# Development of a Prediction Model for Tractor Axle Torque during Tillage Operation
###### Abstract
[25] performed regression analysis on the traction force of a moldboard plow, disk plow, disk narrow, and rotary tiller using the travel speed, tillage depth, and rotor speed as the main variables. [PERSON] and [PERSON] [27] proposed a specific draft prediction model of a disk narrow using multiple regression analysis based on front gang angle, cone index, tillage depth, and travel speed. The literature review revealed that multiple linear regression-based approaches for predicting axle torque during tillage are rare, and most of them focus on the prediction of traction force. In order to use regression analysis to develop a prediction model for a tractor axle model, it is important to select tractor axle torque and key variables that are meaningful and easy to measure. The engine is a power source for the driving axle torque, and representative major data of the engine load, such as engine torque and speed, are closely related to axle torque. To date, most studies have been carried out on tractors equipped with mechanical engines. However, recent tractors have been equipped with electronic engines capable of controller area networks (CAN) communication to respond to Tier-4 environmental regulations. Thus, various types of engine information, including engine torque and speed during field operation, can be measured through CAN, without an additional sensor. Some studies have evaluated a tractor's load condition based on the fuel rate, engine speed, and percent torque data, measured via CAN [28]. Engine load data have difficulty predicting axle torque directly due to the power loss in hydraulic and electrical systems, depending on the working conditions [13], but since there is a significant correlation between engine load and axle torque, engine load can be used as a main variable for predicting axle torque. Tillage depth and travel speed are the main variables used in the model for predicting the required draft of the proposed major tillage tools from American Society of Agricultural and Biological Engineers (ASABE) and are expected to be closely related to axle torque [6; 29]. In addition, slip has been used as a key variable in predicting tractor traction in many studies [16; 20; 30; 31], and some studies have shown that the slip ratio actually affects the axle torque during tillage operation [32]. Therefore, developing a regression model using variables that can affect various axle loads, including measurable variables in the engine, can be a good method for estimating axle torque. In conclusion, axle torque is one of the most important parameters of tractor transmission, which needs to be continuously predicted during operation. In this study, a low-cost sensor-based prediction model that does not require the installation of an expensive wheel torque transducer of the telemetry type, which is the main advantage of using multiple linear regression, is proposed. The accurate estimation of the output axle torque exerted by attached implements through a low-cost sensor can be used for various technologies for managing tractors during field operations. The aim of this study was to develop a prediction model for estimating axle torque by substituting an expensive axle torque sensor, using data on variables that are relatively easy to measure, with a low-cost sensor. Axle torque could be used as an important decision indicator for the optimum design, service life evaluation, and traction performance analysis of transmissions through the prediction model developed in this study. To develop and verify the model, field data were measured through moldboard plow tillage operations. The prediction model was developed based on measured variables using multiple regression. The developed model was verified using the measured actual axle torque from a field experiment.