# Development of a Simulation Model for HMT of a 50 kW Class Agricultural Tractor
## 1 Introduction  
The growing role of agricultural mechanization and the need to save fossil energy are important factors in the fuel consumption and emissions of agricultural machinery, such as tractors [1; 2; 3]. Power transmission is a critical component of a tractor and has evolved from traditional manual transmission (MT) into newer continuously variable transmission (CVT), and dual clutch transmission (DCT) types [4; 5; 6]. Among them, CVT is a variable solution not only to retain the characteristics of stepless speed regulation and maintain a high efficiency but also to improve fuel efficiency by adjusting the engine operating conditions [7; 8; 9]. CVTs can be classified into V belt types, hydrostatic transmissions (HST), and hydro mechanical transmissions (HMT) [10]. V belt-CVT is widely equipped in passenger cars. However, the power level is too low to meet the requirements of agricultural machinery, such as tractors [11; 12]. The hydraulic pump and motor, which is representative of HST, has gained wide interest owing to the small size of its hydraulic components, low weight, and the important advantages it provides compared with other forms of stepless transmission. However, the low power transmission efficiency of less than 70% and high cost is a disadvantage of HST [13; 14]. Accordingly, an HMT structure was proposed. In this transmission structure, a hydrostatic component is set parallel to a planetary gear to improve the overall efficiency and to reduce the difficulty of developing a high power hydrostatic transmission [15]. The control strategy of HMT is determined based on the HMT structure, and the arrangements for the planetary gear (PG) train and hydrostatic components [16]. The following studies were conducted with regard to the HMT structures. A study on the HMT structures was conducted using a new HMT system for the purpose of improving power transmission efficiency. The basic characteristics such as speed ratio, torque, and power transmission efficiency were analyzed and compared with an existing HMT system [17]. The results showed that the efficiency of the developed HMT was higher than the pure hydrostatic transmission and that the new transmission structure achieved the low-speed increased-torque effect, which is important for engineering and agricultural vehicles. In another study, an HMT, composed of an HSU and PG, was analyzed in regard to the characteristics of gear shift using lever analysis and of output speed according to change of HSU stroke [18]. The tractor speed increased as the HSU stroke change from \(-1\) to \(1\) based on the gear stage. The power transmission efficiency of the HMT was the highest and changed parabolic shape when the HSU stroke was zero for each gear shift. In other studies, based on the extended network theory, a simulation program was developed to analyze an HMT system, consisting of two hydrostatic pump motors, several PGs, and a steering differential gear [19]. The results showed that the extended network analysis program could predict the power circulation, as well as the magnitude of torque and speed for each transmission element and could be used as a useful design tool for an overall power transmission system. Various studies have been conducted analyzing the power transmission efficiency of HMT as well as the structural analysis for an HMT. Conventionally, power transmission efficiency has been analyzed as one of the representative performance indicators of the transmission [20]. A study on the design of an HMT was performed as an optimization problem in which the objective function was the average power transmission efficiency. Meanwhile, the design variables were the displacements of the two hydraulic machines and gear ratios of the ordinary and planetary gears [21]. The results show that the optimization problem was solved by a direct search algorithm based on the swarm method, which showed a good speed convergence and the ability to overcome local minima.