Search Results (25)

The transmission accuracy and meshing performance of the gearbox is determined by the internal helical gears pair. Thermal deformation of internal helical gears pair is derived from sliding friction between the contacting teeth surface, resulting in shock, vibration, and misalignments. The purpose of this paper is to compare the influence of a modified gear and an unmodified gear on the temperature field and transmission characteristics of a planetary gear system under the same working conditions. This study presents an innovative temperature field model for gear pairs utilizing Surf152 elements, integrating Hertzian contact theory, tribological principles, and finite element analysis. For the first time, we quantitatively demonstrate the enhancement of thermo-mechanical performance through topological modification in helical gears. Under light-load conditions (200 rpm), the modified gear configuration exhibits a 6.38% reduction in tooth surface temperature and a 46.5% decrease in thermal deformation compared to conventional designs. Experimental validation confirms these improvements, showing an average 62.35% reduction in transmission error. These findings establish a novel methodology for high-precision gear design while providing critical theoretical foundations for planetary gear systems, ultimately leading to significant improvements in both transmission accuracy and operational lifespan. Full article

This paper presents a vibration analysis method for detecting typical faults in gears of the drive train of a 2 MW wind turbine. The data were collected over a one-year period from an operating wind turbine with a gearbox composed of one planetary stage and two helical gear stages. Failures in two pairs of helical gears were identified: one involving pitting and wear in the gears connecting the intermediate-speed shaft to the low-speed shaft, and another one involving significant material detachment in the gears connecting the intermediate-speed shaft to the high-speed shaft. The continuous evaluation of time signals, frequency spectra, and amplitude modulations allowed the most sensitive sensors and frequencies for predicting surface damage on gear teeth in this type of turbine to be determined. A steady-state frequency analysis was performed, enabling the detection of the aforementioned surface faults. This approach is simpler compared with more complex transient-state techniques. By tracking vibration signals over time, the importance of analyzing gear mesh frequencies and their harmonics was highlighted. Additionally, it was found that the progression of gear damage was dependent on the power output of the wind turbine. As a result, the most appropriate ranges of power were identified, within which the evolution of the vibration measurement was associated with the damage evolution. Since many turbines currently in operation have similar designs and power output levels, the present findings can serve as a guideline for monitoring an extensive number of units. Full article

Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primarily relies on finite element simulation, and there still lacks a mesh stiffness analytical model that accounts for tooth surface nonlinear contact. Therefore, this paper proposes an analytical model for nonlinear contact mesh stiffness that comprehensively accounts for tooth surface modification and the flexibility of the ring gear. Firstly, a mesh stiffness calculation model for a sliced tooth pair was established using the potential energy method, which accounted for the influence of gear ring flexibility. Secondly, the tooth deviation ease-off diagram was derived from the modified tooth surface equations, which provided data support for the nonlinear contact analysis. On this basis, slicing element pairs that met the contact conditions were identified by combining elastic deformation with mesh clearance. The comprehensive mesh stiffness in nonlinear contact was calculated by integrating the deformation coordination equation with the principle of minimum potential energy. Finally, using a group of internal helical gear pairs as an example, the validity of the proposed method was verified through finite element simulation. The effects of load, modification amount, and face width on the TVMS and load transmission error (LTE) of an internal helical gear pair were investigated by the analytical model. The results show that the analytical model can provide a reference for the optimal design of internal gear transmission. Full article

Internal helical gear pairs are sensitive to manufacturing and assembly errors, loading deformation, which can result in vibration and noise. Three-dimensional topological modification of tooth surfaces is available to reduce this sensitivity. A 3D topological modification method is proposed by means of an internal helical gear form grinding method. The modified tooth surface model was constructed using spatial meshing theory and matrix transformations. Loaded tooth contact analysis (LTCA) was established to investigate the effect law of modification parameters on gear loading performance. Simulation results indicated that the contact area appeared at the middle area of the tooth surface under design loading conditions, with little edge contact existing. Transmission error decreased by up to 28.4% compared to the tooth without modification. The dynamic meshing performance of the internal helical gear pair was enhanced significantly. A transmission experiment was conducted to verify the effectiveness and validity of the simulation results. Full article

Compared with traditional gear pumps, circular-arc gear pumps have the advantages of silence and small flow pulsation, but the theory of design is underdeveloped. This paper presents a design method for gear pumps with circular-arc helical gear pairs, and the influence mechanism of flow characteristics is studied. First, a model of the gear pair is established, and a design method for the gear pair is proposed. Second, a CFD model is demonstrated, and the influences of the tooth profile parameters (tooth number, modules, and pressure angle) on the flow characteristics are analyzed. Finally, the significance of the influencing factors is analyzed. The results show that when the stagger angle of the two ends of the arc helical gear pair is an integral multiple of π/Z, there is no flow pulsation, and there is little noise. The tooth number and modules are positively correlated with the flow rate and flow pulsation, among which the modules have the most significant influence. The flow rate of the gear pump increases by 4–5 L/min for every 0.2 increase in the modules. The pressure angle and flow rate show a negative correlation trend, but the influence is insignificant. The flow rate is less than 1 L/min for every 2° change in the pressure angle. This paper provides a theoretical basis and reference value for the gear pair design of gear pumps. Full article

