Load Angle Research Articles

A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.

Modified load angle direct torque control for dual star motor using fuzzy logic

Space Vector Modulation (SVM) has emerged as a prominent alternative for motor control, particularly within the framework of Direct Torque Control (DTC-SVM). SVM leverages variations in the load angle, which result from changes in motor torque, to generate the appropriate voltage vectors. The conventional approach to this method involves a single Proportional-Integral (PI) regulator, which is characterized by a constant switching frequency and the capability to reduce ripples in torque, flux, and current. Despite these advantages, the PI regulator may face challenges in maintaining optimal performance under varying load conditions. This study seeks to enhance the performance of the DTC-SVM strategy by integrating Fuzzy Logic into the PI regulator. The primary objective is to improve the accuracy and responsiveness of the load angle control, thereby optimizing the motor's operational efficiency. The proposed SVM-Fuzzy control scheme is designed to address the limitations of the traditional PI regulator, offering a more adaptive and robust solution for motor control. To evaluate the effectiveness of the proposed approach, extensive simulations were conducted using Matlab Simulink. The SVM-Fuzzy strategy was compared against the conventional SVM-PI approach to assess its performance in terms of torque, flux, and current regulation. The SVM-Fuzzy control scheme significantly enhances efficiency, stability, and load angle precision, particularly in Double Star Induction Motors (DSIM). It also ensures the durability and reliability of the motor control system under different operating conditions.

Behaviour of yielding mechanical hybrid rockbolts under complex loading conditions

The original “hybrid bolt” was a pragmatic solution to address installation issues in the use of resin grouted rockbolts in heavily fractured ground and the inadequate capacity of friction rock stabilisers. The original hybrid rockbolt involved installing a resin rebar in a friction rock stabiliser. The development of Yielding Mechanical Hybrid Rockbolts has been driven by efforts to eliminate the use of resin in heavily fractured ground. A typical Yielding Mechanical Hybrid Rockbolt consists of a steel tendon mechanically anchored within a friction unit. The bolt is percussion driven by the rock drill and the mechanical anchor is subsequently activated using rotation. This installation process improves the rockbolt resilience to hole closures and avoids issues associated with the use of resin. Yielding Mechanical Hybrid Rockbolts are used in both squeezing and rockburst prone ground conditions.This paper addresses a significant knowledge gap related to the behaviour of Yielding Mechanical Hybrid Rockbolts under multiple quasi-static conditions. A comprehensive experimental program investigated the complete load displacement performance of Yielding Mechanical Hybrid Rockbolts under axial, shear, and a combination of tensile and shear loads. It was observed that the load capacity increases from axial (0°), combined axial and shear (30°), combined axial and shear (60°), and pure shear (90°). The displacement capacity, however, decreases under the same testing conditions. The results are consistent but there is a slightly greater variability as the loading angle increases from 0° to 90°. It was observed that beyond 60° loading angle there is greater variability in the results as the influence of the shear component manifests itself in greater disintegration of the concrete blocks at the shear interface.

The installation behavior and capacity of piggy-backed anchors for offshore wind turbine

Piggy-backed anchors present a promising solution to address the limitations of single Drag Embedment Anchors (DEAs). A series of centrifugal model tests were performed on the installation of piggy-backed anchors with varying spacings and attachment points in saturated sand using a magnetometer system. The experimental results validated the proposed theoretical prediction model, which can identify the trajectory, capacity, orientation, and soil failure wedge slip surface. Key findings include: (1). the embedment depth of the second anchor in piggy-backed anchors is significantly greater than that of a single anchor, resulting in the total capacity of piggy-backed anchors exceeding twice that of a single anchor at appropriate spacing; (2). investigating spacing effects shows that capacities are less than twice that of the single anchors when spacing is less than 1Lf due to overlapping failure soil wedges; optimal spacing was found to be 2Lf to 3Lf; (3). piggy-backed anchors with attachment points at the back of fluke exhibit better embedment performance and capacity stability compared to those with attachment points at the padeye. Finally, the prediction model explored the capacity performance of piggy-backed anchors at different loading angles at the final embedment depth, revealing a two-stage failure process compared to single drag anchors.

