Effects of the interval geometric deviation and crowning parameters on the automotive differential dynamics

2021 ◽  
pp. 146441932110394
Author(s):  
Wassim Lafi ◽  
Fathi Djemal ◽  
Ali Akrout ◽  
Lassaad Walha ◽  
Mohamed Haddar
Keyword(s):  
Gear Tooth ◽  
Dynamic Performance ◽  
Gear System ◽  
Time Step ◽  
Scanning Method ◽  
Wheel Drive ◽  
Applied Torque ◽  
Differential Mechanism ◽  
Geometric Deviation ◽  
Potential Energy Method

A differential mechanism is an essential component in the majority of automotive applications. Its vitality stems from the fact that it allows a wheel-drive vehicle to take a curve safely. On the other hand, it can ratchet up the vibration in the wheel-drive vehicle due to the excessive gear tooth deflection from applied torque. Some gear tooth modifications can increase or decrease the level of vibration in the mechanism. So far, very little attention has been paid to the effects of the uncertain geometric deviation of the tooth profile and uncertain crowning parameters on the dynamic performance of the mechanism. This study aims to investigate the impacts of these uncertain parameters on the gear systems’ dynamic performance. To this end, the nonlinear interval model of the differential mechanism is proposed. The mesh stiffness for straight bevel gear is modelled through the potential energy method and slice theory, while bearing stiffness elements are calculated at each time step. A refined computational algorithm is proposed to deal with any gear system with multiple interval variables. The scanning method is used as a reference method in this paper. The main outcomes of this study are that the crowning design can slightly reduce the vibration in the mechanism, and the profile errors can increase its vibration level excessively. Besides, the results derived from the refined algorithm show similarities to those determined by the scanning method, and the study shows that the refined algorithm can handle any gear system with uncertain static or time-varying parameters.

Effects of interval friction coefficients on the differential mechanism dynamics

2022 ◽  
pp. 095440702110689
Author(s):  
Wassim Lafi ◽  
Fathi Gharbi ◽  
Ali Akrout ◽  
Mohamed Haddar
Keyword(s):  
Friction Coefficient ◽  
Sliding Friction ◽  
Dynamic Performance ◽  
Mathematical Formulation ◽  
Reference Method ◽  
Least Square Method ◽  
Least Square ◽  
Mesh Stiffness ◽  
Scanning Method ◽  
Differential Mechanism

The presence of a differential mechanism is fundamental in most automotive applications. Its importance stems from allowing a vehicle to take a curve. The differential should be well-lubricated to ensure its smooth operation and mitigate its vibration level. With lubrication conditions deteriorating over time, the sliding friction coefficient becomes difficult to predict its accurate value. Thus, scrutinizing the dynamic performance of the mechanism with deterministic sliding friction can be misleading. This paper aims to investigate the dynamic performance of the automotive differential with the presence of interval sliding friction. To this end, a 3D dimensional model of automotive differential with time-varying mesh stiffness (TVMS) and bearing flexibility is proposed. The influence of sliding friction on TVMS for straight bevel gear is revealed. The Newton-Euler formulation is used to derive the dynamic equations governing the motions of the automotive differential with friction. The Chebyshev inclusion function and the least square method are used to deal with the interval mathematical formulation of the model. The scanning method is used as a reference method in this paper. There are quite similarities between the results derived by the scanning method and that of the interval process method. The reliability analysis of the differential is conducted. The outcome of this research shows that any variation of the sliding friction can alter the dynamic performance of the differential significantly. The differential is more sensitive to the friction coefficient between the ring gear and the drive pinion and between the left-side gear and two planets. The findings should make an important contribution to the analysis of the differential mechanism.

scholarly journals Fault Feature Analysis of Gear Tooth Spalling Based on Dynamic Simulation and Experiments

Materials ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6053
Author(s):  
Zhiguo Wan ◽  
Jie Zheng ◽  
Jie Li ◽  
Zhenfeng Man
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Gear Tooth ◽  
Resonance Region ◽  
Spur Gear ◽  
Gear System ◽  
Parameter Method ◽  
Coupling Vibration ◽  
Shock Response ◽  
Potential Energy Method

Gear dynamics analysis based on time-varying meshing stiffness (TMS) is an important means to understand the gear fault mechanism. Based on Jones bearing theory, a bearing statics model was established and introduced into a gear system. The lateral–torsion coupling vibration model of the gear shaft was built by using a Timoshenko beam element. The lumped parameter method was used to build the dynamic model of a gear pair. The dynamic model of a spur gear system was formed by integrating the component model mentioned above. The influence of rectangular and elliptical spalling on TMS was analyzed by the potential energy method (PEM). The fault feature of tooth spalling was studied by dynamic simulation and verified by experiments. It is found that the gear system will produce a periodic shock response owing to the periodic change of the number of meshing gear teeth. Due to the contact loss and the decrease of TMS, a stronger shock response will be generated when the spalling area is engaged. In the spectrum, some sidebands will appear in the resonance region. The results can provide a theoretical guide for the health monitoring and diagnosis of gear systems.

