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The Lever Analogy: A New Tool in Transmission Analysis
Abstract
A new tool for analyzing transmissions that use planetary gearsets is presented. With this tool, entire transmissions are usually represented by a single lever, and the calculation of most characteristics is as simple as summing moments of a level. A miniature cookbook of levers for various planetary arrangements is included which can be helpful in selecting a planetary to achieve the desired objectives of a user.
... Planetary/Epicyclic gear sets (PGSs/EGSs) have the advantages of high transmission ratios, large torque-weight ratios and compactness in comparison with ordinary gear trains, which make them widely used in fields like automotive, aerospace, marine, wind turbines, and machine tools applications [1][2][3]. Currently, a lot of methods have been proposed for the design and kinematic analysis of PGSs/EGSs, such as the component analysis synthesis method, the line graph synthesis method, the combination solution method, the rod system conversion [4], and the lever analogy method (LAM) [5], etc. The component analysis synthesis method and the combined solution method are traditional methods of analyzing PGSs/EGSs. ...
... The line graph synthesis method, the rod system conversion, and the LAM are graph-based methods. Applying the graph theory to the kinematic analysis of PGSs/EGSs, a simple and practical LAM was first proposed by Benford and Leising [5], which considers the PGS as an equivalent vertical lever based on appropriate assumption and simplification to position PGS. The vertical lever equivalent substitution reflects the characteristics so that the position relationship of PGS rotating members can be reflected faithfully. ...
... The LAM uses the vertical lever equivalent substitution to reflect the kinematic characteristics of PGSs/EGSs so that the position relationship of PGSs/EGSs rotating members can be reflected faithfully. This makes the analysis of complex PGSs/EGSs transmission mechanisms easy and general [5,6]. However, the theoretical mechanism of the traditional LAM has not been revealed and the kinematic information of planet gear can not be analyzed by the LAM. ...
The lever analogy method (LAM) is a translational system representation for the rotating components and is widely used for the kinematic analysis of PGSs/EGSs. However, it includes only the sun gear, ring gear, and carrier, and ignores the kinematic information of the planet gear. The planet gear kinematic information is vital for its bearing life prediction, and speed sequence, power flow, and efficiency analysis of dual-input PGSs/EGSs. The traditional LAM doesn't work when involving the planet gear kinematic information, because the kinematic information of planet gear is eliminated during the process of merging similar items. In this paper, an augmented lever analogy method (ALAM) is proposed to make up for the lack of traditional LAM in analyzing planet gear kinematic information, and analyze the kinematic relationship between planet gear to other components for the dual-input PGSs/EGSs. In this method, the new nodes and lever lengths representing the planet gear are added to the LAM by analyzing peripheral velocity relationships at the meshing points of PGSs/EGSs. In addition, not all the dual-input compound PGSs/EGSs (e.g. the compound PGSs/EGSs with planet gears in series, etc.) can be analyzed by the traditional LAM. The proposed method can easily establish the augmented lever models for all of them and derive the corresponding kinematic expressions. The results show that the proposed ALAM has good visibility and greater versatility, and can accurately and efficiently calculate the rotating speed of planet gears for calculating the speed sequence, power flow, and efficiency of PGSs/EGSs, which can cover all kinds of the PGSs/EGSs, and greatly reduce the technical threshold and time for their kinematic analysis.
... When focusing on planetary gear sets, an interesting approach for easily and quickly determining the kinematics of a coupled epicyclic spur-gear train can be found in [12]. Next, the well-known Lever Analogy was introduced back in 1981 by Benford and Leising [13]. This is still nowadays one of the most effective tools for analyzing the kinematics and the dynamics of planetary gear sets. ...
... A different approach for computing the kinematic relations of a planetary gear set is the Lever Analogy [13]. The considered Ravigneaux planetary gear set can be seen as the combination of two planetary gear sets: ...
... P G1 and P G2 share the same ring and the same carrier inertial elements. The procedure to follow in order to build a Lever Diagram [13] is the following: 1) replacement of each gear with a vertical lever; 2) rescaling, interconnection and/or combination of levers accordingly; 3) identification of the lever connections, according to the gears connections. The lever diagrams of the two planetary gear sets P G1 and P G2 are shown in Fig. 8.a). ...
In this paper, a systematic approach for the dynamic modeling of complex planetary gear sets is presented. The approach relies upon a set of rules for building the system matrices and vectors of the system full dynamic model for any planetary gear set. A congruent state-space transformation is applied to obtain a reduced-order rigid model of the system, which allows for faster simulations. The behavior of the tangential forces accounting for the gears interactions is proven to be obtained from the reduced-order model. Furthermore, the kinematic relations of the considered planetary gear set are automatically generated when developing the reduced-order rigid model. As an example, two systems of interest in the vehicle industry are then modeled with the proposed approach and simulated in Matlab/Simulink: a Ravigneaux planetary gear set and a double-stage planetary gear set.
... When dealing with Power-Split HEVs, see [12][13][14][15]36], an interest arises in the class of -ports physical systems, since Power-Split HEVs are a category of HEVs equipped with an -ports device, typically a planetary gear set [33,34,[37][38][39][40]. A schematic representation of a Power-Split HEV equipped with an -ports planetary gear set is shown in Fig. 1. ...
... Different approaches for modeling planetary gear sets are present in the literature for different purposes. One of the most widespread approaches is the Lever Analogy, introduced by Benford and Leising [37], which is very suitable for system analysis. As an example, this approach is used in [36] to analyze the operating modes of the considered hybrid electric vehicle. ...
In this paper, the problem of power efficiency evaluation for n-ports physical systems is investigated. The efficiency analysis that we perform highlights the necessary and sufficient conditions for the system to be passive, and outlines the guidelines for the efficiency maps computation. After addressing the problem from a formal point of view, the analysis is deepened for the case of two-ports linear and nonlinear physical systems, and for the cases of three and four-ports linear systems. The efficiency analysis and the computation of the efficiency maps are addressed as a function of the power variables characterizing all the energetic ports of the considered systems. Furthermore, the salient properties of the efficiency are highlighted and discussed. The theoretical analysis which is developed is then applied to some physical systems of interest for industries and engineers working in the electromechanical, hydraulic and automotive fields: a DC electric motor driving an hydraulic pump for the two-ports systems class, a single-stage planetary gear set for the three-ports systems class, and a Ravigneaux planetary gear set for the four-ports systems class.
... In the first modified version of the analytical method used in this paper, the kinematics and statics are analysed using the matrix method, which makes the form of the equations which are used more compact and the computer calculations easier to perform [116,117]. In an equally popular variant, angular velocities and torques are determined using the lever analogy method and nomograms [118][119][120][121][122][123][124][125][126][127][128][129][130]. Also very interesting is the combined method of determining the power flow and efficiency epicyclic transmission presented in references [131][132][133][134][135][136][137][138][139][140], where the Lagrange multipliers and kinematic constraints are used to determine the power flow and to verify the normal power flow balance. ...
