# Development of a Prediction Model for Tractor Axle Torque during Tillage Operation
###### Abstract  
In general, the tractor axle torque is used as an indicator for making various decisions when engineers perform transmission fatigue life analysis, optimal design, and accelerated life testing. Since the existing axle torque measurement method requires an expensive torque sensor, an alternative method is required. Therefore, the aim of this study is to develop a prediction model for the tractor axle torque during tillage operation that can replace expensive axle torque sensors. A prediction model was proposed through regression analysis using key variables affecting the tractor axle torque. The engine torque, engine speed, tillage depth, slip ratio, and travel speed were selected as explanatory variables. In order to collect explanatory and dependent variable data, a load measurement system was developed, and a field experiment was performed on moldboard plow tillage using a tractor with a load measurement system. A total of eight axle torque prediction regression models were proposed using the measured calibration dataset. The adjusted coefficient of determination (R2) of the proposed regression model showed a range of 0.271 to 0.925. Among them, the prediction model E showed an adjusted R2 of 0.925. All of the prediction models were verified using a validation set. All of the axle torque prediction models showed an mean absolute percentage error (MAPE) of less than 2.8%. In particular, Model E, adopting engine torque, engine speed, and travel speed as variables, and Model H, adopting engine torque, tillage depth and travel speed as variables, showed MAPEs of 1.19 and 1.30%, respectively. Therefore, it was found that the proposed prediction models are applicable to actual axle torque prediction. a 20201016 June 20201016 June 20201016 June 20201016 June 20201016 June 20  
There have been studies that have taken various approaches to the prediction of axle torque. According to some studies, axle torque can be predicted using traction force and tire specifications [12; 13; 14; 15]. [PERSON] and [PERSON] [14] reported that axle torque can be calculated using the gross traction (GT) and radius of the wheel or tractive device. The GT can be predicted from the model proposed by [PERSON] [16]. However, since the axle torque during tillage operation is differently affected by various variable conditions, such as slip due to the interaction between the drive wheel and the soil, it is difficult to calculate directly using the traction force. Some researchers have used an artificial neural network (ANN) to predict engine torque [17]. [PERSON] et al. [18] proposed an ANN-based prediction method using exhaust gas temperature and engine speed to evaluate engine performance, such as torque and brake specific fuel consumption (BSFC). [PERSON] et al. [19] developed a low-cost sensor (engine speed, fuel mass flow, and exhaust gas temperature) and soft computing-based prediction models to estimate engine torque. As a result, it was reported that the coefficient of determination (R\({}^{2}\)) of the prediction model was 0.99, which means that it could replace the existing expensive method. However, such a prediction model using an artificial neural network has difficulty finding the optimal value of a parameter in a learning process, and problems, such as overfitting, may occur. Therefore, artificial intelligence is mainly used for solving nonlinear problems and need not necessarily be used for solving linear problems. Linear regression analysis can be a good alternative to the methods presented above. Linear regression models have been proposed in various research fields and are used to select explanatory variables that are highly related to actual dependent variables and to develop prediction models [20; 21; 22]. In the field of tractors, there have been many studies using linear regression models to predict tractor traction performance [23; 24; 25] and fuel efficiency [26]. [PERSON] et al.