Search Results (56)

This study presents an analysis of the electromagnetic noise and vibration in a surface-mounted permanent magnet synchronous machine (SPMSM), focusing on their excitation sources. To investigate this, the excitation sources were identified through an analytical approach, and their effects on electromagnetic noise and vibration were evaluated using a finite element method (FEM)-based analysis approach. Additionally, an equivalent curved-beam model based on three-dimensional shell theory was applied to determine the deflection forces on the stator yoke, accounting for the tooth-modulation effect. The stator’s natural frequencies were derived through the characteristic equation in free vibration analysis. Modal analysis was performed to validate the analytically derived natural frequencies and to investigate stator deformation under the tooth-modulation effect across various vibration modes. Furthermore, noise, vibration, and harshness (NVH) analysis via FEM reveals that major harmonic components align closely with the natural frequencies, identifying them as primary sources of elevated vibrations. A comparative study between 8-pole–9-slot and 8-pole–12-slot SPMSMs highlights the impact of force variations on the stator teeth in relation to vibration and noise characteristics, with FEM verification. The proposed method provides a valuable tool for early-stage motor design, enabling the rapid identification of resonance operating points that may induce severe vibrations. This facilitates proactive mitigation strategies to enhance motor performance and reliability. Full article

Due to its small size, high transmission ratio and precision, the harmonic reducer is widely used. The design of the flexspline tooth profile is crucial for the transmission accuracy and service life of harmonic reducers. However, the numerous design parameters and the lack of a unified design standard for the flexspline tooth profile make it challenging to accurately determine these parameters. This can lead to issues such as tooth profile interference and excessive stress on the gear teeth during transmission. To address these issues, we propose a novel rapid design framework for the tooth profile of a double-circular-arc common-tangent flexspline in harmonic reducers. Firstly, the mathematical formula for the flexspline tooth profile with a double-circular-arc common-tangent and its conjugate circular spline tooth profile is derived. Then, two-dimensional and three-dimensional parametric finite element models of the harmonic reducer are established, and radial and axial profile modifications of the flexspline are carried out. Based on the parametric two-dimensional finite element model of the harmonic reducer, the optimized Latin hypercube experimental design method is employed to determine the flexspline tooth profile parameters. The method proposed can be implemented using Python language code and integrated into the Abaqus 2019 software, offering the advantage of meeting the requirements for rapid engineering development. Finally, a case study is presented to verify the effectiveness of the proposed design method. Full article

Induction motors have a simple structure, have low manufacturing costs and are widely used. However, various vibration effects with mechanical or electromagnetic origins are also very common. To analyze the impact of rotor skewing on electromagnetic vibrations in induction motors, this paper investigated the skew factor of skewed rotor slots and proposes an electromagnetic force wave analysis method. The method aimed to optimize the skew angle parameters for vibration amplitude reduction, with its effectiveness verified through simulations and experiments. Taking a 7.5 kW four-pole induction motor with 36 stator slots and 28 rotor slots as the research object, the suppression law of different skew parameters on force waves generated by stator harmonics was obtained. Results show that when the rotor is skewed by an angle equivalent to three stator teeth pitch, electromagnetic forces of different orders are attenuated by approximately 5% on average. Physical rotors with skew angles of 0°, 10°, 12.8°, 14°, and 20° were manufactured for experimental validation, while considering the influence of rotor skewing on starting torque and maximum torque. The study concludes that the amplitude of tooth harmonics varies with the skew coefficient, consistent with the skew factor analysis. By analyzing motor vibration with the skew coefficient, the amplitude relationship of electromagnetic vibration under different optimization parameters can be determined, thereby selecting reasonable skew parameters for rotor optimization. Full article