Computer modelling of technical constructions is increasingly carried out using software that includes more detailed knowledge, which requires an increase in the level as well as an expansion of the scope of the geometric knowledge. A significant part of motion transmission mechanisms are worm drive pairs, for which the separation of the parts dealing with the theoretical and practical problems found in the literature can be experienced in numerous instances. Due to the different technical features, in many cases the helical surfaces are not designed and manufactured in a geometrically correct way, or the best solution is not the compulsory chosen. The geometric model describing the production process of the worm surfaces provides the basis for examining the deviation between the surface mathematically determined by the designer and the surface produced. An integrated mathematical kinematic model was developed for the production geometrical analysis of the elements of cylindrical and conical worm gear drive pairs for machining with a traditional thread grinding machine, which causes a serious pitch fluctuating error among several other problems in the case of machining the conical worm. Modelling of the production process of surfaces and the simultaneous study of the manufacturing errors is basically performed with the toolbox of descriptive geometry, including the use of the projective invariants. Knowing the inheritance of the invariants of projective geometry, the aim was the mathematical generalization of the integrated model and the creation of a projective relationship between the reference surfaces of conical and cylindrical spiral surfaces. As a result, the improved constructive geometric model was created, in which the method of analytically creating the projective geometric relationship between the reference surfaces of conical and cylindrical helicoid surfaces has been described for the first time in this article. This procedure is considered the most important result of the present article. Another significance of the further development presented is that during production of the conical helicoid surface, the thread pitch fluctuation has been eliminated. The results obtained, consisting of an improved geometric model, lead to a new geometry of the technological environment regarding the relative position of the cutting tool and the workpiece as well as the relative motion between them. Full article

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise. 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

The measurement of the meshing stiffness in gear pairs is a technological problem. Many studies have been conducted, but a few results are available. A tailored test bench was designed and realized to measure the Static Transmission Error in two mating gears to address this issue. The bench is capable of testing several kinds of gears, e.g., spur, helical, conical, and internal, and it measures the transmission error concerning the applied torque. The Static Transmission Error is due to the variable stiffness of the gear teeth during a mesh cycle. In this paper, a dynamical method for measuring gear mesh stiffness is presented. The tooth stiffness is estimated from the torsional modal behavior of the rotating parts of the test bench. The dynamics of the system are acquired using accelerometers and very precise encoders to measure the angular accelerations and displacements of rotating parts. The torsional mode shapes are identified; those that show a vibrational behavior of the gears that do not follow the transmission ratio’s sign of the mating kinematic condition are selected because they depend on the flexibility of the teeth. In such a way, the engagement stiffness is estimated from the natural frequencies of the selected mode-shapes and the known inertia of gears and shafts. The experimentally identified results are also compared with numerical values computed with a commercial software for mutual validation. Full article

A study on the dynamic characteristics of non-orthogonal helical face gears with higher-order tooth surface modification is presented in this article. The method of designing the non-orthogonal helical face gears with higher-order tooth surface modification is described. First, MATLAB programming that can be used for the parameterized 3D mesh calculations of non-orthogonal helical face gears with higher-order tooth surface modification are completed. Second, the calculated grid nodes from the MATLAB programming are imported into ABAQUS to generate a three-dimensional mode. The meshing stiffness of the gear pair is then estimated using finite element analysis. Ultimately, a dynamic model of a non-orthogonal helical face gear pair involving second-order and higher-order tooth surface modifications is established. One example is presented to study the dynamic characteristics of non-orthogonal helical face gear pairs with second-order and higher-order tooth surface modifications. The results show that the dynamic response from the second-order tooth surface modification has a higher peak-to-peak amplitude than that of the higher-order modification. Full article

Beveloid gears have the advantages of compensating for axial error, providing smooth transmission, and eliminating turning error. Therefore, they are widely used in applications that require high transmission accuracy and stability. However, research on calculating the time-varying meshing stiffness of beveloid gears is still limited, and there is an urgent need to propose a method that can calculate the meshing stiffness of beveloid gears quickly and accurately. We first established the tooth profile expressions, assuming a pair of beveloid gears meshing with the same rack, and the contact line equations of parallel axis beveloid gear pairs were derived. Next, we analyzed the contact process of beveloid gears. We propose an analytical algorithm based on the slicing method to calculate the meshing stiffness of helical gears, straight beveloid gears, and helical beveloid gears. Then, the influence of different parameters on the meshing stiffness of helical beveloid gears was analyzed by changing the respective parameters. Finally, the finite element method (FEM) was used to verify the correctness of the analytical results, and then the errors were analyzed. The study demonstrates that the results obtained from the analytical algorithm we proposed have the same magnitude as those obtained by the FEM for the time-varying meshing stiffness calculation of beveloid gears. Full article