Revealing the failure mechanism of 2D triaxially braided composites under off-axial tension through mesoscale simulations

The external load angle is known to have a significant influence on the mechanical behavior of two-dimensional triaxially braided composites (2DTBCs). However, the experimental data for 2DTBCs under off-axial loading provide limited information for understanding the failure mechanisms. In this study, a comprehensive mesoscale finite element (FE) model for simulating 2DTBC specimens was established to evaluate the mechanical responses and damage characteristics when off-axial tensile loads are applied. The FE model effectively captured the mechanical response at five distinct angles (0°, 30°, 45°, 60°, and 90°) and revealed the evolving patterns of failure behavior, damage morphology, and out-of-plane deformation mechanisms corresponding to the different loading angles. The findings indicate that, when the external load aligns with the axial fiber bundle direction, the primary failure mechanism involves the fracture of load-bearing fiber bundles. In contrast, deviations from the axial loading direction resulted in failure that was primarily due to the undulation of the bias fiber bundles, resulting in a loading angle–dependent warping at the edge of the specimen due to local shear stress concentration. The findings of this study provide valuable insights that can inform the design of structures with improved application.

Oxidation model of slabs in an industrial-scale walking-beam reheating furnace with mixed loading

This paper develops a comprehensive numerical model of an industrial-scale walking-beam reheating furnace integrated with an improved oxidation model. The model demonstrates good agreement with experimental data, accurately predicting both temperature distribution and the oxidation process. Utilizing this model, the impact of mixed loading and swirl angles on the oxidation process is investigated. The average porosity of the scale, determined experimentally to be 0.25634, is used as a benchmark for the model. Comparisons of results with and without considering porosity highlight its significant impact on scale thickness distribution. This finding is crucial for the descaling process, allowing for a more accurate determination of descaling pressure and the reduction of production costs. Predicting scale distribution based solely on the temperature at a specific time is challenging due to the lag in scale accumulation. The temperature trend over an extended period is more consistent with the scale distribution. For the reheating furnace studied in this paper, the research results reveal that a swirl angle of 25° emerges as the optimal choice with industrial demands. These results underscore the importance of considering porosity and swirl angle effects on scale distribution and oxidation loss rate, offering valuable guidance for industrial processes.

Study on calculation method for dynamic load distribution of thread pair of planetary roller screw mechanism

To reveal the dynamic load distribution characteristics of planetary roller screw mechanism under the high-speed operating conditions, based on the spiral surface equation and deformation coordination relationship, a static contact force calculation method of the roller-screw and roller-nut thread at the contact point is proposed, and a formula for calculating the contact angle after bearing is derived. On this basis, further considering the inertial force generated by using high-speed operation, a dynamic load distribution model for planetary roller screw mechanism thread was established. By comparing with the finite element contact model of planetary roller screw mechansim, the error is below 5%, which verifies the correctness of the model established. Finally, the influence of the parameters such as screw speed, axial load, pitch, and tooth flank angle on the distribution of dynamic load was analyzed. The results show that the inertia force causes the roller to have a tendency to move closer to the nut and away from the screw resulting in a decrease in dynamic contact force on the roller screw side and an increase in dynamic contact force on the roller nut side. The degree of uneven distribution of dynamic load is positively correlated with the screw speed and pitch, and negatively correlated with the tooth side angle. The size of axial load has a significant impact on the distribution of dynamic load.

Effect of lubricants during the rolling process on the mixed mode fracture behavior of the as-rolled material

Friction is one of the major factors in energy consumption and metal depreciation during various mechanical processes. Lubrication is often used during the process of forming metals to cope with friction and its consequences. Mineral lubricants are employed in the rolling process to decrease the rolling force and enhance the quality of the sheets. This research aims to compare the performance of mineral lubricants such as crude oil, gas oil, and CM405A to enhance the production efficiency of the aluminum forming process, especially in the rolling process. The ring compression test was utilized to evaluate the influence of lubrication on the friction coefficient which was extracted through calibration curves. Then, the effect of friction coefficient was experimentally examined during the forming process through rolling. Al 1050 was rolled by the mentioned lubricants. The pre-cracked rolled samples were then tested by fracture test at different loading angles of 0 (pure mode-I), 45(mixed-mode of I and II), and 90(pure mode-II). J-R curves were extracted using elastic–plastic fracture theory based on material characteristics. The fracture tests indicated maximum resistance to crack growth occurred in the sample prepared with CM405A lubricant. In contrast, the lowest crack growth resistance was recorded in the case where crude oil was employed as a lubricant. In the end, the SEM images of the fractured surfaces were explored for a deeper understanding of the fracture behavior. Although a combination of brittle and ductile fracture mechanisms can be observed on the fractured surfaces, cleavage was the dominant phenomenon and fracture mechanisms.