Recently, with policies aimed at strengthening domestic manufacturing and technological innovation, the robotics industry has been growing rapidly, and its applications are expanding across various industrial fields. Accordingly, the importance of high-performance speed reducers with flexibility and precision is gradually increasing. The tooth profiles used in conventional harmonic reducers have structural limitations, such as meshing discontinuity, restrictions on the radius of curvature of the tooth base, and distortion of the contact trajectory, especially when the number of teeth is small. These problems limit the design freedom of the reducer and make it difficult to secure contact stability and durability under precision driving conditions. To solve these problems, this paper proposes a new tooth profile design equation, the IH (Involute Harmonic) tooth profiles and the HTPs (Hybrid Tooth Profiles), using the cycloid curve to overcome the structural limitations of the conventional harmonic tooth profile, which is difficult to design under small-tooth-number conditions, and to enable tooth design without restrictions on the number of teeth. HTP tooth profile is a new gear tooth profile design method that utilizes IH tooth profile and cycloid curve to optimize the meshing characteristics of gears. A tooth profile design tool based on the HTP equation was developed using Python 3.13.3. The tool’s effectiveness was validated through simulations assessing tooth meshing and interference. Using the tool, an R21_z3 reducer with a single-stage high reduction ratio was designed to evaluate practical applicability. A prototype was fabricated using 3D printing with PLA material, and experimental testing confirmed the absence of meshing or interference issues, consistent with simulation results. Through this study, we verified the usefulness of the HTP tooth profile design formula and design tool using the IH tooth profile and cycloid curve, and it is expected that the proposed HTP tooth profile can be utilized as a tooth profile applicable to various reducer designs. Full article

The condition monitoring of gearboxes is crucial to ensuring the reliability and efficiency of modern industrial machinery. The accurate estimation of Time-Varying Mesh Stiffness (TVMS) is a key aspect of modeling gear meshing behavior and generating vibration signals used for fault diagnosis. In this study, TVMS is calculated by using the Refined Finite Element Method (R-FEM), which captures detailed gear-body compliance and distributed load effects. The dynamic model of a two-stage gearbox is then used to generate vibration responses under both healthy and faulty conditions. A comprehensive parametric sensitivity analysis is conducted on critical gear modeling parameters, including tooth profile deviations, mesh convergence in contact zones, assembly tolerance-induced interaxial variations, load-dependent stiffness variations, and hub-radius effects. Experimental validation using a gearbox test bench confirms that the proposed methodology accurately reproduces fault-specific harmonic components. These results indicate that the hybrid FEM–dynamic modeling approach effectively balances accuracy and computational efficiency, thereby providing a robust framework for advanced fault detection and maintenance strategies in gear systems. Full article

This paper proposes a two-dimensional (2D) generalized equivalent magnetic network (GEMN) model suitable for surface-mounted permanent magnet electric machines (SPEMs). The model divides the SPEM into eight types of regions: stator yoke, stator tooth body, stator tooth tips, stator slot body, stator slot openings, air gap, rotor permanent magnets, and rotor yoke. Each region is subdivided radially and tangentially into multiple 2D magnetic network units containing radial and tangential magnetic circuit parameters, forming a regular magnetic network covering all regions of the SPEM. The topology of this magnetic network remains unchanged during rotor rotation and can accommodate various surface-mounted permanent magnet structures including Halbach arrays, which enhances the generality of the model significantly. The proposed model can be used to calculate the 2D magnetic flux density distribution, winding electromotive force, electromagnetic torque, stator iron loss, and permanent magnet demagnetization in the influence of magnetic saturation, stator slotting, and current harmonic. Comparative analysis with the accurate subdomain method (ASDM) and finite element method (FEM) demonstrates that the GEMN model achieves a good balance between computational speed and accuracy, making it particularly suitable for efficient electromagnetic performance evaluation of SPEMs. Full article

A harmonic drive (HD) is a precision reduction device widely utilized in the core joints of high-end equipment such as spacecraft and robots. The design of an excellent tooth profile is the core challenge related to the performance of HD. This investigation aims to propose a design method of a fully conjugated cycloid tooth profile (CTP) for HD. Firstly, the rationality of CTP use for HD is analyzed, and the cycloidal characteristics of the tooth trajectory are studied by use of canonical warping distance. Then, initial CTP equations are constructed, adopting the trajectory mapping results. Presetting the addendum CTP of circular spline, the conjugate CTP of flexspline is then designed using the envelope method. Subsequently, the envelope of the designed flexspline addendum is used to reverse-design the circular spline dedendum. The backlash is calculated to evaluate the CTPs designed with different radial displacement coefficients. Research shows that the tooth trajectory has cycloidal characteristics; therefore, the HDs that use CTP can realize a fully conjugate engagement. Moreover, the variable control parameters enable the proposed CTP expression to have excellent fitting characteristics, resulting in small and uniform mesh backlash distribution. The CTP is expected to become one of the ideal tooth profiles of HD. Full article