... In practice, the Willis formula [12][13][14][15][16][17]163,178] is often used for this purpose, although graph methods (linear, contour, signal flow, bond graphs, matroids, and hypergraphs) are gaining more and more recognition, thanks to their advantages [143,162,[164][165][166][167][168][169][171][172][173][174][175][176][177][179][180][181][182][183][184][185][186]189,192,194]. The nomograph method and, especially, the lever analogy are also promising as universal methods for kinematics, statics, and power flow analysis of the most complex PSHEV planetary transmission [88,[118][119][120][121]126,[128][129][130]160,161,164,188]. The effectiveness of the above-mentioned methods can be additionally increased by the matrix notation of the obtained equations [117,187,196]. ...
So far it is believed that, for every series-parallel planetary gear system (PGS), as a coupled gear, a very harmful phenomenon of power circulation must occur in at least one of its closed circuits. In this paper (Part I) and in the next two (Part II and Part III), it will be shown that it is possible to construct a three-row series-parallel PGS in which this phenomenon can be avoided. For this purpose, in Part I, a detailed analysis of the kinematics and statics of a planetary gear with power circulation inside a closed loop was carried out. The determination of the angular velocities of gears and carriers is carried out using Willis formulas and the graphical-analytical method (for verification), while the torques are determined using free body diagrams. The magnitudes of angular velocities and torques were used to determine the directions of power flows with improved energy balance equations in the reference frame related to the stationary gear body and, additionally, only to verify the energy balance equation in the mobile reference frame related to the carrier hi (i=2,5,8). The improvement of the methods was based on the use of the original concept of distinguishing active torque from reactive torque, as well as active power from reactive power, which made it very easy to determine the directions of the power flow. The determined paths of the power flow, including the power circulation in the analysed PGS, are presented graphically.
... Qin et al. [20], [21] extended the approach to the powertrain design for hybrid tracked vehicles. Moreover, the lever analogy method [22], developed by Benford and Leising for the first time, is another critical tool for simplifying transmission analysis. Barhoumi et al. [23] proposed a systematic conversion method between virtual design variables and physical design space, which eliminates the redundancy in the physical design space during the modeling and optimization process. ...
... Therefore, the MG2 power loss Pmg2,loss can be calculated by [14] 2, 2 2, , (21) where Tmg2,min,base and Tmg2,max,base are the baseline minimum and maximum torque of the MG2. The MG2 mass is scaled by 2 2, 2 mg mg base mg m m s (22) where mmg2,base is the baseline mass of MG2, listed in Table III. ...
Configuration design, component sizing, and energy management are intertwined. However, the full potential of hybrid powertrains has not yet been thoroughly investigated due to the multi-dimensional design space. Therefore, in this paper, a joint optimization method combining particle swarm optimization (PSO) and convex programming (CP) is proposed for the first time. In the outer loop, the PSO algorithm searches for the optimal design for the powertrain configuration. In contrast, the component size and power management are simultaneously optimized by the CP algorithm in the inner loop. A combined driving cycle is designed to integrate both acceleration and energy-saving performance, where an extreme acceleration driving process is intended to act as the acceleration constraint. The results show that, compared to Prius 1
st
, the acceleration and total cost-saving of the optimal 1-PG (planetary gear) powertrain are improved by 13.09% and 11.08%, respectively. In particular, the acceleration and total cost-saving of the optimal 2-PG powertrain (MG2-RSG) are upgraded by 34.23% and 15.18%, respectively. Finally, the effectiveness and efficiency of the proposed method are verified by comparing it with dynamic programming (DP) and multi-objective evolutionary algorithm based on the decomposition (MOEA/D) method.
... A PG consists of the sun gear, the ring gear and the carrier gear with several pinions. Lever analogy [23] is used to demonstrate the dynamics of 1-PG powertrain, as shown in Figure 1. The angular velocities of sun gear, ring gear and carrier gear must satisfy the constraint equation given in Equation (1) [23]. ...
... Lever analogy [23] is used to demonstrate the dynamics of 1-PG powertrain, as shown in Figure 1. The angular velocities of sun gear, ring gear and carrier gear must satisfy the constraint equation given in Equation (1) [23]. In this work, only 1-PG and 2-PG topologies are considered. ...
Modern hybrid electric vehicles (HEVs) like the fourth generation of Toyota Prius incorporate multiple planetary gears (PG) to interconnect various power components. Previous studies reported that increasing the number of planetary gears from one to two reduces energy consumption. However, these studies did not compare one PG and two PGs topologies at their optimal operation. Moreover, the size of the powertrain components are not the same and hence the source of reduction in energy consumption is not clear. This paper investigates the effect of the number of planetary gears on energy consumption under the optimal operation of the powertrain components. The powertrains with one and two PGs are considered and an optimal simultaneous torque distribution and mode selection strategy is proposed. The proposed energy management strategy (EMS) optimally distributes torque demands amongst the power components whilst also controlling clutches (i.e., mode selection). Results show that increasing from one to two PGs reduces energy consumption by 4%.
... The modeling of epicyclic gear trains has been addressed in the literature using different approaches [4] - [6]. One of the most well-known and widespread modeling solutions is the lever analogy [7], from which the static and dynamic relations of epicyclic gear trains can be obtained. The modeling can also be performed using suitable graphical modeling techniques [8]. ...
... The left subplot of Fig. 5 shows the angular velocities ω i , for i ∈ {c, p, s, r}, whereas the right subplot of Fig. 5 shows the time behavior of the tangential forces F ij , for ij ∈ {sp, pr}. For both subplots, the colored characteristics refer to the simulation performed on the full elastic model (1), whereas the red dashed characteristics refer to the simulation performed on the reduced model (7). As for the latter, the red dashed characteristics of tangential forces F ij have been computed using Eq. ...
Model-based simulations are important in the automotive industry to study and evaluate the vehicle behavior. In this paper, the Power-Oriented Graphs (POG) technique is used as a tool for modeling epicyclic gear trains. A full elastic dynamic model of the system is first derived, which can then be reduced by neglecting the elastic contact points between the gears while still being able to recover the time behaviors of the spring tangential forces. The proposed modeling method is then applied to two epicyclic gear trains, and the design of a suitable control allowing to minimize the system dissipations is presented and applied to the second case study.
... Indicated for simple and compound planetary gearsets with exemplary gear tooth counts. Depictions and approach adapted from [81][82][83]. Figure A1. Summary of simple (left) and compound (right) planetary gearset lever diagrams and all permutations of input, output, and constraint for gear ratio, exemplary tooth counts provided. ...
A review of past, current, and emerging electric vehicle (EV) propulsion system technologies and their integration is the focus of this paper, namely, the matching of electric motor (EM) and transmission (TRM) to meet basic requirements and performance targets. The fundaments of EM and TRM matching from a tractive effort and a vehicle dynamics perspective are provided as an introductory context to available or near-production propulsion system products available from OEM and Tier 1 suppliers. Engineering data and details regarding EM and TRM combinations are detailed with a specific focus on volumetric and mass density. Evolutionary trends in EM and TRM technologies have been highlighted and summarized through current and emerging products. The paper includes an overview of the initial EV propulsion system’s sizing and selection for a set of simple requirements that are provided through an examination of three light-duty EV applications. An enterprise approach to developing electrified propulsion modules with suitable applicability to a range of light-duty EVs from compact cars to full-size trucks concludes the paper.