Non-probabilistic interval process method for analyzing two-stage straight bevel gear system with uncertain time-varying parameters

2020 ◽  
pp. 095440622096769
Author(s):  
Wassim Lafi ◽  
Fathi Djemal ◽  
Dhouha Tounsi ◽  
Ali Akrout ◽  
Lassaad Walha ◽  
...  
Keyword(s):  
Bevel Gear ◽  
Gear System ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Time Step ◽  
Two Stage ◽  
Straight Bevel Gear ◽  
Potential Energy Method ◽  
Process Method

A two-stage straight bevel gear system is a gear system that can be used in various applications. The straight bevel gear is known for its complex tooth geometry. Due to the variation of the number of pairs of teeth in contact, the mesh stiffness function can be considered as a time-varying function. However, the mesh stiffness for the straight bevel gear is sensitive to measurement and modeling errors. Thus, at each time step, its value can not assigned to deterministic one. Generally, the uncertain parameters are assumed to be time-independent. In this paper, the interval process method has been used to represent the time-varying uncertain parameters, whose bounds are determined through the potential energy method. The lumped parameter model of two-stage straight bevel gear has been proposed. We have considered that the masses of the straight bevel gear system components and bearing stiffnesses along with time-varying mesh stiffnesses are uncertain parameters which can be represented by the interval process model. The Chebyshev polynomial expansion has been used to approximate the response of the two-stage straight bevel gear system with respect to the interval variables. The lower and higher bounds of the eigenvalues of the system have been determined. The bounds of dynamic displacements of the straight bevel gear system have been computed and compared with those computed by the Monte Carlo method.

scholarly journals Simulation of Differentials in Four-Wheel Drive Vehicles Using Multibody Dynamics

2011 ◽  
Author(s):  
Geoffrey Virlez ◽  
Olivier Bru¨ls ◽  
Pierre Duysinx ◽  
Nicolas Poulet
Keyword(s):  
Test Bench ◽  
Good Accuracy ◽  
Dynamic Performance ◽  
Nonlinear Finite Element Method ◽  
Vehicle Model ◽  
Contact Conditions ◽  
Flexible Bodies ◽  
Wheel Drive ◽  
Complex Phenomena ◽  
Four Wheel Drive

The dynamic performance of vehicle drivetrains is significantly influenced by differentials which are subjected to complex phenomena. In this paper, detailed models of TORSEN differentials are presented using a flexible multibody simulation approach, based on the nonlinear finite element method. A central and a front TORSEN differential have been studied and the numerical results have been compared with experimental data obtained on test bench. The models are composed of several rigid and flexible bodies mainly constrainted by flexible gear pair joints and contact conditions. The three differentials of a four wheel drive vehicle have been assembled in a full drivetrain in a simplified vehicle model with modeling of driveshafts and tires. These simulations enable to observe the four working modes of the differentials with a good accuracy.

Robust mode transition control of four-wheel-drive hybrid electric vehicles based on radial basis function neural network estimation-a simulation study

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ling Li ◽  
Fazhan Tao ◽  
Zhumu Fu
Keyword(s):  
Dynamic Performance ◽  
Transition Process ◽  
Mode Transition ◽  
Robust Controller ◽  
Content Type ◽  
Engine Torque ◽  
Transition Control ◽  
Wheel Drive ◽  
Mode Transition Control ◽  
Four Wheel Drive

Purpose The flexible mode transitions, multiple power sources and system uncertainty lead to challenges for mode transition control of four-wheel-drive hybrid powertrain. Therefore, the purpose of this paper is to improve dynamic performance and fuel economy in mode transition process for four-wheel-drive hybrid electric vehicles (HEVs), overcoming the influence of system uncertainty. Design/methodology/approach First, operation modes and transitions are analyzed and then dynamic models during mode transition process are established. Second, a robust mode transition controller based on radial basis function neural network (RBFNN) is proposed. RBFNN is designed as an uncertainty estimator to approximate lumped model uncertainty due to modeling error. Based on this estimator, a sliding mode controller (SMC) is proposed in clutch slipping phase to achieve clutch speed synchronization, despite disturbance of engine torque error, engine resistant torque and clutch torque. Finally, simulations are carried out on MATLAB/Cruise co-platform. Findings Compared with routine control and SMC, the proposed robust controller can achieve better performance in clutch slipping time, engine torque error, vehicle jerk and slipping work either in nominal system or perturbed system. Originality/value The mode transition control of four-wheel-drive HEVs is investigated, and a robust controller based on RBFNN estimation is proposed. Compared results show that the proposed controller can improve dynamic performance and fuel economy effectively in spite of the existence of uncertainty.

