the safety and reliability of the SWHEs, it is important to understand clearly the natural modes of spirally wound coils in different sizes and their response under external excitation. Therefore, a 3D model of the helix tube is established and the helix tubes are fully investigated. The effects of different geometrical parameters on the frequency and vibration amplitude of the helix tubes are performed at each mode, by using the finite element (FE) method. Then, the vibration amplitude analysis of the helix tube under harmonic excitation is carried out, and the dangerous frequency band of the equipment under different geometrical parameters is obtained, which is mainly around 10 Hz to 40 Hz in current domain. Moreover, sensitivity analysis is presented to have a more in-depth investigation into the effects of vibration deformation and frequency, which shows that the biggest influence factor is the helix angle. Finally, machine learning is used to predict dangerous frequency, then case studies are presented to verify the validity of the regression method in which the random forest (RF) model and extreme gradient boosting (XGBoost) have the smallest error, less than 10%. The results are very important for designing SWHEs on large scale to meet the requirement of industry development.

Research on Double-Arc Cutting Tool Design and Cutting Performance

With the increasing complexity of the workpiece surfaces in aerospace and automotive molding and other areas, an increasing number of cutting tools with different shapes and performance have become necessary. A new kind of cutting tool is developed with a double-arc revolving surface at the tool’s end to improve the processing quality in numerical control milling, referred to as a double-arc cutting tool (DACT) in this paper. The parametric geometric model of the DACT is established. Three types of cutting-edge curves are proposed (a cutting edge with a constant helix angle, a cutting edge with a constant pitch, and an orthogonal spiral cutting edge). Corresponding numerical simulation results are also provided as graphical representations. A DACT is manufactured and tested to verify its feasibility. Finally, two contrast experiments are conducted to prove that DACT has a higher processing quality than a ball-end mill (BEM). The advantage of the DACT is verified, which provides a theoretical basis for higher quality machining. The parametric design and application research provides a new method and theoretical basis for other new types of cutting tools.

Study on the toroidal helix and manufacturing method of enveloping hourglass worm tooth surface

As a complex space enveloped surface, the tooth surface of dual-lead helical gear enveloping hourglass worm is characteristic with difference tooth profile, unequal pitch and variable tooth thickness. To grasp the geometry characteristics and precision manufacturing method of it, the analytical method for toroidal helix is presented. The mathematical model of toroidal helix is developed, and the geometry characteristics of helix angle, axial tooth thickness, and tooth surface undercutting are analyzed. The helix angle of toroidal helix presents the convex shape, and the undercutting characteristic is affected by the pressure angle, helix angle, transmission ratio, and normal modulus. Based on the toroidal helix of tooth surface, the precision manufacturing method is proposed, and the measuring method is developed. The hourglass worm sample was manufactured and measured, and the transmission accuracy of hourglass worm drive is tested. The results show that the manufacturing and measuring method of toroidal helix is effective and feasible.

3D FEM Simulation of Titanium Alloy (Ti6Al4V) Machining with Harmonic Endmill Tools

AbstractUsually, end milling operations have been carried out using conventional uniform helix tools with fixed helix angles. Thus, many studies have been conducted to study the effects of these tools on the thermomechanical properties of a milling process. Recently, there have been works that point to the benefits of using harmonic endmills. Harmonic endmills consist of cutting edge profiles that have continuously harmonically varying helix angles. The variation is described using a harmonic function of axial position (elevation) of points on the cutting edge. In this work, a 3D finite element simulation using ABAQUS, is carried out for the complex milling process of Titanium alloy Ti6Al4V. The envelope of the harmonic tool is first generated using a set of MATLAB codes and stored in a Standard Triangle Language (.stl) format. The machine tool is introduced into an FEM program which has been designed to provide for dynamic effects, thermo‐mechanical coupling, material damage law and the criterion for contact associated with the milling process. A Johnson‐Cook material constitutive equation which combines the effects of strain hardening, strain softening, and temperature softening is used. To account for the chip separation criterion, the Johnson Cook damage evolution equation is used. The milling process simulation for Ti6Al4V is then carried out. In the end, the stress distribution and the cutting forces are obtained.