... A lever diagram is commonly used to describe the relationship between the stable-state rotational speed and torque between planetary gear components (Benford and Leising 1981). As shown on the right side of Fig. 1, considering the planetary gear as a lever, the sun gear, carrier, and ring gear are arranged as nodes on the lever in order, in which the rotational speed of each component is the displacement of the lever node, and the torque is the force of the lever, both following the lever balance. ...
... In the literature, different formulations are found for describing the behavior of a planetary gearset depending on the level of accuracy to be achieved. The lever analogy diagram [23] has been widely used due to its simplicity and the equations to correlate the different speeds and torques of carrier, sun and ring gears have been formulated by Liao et al. [24]. In general, after constructing the free body diagram for a single planetary gearset, an assessment of the forces acting on each gear can be made, leading to the formulation of relationships as depicted in the subsequent equations: ...
Reducing computational time has become a critical issue in recent years, particularly in the transportation field, where the complexity of scenarios demands lightweight controllers to run large simulations and gather results to study different behaviors. This study proposes two novel formulations of the Optimal Control Problem (OCP) for the Energy Management System of a Plug-in Hybrid Electric Vehicle (PHEV) and compares their performance with a benchmark found in the literature. Dynamic Programming was chosen as the optimization algorithm to solve the OCP in a Matlab environment, using the DynaProg toolbox. The objective is to address the optimality of the fuel economy solution and computational time. In order to improve the computational efficiency of the algorithm, an existing formulation from the literature was modified, which originally utilized three control inputs. The approach involves leveraging the unique equations that describe the Input-Split Hybrid powertrain, resulting in a reduction of control inputs firstly to two and finally to one in the proposed solutions. The aforementioned formulations are referred to as 2-Controls and a 1-Control. Virtual tests were conducted to evaluate the performance of the two formulations. The simulations were carried out in various scenarios, including urban and highway driving, to ensure the versatility of the controllers. The results demonstrate that both proposed formulations achieve a reduction in computational time compared to the benchmark. The 2-Controls formulation achieved a reduction in computational time of approximately 40 times, while the 1-Control formulation achieved a remarkable reduction of approximately 850 times. These reductions in computational time were achieved while obtaining a maximum difference in fuel economy of approximately 1.5% for the 1-Control formulation with respect to the benchmark solution. Overall, this study provides valuable insights into the development of efficient and optimal controllers for PHEVs, which can be applied to various transportation scenarios. The proposed formulations reduce computational time without sacrificing the optimality of the fuel economy solution, making them a promising approach for future research in this area.
... In the first modified version of the analytical method, the kinematics and statics are analyzed using the matrix method, which makes the form of equations more compact and easier to perform computer calculations [129,130]. In an equally popular variant, angular velocities and torques are determined using the lever analogy method and nomograms [131][132][133][134][135][136][137][138][139]. The analytical geometry method [140] consists in plotting circuit relationship graph (circuit lines on the angular speed plane) and circuit relationship graph with kinetic energy increment. ...
Comparisons of power flows and efficiencies in two structurally quite similar cylindrical series-parallel planetary gear systems (PGSs) were performed in three separate parts of this paper. Each of these single degree of freedom (DoF) systems consists of three different 2KH subsystems connected in series-parallel. The main goal was to prove that apart from complex, structurally and dynamically coupled PGSs, there are also complex and only structurally coupled PGSs, in which the phenomenon of power flow circulation inside closed loops does not occur. Such a half-coupled type of PGS is herein called pseudo-coupled. Therefore, Part I discusses in detail the geometry, kinematics and statics of coupled PGSs in order to determine power flow paths. A comparison of the directions of power flow in both types of PGSs can be made in Part II after determining the power flow paths in the second planetary gear in a similar way. The directions of power flow in both types of PGSs were determined in a relatively simple way, thanks to the distinction between active and passive torques and thus active and passive shafts of individual subsystems. The efficiency comparison made in Part III will show whether power circulation has an influence on the efficiency value, at least in these two types of PGSs.
... As an example, an approach for determining the kinematics of a coupled epicyclic spur-gear train is proposed in Freudenstein and Yang (1972). Later on, the Lever Analogy (Benford & Leising, 1981) was introduced, which is still one of the most employed tools for the kinematic and dynamic analysis of planetary gear sets. Other approaches can be found, adopting different degrees of simplification, including the use of basic physics laws assuming rigid connections employed in Zhang, Shen, and Kako (2020) for the modeling of the planetary gear set, for instance. ...
This paper addresses a methodology for the systematic modeling of complex gear systems. The methodology is based on the use of a unified general model, working for all complex gear systems: time-variant as well as time-invariant, having parallel or oblique rotation axes. The model equations are automatically written following the outlined procedure and applying the presented algorithms, making this approach less prone to mistakes with respect to other approaches. Next, a reduced model assuming rigid gear connections and introducing no loss of information is proposed, which directly gives the kinematic relations between the gears angular speeds and input torques. In order to show some case studies, the proposed methodology is applied to three systems of interest for vehicle dynamics and powertrain modeling. The considered case studies are a differential structure having a bevel gearing system with non-perpendicular gear shafts, a vehicle differential and a full toroidal variator, which is suitable for applications such as KERS (Kinetic Energy Recovery System) and IVT (Infinitely Variable Transmission). Furthermore, the control of a full toroidal variator acting as a KERS with reference to an automotive case study and the comparison of the proposed modeling methodology with two other approaches are addressed.
... The combination of input and output powersplit modes using a single PG and synchronizer, which reduces the loss of power flow in energy conversion, has been realized [6]. In the literature [7][8][9], the distribution of mechanical points of compound power-split PGs was optimized by utilizing the lever [10] and matrix methods to realize the combination of input power-split and compound powersplit modes, which widened the efficient operation range of the transmission system. However, the above methods lack systematic theoretical guidance and are not easily applicable to other configurations. ...
Existing design methods for hybrid power system configurations obtain new solutions based on experience, structure improvement or optimization, exhaustive searching, and the screening of schemes at the expense of less innovation and less efficiency. Furthermore, these methods lack mechanisms involving automotive theory to guide powertrain configuration design. In this study, a design method of configuration with a single motor based on basic schemes of speed and torque decoupling was proposed from the perspective of the hybrid electric vehicle fuel-saving mechanism. First, the coupling characteristics of speed and torque in the basic scheme were analyzed from four perspectives. Thereafter, new configurations that meet operation requirements were derived via configuration reconstruction, which combined the better basic schemes with brakes, clutches, and transmissions. A multidimensional evaluation and screening method based on dynamic performance, economic performance, and adaptability was built. A comparison of S-4 with Toyota Hybrid System, which was performed to demonstrate the feasibility of the design method, revealed that both configurations perform similarly in terms of economic performance, but the dynamic performance of the S-4 is greater by approximately 50%. The times required to attain 100 km/h from 0 km/h for THS and S-4 are 13.5 s and 6.69 s, respectively.