Tip relief is a critical design feature of modern spur gears, aimed at improving dynamic performance through a typical design strategy involving peak-to-peak minimization of mesh excitations. However, due to the hyperstatic nature of simultaneous tooth engagements, the applied torque not only affects mesh deformation amplitudes as normally considered but also alters mesh excitation waveforms, leaving great challenges for the typical design to meet various operating conditions. This paper develops an analytical framework to reshape mesh excitation waveforms, aimed at flexibly reducing vibration intensities across different operating loads and speeds. The load-dependency of excitation harmonics with tip relief is efficiently characterized by an improved analytical mesh excitation model. A tip relief design method is proposed, which automatically recombines harmonic contents of mesh excitations to adapt target operating speeds. Comparisons with finite element models and experiments confirmed the accuracies of quasi-static and dynamic analyses. Parametric studies and application examples further demonstrate the acceptable feasibility and effectiveness of the present method. Full article

Considering the elasticity of gear solid bodies, the load applied to gear teeth will force theoretically separated gear teeth to get into engaging state in advance. This phenomenon is named as the extended tooth contact (ETC). Effects of the ETC directly influence the time-varying mesh stiffness of gear pairs and subsequently alter nonlinear dynamic characteristics of gear transmission systems. Time-vary mesh stiffness, considering effects of the ETC, is thus introduced into the dynamic model of the gear transmission system. Periodic motions of a gear transmission system are discussed in detail in this work. The analytical model of time-varying mesh stiffness with effects of the ETC is proposed, and the effectiveness of the analytical model is demonstrated in comparison with finite element (FE) results. The gear transmission system is simplified as a single degree-of-freedom (DOF) model system by employing the lumped mass method. The correctness of the dynamic model is verified in comparison with experimental results. An incremental harmonic balance (IHB) method is modified to obtain periodic responses of the gear transmission system. The improved Floquet theory is employed to determine the stability and bifurcation of the periodic responses of the gear transmission system. Some interesting phenomena exist in the periodic responses consisting of “softening-spring” behaviors, jump phenomena, primary resonances (PRs), and super-harmonic resonances (SP-HRs), and saddle-node bifurcations are observed. Especially, effects of loads on unstable regions, amplitudes, and positions of bifurcation points of frequency response curves are revealed. Analytical results obtained by the IHB method match very well with those from numerical integration. Full article

Gear skiving is a highly productive method for manufacturing gears, especially internal gears. Circular arc internal gears are important parts of Rotary Vector (RV) reducers and harmonic reducers. This study presents the implementation of the gear skiving technique using a cylindrical tool to enhance the precision and efficiency of machining circular arc internal gears. By establishing the mathematical model for skiving a circular arc internal gear based on the conjugation theory of two surfaces, the barrel-shaped conjugate surface was solved by deducing gear meshing equations. A design method is proposed for a cylindrical skiving tool by utilizing the barrel-shaped conjugate surface with an off-center tool position along the axis. The cutting edge of the tool rake face was then obtained through cubic spline interpolation from the conjugate surface. The influence of the tool rake face offsets on the cutting rake angle and clearance angle is also discussed by defining the normal cutting plane of the tool. The correctness of the proposed cylindrical skiving tool was validated through simulation and actual skiving experiments. The experimental results demonstrated that the tooth profile error of the gear fell within ±0.004 mm, thereby satisfying the accuracy requirement for pin wheel housing gears. These research findings can contribute to advancements in novel cylindrical skiving tools. Full article

Harmonic drives (HDs) with short flexspline (FS) always suffer from small meshing areas and severe stress concentration caused by large cone angles when a short FS is assembled and loaded. To address this issue, a tooth longitudinal modification method for the circular spline (CS) with a double circular arc common-tangent tooth profile (DCTP) is proposed. Using neutral layer and envelope conjugation theories, a mathematical model of the conventional straight CS tooth was developed. A shaping cutter for this tooth profile was then designed through coordinate transformation and meshing principles. The proposed longitudinal modification for the CS was achieved by adjusting the cutter’s trajectory. A precise finite element model of the HD was developed, revealing that tooth longitudinal modification can reduce the maximum contact pressure by 69.6% and significantly increase the contact area for HDs with short FS. This work provides valuable technical references for improving the contact state of HDs with short FS. Full article