Experimental and numerical analysis of Brazilian splitting mechanical properties and failure mechanism for composite discs

The properties of structural planes and the strength of rock matrix significantly influence the splitting characteristics of composite rock masses. To investigate the effects of structural plane and differences in matrix strength on the mechanical behavior and failure characteristics of composite jointed rock bodies, composite jointed disc specimens with varying structural plane roughness and matrix combinations were prepared. These specimens were then subjected to Brazilian split tests under different loading angles ranging from 0° to 90°. Results indicate that the failure mode of the specimens is determined by the angle of the structural plane. As the structural plane angle increases, the failure mode transitions from structural plane failure to combination failure and finally back to structural plane failure. Increased roughness of the structural plane reduces the extent of structural plane failure, while matrix strength has no significant impact on the failure mode. The failure load of the specimens increases with increasing structural plane angle, roughness, and matrix strength. The influence of structural plane roughness and matrix strength on the mechanical properties of the specimens grows with increasing structural plane angle. Increases in structural plane roughness and matrix strength significantly enhance the strain energy and dissipated energy of the disc model. Finally, an analysis of the stress state on the structural planes is combined with an exploration of the failure mechanisms of the specimens.

Crashworthiness of hierarchical multi-cell square tubes under axial and oblique crushing

Hierarchical tubes have been proved to be excellent energy absorbers under axial compression. However, there are limited studies exploring their oblique crushing performance. Therefore, the oblique crushing characteristics of hierarchical tubes, bio-inspired hierarchical multi-cell square tubes (BHMS), hierarchical multi-cell square tubes (HMSA and HMSB), have been numerically studied. The influencing factors of loading angle and hierarchical order on deformation modes, force-displacement curves, and energy absorption (EA) behaviors were explored. It is found that BHMS tubes present the superior crushing performance among these hierarchical square tubes. Moreover, BHMS tubes display the excellent crushing characteristics in comparison with single square tubes. Specifically, the specific EA of BHMS-3 tubes is 213%, 212%, 66%, and 42% greater than that of single square tubes at loading angles of 0°, 10°, 20°, and 30°. The findings demonstrate the priority of hierarchical square tubes under oblique crushing, and provide the reference and insight for the design of energy absorbers.

Dynamic model of magnetic transmission

In the work, a non-contact electromechanical energy converter with permanent magnets, which is known as magnetic transmission, is studied. Magnetic transmissions have certain structural advantages compared to mechanical transmissions, namely: high reliability, efficiency, lower losses, non-contact transmission of mechanical power, no maintenance costs, and simplicity of construction. The use of magnetic transmissions for systems of conversion of low-potential mechanical energy into electrical energy is especially relevant: wind energy, water energy, energy of mechanical vibrations, etc. The use of magnetic gearboxes in autonomous wind power plants can be more promising from an economic and technical point of view compared to traditional mechanical transmissions. A numerical simulation mathematical model of magnetic transmission with permanent magnets has been developed. The use of magnetic transmission, for example, for autonomous wind power systems allows to increase the reliability of the operation of such installations, reduce operating costs and increase the efficiency of their operation. In emergency modes of operation, the use of magnetic transmission allows to avoid destruction or emergency shutdowns of electrical equipment. The developed simulation model of magnetic transmission takes into account the pulsations of the electromagnetic moment due to the discrete structure of the magnetic transmission and the change of the model parameters when the input moment changes: pulsations, losses in the magnetic core and permanent magnets, the change of the load angle and the transmitted electromagnetic moment. A feature of the developed model of the magnetic transmission system is that a change in the load of the electric power source leads to a change in the operating point on the mechanical characteristics of the rotor of the wind turbine. Conversely, when the wind parameters change, the output parameters of the source of electrical energy change: power, voltage, current and electromagnetic moment.