... Lai [6] proposed a flexible-rigid coupling dynamic (FRCD) model by coupling the condensed substructure of finite element (FE) flexible bodies with rigid dynamic model and investigated the effect of sun gear positions on the dynamic response of the long planet and the mechanism for the vibration of the floating ring gear. Benford [7], Kim [8], Kahraman [9], Lang [10] and Tian [11] carried out statics and kinematics analysis on gear components of planetary automatic transmission. For statics analysis of compound planetary gear sets, Kahraman [9] proposed a generalized formula for speed and force analysis of gear parts of planetary automatic transmission, which has certain applicability to compound planetary gear sets. ...
The dynamics analysis of a planetary gear set transmissions requires the creation of completely different models for different gears, which is very tedious. In this paper, a generalized dynamics modeling process is proposed for a three planetary gear set transmissions, and a generalized dynamic model for multiple gears is established by using the lumped mass method. The analysis of meshing force characteristics is carried out for the second gear position, and the meshing frequency coupling phenomenon between the meshing forces of the three planetary gear sets is investigated. The results show that, for the current gear set of meshing force, the meshing frequency components of other gear sets only appear in a part of the speed, and with the increase in speed, certain low-frequency components of other sets that exist at low speed will decrease or even disappear, and the coupling relationship between the meshing forces of different planetary gear sets is not symmetrical.
... Figure 2 illustrates the considered HEV powertrain layout which embeds an ICE and two electric motors (EMs) as vehicle propellers. The related driveline features two planetary gear (PG) sets, i.e., mechanical devices that are constituted by a ring gear, a carrier, and a sun gear as illustrated in Figure 2 using the lever analogy approach [49]. They allow the HEV powertrain to operate as an electrically variable transmission (eVT). ...
This article presents a method to estimate the State of Charge (SOC) in Lithium-ion batteries of Hybrid Electric Vehicles (HEVs) with Artificial Neural Networks (ANNs). The inputs of the SOC estimation algorithm are the measured values of current, voltage, and temperature. In the article, two different battery packs are considered for a power-split full HEV. The training and validation datasets needed for developing the ANNs are generated exploiting a numerical model of two different configurations of an HEV performing real-world driving missions or the Worldwide Harmonized Light Vehicle Test Procedure (WLTP) cycle, while the testing dataset is collected experimentally on battery cells. Specifically, the capacity values for the considered battery pack sizes are 1.82 kWh and 1.06 kWh. The proposed method uses a Nonlinear AutoRegressive with eXogenous input (NARX) recurrent ANN, which has been observed to have reasonable computational cost in prior research. The performance of the investigated technique is demonstrated by estimating the SOC with a low estimation error for both the considered battery sizes. Coulomb counting is used to compute the reference value of the SOC during the real charge/discharge cycles. An analysis of the robustness of the proposed estimation method to offset errors on the measured input current is also performed.
... sun, carrier, ring) is blocked, similarly to the study performed in [42]. It is possible to employ for this objective the lever analogy for planetary gear sets, which was introduced by Benford and Leising [43] and further exploited by Liao [44,45]: a gearset may be schematically replaced by a single vertical lever; the input, output, reaction torques are represented by horizontal forces that act on the lever and the angular velocities of the gears are represented by the lever motion relative to the reaction point. A rightward movement corresponds to clockwise rotation. ...
The electrification of propulsion systems in light passenger vehicles is essential to reach the objectives set by the different organizations that protect the environment. However, due to various aspects such as politician decisions, bad press, high powertrain production costs and a moderate reduction in energy consumption, purely electric vehicles are being a priority for several car manufacturers as well as for governments instead of hybrid vehicles. This article shows how hybrid electrification, using a low temperature combustion engine, is capable of reducing the energy consumption while drastically minimizing the particle matter (mainly soot) and NOx emissions, in a power split propulsion system. This is possible by means of a precise control of the operating conditions of the engine. To operate in the hybrid powertrain efficiently and with low emissions, several energy managements controller strategies are studied. In this work, adaptive Equivalent Minimization Control Strategy (ECMS) and Rule-Based Control (RBC) are used as online controller, and the dynamic programming optimal control is used to size the powertrain. In this sense, the electric machine maximum power, battery energy content, power split device gear ratio as well as the control parameter are studied. Both emissions and fuel consumption are included in the optimization function. The results show that it is possible to reduce the fuel consumption by 17.5% with an energy minimization-oriented strategy. In addition, ECMS is more effective to control both emissions and fuel economy. If a double target is applied, the fuel consumption is reduced to 5% while achieving Euro 6 emissions levels without the need for NOx and particulate matter aftertreatment systems. This strongly reduces the total cost of the propulsion system compared to a conventional vehicle, thus compensating the cost increase due to the hybridization without considering the fuel saving costs.
... The planetary gear acts as a reduction gear in the EV#2 and parallel modes. The speed relationships for the EV#1, EV#2, and parallel modes are shown in Figure 2. In the power split mode, the speed and torque equations can be derived via lever analysis as follows [21]: ...
This paper presents an advanced rule-based mode control strategy (ARBC) for a plug-in hybrid electric vehicle (PHEV) considering the driving cycle characteristics and present battery state of charge (SOC). Using dynamic programming (DP) results, the behavior of the optimal operating mode was investigated for city (UDDS×2, JC08 ×2) and highway (HWFET ×2, NEDC ×2) driving cycles. It was found that the operating mode selection varies according to the driving cycle characteristics and battery SOC. To consider these characteristics, a predictive mode control map was developed using the machine learning algorithm, and ARBC was proposed, which can be implemented in real-time environments. The performance of ARBC was evaluated by comparing it with rule-based mode control (RBC), which is a CD-CS mode control strategy. It was found that the equivalent fuel economy of ARBC was improved by 1.9–3.3% by selecting the proper operating mode from the viewpoint of system efficiency for the whole driving cycle, regardless of the battery SOC.
... Ignored were the stiffness-damping elastic effect on the MG1 shaft, MG2 shaft, engine output shaft, drive shaft, as well as the dynamic meshing force and efficiency loss between gears. Based on the lever method [35], the torques of MG1 and MG2 during the engine startup can be expressed as follows: ...
For a power-split plug-in hybrid electric vehicle (PS-PHEV), the control system cannot effectively reduce jerks under some engine-starting conditions due to the pulsating torque of the engine, elastic characteristics of the transmission, battery power limitations, and the limitation of the maximum torque of the motor. To solve this problem, a dynamic torque-coordinated control method considering engine starting conditions (DTCC-ESC) is proposed in this paper. The proposed DTCC-ESC mainly includes three parts: the engine segment active control before and after engine ignition to minimize the impact of the engine ripple torque on the shocks of the powertrain system; the feedforward control of the engine starting conditions and the feedback control of the engine’s optimal target speed; and the active damping feedback compensation control for system resonance to reduce system vibrations. The results show that the proposed DTCC-ESC can effectively improve driving comfort under different engine starting conditions.
... The analogy between the geometric properties of a lever and the speed and torque of different gears of a PG was proposed as an effective tool for powertrain analysis [56]. The single PG and lever model are shown in Fig. 7. Ring gear, carrier, and sun gear are represented by three nodes (R, C, S) on a lever. ...
