Gear Parameters Research Articles

МОДЕЛИРОВАНИЕ ПЕРЕКЛЮЧЕНИЯ ПЕРЕДАЧ АВТОМОБИЛЬНОЙ ТРАНСМИССИИ С ГИДРОТРАНСФОРМАТОРОМ

The aim of the work is to evaluate the influence of gear shift parameters on the performance indicators of an automobile transmission with a torque converter (TC). The research objective is to develop a computer dynamic model of an automobile transmission with a three-row planetary gearbox and a TC to assess the transmission quality. The research applies the method of computer simulation using the software package “Universal Mechanism”. The novelty of the work is building a computer dynamic model of an automobile transmission with a three-row planetary gearbox and a torque converter to study the processes of gear shifting. The work results in developing a computer model to study the dynamic processes in a car transmission to assess the influence of gear shift parameters on the performance indicators of a car transmission with a TC. Recommendations are given on choosing gear shift control parameters. The work findings state that increasing the rise time of the friction clutch tup compression force raises the TC efficiency and the synchronization time of the clutch disks, reduces the values of the maximum angular acceleration and the change rate in the angular acceleration of the vehicle wheels (Jerk), increases the work of the friction forces of the clutches (W) when shift up is engaged and reduces W when shift down is engaged regardless of the TC blocking. When upshifting is actuated, one can recommend the minimum value of tup, which provides an acceptable value of Jerk.

Application of Kriging Model to Gear Wear Calculation under Mixed Elastohydrodynamic Lubrication

The calculation of tooth wear under mixed elastohydrodynamic lubrication is very complex and requires consideration of many conditions such as load distribution in the tooth meshing zone, micro-convex elastoplastic deformation and tooth surface temperature. The accurate calculation of tooth wear requires a lot of time and effort. In order to calculate tooth face wear under mixed elastomeric flow lubrication quickly and accurately, a new proxy model of tooth face wear is developed using the Kriging method. The pressure distribution required for the wear calculation was obtained utilizing the modified Reynolds equation and ZMC elasto-plastic model. The numerical calculation model of gear wear was derived using the modified Archard wear model. The Kriging model was used to construct a proxy model between gear parameters and tooth wear, and the degree of approximation and goodness of fit of the Kriging model were investigated. The results are as follows. The wear depth at each position is different, the smallest at the pitch, the largest near the tooth root, and the pinion has a larger wear depth than the gear. The Kriging model is highly efficient and accurate in its computation and overcomes the shortage of excessive time spent on the calculation of numerical calculation models.

A New Method of the Positioning and Analysis of the Roughness Deviation in Five-Axis Milling of External Cylindrical Gear

Abstract Five-axis milling is a modern, flexible and constantly developing manufacturing process, which can be used for the machining of external cylindrical gears by means of cylindrical end mills and special disc mills on universal multi-axis machining centres. The article presents a new method of positioning the tip and the axis of the end mill and the disc cutter in order to ensure a constant value of deviation of the theoretical roughness Rth along the entire length of the tooth profile. The first part presents a mathematical model of the five-axis milling process of the cylindrical gear and an algorithm for calculating the Rth deviation values. The next section describes the positioning of the end mill and the disc cutter. Then, a new method for the empirical determination of the distribution of the involute root angle Δui and the data description by means of the interpolation function are presented and described. In the conducted numerical tests, the influence of the geometrical parameters of the cylindrical gear on the deviation Rth is determined, assuming a constant Rth value in the five-axis milling process.

Scalable multi-distance measurement approach for the optical assessment of tooth-individual shape parameters of large gearings

Abstract The demand for scalable measuring systems for the fast measurement of tooth-individual shape parameters of large gears is increasing. Due to a limited measuring speed and a limited measuring volume, standard tactile gear measuring systems are only conditionally suitable for comprehensive measurements of large gears. Therefore, the applicability of a scalable optical multi-distance measurement approach consisting of an optical sensor and a rotary table with a model-based evaluation is studied. As a fundamental gear shape parameter, the base circle radius of a large gearing is evaluated and the achievable measurement uncertainty is estimated. As a result, the tooth-individual base circle radius is determined on average with an expanded measurement uncertainty (k = 2) of one quarter of the required tolerance, and the realized measurement setup enables the measurement of all teeth within 1 minute. Hence, the scalable optical multi-distance measurement approach is appliacable for the fast measurement of tooth-individual shape parameters of large gearings.