Investigation of the Electrical Impedance Signal Behavior in Rolling Element Bearings as a New Approach for Damage Detection

The opportunities of impedance-based condition monitoring for rolling bearings have been shown earlier by the authors: Changes in the impedance signal and the derived features enable the detection of pitting damages. Localizing and measuring the pitting length in the raceway direction is possible. Furthermore, the changes in features behavior are physically explainable. These investigations were focused on a single bearing type and only one load condition. Different bearing types and load angles were not considered yet. Thus, the impedance signals and their features of different bearing types under different load angles are investigated and compared. The signals are generated in fatigue tests on a rolling bearing test rig with conventional integrated vibration analysis based on structural borne sound. The rolling bearing impedance is gauged using an alternating current measurement bridge. Significant changes in the vibration signals mark the end of the fatigue tests. Therefore, comparing the response time of the impedance can be compared to the vibration signal response time. It can be shown that the rolling bearing impedance is an instrument for condition monitoring, independently from the bearing type. In case of pure radial loads, explicit changes in the impedance signal are detectable, which indicate a pitting damage. Under combined loads, the signal changes are detectable as well, but not as significant as under radial load. Damage-indicating signal changes occur later compared to pure radial loads, but nevertheless enable an early detection. Therefore, the rolling bearing impedance is an instrument for pitting damage detection, independently from bearing type and load angle.

Understanding plasticity in multiphase quenching & partitioning steels: Insights from crystal plasticity with stress state-dependent martensitic transformation

This study develops a novel crystal plasticity (CP) model incorporating deformation-induced martensitic transformation (DIMT) and transformation-induced plasticity (TRIP) effect to predict the complex interplay between microstructural evolution and mechanical behavior in a third-generation advanced high-strength steel QP980. This model introduces phenomenological theory of martensite crystallography (PTMC) based TRIP theory and DIMT kinetics grounded on nucleation-controlled phenomenon. Notably, the DIMT model is improved by utilizing a geometric approach for calculating shear band intersections. A virtual multiphase representative volume element (RVE) based on the Voronoi tessellation is generated for the QP980 steel, which comprises ferrite, martensite, and retained austenite (RA). The study highlights how phase transformation affects mechanical properties, notably the strengthening from transformed martensite and the mechanical alterations in RA due to the TRIP effect. The DIMT kinetics dependent on stress states such as uniaxial tension (UT), uniaxial compression (UC), plane strain tension (PST), and equi-biaxial tension (EBT) are analyzed using the developed model. The role of microstructural surroundings on martensitic transformation is also examined. Furthermore, analysis under biaxial loading angles using the model reveals an asymmetric yield surface, with more pronounced changes in yield stress in the tensile region due to accelerated transformation behaviors, as opposed to the more gradual transformations in the compressive region. This study provides valuable insights into the deformation mechanisms of the third-generation advanced high-strength steels including relationship between plastic anisotropy, transformation kinetics, and microstructural evolution.

Mechanical properties of lotus petiole bio-inspired structures under quasi-static radial load

The lotus petiole in nature is characterized by its porous structure and high bending resistance. Inspired by this, in this paper, random sampling of lotus petiole was carried out to clarify the porous distribution pattern of lotus petiole in cross section. On this basis, the original structures with 12 and 13 wells (Os-12w, Os-13w) were constructed, and equal mass hollow circular tube (Emhct) was also designed for comparison. Based on the experimentally verified finite element models, Os-12w, Os-13w and Emhct were comparatively analyzed. In addition, comparisons were made with five other bionic circular structures Compared to the rest of the structures, Os-13w performs better in all comprehensive properties. The bending and traction in the core region of the bionic structure caused the surrounding structures to join in the buckling earlier, creating a global crushing trend. More interestingly, further bending and traction in the core region creates a negative Poisson's ratio phenomenon. In addition, the results of the parametric study show that the optimum loading angle of Os-12w is between 60° and 90°, and the proper adjustment of its core cross-section characteristics can improve the mechanical properties of the structure. This study provides some reference for the development of thin-walled porous structures under radial loading conditions.