Electrified vehicles are considered a promising technology for energy savings and emission reductions. Both powertrain design (configuration design and component sizing) and energy management strategies (EMSs) for electrified vehicles have been studied extensively. However, powertrain design and energy management need to be examined holistically and optimized simultaneously, from a mechatronic viewpoint, for maximizing the potential of electrified powertrains. This paper provides a comprehensive, critical review of the current state and prospects of electrified powertrain design and energy management. The research status in both powertrain design and energy management development is reviewed and discussed. First, the modeling techniques for rapid configuration design are thoroughly reviewed and summarized. Then, the optimization methods for component sizing are elucidated. Next, the classical EMSs are categorized, and several near-optimal strategies used for powertrain design are elaborated. Finally, the current challenges and future trends of electrified powertrain design and control are discussed, which provides a useful reference to researchers in this area.
... In EV operation, as shown in Figure 2 [47]. The governing torque and speed equations, derived using the lever analogy of planetary gear sets [52], of the drive unit in EV mode are provided in . Low extended range (LER) is the first of three hybrid modes produced by the drive unit. ...
The continued push for the reduction of energy consumption across the automotive vehicle fleet has led to widespread adoption of hybrid and plug-in hybrid electric vehicles (PHEV) by auto manufacturers. In addition, connected and automated vehicle (CAV) technologies have seen rapid development in recent years and bring with them the potential to significantly impact vehicle energy consumption. This dissertation studies predictive control methods for PHEV powertrains that are enabled by CAV technologies with the goal of reducing vehicle energy consumption. First, a real-time predictive powertrain controller for PHEV energy management is developed. This controller utilizes predictions of future vehicle velocity and power demand in order to optimize powersplit decisions of the vehicle. This predictive powertrain controller utilizes nonlinear model predictive control (NMPC) to perform this optimization while being cognizant of future vehicle behavior. Second, the developed NMPC powertrain controller is thoroughly evaluated both in simulation and real-time testing. The controller is assessed over a large number of standardized and real-world drive cycles in simulation in order to properly quantify the energy savings benefits of the controller. In addition, the NMPC powertrain controller is deployed onto a real-time rapid prototyping embedded controller installed in a test vehicle. Using this real-time testing setup, the developed NMPC powertrain controller is evaluated using on-road testing for both energy savings performance and real-time performance. Third, a real-time integrated predictive powertrain controller (IPPC) for a multi-mode PHEV is presented. Utilizing predictions of future vehicle behavior, an optimal mode path plan is computed in order to determine a mode command best suited to the future conditions. In addition, this optimal mode path planning controller is integrated with the NMPC powertrain controller to create a real-time integrated predictive powertrain controller that is capable of full supervisory control for a multi-mode PHEV. Fourth, the IPPC is evaluated in simulation testing across a range of standard and real-world drive cycles in order to quantify the energy savings of the controller. This analysis is comprised of the combined benefit of the NMPC powertrain controller and the optimal mode path planning controller. The IPPC is deployed onto a rapid prototyping embedded controller for real-time evaluation. Using the real-time implementation of the IPPC, on-road testing was performed to assess both energy benefits and real-time performance of the IPPC. Finally, as the controllers developed in this research were evaluated for a single vehicle platform, the applicability of these controllers to other platforms is discussed. Multiple cases are discussed on how both the NMPC powertrain controller and the optimal mode path planning controller can be applied to other vehicle platforms in order to broaden the scope of this research.
... One of the most common and simple methodologies in the first type is the lever analogy [11], which was achieved by establishing the analogy between geometric properties of a lever and speed/ torque relationships between different components on a PG. Some modifications were achieved in Refs. ...
Increasingly strict emission and fuel economy standards stimulates the researches on hybrid electric vehicle techniques in automobile industry and one of the most important techniques is the design of powertrain configurations. In this paper, a theoretical design methodology for hybrid electric vehicle powertrain configurations is proposed to find the configurations with excellent performance in a large pool of configurations. There are two main parts in a powertrain configuration, power/coupling devices (engine, electric machine, wheel and planetary gear set) and mechanical connections between these devices. Different connections will lead to the configurations having different performance. This paper divides all connections in configurations into three categories and a novel matrix representation method is developed to express these kinds of connections so as to reflect system dynamics and physical structure of configurations. With the support of the matrix representation method, configuration selections from large pools can automatically be completed by computer and manually calculation and comparison can be avoided, which saves much energy and time. Finally, the proposed method is vigorously verified by simulations.
... Subscripts of the torque follow the same notations as in the case of the radius. For easy understanding of these kinematics of a planetary gear-set, lever analogy is commonly used as shown in Figure 2 [30]. The speed relation of a PGS can be expressed as the incline of a lever. ...
Vehicle transmission which has discrete gear-stages inevitably produces torque drop during shifting gears. This torque drop should be minimized because it may lead to uncomfortable driving feeling and degradation of acceleration performance. In accordance with the spread of electric-powered vehicle technology, this study proposes novel transmission architecture to eliminate torque drop during shifting gears by using one electric motor and verifies its operating concept through experiments with a test-bench. The proposed transmission, called CGST (clutchless geared smart transmission) can synchronize the gear-shaft to be engaged for the next gear-stage with the output shaft by using a planetary gear-set and an electric motor. The CGST has a dual input gear-box with even and odd gear-stages on different input shafts, and the planetary gear-set and the electric motor control the speeds of each input shafts to smoothly engage the next gear-stage. This idea was verified by the simplified test-rig in this study. Three distinct scenarios for gear-shift including starting from engine idling, odd to even gear-shift, and even to odd gear-shift were conducted in the experiment. The shifting performance of the CGST was evaluated by comparing it with the results of the manual transmission (MT). As a result, the CGST shows only 24% of torque drop of the MT, and torque oscillation followed after gear-shifting is reduced by 26%. Although the developed test bench was of limited size, the possibility and expected performance of the CGST have been confirmed as the solution for seamless transmission.