Vibration Suppression Technology of Integrated NC Machining of Lightweight Monolithic Panel

The new generation spacecraft module is formed by spinning as a whole, and then the whole module is processed by integrated numerical control. Due to the characteristics of the large diameter and thin wall of the module, it is easy to produce vibration in the processing. In this paper, aiming at the vibration problem of integrated CNC machining cabin body, a method of using reconfigurable fixture internal support to suppress the vibration of weak rigid cabin body overall processing is proposed, and the ANSYS finite element analysis software is used to simulate and analyze the internal support force. The results show that the thickness uniformity of the bottom skin is similar, the dimensional accuracy is higher, and the effect of suppressing cutting chatter is obvious. This paper also improves the design of the milling tool with an unequal helix angle, adds DLC tool coating, and increases the tool rake angle. The simulation results of cutting force based on the FORCE module show that the cutting force is reduced by 31% and chatter in machining is suppressed compared with that before the tool is improved. Through the cycloid milling strategy, the wrap angle between the tool and the workpiece is reduced. It reduces the cutting force, reduces the cutting heat, and ensures the consistency of the product wall thickness and the roughness requirements. The experimental results show that these methods can effectively suppress the vibration in the processing and control the thickness of the integrated numerical control processing panel between 1.47-1.77 mm.

Influence of the Spiral Angle of the Blade on the Material Loading Characteristics of the Slurry Pump

To study the effect of rotational speed on the internal flow characteristics and operating performance of a deep-sea mining slurry pump, a new type of slurry pump delivery system with changing vane helix angle is adopted in this paper. Based on the coupled computational fluid dynamics-discrete element method (CFD-DEM), the realizable k-ɛturbulence model and SIMPLE algorithm are applied to numerically simulate the solid-liquid two-phase flow field in the slurry pump to study the effect of rotational speed on the flow characteristics and distribution of particles in the slurry pump. The results show that with the increase in rotational speed, the separation of the boundary layer at the impeller runner is promoted, which weakens the particle overflow capacity and increases the hydraulic loss. The impact at the inlet of the guide vane runner is more violent. The fluid flow separation at the inlet is suppressed. The overflow capacity is increased and the hydraulic loss is weakened. With the increase in rotational speed, the more the average number of collisions between particles and vanes in each time period, the more the particles collide with the impeller and space. The collision probability and collision speed of the guide vane overflow parts become larger, thus laterally reflecting that the larger the rotational speed, the greater the wear rate of particles on the blade is.

Numerical investigation on the helix angle to smoothen aerodynamic torque output of the 3-PB Darrieus vertical axis wind turbine

Numerical investigation on the helix angle to smoothen aerodynamic torque output of the 3-PB Darrieus vertical axis wind turbine

Process Design for Manufacturing Fiber-Reinforced Plastic Helical Gears Using a Rapid Heating and Cooling System

In this study, a lightweight fiber-reinforced plastic (FRP) helical gear was fabricated to investigate the potential application of FRP in automobile parts that require high loads and reduced noise. High-performance aramid FRP processed using the wet-laid method was used in the tooth region, and SCR420 steel was used in the inner hub region. A hot-forming system that combines rapid induction heating and water channel cooling methods was developed to reduce the cycle time. The cooling water flow conditions were analyzed to precisely control the mold temperature. Additionally, a rotating extraction system was developed to mitigate the extraction difficulty owing to the helix angle to the extraction direction. Using the innovative hot-forming system developed in this study, a helical gear without any process-induced defects was fabricated with a significantly reduced cycle time. The performance of the gear was successfully estimated using gear durability, torsional strength, and motion noise tests. The use of FRP materials offers significant potential to realize lightweight components; however, certain challenges related to their properties that may limit their application must be addressed on a case-by-case basis.

Low-velocity impact resistance behaviors of bionic double-helicoidal composite laminates

To improve the low-velocity impact resistance of composite laminates, a bionic double-helicoidal composite laminate (BDHCL) emulated from the micro-structure of coelacanth scales is proposed. The micro-structure is a double helicoidal Bouligand structure in which two adjacent collagen layers are arranged into an orthogonal bilayer and then rotating at a small helix angle. Three types of helicoidal configurations with different derivatives are designed, including sine rotation angle (SRA), linear rotation angle (LRA), and exponential rotation angle (ERA). The progressive intra-laminar and inter-laminar damage model is adopted to capture the failure behaviors of material. The impact behaviors of BDHCLs with several helix angles and included angles of the bilayer are studied. The results show that the double-helicoidal Bouligand structure has a higher resistance load and shallower penetration depth. The impact resistance of ERA laminate has the maximum improvement among the above three types of helix angle. A certain included angle of bilayer for the BDHCL will exhibit excellent impact resistance.