Objectives: The main objective of this study was to assess whether there are differences in the muscular and occlusal levels between wind players and the general population, in addition to assessing the different repercussions depending on the embouchure type. Material and Methods: Two cohorts were chosen: one of them comprised intermediate students related to the practice of a wind instrument (n = 39), and the other one, harmonized with the former, comprised secondary students that served as a control group (n = 19). Overjet, overbite, presence of lip abrasion and/or erosion, Angle’s molar class, Little’s irregularity index, dental abrasion, presence of labial herpes, presence of tooth sensitivity, and presence of articular noises muscle pain were evaluated. Results: Significant statistical differences between the groups were found regarding overjet, overcrowding of teeth, lower lip erosion, and dental abrasion, which was higher in musicians. Lastly, within the group of musicians, it was proven that tooth sensitivity was higher in the group of brass musicians. Conclusions: Wind instrument practice may be a risk factor for developing some orofacial involvement, and there are no differences among the various existing mouthpieces. Full article

Low-frequency harmonic interference is an important factor that affects the performance of low-speed direct-drive servo systems. In order to improve the low-speed smoothness of direct-drive servo, firstly, the causes of the first and second harmonics of electromagnetic torque and tooth harmonics are analyzed based on the mathematical model of PMSM (permanent magnet synchronous motor) and the principle of vector control. Accordingly, the CC-EUMA (Electrical angle Update and Mechanical angle Assignment algorithm for Center Current) and SL-DQPR (Double Quasi-Proportional Resonant control algorithm for Speed Loop) algorithm are proposed. Second, to confirm the algorithm’s efficacy, the harmonic environment is simulated using Matlab/Simulink, and the built harmonic suppression module is simulated and analyzed. Then, a miniaturized, fully digital drive control system is built based on the architecture of the Zynq-7000 series chips. Finally, the proposed suppression algorithm is verified at the board level. According to the experimental results, the speed ripple decreases to roughly one-third of its initial value after the algorithm is included. This effectively delays the speed ripple’s low-speed deterioration and provides a new idea for the low-speed control of the space direct-drive servo system. Full article

Flexsplines in harmonic gear reducers are usually characterized by a large number of teeth, small modulus, and poor stiffness, which makes them difficult to measure using conventional gear measuring centers. In order to efficiently evaluate the quality of flexsplines in harmonic gear reducers, a rapid measurement method for flexspline pitch using offset point laser sensors (PLS) is proposed. This paper investigates the principle of measuring the tooth flank of the flexspline under the offset of the PLS, establishes a model for collecting and analyzing gear surface data, builds an experimental system, calibrates the six pose parameters of the sensor using the geometric features of the flexspline’s outer circular surface, and completes the reconstruction of the left and right gear surfaces of the flexspline based on the measured data. In the experiment, the gear surface obtained by the proposed method is largely consistent with that measured by the video imaging method, and the repeatability of both single pitch deviation and cumulative pitch deviation is within ±3 µm. Full article

The current paper presents helical gearbox defect detection models built from raw vibration signals measured using a triaxial accelerometer. Gear faults, such as localized pitting, localized wear on helical pinion tooth flanks, and low lubricant level, are under observation for three rotating velocities of the actuator and three load levels at the speed reducer output. The emphasis is on the strong connection between the gear faults and the fundamental meshing frequency GMF, its harmonics, and the sidebands found in the vibration spectrum as an effect of the amplitude modulation (AM) and phase modulation (PM). Several sets of features representing powers on selected frequency bands or/and associated peak amplitudes from the vibration spectrum, and also, for comparison, time-domain and frequency-domain statistical feature sets, are proposed as predictors in the defect detection task. The best performing detection model, with a testing accuracy of 99.73%, is based on SVM (Support Vector Machine) with a cubic kernel, and the features used are the band powers associated with six GMF harmonics and two sideband pairs for all three accelerometer axes, regardless of the rotation velocities and the load levels. Full article