div>Torsional vibration generated during operation of commercial vehicles can negatively affect the life of driveline components, including the transmission, driveshafts, and rear axle. Undesirable vibrations typically stem from off-specification parts, or excitation at one or more system resonant frequencies. The solution for the former involves getting the system components within specification. As for the latter, the solution involves avoiding excitation at resonance, or modifying the parameters to move the system’s resonant frequencies outside the range of operation through component changes that modify one, or more, component inertia, stiffness, or damping characteristics. One goal of the effort described in this article is to propose, and experimentally demonstrate, a physics-based gear-shifting algorithm that prevents excitation of the system’s resonant frequency if it lies in the vehicle’s range of operation. To guide that effort, analysis was conducted with a numerical simulation model incorporating nonlinear driveline dynamics resulting from engine operation (including misfire and cylinder deactivation), excitation from multiple universal joints, the transmission, and a vehicle speed feedback controller, a contribution the authors have not seen in the pre-existing literature. The experimentally validated simulation results demonstrate that the torsional oscillating mode corresponding to the torque converter or turbine exhibits sensitivity to clutch activation, and variations in system parameters. Consequently, variation in system parameters alters the natural frequency of the system, potentially aligning it with the vehicle’s operational frequency range in specific gear ranges. Experimental on-road tests, described here, demonstrate that for the truck-under-test one of the natural frequencies of the system is within the range of operation for gears 4, 5, and 6 for certain vehicle speeds. Resonance in these gears was successfully prevented, and experimentally demonstrated, by using the proposed algorithm without sacrificing the performance of the vehicle.</div
div class="section abstract"> In the face of growing concerns about environmental sustainability and urban congestion, the integration of eco-driving strategies has emerged as a pivotal solution in the field of the urban transportation sector. This study explores the potential benefits of a CAV functioning as a virtual eco-driving controller in an urban traffic scenario with a group of following human-driven vehicles. A computationally inexpensive and realistic powertrain model and energy management system of the Chrysler Pacifica PHEV are developed with the field experiment data and integrated into a forward-looking vehicle simulator to implement and validate an eco-driving speed planning and energy management strategy assuming longitudinal automation. The eco-driving algorithm determines the optimal vehicle speed profile and energy management strategy. Then, a microscopic traffic model that represents the driving behaviors of the human-driven vehicle queue is introduced to investigate the overall energetic impact of the eco-driving strategy on human-driven vehicles in urban routes. Two different scenarios are considered, one involving human-driven vehicles following a lead human-driven vehicle, and the other with the human-driven vehicles led by the CAV. The results reveal that CAV not only achieves high energy savings for the CAV itself but also improves the fuel economy of the following human-driven vehicles without featuring any cooperative driving. The findings highlight that even with a low penetration rate, CAVs could reduce the overall energy usage of a cohort of uncoordinated vehicles in urban traffic scenarios by as much as 7% - 27% when used as virtual eco-driving controllers.
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Compared with single-mode power-split hybrid electric transmission, multi-mode power-split hybrid electric transmission can achieve high power, wide speed range, and high efficiency, which is the most suitable hybrid electric transmission scheme for heavy vehicles. Mode switching quality is the key factor restricting the application of multi-mode power-split hybrid electric transmission. Therefore, a design method for multi-mode power-split hybrid electric transmission which can ensure mode switching without speed difference is proposed. Firstly, based on the lever analogy method and analysis on characteristics of mechanical points, three conditions of mode continuity and methods to satisfy these conditions on function level are obtained. Then the design method can be divided into three steps: (1) design the function model of each mode scheme to achieve the conditions of mode continuity; (2) design the configuration of each mode scheme according to the function model and comprehensive consideration of mode continuity, structural simplification and operation logic, and combine the configuration of each mode into an integral scheme by arranging clutches/brakes; (3) inversely convert the lever model in the configuration scheme to planetary gear set to obtain specific transmission scheme. Finally, to demonstrate the feasibility of the design method, one of the design results is taken as an example to carry out mechanical structure design, kinematics and power flow analysis.
Power-split hybrid transmissions are the core components of power-split hybrid electric vehicles (HEVs), and the quest for a more energy-efficient and higher-performing power-split hybrid transmission has long been the focus of study. In contrast to previously published methodologies, this paper proposes a novel approach for directly synthesizing power-split hybrid transmissions that makes use of the results of previously synthesized planetary gear trains (PGTs) rather than necessitating a resynthesis of their PGTs. A new topological graph that can construct a bridge between the PGTs and power-split hybrid transmission has been developed, reducing the computational complexity in the synthesis process. The new topological graph is obtained by adding topological characteristics of the power-split hybrid transmission to the PGT graph. A standard structure matrix is proposed to further screen out all the isomorphic configurations. The present method can generate various types of multi-PGT hybrid transmissions while avoiding mechanical structural interference. The design process of configurations for power-split hybrid transmission with three-column PGTs (3-PGT) is used as an example to prove the rationality of the method.
Dual-motor powertrain (DMP) has been proven to help Electric vehicles (EVs) achieve better dynamic performance and energy economy. This study proposes a novel dual-motor powertrain, which can realize four alternative working modes to meet complicated and volatile driving cycles. To capture the transient characteristics of this powertrain, its detailed dynamic model is established. To achieve uninterrupted-torque mode shift, simplified model-based shifting strategies are developed. Specifically, the proposed mode-shifting strategies are derived by coordinating the relationship between torques and speeds applied by two motors and the band brake. To verify the validity and effect of the proposed mode-shifting strategies, Hardware-in-the-Loop (HIL) experiments are undertaken. According to the experiment results, it can be clearly seen that the proposed strategies can realize seamless mode shifting. This study provides a systematic solution for mode shifting transient control of this proposed DMP and its HIL experiment.
Tractor-implement combination generally involve the forward and reverse motion to perform the required task, which causes the tractor to frequently change its direction of movement. Automating the shuttle shifting process can reduce the labor intensity of the driver and improve the field efficiency and comfort. In this study, a power shuttle motion inverter is designed with a planetary gear train and clutch/brake. The dynamics model of the tractor power-train and a simulation model are established. Two types of the shuttle shifting process are designed and analyzed by the lever analogy method. To improve the shifting quality, control strategies for the shuttle shifting processes are formulated by analyzing the changing characteristics of the force exerted on the tractor-implement combination during the shifting processes. The analysis results show that quick and comfortable shuttle shifts are achieved during the process of moving from the forward to reverse directions and vice versa.
div class="section abstract"> The proliferation and increased complexity of electrified powertrains presents a challenge to the associated controls development. This paper outlines the strategy of common supervisory and domain torque management for such powertrains. The strategy covers the multitude of powertrain architectures that exist in the market today while maintaining the fundamental pillars of physics-based torque controls, state-of-the-art optimization methodologies, and common-core hybrid system constraints.
The electrified powertrain torque controls that Stellantis LLC. uses include key constituents such as optimization of powertrain state that relate to optimum engine speed and transmission gear, optimization of engine and motor torques, engine start-stop management, and hybrid shift execution which manages powertrain state transitions by interacting with various external transmission systems. The common backbone of these constituents are the dynamic/kinematic equations of the powertrain. Centralizing these dynamic and kinematic equations within the control structure allows for the downstream control constituents mentioned above to remain common for all electrified powertrain architectures. An added benefit of this strategy is the streamlining of calibration methodology and effort.
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Hybrid power configuration has two kinds of power sources, how to design the configuration to couple the energy of the two power sources is an important part of the development of hybrid power technology. In the systematic design scheme of hybrid power, most scholars focus on the design of planetary gear hybrid power configuration, but lack of systematic design scheme of fixed-shaft hybrid power configuration. In this paper, based on the equivalent tree graph method, the fixed-shaft hybrid configuration is transformed into the corresponding tree graph representation, and all possible configurations are generated by the combination of the trunk, branches and leaves. Add the corresponding design constraints, use Matlab to realize automatic generation and screening, and finally obtain the required configuration after specification. The configuration is verified in the Simulink & Amesim co-simulation environment. The results show that the proposed single-motor fixed-shaft hybrid power configuration has certain advantages in economy compared with the traditional P2 and P3 configurations, and its dynamic performance is the same as that of P2 configurations and superior to P3 configurations.
