Dynamics Equations of Planetary Gear Sets for Shift Quality by Lagrange Method

2008 ◽  
Author(s):  
Patinya Samanuhut ◽  
Atilla Dogan
Keyword(s):  
Equations Of Motion ◽  
Planetary Gear ◽  
Torque Converter ◽  
Vehicle Model ◽  
Lagrange Method ◽  
Engine Torque ◽  
Shift Quality ◽  
Planetary Gear Sets ◽  
And Shifts ◽  
Single Set

The equations of motion of planetary gear sets including pinion dynamics are derived using the Lagrange method. The Lagrange method provides a systematic procedure for derivation and yields a single set of equations that are valid for all gears and shifts for a given configuration. This procedure is applied to the coupled planetary gear set in GM Hydramatic 440 transmission. The planetary gear set equations along with a simplified engine, torque converter, friction elements and vehicle model are simulated for 2–3 and 3–4 shifts. The simulation results demonstrate that the equations derived for planetary gear sets can be used for studying shift quality.

Torsional Vibration Analysis of a Hydrodynamic Split Torque Transmission

1967 ◽  
Vol 89 (4) ◽  
pp. 605-610
Author(s):  
D. A. Klokkenga
Keyword(s):  
Experimental Data ◽  
Torsional Vibration ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Torque Converter ◽  
Transmission System ◽  
Engine Torque ◽  
Lagrange’S Equation ◽  
Torque Transmission

The steady-state torsional vibration for one mode of an engine transmission system was analyzed, and the analysis was verified by experimental data. The engine transmission system included a diesel engine, torque divider which consisted of a fixed housing, single-stage torque converter and a planetary gear set, and a dynamometer. The equations of motion are derived by an energy method (LaGrange’s equation) and a numerical solution of these equations is obtained with the aid of a digital computer. The analytical and experimental results agree when empirical values for torque converter damping are used.

A Systematic Approach for Dynamic Analysis of Vehicles With Eight or More Speed Automatic Transmission

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Sangchul Lee ◽  
Yi Zhang ◽  
Dohoy Jung ◽  
Byungchan Lee
Keyword(s):  
Dynamic Behavior ◽  
Test Data ◽  
Performance Metrics ◽  
Automatic Transmission ◽  
Control Unit ◽  
Torque Converter ◽  
Fine Tuning ◽  
Transmission Control ◽  
Engine Torque ◽  
Shift Quality

In this study, a dynamic model of a vehicle with eight or more speed automatic transmission (A/T) has been developed for the analysis of shift quality and dynamic behavior of the vehicle during shift events. Subsystem models for engine, torque converter, automatic transmission, drivetrain, transmission control unit (TCU), and vehicle are developed and integrated with signal information interface. The subsystems included in the model were carefully selected to improve the accuracy of the model by comparing the simulation results with the test data. The systematic modeling approach based on matrix operation proposed in the study enables calibrating and fine-tuning the transmission control unit for shift quality in a virtual vehicle environment. The model presented in the study is validated with the vehicle test data and the comparison shows very good agreement. This paper presents a generalized modeling methodology for multiratio automatic transmissions that require both direct and indirect shifts. The model developed in the study provides a valuable analytical tool for the calibration and tuning of the transmission control unit by allowing quantitative analysis on the dynamic behavior and the performance metrics of an automatic transmission.

A study of shift control using the clutch pressure pattern in automatic transmission

2003 ◽  
Vol 217 (4) ◽  
pp. 289-298 ◽  
Author(s):  
Woosung Han ◽  
Seung-Jong Yi
Keyword(s):  
Dynamic Models ◽  
Equations Of Motion ◽  
Automatic Transmission ◽  
Torque Converter ◽  
Optimum Pressure ◽  
Planetary Gears ◽  
Transient Characteristics ◽  
Engine Torque ◽  
Shift Control ◽  
Road Load

It is necessary to understand the overall system including engine, torque converter, multiplate clutch, band brake, one-way clutch, planetary gears, road load and tyre to analyse the performance of the vehicle powertrain. The performance of the powertrain can be analysed using dynamic models including transient characteristics and the equations of motion are derived from the dynamic models of the powertrain. In this study, the shift transient characteristics of the vehicle equipped with a Ravigneaux-type planetary gears automatic transmission has been investigated. A shift control using engine torque reduction and optimum pressure trajectory has also been investigated in order to enhance transient characteristics during shift.

Development of 2 Stage CVT Shift Control Algorithm to Reduce Torque Variation During 1-2 Upshift of Planetary Gear

2012 ◽  
Author(s):  
Jeongman Park ◽  
Sunghyun Ahn ◽  
Oheun Kwon ◽  
Youngho Jun ◽  
Minhyo Kim ◽  
...  
Keyword(s):  
Control Algorithm ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Shift Quality ◽  
Response Characteristics ◽  
Shift Control ◽  
Variable Transmission ◽  
Vehicle Simulator ◽  
Simulation Results ◽  
Fuzzy Control Algorithm

In this paper, a 2 stage continuously variable transmission (CVT) shift control algorithm is proposed for the 1–2 upshift of the planetary gear to achieve the shift quality. A fuzzy control algorithm is designed considering the relatively slower response characteristics of CVT. In order to evaluate the performance of the control algorithm, a 2 stage CVT vehicle simulator is developed including a dynamic model of the CVT powertrain. From the simulation results, it is found that CVT gear ratio changes faster in the inertia phase and remains constant after the inertia phase of the planetary gear shift, which provides the reduced torque variation by the proposed control algorithm.