Design and Test of Differential Planetary Gear System for Open Rotor Power Gearbox

2013 ◽  
Author(s):  
Hideyuki Imai ◽  
Tatsuhiko Goi ◽  
Kenichi Kijima ◽  
Tooru Nishida ◽  
Hidenori Arisawa ◽  
...  
Keyword(s):  
Performance Test ◽  
High Efficiency ◽  
High Reliability ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Design Concept ◽  
Gear System ◽  
Open Rotor ◽  
Planetary Gear System ◽  
Validation Tests

The open rotor engine is a next generation aero-engine that satisfies the demand for high fuel efficiency and low CO2 emission. A differential planetary gear system is incorporated in the open rotor engine to connect the turbine output shaft and fan rotors in order to counter-rotate the fan rotors as well as allow the turbine and fan rotors to operate at more efficient speeds. The open rotor gear system is required to have not only 20,000 hp high power transmission, but also an increasingly high efficiency, high reliability and light weight. To achieve these requirements, the following design works were conducted; (1) a low misalignment and lightweight carrier, (2) a flexible structure to absorb the displacement caused by the flight load, (3) an optimum gear tooth modification and (4) reduction of oil churning and windage losses. Also, extensive analyses and simulations such as lube oil flow CFD, FEA and tooth contact analysis were conducted. A full scale prototype gear system was manufactured and validation tests were conducted using a newly constructed test rig to validate the design concept. A slow roll test, rated performance test and efficiency test were conducted. And the design concept was found to be valid. This paper describes details of the prototype design and the results of the validation tests.

Load Effects on the Dynamics of Spur Gear Transmissions

2010 ◽  
Author(s):  
Alfonso Fernandez del Rincon ◽  
Fernando Viadero Rueda ◽  
Miguel Iglesias Santamaria ◽  
Pablo Garcia Fernandez ◽  
Ana de-Juan de Luna ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Hybrid Approach ◽  
Angular Position ◽  
Spur Gear ◽  
Computational Effort ◽  
Contact Forces ◽  
Mode Shapes ◽  
Computational Time ◽  
Applied Torque ◽  
Rolling Elements

Gear transmissions in general and spur gears in particular exhibit a different dynamic behavior depending on the level of the transmitted load. This fact justifies the interest in the study of the role of the load in gear dynamics not only in the context of design, vibration and noise control but also for condition monitoring. This task requires the development of advanced models achieving a compromise between accuracy and computation time. In this work, gear and bearing non-linearities associated with the contact among teeth and roller elements have been included, taking into account the flexibility of gears, shafts and bearings. Besides, parametric excitations coming both from gear and bearing supports, as well as clearance, were also considered. Gear contact force calculations are carried out following a hybrid approach which combines both analytical and numerical tools. This lets to achieve accurate results with an acceptable computational effort and thus dynamic analysis becomes feasible. This approach was improved and the calculation speeded up from the point of view of computational time. This was performed by using a pre-calculated value for gear tooth stiffness as a function of load and the angular position when it operates under stationary conditions. On the other hand, bearings were formulated just as deflections of Hertzian type. This means that bending and shearing of races and rolling elements are neglected. However, the variation in the number of loaded rolling elements as a function of the load and the angular position was taken into account. Shaft flexibilities were added to gear and bearing models to define a simple transmission that was used to study the vibratory behavior under different levels of applied torque. In a preliminary study, this model was linearized for several loads, obtaining the corresponding frequencies and mode-shapes in order to assess their variation with this parameter. Finally, dynamic simulations were carried out, showing the modifications undergone by the orbits, meshing contact forces and transmitted bearing forces.

On Dynamic Tooth Load and Stability of a Spur-Gear System Using the State-Space Approach

1985 ◽  
Vol 107 (1) ◽  
pp. 54-60 ◽  
Author(s):  
A. S. Kumar ◽  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
State Space ◽  
Dynamic Load ◽  
Initial Conditions ◽  
Gear Tooth ◽  
Spur Gear ◽  
The State ◽  
Gear System ◽  
Computational Time ◽  
Steady State Condition ◽  
The Stability

In this study, a new approach using the state-space method is presented for the dynamic load analysis of spur gear systems. This approach gives the dynamic load on gear tooth in mesh as well as information on the stability of the gear system. Also a procedure is given for the selection of proper initial conditions that enable the steady-state condition to be reached faster, conditions that result in considerable savings in computational time. The variations in the dynamic load with respect to changes in contact position, operating speed, backlash, damping, and stiffness are also investigated. In addition, the stability of the gear system is studied, using the Floquet theory and the well-known stability conditions of difference systems.