Efficient hierarchical robust adaptive control of mode transition for parallel hybrid electric vehicles

A fast and smooth mode transition process for parallel hybrid electric vehicles (HEVs) can improve vehicle drivability. At the same time, system uncertainty resulting from friction, gearbox, parameter perturbation, production deviations, and external disturbance of the mode transition process makes control design challenges. In this regard, this paper introduces a novel efficient hierarchical robust adaptive mode transition control strategy to achieve an accurate and fast engagement of the clutch of a parallel HEV during mode transition in the case of uncertain system parameters and unmeasurable actual clutch torque in this paper. At the upper level of the controller, a robust adaptive sliding mode control (RASMC) is proposed to calculate the clutch transmitted required torque based on the current states of the electric motor (EM) and engine, and the control parameters are optimized via the particle swarm optimization (PSO) algorithm by compromising the vehicle jerk and the clutch slipping energy loss. Moreover, a fuzzy controller is designed to calculate the expected clutch engaging speed by employing the deviation of the desired and actual clutch torques, and the actual clutch torque is not a measured value but an estimate obtained by a proportional-integral (PI) observer. At the lower level, an adaptive finite-time control (AFTC) scheme is developed to overcome the gear backlash, parameter perturbation, and external disturbance during the clutch position tracking process. The effectiveness and advantage of the proposed control strategy are verified by both MATLAB/Simulink simulations and the hardware-in-loop (HIL) test.

Meshing limit line of face worm gear drive with hardened cylindrical worm

This paper systematically establishes the computation method of the meshing limit line for the face worm gear drive with a hardened cylindrical worm. The meshing theory based on the reference point in the tooth surfaces is developed for the face worm gear drive. The reference point is reasonably determined based on the study of the meshing limit line characteristics. The calculation method of the coordinates of the reference point is proposed. The formula for the limit pressure angle at the reference point is obtained. Numerical results show that two meshing limit lines can be obtained on each flank of the worm tooth surface by iteratively solving the system of non-linear equations with four unknowns. These two meshing lines are near the inner end of the worm addendum. When the meshing limit lines are outside the worm tooth surface, the conjugacy of the worm tooth surface is good. Besides, studies of numerical examples find that poorly matched parameters of the face worm gear drive can result in the meshing limit line entering the worm tooth surface first from the inner end of the addendum, which reduces the conjugacy of the worm tooth surface. To avoid this, the conjugacy of the worm tooth surface can be checked by examining the limit pressure angle of the reference point when designing the face worm gear drive.

Rapid hob tip corner optimization of spur gears for increasing bending strength

Spur gears are widely applied in transmissions of heavy load cases, such as turbines, ships, mining devices, and other industrial applications. Increasing the tooth root bending strength offers great potential to increase the power density of gearboxes. To obtain a higher bending strength without increasing manufacturing costs, this study intends to find an optimal tooth root contour by optimizing the hob tip corner geometry. A rapid optimization method is thus proposed, consisting of a quick hobbing simulation to generate the tooth root fillet for arbitrary hob tip corners, a fast meshing adaptation mapping rule to guarantee the high mesh quality of different gear tooth geometries, and an analytical equation for calculating the maximum principal stress of the tooth root margin. The results show that the computing time only takes 5–8 min for each optimization, and an average potential of 15% is obtained for various gear parameters. Furthermore, a unified optimal hob tip contour, suitable for a wide range of gears, is also found with an average optimization potential of 13%. This study contributes greatly to the rapid optimization of the tooth root geometry and the corresponding hob tip geometry for high bending strength.