Peristaltic pumps are widely used in biomedical applications to ensure the safe flow of sterile or medical fluids. They are commonly employed for drug injections, IV fluids, and blood separation (apheresis). These pumps operate through a progressive contraction or expansion along a flexible tube, enabling fluid flow. They are also utilized in industrial applications for sanitary fluid transport, corrosive fluid handling, and novel pharmacological delivery systems. This research provides valuable insights into the selection and optimal design of the powertrain stages for peristaltic pumps implemented in drug delivery systems. The focus of this paper lies in the simulation and optimization of the performance of a power transmission gearbox by examining the energy consumption, sound levels, reliability, and volume as output metrics. The components of the powertrain consist of a helical gear pair for the first stage, a bevel gear pair for the second one, and finally a planetary transmission. Through extensive simulations, the model exhibits promising results, achieving an efficiency of up to 90%. Furthermore, alternative configurations were investigated to optimize the overall performance of the powertrain. This process has been simulated by employing the KISSsoft/KISSsys software package. The findings of this investigation contribute to advancements in the field of biomedical engineering and hold significant potential for improving the efficiency, reliability, and performance of drug delivery mechanisms. Full article

Due to the special meshing of convex and concave tooth profiles, an S-shaped tooth profile gear with a few teeth has the advantage of reducing the contact stress and improving the contact ratio. However, the theoretical inseparability of the center distance of an S-shaped tooth profile and shaft misalignments, including center distance errors and axis parallelism errors caused by manufacturing or installation errors, can easily cause tip contact and produce transmission errors. Accordingly, it is necessary to analyze the influence of shaft misalignments on the meshing performance. In this paper, a unified mathematical model of spur and helical gears with an S-shaped tooth profile is established and an analytic method for determination of the contact pattern, meshing path, and transmission error of a gear pair with shaft misalignments is proposed. Then, the validity of the analytic method is proved by practical examples and the influence of shaft misalignments on the contact pattern of an S-shaped tooth profile gear pair is obtained. Through comparison with an involute gear with the same parameters, it is found that shaft misalignments within a certain range result in an acceptable transmission error and contact area migration of the S-shaped tooth profile gear pair similar to that of the involute gear pair. Full article

This paper presents an efficient method for obtaining the dynamic mesh stiffness and dynamic response of a helical gear pair. Unlike the traditional dynamic model that utilizes a time-dependent sequence, the mesh stiffness using the presented method is updated according to the gear displacement vector at each sub-step of the numerical calculation. Three-dimensional loaded tooth contact analysis (3D LTCA) is used to determine the mesh stiffness, and a surrogate model based on sparse polynomial chaos expansion (SPCE) is proposed to improve the computational efficiency, which is achieved by reducing the number of coefficients in the polynomial chaos expansion (PCE) model though a quantum genetic algorithm. During the calculation, the gear displacement vector at each sub-step is converted into the changes in center distance, misalignment angle, and mesh force, which are then introduced into the SPCE model to update the mesh stiffness for subsequent calculations. The results suggest that the SPCE model exhibits high accuracy and can significantly improve the computational efficiency of the PCE model, making it suitable for dynamic calculations. Upon updating the mesh stiffness during the dynamic calculation, the mesh stiffness declines, the dynamic transmission error (DTE) increases, and the frequency components of the responses change significantly. Full article

Due to the existence of machining and installation errors, axis parallelism error of gear pairs occurs, which causes eccentric load and mesh in-out impact, thus weakening loaded transmission character. To solve this problem, the axis parallelism error of gear pairs was equated with tooth axial inclination error based on the gear-meshing principle. On this basis, we established the tooth modification model with tooth axial inclination error as the variable according to involute helical gear form-grinding process. Then, the degradation of loaded transmission character caused by axis parallelism error of gear pairs was quantitatively analyzed. The gear grinding, gear measuring, and gearbox vibration measuring were, respectively, performed on high-precision CNC horizontal gear form-grinding machine tool L300G, Gleason 350 GMS, and JWY-II multifunctional gearbox loading test bench. The results show that the proposed method can effectively reduce eccentric load and mesh in-out impact and significantly improve loaded transmission character. Therefore, it can provide a theoretical and experimental basis for the research of high-performance gear-grinding technology of gear-grinder machines. Full article