Synthesis of multi-mode electric-mechanical variable transmission (EVT) mainly involves two contents: the topology of planetary gear mechanism (PGM) and the determination of their characteristic parameters. This article deals with the computationally intensive problems caused by numerous potential schemes and proposes an automatic and systematic design process for multi-mode EVTs based on 3-row PGM. First, all the non-isomorphic 4-degree-of-freedom (4-DOF) topologies are enumerated by combining the modified digraph model with the determinants of their adjacency matrices. Second, the rules with guiding significance for configuring shift elements and motor/generators (M/Gs) are summarized to eliminate all infeasible configurations. And all the mechanical points (MPs) that come from the kinematic equations play an important role in the selection of new schemes. Third, the method of Monte Carlo simulation handles the problem of solving many different forms of multivariate nonlinear functions to sort the rational mode sequences. Finally, the characteristic parameters of each planetary gear set are optimized by NSGA-II. The feasibility of the method is verified by synthesizing six novelty 3-mode EVTs and it is also applicable to similar problems.
Power-split hybrid electric vehicle (PSHEV) has outstanding energy-saving potential, which is one of the effective solutions to alleviate energy shortage and environmental pollution. The powertrain configuration of PSHEV is the basis of energy management, which determines the operating mode, control algorithm selection, optimization potential, and directly affects the vehicle’s comprehensive performance. Analyzing and summarizing the existing research results will be beneficial to promote the further development of the design theory of powertrain. In this article, the generation, screening, and optimization techniques of PSHEV powertrain configuration are systematically compared and analyzed. First, the classification and modeling of PSHEV are analyzed and summarized. Second, the generation method of the PSHEV powertrain is analyzed in detail. Thus, three types of formation methods for the design space of PSHEV powertrain configuration are summarized. Then, the feasible solution is explored via configurations screening, which further reduces the difficulty of industrial application. Meanwhile, the feasible design space is further optimized to obtain the competitive solution, so as to meet the design requirements. Finally, the technology challenges of PSHEV powertrain configuration research are discussed, which pointed out the application direction of configuration design method in electric vehicles and fuel cell vehicles.
Integrated design of topology and characteristic parameters for Planetary Gear Trains (PGTs) is critical for automatic transmissions (AT) because they are closely related to clutching sequences and gear ratios. A systematic method consisting of four steps for the synthesis of multi-speed ATs is proposed based on four-row Ravigneaux-based PGTs. First, the digraph model and adjacency matrix are employed to enumerate all the non-isomorphic four-degree-of-freedom (four-DOF) and three-DOF topologies. Second, the rules for configuration of gear shift elements are summarized to eliminate their infeasible combinations, and the speed matrix equations are established to obtain all potential gear ratios with given number of brakes and clutches. Third, Monte Carlo simulations based on the Latin hypercube sampling—Chi square (χ2) test method is adopted to classify all the gears into four groups to significantly reduce the number of gear permutations. Finally, the characteristic parameters are optimized by the internal penalty function method. The method is verified by synthesizing eight-speed and nine-speed Ravigneaux ATs.
A novel compound power-split hybrid power system based on two planetary gear sets for commercial vehicles is developed. The equivalent lever diagram is used to investigate the components speed and torque characteristics of the system, and then the system dynamic torque control and transmission efficiency are described in equations. Six types of operating modes which are divided into two pure electric modes and four hybrid modes are analyzed by the simplified combined lever diagrams, and their torque decoupling in form of formula is derived. The hybrid transmission (HT) external characteristic is analyzed simultaneously. A control strategy which implements the rule-based (RB) method for the system is depicted. To evaluate the performance of a hybrid vehicle equipped with this hybrid system, the vehicle control and physical models are developed. Then power performance and economic performance simulations are performed. Meanwhile, corresponding tests are carried out to validate simulations. Simulation and test results indicate that, the fuel consumption for C-WTVC of the vehicle equipped with the proposed hybrid system is about 11 L/100 km and it declines by 21% compared with 14 L/100 km of the traditional vehicle.
To find the optimal powertrain design for hybrid and electric vehicles in terms of energy efficiency and performance, often automatised optimisation tools are applied. These require a mathematical model of the powertrain configuration, which is usually done on the level of components, such as planetary gear sets (PGS), clutches and brakes. This, however, leads to a huge design space with lots of functional redundancy. In fact, each functional powertrain mode can be realised by various component combinations. In this paper, a novel mode-based modelling technique for arbitrary hybrid and electric powertrain configurations with up to one internal combustion engine (ICE) and two electrical machines (EMs) is proposed. This allows to easily analyse multi-mode hybrid and electric powertrains on a purely functional basis. Additionally, it reduces the set of mode describing parameters to the minimum amount required. First, an existing graphical representation of hybrid powertrains with one ICE and one EM is analysed and formalised. Based on that, virtual powertrain nodes are defined. These are used to compose all hybrid and electric powertrain modes. Five of them are presented in detail and plotted within a three dimensional ratio plot. Using a first case study, it is shown how the ratio plot can be used to analyse arbitrary multi-mode powertrains. Within a second case study, it is demonstrated how optimal parameter sets for single-mode powertrain configurations can be identified using the derived model.
Hybrid electric vehicles (HEVs) utilize multiple power sources to minimize fuel consumption, which, generally, comprises one or two electric motors added to the conventional configuration. Based on the power flows from the sources to the wheels, the powertrain configurations are classified into three different types, such as series, parallel, and power-split. Although the classification is helpful for engineers to understand the layout of the system, it might not be useful for analyzing the operation of the system. This study proposes new classification concept, so that the powertrain configurations can be classified into two categories according to the operating mode, as either a variable type or a fixed type, which can be very practical for building mathematical models and analyzing the systems. The mathematical models are developed based on parameters characterizing the operations, and the modeling technique is tested in four real-world hybrid vehicles in order to see the feasibility. The new classification concept brings significant advantages for engineers who want to study hybrid systems because it is possible to accelerate the development process by reusing the generic models even for different powertrain configurations, which can be used for analyzing, evaluating, and optimizing the hybrid powertrain systems.
In control problems of hybrid electric vehicles, concepts using Pontryagin’s minimum principle produce near-optimal solutions for minimizing fuel consumption. The costate in these control concepts can be interpreted as a parameter that represents the value of the electrical consumption because it is used for calculating the equivalent fuel consumption of the electric use. Therefore, it is possible to balance the state of charge (SOC) of the battery by adjusting the costate. In this study, an analysis was conducted to determine the correlation between future driving information and the costate by investigating the simulation results from different costate values. To analyze the impact of the driving conditions on the SOC balance, the driving cycles are classified into three groups, such as city, rural, and highway, using a support vector machine based on a supervised learning algorithm that categorizes the cycles with the hyperplane constructed from training data labeled in advance. Based on the analysis of the results, it is shown that the costate have different characteristics according to the classified future driving, and stochastic models for optimal costates can be obtained according to the categorized driving groups. The approximation model produced from the data-driven analysis makes it possible to design a controller that determines an appropriate costate according to upcoming future driving conditions such that a real-time controller using updated costates can be developed if the future driving conditions are provided by navigation systems and connectivity technologies.