Exact Formulation for the Curvature of Gothic Arch Ball Screw Profiles and New Approximated Solution Based on Simplified Groove Geometry

The correct evaluation of the curvatures of ball screw grooves allows the accurate design of the constructive parameters of this mechanism and enhancing its performance. The formulation commonly used in the literature, however, refers to ball bearing geometry, ignoring the shape of the section’s profile and the helix angle. In this paper, the exact formulae for calculating the principal curvature radii of the screw shaft and the nut grooves are analytically derived and presented. These equations, obtained through a rigorous differential geometry approach, consider the helix angle and a gothic arch profile. An approximated formulation is proposed simplifying the exact solution under the assumption of a circular groove profile. These new simple formulae accurately reproduce the exact curvature radii values with a mean relative error of approximatively 0.51% and 0.40%, respectively, for the screw shaft and nut grooves, against the value of more than 50% obtained by using the literature formulae for common off-the-shelf ball screws, especially those with high helix angles. Furthermore, they allow a computational time saving of 98%, making them suitable for being incorporated in high-fidelity dynamic models of ball. Finally, two MATLAB functions are provided to easily evaluate the complex curvature exact solution.

Observation of the skyrmion side-face state in a chiral magnet

We identify a three-dimensional skyrmion side-face state in chiral magnets that consists of a thin layer of modulated surface spirals and an array of phase-locked skyrmion screws. Such chiral spin structures lead to a characteristic X-shaped magnetic diffraction pattern in resonant elastic x-ray scattering, reminiscent of Photo 51 of the DNA double-helix diffraction. By measuring both thin plates and bulk ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$ crystals in the field-in-plane geometry, we unambiguously identify the modulated skyrmion strings by retrieving their chirality and helix angle. The breaking of the translational symmetry along the side faces suppresses the bulk-favored conical state, providing a stabilization mechanism for the skyrmion lattice phase that has been overlooked so far.

Novel real-time monitoring method of depths of cut and runout for milling process utilizing FFT analysis of cutting torque

For smart manufacturing systems, it is required to monitor the cutting process in real-time to recognize the present state of the process. In this study, a novel method to monitor important parameters (i.e., axial/radial depths of cut and end mill runout) in the square end milling process by analyzing frequency components of the cutting torque is proposed. The proposed method assumes easily achievable information about the cutting conditions (i.e., spindle speed and feed rate) and tool parameters (i.e., helix angle, nominal radius, and number of flutes) as the given inputs. The presented method only utilizes measured torque data and the given inputs; therefore, it does not require any previously tuned information (e.g., specific cutting forces). From the perspective of the cutting torque model, analytical relationships between the process parameters to monitor and the frequency components of the cutting torque are clarified. On the basis of the mathematical expressions derived from the model, the proposed method offers a monitoring scheme of axial/radial depths of cut and runout. In addition, an index is suggested to offer information on reliability of the monitored outputs to the user. As results of experimental tests, the proposed method successfully monitored axial/radial depths of cut and runout and evaluated the reliability of the outputs.

A comparative study on drillability of Inconel 625 alloy fabricated by wire arc additive manufacturing

In recent years, the cost-effective wire arc additive manufacturing (WAAM) method is increasingly replacing traditional production methods for Ni-based superalloys. However, the effect of high heat input and elemental segregation in the WAAM method on machinability has not yet been adequately investigated. For this purpose, drilling of wrought and WAAM Inconel 625 samples with thermal (i.e., die-sinking micro-EDM and micro-EDM) and mechanical drilling techniques (i.e., orbital and conventional drilling) was investigated in this study. It was observed that thermal drilling methods formed a white layer with a thickness of 20-25 μm and 35-50 μm in the cross-section of wrought and WAAM specimens, respectively, while no white layer was formed in the mechanical methods. The average surface roughness of the inside hole, Ra, obtained in the conventional drilling process has improved by 46.15 %, 94.62 %, and 92.82 %, compared to the orbital, die-sinking, and micro-EDM methods, respectively. Because the drill cutting form and helix angle used in this method facilitated chip evacuation. The best surface roughness was obtained respectively by conventional (0.27–029), orbital (0.51–0.53), die-sinking (4.54–5.88), and micro-EDM drilling (3.54–4.25) methods. In addition, a larger kerf angle is obtained in the WAAM sample compared to the wrought one due to higher residual stress and higher dislocation density in the WAAM alloy. On the other hand, the higher hardness value of WAAM samples provided better surface quality in mechanical drilling methods than wrought material. An increase in surface hardness values up to 25 μm from the surface was detected due to the recast layer formed in thermal drilling methods and the strain hardening occurring on the surface in mechanical drilling methods.