Research on gear mesh stiffness of helical gear based on combining contact line analysis method

A new analytical model of mesh stiffness of helical gears is proposed using a combination of contact line analysis with slice method, which can well predict the dimensionless time-varying mesh stiffness. Based on the derived formula, the influence of gear basic parameters on mesh stiffness fluctuation coefficient is studied. The simulation shows that the influence of the overlap ratio on the mesh stiffness fluctuation coefficient is greater than that of the transverse contact ratio. By designing reasonable helix angle and tooth width, the overlap ratio is close to an integer, and then the mesh stiffness fluctuation coefficient can obtain a local minimum value, which is an effective way to reduce the vibration and noise of gear system.

Effects of gear structural parameters on unsteady-state temperature field of large transmission ratio gear and tooth root thermal stress

A calculation method of tooth root stress for large transmission ratio gear and rack is proposed using a broken-line section model and thermal-mechanical coupling analysis. To describe the transient meshing dynamics between the gear and the rack, a contact deformation model between the gear and the rack is fitted by using the least square method, and the meshing temperature field is calculated using the Blok flash temperature theory. The method of the broken-line section is modified based on the fatigue crack growth path at the tooth root. A new broken-line section model to calculate the tooth root stress is established, and a stress permeability factor is introduced to identify the width of the broken line. Using the meshing temperature field of gear and rack, the calculation formulas of root bending stress and root compression stress are derived by the integral-iterative method under thermal-mechanical coupling, and the correctness of the maximum tooth root stress model is validated by the finite element method (FEM). Compared with other methods for analyzing the thermal strength of gear roots, the proposed novel broken-line section method has simpler calculations and higher accuracy, and it can systematically analyze the effect of structural parameters on the dynamic strength of gear transmission mechanisms under actual working conditions.

Effect of Gear Design Parameters on Stress Histories Induced by Different Tooth Bending Fatigue Tests: A Numerical-Statistical Investigation

The characterization of new materials for enabling gear design is definitely a fundamental objective in the gear industry and research. Single Tooth Bending Fatigue (STBF) tests can be performed to speed up this process. However, it is well known that STBF tests tend to overestimate material strength compared to tests performed directly on meshing gears (MG) which, in turn, require an excessively long test time. Therefore, it is common practice to use a constant correction factor fkorr of 0.9 to translate STBF results for designing actual MG (e.g., via ISO 6336). Recent works involving a combination of Finite Element Models (FEM) and multiaxial (non-proportional) fatigue criteria based on the critical plane concept have highlighted that the assumption of considering fkorr as a constant independent of the gear design parameters leads to inaccurate results. However, in previous studies, no correlation between fkorr and gear design parameters has emerged. In the present paper, the influence of the normal pressure angle (αn), the profile shift coefficient (x*), and the normal module (mn) on fkorr was investigated by analyzing FEM simulations with the Findley fatigue criterion. 27 gear geometries were studied by varying the above 3 parameters in 3 levels (full factorial DOE). These geometries were simulated in both MG and STBF configurations. The results of the 54 FEM simulations were analyzed by applying the Findley fatigue criterion and the corresponding fkorr were calculated. The correlation between fkorr and αn, x* and mn was investigated using the Analysis of Variance (ANOVA) technique. The results show that the only gear design parameter influencing fkorr is x* hence, a regression model for fkorr including x* has been developed. This latter has been then adopted for calculating and comparing fkorr values from other combination of the parameters found in literature, giving good correspondence.

Spherical gear coupling design space analysis for high misalignment applications

Spherical gear couplings are machine elements that enable power transmission between highly misaligned shafts. The highly crowned tooth surfaces and the presence of undercut sections, have been a matter of disagreement between existing geometry generation methods available in the scientific literature. The main reason for this, are the geometry variations which arise in the generated parts, and consequently, the effect of such variations on the contact point location and clearance distribution. In this paper the influence of the main design parameters of spherical gear couplings (namely, the crowning ratio, the pitch diameter, the pressure angle, etc.), on the geometrical properties of the gear tooth surfaces are investigated. An algorithm to calculate the maximum misalignment angle is proposed, which is one of the most crucial design parameters. It shows that the values obtained with models existing in the literature are not applicable to highly crowned spherical gear couplings. Finally, design criteria are described to help the designer choose proper spherical gear coupling tooth geometry parameters to fit in a certain space and achieve a given maximum misalignment angle without further geometrical issues (undercut or pointed teeth).