scholarly journals Perancangan dan Realisasi Kontrol Prototype Landing Gear System Menggunakan PLCmikro berbasis Mikrokontroller PIC16F877A

2014 ◽  
Vol 2 (1) ◽  
pp. 15
Author(s):  
RATNA SUSANA ◽  
USEP ALI ALBAYUMI ◽  
NICKY ILHAM TRIADHY
Keyword(s):  
Solenoid Valve ◽  
Landing Gear ◽  
Ladder Diagram ◽  
Gear System ◽  
Centralized Control ◽  
Flight Altitude ◽  
Analog Input ◽  
Information Processes ◽  
Wheel Drive ◽  
Led Lights

ABSTRAKLanding gear system merupakan suatu sistem penggerak pada roda pesawat yang menggunakan electromechanic system dengan sejumlah relay tanpa control terpusat. Melalui penelitian ini, electromechanic system tersebut diubah menjadi landing gear system yang dikendalikan secara terpusat menggunakan mikrokontroller dan diprogram oleh ldmikro berbahasa ladder diagram yang kemudian lebih dikenal dengan nama “PLCmikro”. Input discreate digunakan untuk menggerakkan aktuator solenoid valve agar piston double acting cylinder dapat bekerja sesuai sistem yang diinginkan. Input analog digunakan sebagai informasi ketinggian pesawat minimum agar pesawat tetap aman terbang di udara. Control Landing gear system yang direalisasikan berhasil menggerakkan piston masuk maupun keluar dari tabung, memberikan informasi proses pergerakkan piston yang bermasalah dan posisi roda yang telah masuk atau keluar dari pesawat berupa lampu LED. Sistem ini juga berhasil membaca informasi ketinggian minimum pesawat dari potensiometer serta mengubahnya menjadi informasi suara dan lampu LED.Kata kunci: Landing gear system, PLCmikro, Ldmikro, ladder diagram, double acting cylinder.ABSTRACTThe landing gear system an aircraft wheel drive system that uses electromechanic system with a relay without any centralized control. Through this study, the electromechanic system was changed to landing gear system with a centrally controlled by using microcontroller and programmed with ldmikro ladder diagram language which came to be known by the name of "PLCmikro". Discreate input used to drive the actuator solenoid valve double acting cylinder so that the piston can work as desired system. The analog input is used as the minimum flight altitude information to keep the plane safe to fly in the air. Landing gear control system is realized successfully drive the piston in and out of the tube, providing information processes are problematic piston movement and wheel position that has entered or exited the plane in the form of LED lights. The system also successfully read the minimum altitude aircraft information of the potentiometer and turn it into information sounds and LED lights. Keywords: Landing gear system, PLCmikro, Ldmikro, ladder diagram, double acting cylinder.

Investigation on the Backlash of Roller Enveloping Hourglass Worm Gear: Theoretical Analysis and Experiment

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Xingqiao Deng ◽  
Jie Wang ◽  
Shike Wang ◽  
Shisong Wang ◽  
Jinge Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Comparison ◽  
Gear Tooth ◽  
Worm Gear ◽  
Gear System ◽  
Design Parameters ◽  
Comparison Results ◽  
Worm Gears ◽  
Base Circle ◽  
Roller Radius

This paper proposes a single-roller enveloping hourglass worm gear design and verifies its advantages compared to the existing double-roller worm gear system and the conventional worm gear set. Our hypothesis is that the single-roller worm gear with appropriate configurations and parametric values can eliminate the backlash in mating gear transmission while maintaining advantages of the double-roller worm gears. Also, the self-rotation of the rollers when they are in the worm tooth space (TS) will help the gear system to avoid jamming and gear tooth scuffing/seizing problems caused by zero backlash and thermal expansion. In order to test that hypothesis, a mathematical model for the single-roller enveloping hourglass worm gear is developed, which includes a gear engagement equation and a tooth profile equation. Using that model, a parametric study is conducted to inspect the influences of center distance, roller radius, transmission ratio, and the radius of base circle on the worm gear meshing characteristics. It is found that the most effective way in eliminating the backlash is to adjust the roller radius and the radius of base circle. Finally, a single-roller enveloping hourglass worm gear set is manufactured and scanned to generate a 3D computer model. That model is compared with a theoretical model calculated from the developed mathematical model. Comparison results show that both models match very well, which verifies the accuracy of the developed mathematical model and our initial hypothesis that it is possible to achieve transmissions with zero backlash by adjusting the design parameters.

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