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Computer-Aided Calculation of Planetary Gear Sets
Abstract
The paper presents computer-aided calculation of planetary gear systems in automotive transmissions. We distinguish between two approaches to make the calculations: the direct problem and the inverse problem. The direct problem starts with a given nested gear set, calculated by means of the matrix method. This method, previously used only for nested gear trains consisting of simple planetary gear sets, is extended for computation of the Ravigneaux gear-sets as well. The matrix method-based program is presented. The inverse problem starts with the known kinematic parameters of a gear set. Two known methods used for defining of structure of nested planetary gear-box are briefly described: the iterative approach and the analytic parametric approach.
... It seems appropriate in the Kinematics and Dynamics of Machines course to present a simpler method of analyzing and characterizing gear trains. The method is called the Lever Analogy Diagrams which are commonly utilized in industry [1][2][3][4] . ...
... Šalamoun in 70's of last century [1]. In 2007 this method was further elaborated for calculation of reduced or Ravigneaux PGSs [2]. In 2010 the usage of matrix method for any type of mechanism was introduced [3]. ...
The article is divided into two parts. The first part is dedicated to the analysis of mechanical systems by means of the matrix method. The power of the matrix method lies in its easy implementation in computer calculations. In this article we will present the program "SunGear." This program is devoted to calculation of such Power-split systems and complete analysis of mechanical stepped planetary gearboxes. The second part of the article will describe the analysis of Power-split systems. In our study we focus on Power-split systems with mechanical CVT. The analysis will be presented by means of two examples: a)IVT (no shift elements) with the spread from reverse (ratio equals -2) up to the overdrive with a ratio of 0,6. The power is split between CVT (spread 0,25 up to 4) and mechanical gear set. The differential (planetary or bevel gear device with 2 degrees of freedom) is placed on the input or on the output of the mechanism. A set of 24 different compositions of mechanisms which fulfill the given kinematic constraints was obtained. The comparison of all found solutions is made mainly based on the overall efficiency and magnitude of circulating power. According to the analysis the guidelines for design of an efficient IVT system were developed.b)Power-split CVT, where the combination of differential, CVT and mechanical gearset is made mainly to increase the torque capacity in case of usage of mechanical CVT and for increase of efficiency in case of usage of hydrodynamic of hydrostatic CVT. As distinct from the IVT's the Power-split CVT systems can be designed without circulating power. The guidelines of design of Power-split CVT systems without circulating power will be presented.
... There are numerous other publications [3,4,5,6,7,8,9,10,11,12,13] devoted to the different aspects of modeling, analysis, design and control optimization of the power-split HEV propulsion systems shown in Figure 1. The approach described in the current paper is unique in its look at potential configurations relative to vehicle operating requirements. ...
Hybrid electric vehicle (HEV) systems offer significant improvements in vehicle fuel economy and reductions in vehicle generated greenhouse gas emissions. The widely accepted power-split HEV system configuration couples together an internal combustion engine with two electric machines (a motor and a generator) through a planetary gear set. This paper describes a methodology for analysis and optimization of alternative HEV power-split configurations defined by alternative connections between power sources and transaxle. The alternative configurations are identified by a matrix of kinematic equations for connected power sources. Based on the universal kinematic matrix, a generic method for automatically formulating dynamic models is developed. Screening and optimization of alternative configurations involves verification of a set of design requirements which reflect: vehicle continuous operation, e.g. grade test; and vehicle dynamic operation such as acceleration and drivability. Only the former are consider in this paper. The method automatically defines a design parameter space for each configuration which eventually would allow configuration evaluation and optimization, e.g. sizing of power sources or optimization of transaxle gear ratios.
... It seems appropriate in the Kinematics and Dynamics of Machines course to present a simpler method of analyzing and characterizing gear trains. The method is called the Lever Analogy Diagrams which are commonly utilized in industry [1][2][3][4] . ...
The planetary gear trains are widely used in many automotive, aerospace and marine applications. The planetary gear trains are introduced to undergraduate mechanical engineering students in the course of Kinematics and Dynamics of Machines. Traditional methods of analyzing planetary gear trains, by means of torque and speed calculations, tend to be slow and cumbersome. The complexity involved has, no doubt, kept many students from becoming familiar with the capability of planetary gearing. It is our intent in this paper to describe the lever analogy method of analysis and to present a miniature 'cookbook' of levers for various planetary arrangements.
... With the numerous options for the configuration design variations, such an iterative process only can be achieved with a systematic method with many underlying techniques, which including automated model generation and simulation with optimal design and optimal control techniques. Computer-aided method for gear design is not a new concept (Achtenova and Svoboda, 2003). In fact, many systematic ways to search among different designs have been proposed for transmission designs (Freudenstein and Yang, 1972; Kaharaman et al., 2004). ...
Hybrid electric vehicles (HEV) represent one of the most promising fuel-saving technologies in the short-term for improving fuel economy of ground vehicles. Their viability has been amply demonstrated in a few successful commercial models. Among the common configurations, the power-split (i.e., combined parallel/series) configuration offers superior design and control flexibility and achieves highest overall efficiency. Therefore, most of the full-hybrid vehicles planned for the near future from Toyota, Lexus, GM, Chrysler, and Ford are all split hybrids. In this dissertation, a model-based configuration and control optimization analysis of power-split HEV is presented.
An integrated dynamic model was first developed for power-split HEV powertrain systems. From this simulation model, a math-based universal model format is generalized. It presents different designs of power-split powertrains regardless of the various connections between gear nodes and power sources. Based on this universal format, a methodology that automatically generates dynamic models is developed. It not only enables rapid generation of powertrain models, but also allows the process of automatically exploring possible configuration designs.
We next introduce a design screening process and a combined configuration and control optimization strategy. In the design screening process, various design requirements including transmission efficiency, drivability, power source component sizing are utilized to evaluate possible configurations and select valid design candidates. In the combined configuration and control optimization strategy, a control design procedure based on deterministic dynamic programming (DDP) was employed to find the optimal operation of the vehicle system and achieve the performance benchmarks for different configuration candidates. The optimal design solution is then achieved by comparing these benchmarks. This methodology allows design engineers to study powertrain configurations more scientifically and efficiently.
Finally, with the DDP suggesting the potential performance benchmark of the selected powertrain configuration, two alternative control strategies, stochastic dynamic programming and equivalent consumption minimization strategy, are developed to approach this performance benchmark. Both of these two control designs can be implemented in real-time and show close agreement with the DDP results in the simulation.
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