COMPARISON OF CHATTER CONTROL OF VARIABLE AND REGULAR HELIX TOOLS IN THE ALUMINUM END-MILLING PROCESS

In the chatter, machining operations are undesirable because of the phenomena that affect product results, machining accuracy, tool life, and high operating value. Chatter is a vibration phenomenon that occurs in cutting tools due to the self-excitation of the influence of cutting parameters during the operation process of the machine. Types of chatter in machinery are regenerative and resonant. Because the pitch angles of variable helix tools vary, the helix angles of variable tools produce different tooth passing frequencies on each tool eye next to each other and can be used to prevent and control resonance. This study aimed to compare chatter control from the variable helix and regular-angle tools in the aluminum end milling process. The method is carried out through the end milling process experiment to determine the chatter control of the variable helix and regular-angle tools through the stability loop diagram. The results from this study were obtained by comparing control chatters in the milling process through controlling variable and standard helix angles as a guideline to produce the best surface roughness in the end milling process made from aluminum. The comparison of estimated control charts from variable helix tools is more comprehensive than regular helix tools.

Contribution of atrial myofiber architecture to atrial fibrillation.

The role of fiber orientation on a global chamber level in sustaining atrial fibrillation (AF) is unknown. The goal of this study was to correlate the fiber direction derived from Diffusion Tensor Imaging (DTI) with AF inducibility. Transgenic goats with cardiac-specific overexpression of constitutively active TGF-β1 (n = 14) underwent AF inducibility testing by rapid pacing in the left atrium. We chose a minimum of 10 minutes of sustained AF as a cut-off for AF inducibility. Explanted hearts underwent DTI to determine the fiber direction. Using tractography data, we clustered, visualized, and quantified the fiber helix angles in 8 different regions of the left atrial wall using two reference vectors defined based on anatomical landmarks. Sustained AF was induced in 7 out of 14 goats. The mean helix fiber angles in 7 out of 8 selected regions were statistically different (P-Value < 0.05) in the AF inducible group. The average fractional anisotropy (FA) and the mean diffusivity (MD) were similar in the two groups with FA of 0.32±0.08 and MD of 8.54±1.72 mm2/s in the non-inducible group and FA of 0.31±0.05 (P-value = 0.90) and MD of 8.68±1.60 mm2/s (P-value = 0.88) in the inducible group. DTI based fiber direction shows significant variability across subjects with a significant difference between animals that are AF inducible versus animals that are not inducible. Fiber direction might be contributing to the initiation and sustaining of AF, and its role needs to be investigated further.

The comparison of diffusion tensor imaging in human hearts between 1.5 T and 3.0 T

BackgroundThe aim was to compare the diffusion tensor imaging (DTI) indices derived from human hearts between 1.5 T and 3.0 T scanners. Additionally, the reproducibility of DTI indices was assessed between 1.5 T and 3.0 T scanners.MethodsA total of 18 ex-vivo hearts were derived from patients who underwent heart transplantation. The DTI schemes were performed at 1.5 T and 3.0 T, respectively. Then, the same slices from each ex-vivo heart were selected for image analysis. The student’s t-test or Wilcoxon-rank test was used to compare the statistical differences. The agreement of DTI indices was mainly reported as the interclass correlation coefficient (ICC).ResultsNo significant differences (all P > 0.05) were found in the DTI indices between 1.5 T and 3.0 T scanners. Interestingly, the ICC of all DTI indices was relatively lower with a low b-value. The reproducibility of the helix angle (HA) was relatively lower when compared to the other DTI indices.ConclusionThe DTI indices of ex-vivo human hearts between 1.5 T and 3.0 T scanners had no significant differences. The consistency of DTI indices needed caution using a low b-value with different field strengths, and the relatively low reproducibility of HA should be considered.

Rotational multimaterial printing of filaments with subvoxel control.

Helical structures are ubiquitous in nature and impart unique mechanical properties and multifunctionality1. So far, synthetic architectures that mimic these natural systems have been fabricated by winding, twisting and braiding of individual filaments1-7, microfluidics8,9, self-shaping1,10-13 and printing methods14-17. However, those fabrication methods are unable to simultaneously create and pattern multimaterial, helically architected filaments with subvoxel control in arbitrary two-dimensional (2D) and three-dimensional (3D) motifs from a broad range of materials. Towards this goal, both multimaterial18-23 and rotational24 3D printing of architected filaments have recently been reported; however, the integration of these two capabilities has yet to be realized. Here we report a rotational multimaterial 3D printing (RM-3DP) platform that enables subvoxel control over the local orientation of azimuthally heterogeneous architected filaments. By continuously rotating a multimaterial nozzle with a controlled ratio of angular-to-translational velocity, we have created helical filaments with programmable helix angle, layer thickness and interfacial area between several materials within a given cylindrical voxel. Using this integrated method, we have fabricated functional artificial muscles composed of helical dielectric elastomer actuators with high fidelity and individually addressable conductive helical channels embedded within a dielectric elastomer matrix. We have also fabricated hierarchical lattices comprising architected helical struts containing stiff springs within a compliant matrix. Our additive-manufacturing platform opens new avenues to generating multifunctional architected matter in bioinspired motifs.