Analysis of retraction performance of aircraft landing gear in high and low temperature environment

Abstract In order to solve the problem that the internal mechanism parameters of the aircraft landing gear are difficult to measure and retractable, the retractable performance of the landing gear under high and low temperature environments is studied. This paper simplifies the retractable mechanism of the landing gear by analyzing the motion mechanism of the aircraft landing gear. The degree of freedom of the retractable mechanism is calculated to verify the accuracy of the simplified rear landing gear retraction mechanism. The simulation model of landing gear retraction mechanism under high and low temperature environment is constructed by Patran. The component deformation and shaft clearance of the retractable mechanism under low temperature (-55°C) and high temperature (74°C) environments are analyzed from the overall and detail dimensions. The quantitative effect of ambient temperature on the deformation of the retractable mechanism of the landing gear is studied. Then Adams is used to establish the kinematics simulation model of the retractable mechanism, and the friction coefficient of the kinematic pair under different ambient temperatures is incorporated. Based on the historical data of the high and low temperature environmental test of the landing gear, the correctness of the model is verified. The influence of the environmental temperature on the driving torque, movement angle and movement time of the retractable mechanism is quantified. The problem that the deformation parameters and motion characteristics of the retractable mechanism of the landing gear are difficult to measure is solved, and the research method of retractable performance of the landing gear mechanism under different ambient temperatures is formed.

기어시스템에서 설계변수에 따른 전달오차와 물림강성 해석

The gear has a wide range of transmitted force as various gear ratios are possible using a combination of teeth. It can transmit power reliably and cause relatively little vibration and noise. For this reason, the application of reducers of electric vehicles is being expanded. Vibration noise generated from gears is propagated into the quiet interior of a vehicle, causing various claims. In most gear studies, transmission error has been pointed out as the main cause of vibration noise of gears. Transmission errors have various causes, including design factors, manufacturing factors, and assembly factors. In general, when predicting transmission error through finite element analysis, design factors play an important role without considering manufacturing factors or assembly factors. In this study, relationships among important design variables (gear module, compensation rate, load torque, and transmission error) in gear design were investigated using analytical and experimental methods. In addition, a method of predicting gear meshing stiffness through the predicted gear transmission error was proposed to obtain variation of meshing stiffness due to changes of gear design parameters.

Сравнение эвольвентного и циклоидального зацеплений волновых зубчатых передач

Harmonic drives with an involute tooth profile have such faults as noise effects, tooth skips, jamming, increased tooth wear, etc. One of the reasons for the appearance of these shortcomings is the interference of the teeth, which can be caused by an incorrect choice of gear parameters, errors in the manufacture and mounting transmission elements. Interference occurs due to small gaps at the entrance to the engagement of the teeth. To increase these gaps, it is proposed to use cycloidal tooth shapes. To determine the minimum clearance at the entrance to the teeth engagement in involute and cycloidal gears theoretical studies have been carried out. It is shown that in the cycloidal engagement the minimum gap at the entrance to the engagement is much larger than in the involute one. The influence of the moment of resistance on the output shaft and the radial displacement of the cam axis on the specified clearance has been studied.