The hybrid tracked vehicles(HTV) usually adopt series hybrid powertrain with extra steering mechanism, which has relatively low transmission efficiency and reduces the flexibility of structural arrangement. To overcome the disadvantages, a new kind of single-mode powertrain has been proposed. The power-split hybrid powertrain is composed of three planetary gear (PG) sets connected to one engine, left and right track outputs, and three motors. The proposed powertrain can realize steering while going forward by controlling the output torque on each side without extra steering mechanism or steering shaft. Due to the diversity of the connection way between components and planetary gear sets, a rapid configuration design approach is proposed for the design selection of HTV. The automated dynamic modelling method can show the one-to-one correspondence with the selected feasible groups by establishing two characteristic matrices, which is more simple than other researches. The analytically-based method is proposed to classify all possible connection designs into several groups to decrease the searching scope with improved design efficiency. Finally, the optimal control strategy is used to find the design with optimal fuel economy under typical condition of HTV. The case study is implemented by the proposed design approach which demonstrates better design performances compared with the existing series-hybrid HTV.
Existing research on parallel hybrid electric vehicles (HEV) mainly focuses on optimizing the component sizes and control strategies of the single-motor parallel hybrid electric powertrain (SMPHP), and less analyzes the influence of powertrain configuration on the performance of the vehicle. Therefore, the influence of the power coupling type and transmission type of the powertrain configuration on the fuel economy and drivability performance of parallel HEVs is studied in this paper. Considering three types of powertrain topologies (P2 torque-coupled, P2 dual-mode coupled and P3 torque-coupled) and two types of automatic transmissions (DCT and CVT), six typical types of SMPHP configurations to be discussed are determined. To obtain their optimal fuel economy and drivability performance, a multi-objective optimization and analysis method based on dynamic programming and multi-objective particle swarm optimization algorithm is proposed to optimize the component sizes and control variables of powertrain configurations. Finally, the optimal performance and component size optimization results of six typical SMPHP configurations are analyzed and compared, and the influence of powertrain configuration on the performance and components sizing of the SMPHP is obtained, which contributes to the configuration design of the parallel hybrid electric powertrain.
Through the analysis of a CHS (Chinese hybrid system) compound power-split configuration, it is found that enhancing the system’s speed decoupling ability can reduce the electric power loss, optimize the engine operating point distribution, and enhance the vehicle dynamics. This paper proposes a novel compound power-split configuration with a two-speed AMT (Automated manual transmission), which includes an electric-vehicle mode, a low-speed power-split mode, and a high-speed power-split mode. First, the electric power characteristics and rotational speed/torque characteristics of the CHS compound power-split configuration are analyzed using the lever method, theoretically demonstrating the rationality of the two-speed AMT+ compound power-split configuration. Then, the genetic algorithm is employed to optimize the multi-parameters and multi-objectives in terms of the vehicle dynamics and economy. Finally, a comparative simulation and analysis of the vehicle’s economic and dynamic properties is performed for the new two-speed AMT+ compound power-split configuration and the original CHS compound power-split configuration. The results show that the vehicle economy is increased by 6.9 % for the new configuration, the acceleration time per 100 kilometers is decreased by 27.5 %, and the maximum speed is increased by 13.2 %.
The configuration of nine-speed automatic transmission (AT) is one of the most important factors to determine its performance, and the pursuit of a better configuration of AT has always been the research focus. This paper proposes a new structural decomposition method, based on which the configuration synthesis of nine-speed AT with a cut-link is conducted by the combination of two independent planetary gear trains (PGT). Firstly, two different decomposition types are introduced, and the structure of nine-speed AT with four planetary gear sets (PGSs) and two degrees of freedom (DOF) is divided into two substructures with one-DOF. Secondly, all the topological graphs of substructures in the two decomposition types are obtained by screening in our atlas database. Thirdly, the layouts of shifting elements (SEs) are analyzed based on the lever method, and all the possible layouts of SEs are obtained. Finally, the substructures are combined according to the layouts of SEs to synthesize the configurations of nine-speed AT. As a result, 168 different configurations of AT are obtained including some classical and new configurations. Furthermore, the method can be extended to the synthesis of other multi-speed ATs.
In the planetary automatic transmission design, efficiency is one of the primary performance indicators determining the final selection from multiple candidates. However, efficiency evaluation is the last step of conceptual design, thereby causing the trial result is often known at the end of the design. A new methodology based on geometry is presented for multistage planetary automatic transmission design, ranging from clutching sequence synthesis to efficiency evaluation. The emphasis is placed on a unified model for design steps with different analysis principles to predict power transfer characteristics earlier. Some new results and improvements are also presented, such as general speed ratio change law, simultaneous traversal of different shift types, and the efficiency formula. An example is provided to illustrate the applicability to a 3-DOF planetary automatic transmission and shows that early identification of power transfer characteristics can lock in necessary subsequent calculations, thereby eliminating unnecessary analysis and speeding up the design process.
div class="section abstract"> This paper describes a methodology for investigating the controls coordination of clutch and propulsion torque sources relative to clutch energy, electrification energy consumption and output torque profile for offgoing controlled downshifts in P2 parallel xHEV powertrain configurations. The focus is on an 8 speed planetary automatic transmission, but the approach is equally applicable to any powerflow design with clutch-to-clutch shifting. The modeling technique is for an overall control strategy relative to achieving a targeted transmission input speed profile. A reduced order model of the transmission system is presented that accounts for input shaft acceleration and compensation of inertial contributions to offgoing clutch torque and transmission output torque. The coordinated control of offgoing clutch, engine and P2 electric motor torques are explored in the context of power on and off downshifts for clutch energy, P2 energy consumption and output torque trajectory that directly translates to responsiveness and/or perceived shift quality. The presence of a torque converter and lockup clutch and the influence of the lockup clutch state control on downshifting coordination and torque disturbance is also incorporated in the analysis. Potential improvements in downshift response, clutch controllability and output torque trajectory are provided for the particular 8 speed transmission powerflow considered. The methodology presented can easily be applied to any clutch-to-clutch transmission architecture and powerflow, whether planetary, dual clutch or other.
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In this paper, based on two planetary gear sets, a novel compound power-split hybrid power system for commercial vehicles is presented. Firstly, mathematical models of the system dynamic torque control and the system efficiency are established by using an equivalent lever diagram and analyzing the power flow respectively. Then the system operating modes which are divided into two pure electric modes and one hybrid mode and corresponding control strategies are analyzed by the combined lever diagrams. Finally, control strategies in different modes to looking for the optimal system efficiencies are designed and validated by the bench test. In order to prolong its service life, the battery is charged with small power in the hybrid mode. The design and test results indicate that the optimal system efficiency control strategies are reasonable and reliable. The maximum value of the optimal system efficiency can reach about 0.92 in the pure electric mode, and 0.39 in the hybrid mode. And the proportion of the engine operating points with the brake specific fuel consumption (BSFC) lower than 215 g/kWh is 81%. The co-simulation results show that the maximum system efficiency can achieve 14.9% fuel consumption per 100 km drop compared with the minimum system efficiency for an 80 km/h constant speed condition, which indicates that the optimal system efficiency control strategy can greatly improve the vehicle fuel economy. This study can offer a research direction for energy management of hybrid power systems.
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