The effects of three-dimensional bedding on shale fracture behavior: Insights from experimental and numerical investigations

The three-dimensional (3D) structural characteristics of the bedding planes exhibit strong anisotropy in the fracture behavior of shale. Previous studies on the anisotropy of shale fracture characteristics focused on 2D bedding effects, while 3D bedding effects that comprehensively consider bedding angles α and β have been rarely investigated. Therefore, the fracture behavior of shale with 3D bedding planes was studied based on laboratory experiments and numerical simulation. The results indicated that the apparent fracture toughness (AFT) of shale decreased with increasing bedding angle α. The fracture toughness of shale with a bedding angle of α = 0° was 2.26 MPa·m0.5 (β = 0°). However, when the loading angle α increased to 90°, the AFT decreased by 67.70 %. The increase in bedding angle β could improve the AFT significantly, and the higher the loading angle α, the more significant the improvement. The improvement amplitude at α = 90° reached 156.65 %. Due to the enhanced ability of shale to resist crack propagation by the bedding angle β, the trend of dissipation energy under the influence of 3D bedding effects was consistent with the AFT, and the two were positively correlated. Affected by the 3D bedding effect, three typical failure modes of shale have been observed: bedding failure, matrix failure, and mixed failure mode. Based on the calculation of the fractal dimension of the fracture surface, the roughness of the fracture surface under different failure modes was mixed failure > matrix failure > bedding failure. In addition, a 3D numerical model was established based on the DEM method, and the influence of new cracks on fracture toughness was considered after verifying the effectiveness of the numerical model. The length of newly formed cracks at the tip of shale prefabricated cracks exceeded 4.0 mm under critical load. Ignoring the length of new cracks will underestimate the fracture toughness of shale by about 30 %. Finally, the influence of 3D bedding planes on the crack propagation path was discussed.

Optimized Fault Detector Based Pattern Recognition Technique to Classify and Localize Electrical Faults in Modern Distribution Systems

This research presents a method that integrates artificial neural networks (ANN) and discrete wavelet transform (DWT) to identify and classify faults in large power networks, as well as to pinpoint the zones where these faults occur. The objective is to enhance reliability and safety by accurately detecting and categorizing electrical faults. To manage the computational demands of processing the extensive and complex data from the power system, the network is divided into optimal zones, each made visible for fault detection. Niche Binary particle swarm optimization (NBPSO) is employed to place the fault detectors (FD) in each zone. This allows for precise measurement of fault voltage and current phasors without significant cost. The ANN module is tasked with identifying the fault area and locating the exact fault within that zone, as well as classifying the specific type of fault. Discrete Wavelet Transform is used for feature extraction, and a phase locked loop (PLL) is used for load angle computation. The proposed method's validity has been tested on the IEEE-33 bus distribution network.

A mechanical study of the influence of ankle joint angle on translational traction of soccer boots

The shoe–surface interaction for soccer players has both safety and performance implications. This interaction has been widely researched in terms of outsole configuration and surface type. However, these investigations, particularly those involving translational traction, often neglect the approach angle of the foot in terms of a real-world setting. This investigation considers the foot position prior to injuries such as anterior cruciate ligament tears, and observes how the translational traction alters with various angles for simulated plantarflexion, dorsiflexion, calcaneal inversion and calcaneal eversion. It was hypothesised that, as these angles increased, the translational traction would decrease as there would be less contact area between the boot and the surface compared to the neutral, flat footform. A custom-built testing apparatus recorded the translational traction of a soccer boot moving in four different directions at different loading angles on both a natural grass and artificial grass playing surface. A one-way ANOVA was performed, with a post-hoc Tukey Test to determine the significant differences between the translational traction between each angle. It was found that the geometry of the outsole configuration, more specifically, the apparent contact area between the shoe and surface played a significant role in the level of traction obtained. These results highlight the importance of stud geometry, particularly with respect to movements when the foot is angled as it would be in a potential injury scenario. Manufacturers should consider the profile of studs relative to the expected movements to not induce excessive traction, which could lead to potential foot fixation and injury.