Influence of cycloid-pin gear design parameters on bearing capacity and optimized design

Influence of cycloid-pin gear design parameters on bearing capacity and optimized design

Research on an Improved Sliding Extracting Algorithm of Composite Deviation for Wind Turbine Gear

One tooth radial composite deviation and one tooth tangential composite deviation are important parameters of wind turbine gears whose operation life cycle can be influenced. An improved sliding extracting algorithm of composite deviation is proposed. It just only calculates those parts that need to be recalculated, avoids a large number of invalid searching calculations, and greatly improves the efficiency. The experimental results show that the improved sliding extracting algorithm of composite deviation has the same results as the traditional extracting algorithm, and the efficiency of the extracting algorithm is improved nearly 100 times. The improved sliding extracting algorithm of total composite deviation is proposed in this paper, and theoretically the algorithm efficiency is one time than traditional algorithm. The algorithms proposed in this paper can improve the efficiency of radial composite deviation and tangential composite deviation, and can be applied to gear singleflank rolling tester and gear double-flank rolling tester, especially in wind turbine gear field.

ADAPTATION OF RAIL PASSENGER CAR SUSPENSION PARAMETERS TO INDEPENDENTLY ROTATING WHEELS

This study aimed to adjust the rail passenger car running gear parameters by adapting them to independently rotating wheels. The most important aspect was the safety of the passenger car running in terms of derailment; thus, the values of the Nadal criterion were calculated first. Another aspect to consider is passenger comfort based on the values of Sperling’s comfort index according to the rail passenger car speed. The modes of suspension behaviour during operation were considered in two typical conditions: on a straight track section and on a curve with a 200-m radius. Calculations were performed using Universal Mechanism software. The results are interpreted in the paper, and the final conclusions of this study are given.

Modification and Noise Reduction Design of Gear Transmission System of EMU Based on Generalized Regression Neural Network

In view of traction gear vibration and noise affecting the performance of the transmission system and the comfort of passengers when the electric multiple units (EMU) is running at high speed, taking the traction gear transmission system of an EMU as the research object by using Romax software to construct the parametric modification model of the gear transmission system based on gear modification theory. Combined with multibody dynamics, the vibration response characteristics of the transmission system are simulated and analyzed. A radiated noise prediction model is established using the acoustic boundary element method, based on the generalized regression neural network (GRNN). To further explore the influence of gear modification methods and parameters on vibration and noise characteristics and minimize gear transmission’s radiation noise. A particle swarm optimization (PSO) algorithm is designed to solve the optimal modification parameters. The simulation results reveal that after the optimization and modification, the gear transmission error is significantly reduced, the contact status is considerably improved, and the root mean square value of the acoustic power level is reduced by 13.10 dB, which is a reduction of 14%. It shows that the design can effectively reduce the radiation noise of EMU gear trans-mission system.

Analysis of Effects of Change of Gear Parameter Module on Transmission Error in Spur Gear using Interference Volume Method

Gear drives are the most used elements in power transmission systems. Any defect in the gear of these drives leads to noise and vibrations, which affect power/torque transmission. Transmission Error (TE) is one of the critical causes that arises due to the tooth geometry error, cracks in gear, profile error etc. Our work demonstrates, the consequences occurring due to the changes in gear parameter module on TE for spur gear pair of 1:1 gear ratio with pitch error, using the interference volume method. The spur gear without pitch error and with pitch error having the involute profile of standard tooth dimension system and stub tooth dimension system are modelled and assembled in CAD software SOLIDWORKS. The interference volume values obtained from the gear pairs are recorded for one mesh cycle. Various graphs plotted between the angle of rotation and interference volume values for one mesh cycle. It is found from the analysis that as the module and pitch error increase TE also increases. The effect of variation of module and pitch error is more in the standard tooth dimension system than the stub tooth dimension system.

A holistic approach for gear skiving design enabling tool load homogenization

Gear skiving is a highly productive manufacturing process for internal gears. Due to its challenging cutting conditions often insufficient tool life is achieved and localized wear occurs. There is a lack of tool parameters in process design that allow for an uniform and comparable characterization of the process kinematics and tool geometry. In this paper, a new method for calculating process kinematics and tool profile based on parameters of profile-shifted conical gears and an approach for tool load homogenization are presented. The high potential of the methods is demonstrated by comparative tool life tests with an improvement of 300%.