Historically, machinery with wheels and tires has dominated the agricultural machinery market, despite the rapidly growing popularity of rubber tracks. However, notwithstanding the rather long development history of wheels, unresolved problems remain. Most of these are associated with a reduction in the harmful effects on the soil. The aim of this study was to reduce the levels of load on agricultural soils by the drive wheels of agricultural machinery through optimization of the geometric dimensions of the flat and deformed soil surface contact areas of an elastic wheeled vehicle. The tire used for agricultural machinery was modeled mathematically, principally using the properties of Cassinian curves. Some tire dimensions and materials do not satisfy the folding condition, which specifies that the ratio of distances used in specifying Cassinian ovals, $a/\mathit{c}$, should not exceed 1.41. Based on the geometric definition of a Cassinian oval, the shape of the contact profile surface of an elastic tire–soil interaction is determined by the ratio $a/c$. Different $a/\mathit{c}$ ratios correspond to different tire shapes. When $a/\mathit{c}$ = 1.2, the profile shape of the undertread of the tire does not satisfy the folding condition. Using the geometric properties of a common circle and Cassinian ovals, it was possible to determine a value of angle $\alpha \approx {48}^{°}$. This angle is optimal for the tire–soil contact surface and, also satisfies the without folding condition. The presented method may be applicable to bias-ply and radial-ply tires, so it is not specifically applicable for one of these over the other.

从历史上看，尽管橡胶履带迅速普及，但带轮子和轮胎的机械一直主导着农业机械市场。然而，尽管车轮的发展历史相当长，但仍未解决的问题仍然存在。其中大部分与减少对土壤的有害影响有关。本研究的目的是通过优化弹性轮式车辆平坦和变形土壤表面接触区域的几何尺寸，降低农业机械驱动轮对农业土壤的负载水平。用于农业机械的轮胎通过数学建模，主要使用卡西尼曲线的特性。部分轮胎尺寸和材料不满足折叠条件，$\mathrm{一种}/\mathit{C}$，不应超过 1.41。基于 Cassinian 椭圆的几何定义，弹性轮胎-土壤相互作用的接触轮廓表面的形状由比率决定$\mathrm{一种}/C$. 不同的$\mathrm{一种}/\mathit{C}$比率对应于不同的轮胎形状。什么时候$\mathrm{一种}/\mathit{C}$= 1.2，轮胎底面的轮廓形状不满足折叠条件。使用普通圆和卡西尼椭圆的几何特性，可以确定角度值$\alpha \approx {48}^{°}$. 该角度对于轮胎与土壤接触面是最佳的，并且也满足无折叠条件。所提出的方法可能适用于斜交轮胎和子午线轮胎，因此它不是特别适用于其中之一而不是另一种。