Modeling the Dynamic Loads Affecting a Bridge Crane during Start-Up

Introduction. The dynamic loads during the start-up of a bridge crane can cause excessive stress in the structure and components, leading to potential safety hazards and increased wear and tear. To reduce the influence of the dynamic loads, various strategies can be implemented including optimization of the acceleration and deceleration profiles, using the soft start controls, implementing the vibration damping systems. It is vital to ensure that the proper crane maintenance and inspection protocols are in place. By reducing the impact of dynamic loads during the start-up, the overall performance and longevity of a bridge crane can be improved, ultimately enhancing safety and efficiency of the industrial operations. The present research offers a new approach to improving the efficiency and safety of industrial operations by providing a more precise account of the dynamic loads during the start-up of a bridge crane. The objective of this study is to develop a mathematical model for investigating the mechanical properties of the bridge cranes by analyzing the dynamic loads that occur during lifting operations.Materials and Methods. The development of the mathematical model was based on the kinetic model of the system, which included three connecting blocks and two flexible connections for a more accurate description of the bridge crane structure. Lagrange’s equations incorporating the information about the geometry and structure of a bridge crane were used. They made it possible to describe the motion of a system with the multiple elements and degrees of freedom. Processing and analysis of the results of the mathematical model were carried out in the MATLAB program using the Runge-Kutta method.Results. As a result of the research, a mathematical model was developed to study the dynamic loads affecting a bridge crane during lifting operations. Graphs describing the dependences of speed, acceleration, load, and rope angle over time, and their influence on the crane beam were plotted. The changes in these parameters over time, including their maximum values, were analyzed. The reasons for load changes and factors influencing the extension of lifting machines’ service life as well as reducing metal consumption during production thereof were identified.Discussion and Conclusion. The developed mathematical model and its numerical solution using the specialized software (MATLAB) allow for conducting the dynamic analysis of the bridge crane structures and determining the optimal design solutions. The analysis of the factors influencing the load changes leads to the conclusion that the use of this model can significantly reduce the load magnitudes and metal consumption, as well as increase the service life of lifting machines. The results obtained with the developed mathematical model and its numerical solution are useful for optimizing the crane structures, providing compliance with the operational requirements, and extending the service life of lifting machines.

The study of a novel magnetic crankshaft

This paper introduces a revolutionary mechanism, the Four-Translator Magnetic Crankshaft (FTMC), designed to address inherent limitations of the Magnetic Lead Screw (MLS) in energy storage and driving efficiency. The FTMC combines features of the MLS and a traditional cross crankshaft, enabling efficient energy conversion between continuous rotatory motions and reciprocating linear motions. The study presents the FTMC's working principle, theoretical calculations, 3D finite element analysis (FEA) validation, and comprehensive performance analyses. The FTMC's rotor, featuring a unique magnet array, allows for continuous rotation while the four translators reciprocate with a 90-degree phase difference. This breakthrough resolves the energy storage challenge faced by MLS, leading to enhanced efficiency and frequency. The paper explores the FTMC's static and dynamic performance, demonstrating its superiority in achieving 4.6 times higher reciprocating speeds or 93.3 % lower driving torque compared to the same-sized MLS in the limiting case. Furthermore, the study proposes an innovative assembly design with a 2-air gap topology, addressing potential radial attraction issues and reducing translator mass. The anticipated performance under ideal conditions, based on 3D FEA results, showcases the FTMC's ability to transmit about 1.4 kW power with efficiencies exceeding 75 % at rated load angles and 30 Hz driving frequencies. Theoretical insights into the FTMC's capabilities open promising avenues for future research and prototyping. Experimental validation is recommended to confirm the mechanism's maximum driving ability, offering significant advancements in Magnetic Lead Screw and high-speed magnetic drive systems. Future studies should focus on prototype manufacturing and controllable load test bench design to validate the presented theoretical analysis.

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Abstract. Stiffness excitation is one of the important excitations for the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear system. Accurate calculation of the gear meshing stiffness is of great significance to investigating dynamic characteristics of the VH-CATT cylindrical gear system. Firstly, based on the forming theory of the modified tooth surface, the modified tooth surface equation of the VH-CATT cylindrical gear was deduced, and the 3D reconstruction was realised. Next, the load tooth contact analysis (LTCA) model of the VH-CATT cylindrical gear was developed to calculate the meshing stiffness of the VH-CATT cylindrical gear, and it was verified by the finite-element calculation. Finally, the influence of the load and modification parameters on the VH-CATT cylindrical gear stiffness was investigated. Research shows that the stiffness calculation method of the VH-CATT cylindrical gear based on LTCA is accurate. The meshing stiffness of the VH-CATT cylindrical gear in the double-tooth meshing area is large, and the meshing stiffness of the VH-CATT cylindrical gear in the single-tooth meshing area is small. The stiffness of the VH-CATT cylindrical gear increases with an increase in the load and cutter inclination angle, the stiffness of the VH-CATT cylindrical gear only in the double-tooth meshing area decreases with an increase in the parabolic coefficient, and the stiffness of the VH-CATT cylindrical gear increases with a decrease in the blade parabolic vertex position value. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising design.