# Performance Evaluation of a Compound Power-Split CVT for Hybrid Powertrains
## 1 Introduction  
Electrification of the powertrain is a big challenge for the current automotive industry [1]. One of the criticalities of this research area is the improvement of performance, fuel economy and driveability of Hybrid Electric Vehicles (HEV) [2]. Amongst the current hybrid powertrain architectures, the Power-Split Continuously Variable Transmission (PS-CVT) is the most promising technology, since HEVs often present multiple power sources that can be well managed by transmissions with multiple inputs [3]. Continuously Variable Transmissions (CVTs) were studied as early as late 19 th century, when it was recognized that varying the drive ratio during vehicle operation would improve the performance [4]. Of the early designs, there have only been a few that have received significant attention from automotive designers. These CVTs can be classified into five categories, depending on their working principle: friction, traction, hydrostatic, electric, and variable geometry [5]. Conventional CVT units presents some limitations such as limited torque capacity and ratio coverage when compared to conventional units [6]. It has been proven that it is possible to overcome these limitations by combining the CVT with one or more epicyclic gears to create a power-split transmission [7]. An example of an early power-split design is the Perbury transmission proposed in 1940 and based on a toroidal variator (traction type CVT) and a planetary gear-set [8]. Interest in power-split technology for automotive applications began in the 1980s. Products of this renewed interest are the Toyota Hybrid System and the Allison Hybrid Synergy by General Motors [9]. Since then, researchers have been attracted by this architecture [10]. [PERSON] et al. [11] presented an optimization procedure for designing the input and output coupled PS-CVT with higher efficiency. [PERSON] et al. [12] proposed a two-mode PS-CVT with a mode control strategy to minimize fuel consumption. [PERSON] et al. [13] explored potentialcompound power-split configurations with two planetary gear sets to understand how to design the best compound power-split configuration. The PS-CVT architectures can be classified as single-mode (i.e., input split or output split) or multi-mode, in which the power split type is selected engaging and disengaging clutches included in the transmission layout. In general, single-mode PS-CVTs show low efficiency at high speed when compared to more complex solutions that include at least two epicyclical gear trains and one or more locking systems [14; 15; 16]. These solutions are also called compound type power split and an example is given by Global Hybrid Cooperation, a joint project by GM, Daimler, and BMW [17]. Our research group has recently studied the power flows and efficiency of the PS-CVT [18; 19; 20]. In these previous works, the analysis of a \"four-port-mechanical-power split device\" was proposed. This device consists of an electric Continuously Variable Transmission (eCVT) and a power split device (Figure 1). The former is obtained connecting two electric motors; the latter is composed by two planetary gear sets named PG1 and PG2. Figure 1 shows the four possible set-ups. While types A, B and D have been discussed in [18; 20; 19], in this paper, we focus on type C. The power flow and the efficiency of this \"four-port-mechanical-power split device\" are defined and its performance assessed with a numerical example. The practical value of this paper is to provide the designer of such architecture with a tool to estimate advantages and disadvantages of implementing this topology within a powertrain, e.g., the type of power flow that will occur, the power that will flow in the eCVT and the overall efficiency, knowing just the design parameters, that are the geometry of the planetary gear trains, the ratio spread of the eCVT and the required overall speed ratio spread. Section 2 shows the formulation of the kinematic model of the transmission.