# Development of a Prediction Model for Tractor Axle Torque during Tillage Operation
## 5 Conclusions  
Tractor axle torque can be used by engineers as an index for making various decisions in transmission fatigue life analysis, optimal design, and life evaluation. However, the existing axle torque prediction method requires an expensive torque sensor. Therefore, this study developed a prediction model that can replace the existing expensive axle torque sensor. The purpose of this study was to develop a model that predicts tractor axle torque during tillage operation. In this study, a prediction model was proposed through regression analysis using the main variables affecting tractor axle torque.  
The engine parameters (engine torque and engine speed), tillage depth, travel speed, and slip ratio were selected as explanatory variables for the axle torque, which is the dependent variable. These were measured from the engine CAN communication, the built-in potentiometer installed on a three-point hitch, and the separately installed travel speed sensor. Field experiments were conducted using a tractor with a load measurement system to collect data for the explanatory variable and the dependent variable. The collected data were classified into a calibration set (75%) and a validation set (25%), which were used to develop and verify the regression analysis. A total of eight axle torque prediction regression models were proposed using each explanatory variable. The adjusted R\({}^{2}\) of the proposed regression model showed a range of 0.271 to 0.925. Among them, the prediction model E--with engine torque, engine speed, and travel speed as explanatory variables--showed an adjusted R\({}^{2}\) of 0.925. All the prediction models were tested for the basic assumptions of the regression analysis: linearity, normality, independence, homoscedasticity, and multicollinearity. All the prediction models proposed using the validation set were verified. As a result, all the prediction models showed an MAPE of less than 2.8%, and, in particular, Models E and H showed MAPEs of 1.19 and 1.30%, respectively, demonstrating a high accuracy. Therefore, it was found that the proposed prediction models are applicable to actual axle torque prediction.  
This research is intended to propose a prediction model for each source, taking into account the data that the user can collect, because it is difficult for users to collect all the data. Since most previous studies focused on models for predicting engine torque, traction force, and fuel consumption, the main contribution of this study was to develop a low-cost sensor data-based axle torque prediction model. Despite these contributions, this study has limitation that the proposed model was developed and validated using data measured under limited working environment conditions (attached implement, gear stage, soil environment, and so on). The prediction model must be supplemented using data according to various conditions, because the tractor axle torque depends on various working conditions, such as the soil, gear stage, attached implement, ballast, etc. Therefore, in a future study, field data according to the various working conditions will be measured through experiments, and the prediction model will be expanded.  
Conceptualization, W.-S.K. and Y.-J.K.; methodology, W.-S.K., Y.-S.K., and S.-U.P.; resources, S.-U.P.; software, W.-S.K.; formal analysis, S.-Y.B., S.-M.B., and Y.-S.K.; investigation, S.-Y.B., S.-M.B., and Y.-S.K.; writing--original draft preparation, W.-S.K.; writing--review and editing, W.-S.K.; supervision, Y.-J.K.; project administration, Y.-J.K. All authors have read and agreed to the published version of the manuscript.  
This work was carried out with the support of \"Cooperative Research Program for Agriculture Science and Technology Development (Project No. PJ013517012019)\" Rural Development Administration, Republic of Korea.  
The authors declare no conflict of interest.