The Research on Natural Characteristic and Eigensensitivity of Ravingneaux Compound Planetary Gear Sets

2013 ◽  
Vol 446-447 ◽  
pp. 590-596
Author(s):  
Bo Qian ◽  
Shi Jing Wu
Keyword(s):  
Natural Frequency ◽  
Planetary Gear ◽  
Torsional Stiffness ◽  
Ring Gear ◽  
Vibration Model ◽  
Planetary Gear Sets ◽  
Planet Gear ◽  
Natural Characteristic ◽  
Gear Ring ◽  
The Moment

The dynamic model of Ravingneaux compound planetary gear sets has been built. Then the Natural frequency and vibration model have been solved in the Ravingneaux compound planetary gear sets. The eigensensitivity to parameters have been researched based on the dynamical model. The varying trend of natural frequency according to the varying of parameters have been researched, which include gear mass (sun gear, ring gear , or planet gear), the moment of inertia of gears, the support stiffness , the torsional stiffness.

An Analytical and Numerical Investigation of Modulation Sidebands of a Planetary Gear Under Fluctuated External Torque

2018 ◽  
Author(s):  
Yunbo Yuan ◽  
Wei Liu ◽  
Yahui Chen ◽  
Donghua Wang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Operating Conditions ◽  
Radial Acceleration ◽  
External Torque ◽  
Gear Mesh ◽  
Planetary Gear Sets ◽  
Static Transmission Error ◽  
Frequency Modulations ◽  
Mesh Phasing

Certain operating conditions such as fluctuation of the external torque to planetary gear sets can cause additional sidebands. In this paper, a mathematical model is proposed to investigate the modulation mechanisms due to a fluctuated external torque (FET), and the combined influence of such an external torque and manufacturing errors (ME) on modulation sidebands. Gear mesh interface excitations, namely gear static transmission error excitations and time-varying gear mesh stiffness, are defined in Fourier series forms. Amplitude and frequency modulations are demonstrated separately. The predicted dynamic gear mesh force spectra and radial acceleration spectra at a fixed position on ring gear are both shown to exhibit well-defined modulation sidebands. Comparing with sidebands caused by ME, more complex sidebands appear when taking both FET and ME into account. An obvious intermodulation is found around the fundamental gear mesh frequency between the FET and ME in the form of frequency modulations, however, no intermodulation in the form of amplitude modulations. Additionally, the results indicate that some of the sidebands are cancelled out in radial acceleration spectra mainly due to the effect of planet mesh phasing, especially when only amplitude modulations are present.

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

2015 ◽  
Author(s):  
Nicholas D. Leque ◽  
Ahmet Kahraman
Keyword(s):  
Three Dimensional ◽  
Planetary Gear ◽  
Load Sharing ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Proposed Model ◽  
Manufacturing Errors ◽  
Manufacturing Tolerancing ◽  
Planetary Gear Sets

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional formulation of N-planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all three types of manufacturing errors, namely constant errors such as planet pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

scholarly journals Tracking control and robustness study of shifting process

2018 ◽  
Vol 46 (2) ◽  
pp. 99-106
Author(s):  
Xin-xin Zhao ◽  
Chao Guan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Tracking Control ◽  
Pid Controller ◽  
Automatic Transmission ◽  
Good Control ◽  
Simulation Software ◽  
Control Effect ◽  
Engine Torque ◽  
Shift Quality

Heavy dump vehicles are usually working with big load changes and bad work environment, thus change the friction performance of transmission clutches, as well as great affect the shift quality seriously, which influence the vehicle performance. Many researchers developed a lot to design a useful automatic transmission control system. Using PID tracking control and Monte Carlo method, the controller based on an dynamic model was set up to analyze the shifting process of automatic transmission and its robustness in this paper．The shift process was divided into four stages, low-gear phase, torque phase, inertia phase and high-gear phase. The model presents the process from the first gear to the second gear when the torque has big change．Since the jerk and the friction work of clutch are both related to the speed of clutch which was easier to control, it was chose as the target to control the oil pressure for satisfying the requirement of shift quality．The simulation software, Maplesim and Simulink, were used to build the vehicle model and shifting controller for simulation under different working conditions, and the maximum jerk was changed from 34 m/s3 to 12 m/s3 after the optimization. In this paper the Monte Carlo has been used to quantize and evaluate the robustness of the closed-loop system for the friction coefficients and output torque of turbine variation leading by the friction feature parameters and throttle angle changed. Monte Carlo method was used to analyze the effectiveness and robustness of PID controller, which proves that it has good control effect when the throttle is ongoing minor fluctuations. When the throttle is full opening, a quadratic optimal controller based on disturbance is designed by the method of multi-objective optimization. When it changes within 20 percent, PID controller was designed under the guidance of tracking thoughts. The results also show that the controller could still obtain better effect when the friction coefficient ranged from -40 % to 40 % as well as engine torque changed from -20 % to 20 %, which indicates the robustness of controller.

Signal Flow Graphs for Spatial Gear Trains

1994 ◽  
Vol 116 (1) ◽  
pp. 326-331 ◽  
Author(s):  
R. Ma ◽  
K. C. Gupta
Keyword(s):  
Operations Research ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Gear Train ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
System Variables ◽  
Flow Graphs

Signal flow graphs (SFG) have been applied in many areas such as circuit analysis, controls, mechanical vibrations, statistics, and operations research. They have also been applied to the analysis of planetary gear trains which are planar, i.e., where all of the gear axes are parallel. In this paper, signal flow graphs are applied to spatial planetary gear trains. Some additional terminology and rules which are needed for this important application are developed in this paper and illustrated by examples. The significance of applying SFG to a gear system is that the graph describes the interrelationship among the system variables by linking causes and effects, offers the information about the topology of system connection, and the kinematic equations of motion can be written easily by inspection. In this way, it helps use to visualize and understand spatial gear train systems better.

Sign in / Sign up

Export Citation Format

Share Document