Mathematical model of soil digging spherical excavator bucket

Introduction. The article presents a new design of a bucket of a single bucket hydraulic excavator, which allows you to increase the performance of these machines. Increased efficiency is achieved due to the installation of buckets of larger volume without changing characteristics of hydraulic drive. The purpose of the presented work is to select the volume of the spherical ladle for the digging process. The task of research is to obtain the dependencies of ladle and soil speeds on the parameters of the digging process. Selecting the volume of the spherical ladle will determine how much it can be increased compared to the volume of the serial ladle to carry out the digging process.Materials and methods. The process of digging a new bucket was considered in the form of a two-scale KelvinVoigt rheology model. This model was described by a system of second-order differential equations. The system solved the Cauchy problem, which made it possible to determine the general solution of the equation satisfying the two equations of the system. As a result, derivatives from ladle and soil movements were determined, which are nothing more than ladle and soil speeds.Results. The solution of the above system made it possible to obtain dependencies of ladle speeds and soil masses on parameters of the digging process. The digging process is possible at positive speed values. When substituting depending on the process parameters under the condition of velocity positivity, you can determine the volume of the spherical ladle.Practical significance. To simplify and put into practice the obtained dependencies, an algorithm was compiled to calculate the volume of the spherical ladle. The presented algorithm can be implemented in a computer program.