# Modeling Movement Stability of Machine-Tractor Units Based on Modular Type Tractor
## 3 Materials and Methods  
The subject of the study is modeling the motion stability of machine-tractor units based on a modular tractor. The study's main hypothesis was that blocking the TM vertical hinge could significantly increase the motion stability of the wide-width MTU based on a modular tractor. To check the adequacy of the MTU mathematical model based on a modular tractor (Figure 1), we used a unit assembled according to diagram A (Figure 3). The KY-14102 tractor (Ukravtozapchastina LLC, Kyiv, Ukraine) was used as an energy module (Table 2). \begin{table}
\begin{tabular}{c c c} \hline
**Index** & **Designation** & **Values** \\ \hline Energy module: & KY4102 & \\ Operating mass (kg\(\cdot\)Mg\({}^{-1}\)) & \(m_{t}\) & 4100/4.1 \\ Power engine (kW) & \(N_{e}\) & 100 \\ Energy saturation (kW\(\cdot\)Mg\({}^{-1}\)) & \(E_{p}\) & 24.4 \\ Wheelbase (m) & \(L\) & 2.40 \\ Mass cent longitudinal coordinate (m) & \(a_{T}\) & 0.95 \\ Distance from the rear wheels to the TM hinge (m) & \(l\) & 1.30 \\ Technology module: & TM & \\ Operating mass (kg) & \(m_{m}\) & 2600 \\ Mass center longitudinal coordinate (m) & \(a_{m}\) & 0.20 \\ Distance from hinge axle of wheels (m) & \(b\) & 1.30 \\ Cultivator: & KRN-4.2 & 300 \\ Operating mass (kg) & & 4.2 \\ Operating width (m) & & \\ \hline \end{tabular}
\end{table} 
Table 2: Technical characteristics of the MTU. The modular tractor was used with three KRN-4.2 cultivators (Elvorti, Kropyvnytskyi, Ukraine) designed for inter-row cultivation of row crops with row spacing of 70 cm. According to diagram B (Figure 3), one cultivator was hung behind the EM. Two other cultivators were connected to the front linkage of the energy module using a semi-mounted hitch. When operating movement, the vertical hinge, which joins the EM and TM, was automatically locked by a unique device. It unlocked when driving on the headland. This allowed the TM and the side machines to turn relative to the EM and realize the movement of the MTU with a minimum radius. Moreover, since this modular tractor has parameters \(l=b\) (see Table 2), the TM wheels moved along the tracks of the EM rear wheels on the headland. In this case, the TM did not limit the agility of the EM. A modular machine-tractor unit was studied for inter-row processing of sunflower seedlings. Two sites were allocated on the field, each 250 m long. The first 25 m of the site was used to overclock the MTU. Measurements were carried out on the remaining part (225 m). In the process of field research, the following were recorded: heading angle MTU (\(\varphi\)); EM's wheels steering angle (\(\alpha\)); traction resistance (N) of cultivators KRN-4.2 (\(R_{tr}\)); time (\(t\)) for the MTU to pass the test site. To measure the angle \(\alpha\), a variable SP-3A resistor (Daier, Liushi Town, Yueqing City, Zhejiang, China) with a nominal value of 470 Ohms and a linear characteristic was used. It was installed on the kingpin axis of the left front EM wheel (Figure 4). The heading angle \(\varphi\) was recorded using a GY-521 6 DOF gyroscope on an MPU-6050 chip (TDK InvenSense, San Jose, CA, USA). Hanging frames with strain gauge elements were used to record the traction resistance of cultivators, which made it possible to record traction resistance of up to 30 kN. The unit's time passed the test section was recorded with an electronic stopwatch PC 396 (Hefei Strong Sports Co., Ltd., Anhui, China) with a measurement accuracy of 0.01 s. The measurement data determined the MTU movement velocity using the formula = 225/\(t\) (m/s). Electrical signals from the variable resistance, gyroscope, and strain gauge elements were recorded using an Arduino Uno device (Arduino S.r.l, Monza, Italy). The obtained data were used to calculate the parameters' variances and normalized spectral densities \(\alpha\), \(\varphi\), and \(R_{tr}\). The measurement error of the \(\alpha\) parameter did not exceed 1\({}^{\circ}\), the \(R_{tr}\) parameter--no more than 0.5%, and the \(\varphi\) parameter--less than 2%.