Optimization of a three point hitch in an agricultural tractor

The three point hitch was fitted on a tractor for the first time by Ferguson in 1935, and has been modified in the following years till the electronically controlled modern versions. During the last decades the geometry of the three point hitch has been regulated from standards. In particular, the ISO 730 specifies the geometrical constraint of the system in function of the tractor power and the physical and dimensional parameters as the mass and the wheelbase of the tractor. These constraints have been fixed to restrict the implement movements and, as a consequence, to reduce the risks related to the use. The directive 74/151/CEE determines limits on the maximum load on the front axle of the tractor and, as a consequence, on the maximum lifting load by the three point hitch. This constraint has been imposed to guarantee tractor stability. The remaining degrees of freedom are usually used from the designers to maximize the lifting load. This measure is also required by the OECD Code 2 standard. The goal of the paper is to define a methodology in order to design the three point hitch of a tractor, able to respect the standard ISO 730, the tractor stability according to the directive 74/151/CEE, and maximize the lifting load using a constrained optimization technique. An optimization problem with constraints has been defined using as its objective a function to maximize the equation that defines the lifting load capacity in function of the three point hitch geometry, and fixing the force deriving by the hydraulic cylinders. The constraining equations have been defined according to the standard ISO 730 with respect to the geometric limits of the three point hitch and according to directive 74/151/CEE with respect to the dynamics of the tractor. The vertical and horizontal distance of the lower link pivot point, of the upper link pivot point and of the lift arm pivot point from the real-wheel axle; the length of the upper link, of the lift arms, of the lower links, and of the lift rods; the stroke of the cylinder and the distance of lower link pivot points to lift rod pivot have been defined as variables. The methodology has been used to design a three point hitch for a specific tractor and to perform a sensitivity analysis to analyze the influence of each variable on the load capacity of the three point hitch, showing the crucial designing variables. The optimization technique firstly permitted to design the three point hitch in a reduced time, and also allowed to give some guidelines on the dimensioning through the sensitivity analysis. The sensitivity analysis has shown how the length of lift rods allows to increase the load capacity of the hitch as well as the regulation range. The distance of lower link pivot points to lift rod pivots is the parameter that deeply influences the uniformity of the load capacity in the height range.