Mathematical model of soil digging spherical excavator bucket

• Published in: Vestnik SibADI (Online) Vol. 18; no. 6; pp. 688 - 698
• Main Author: Buriy, G. G.
• Format: Journal Article
• Language: English; Russian
• Published: Siberian State Automobile and Highway University 17-01-2022
• Subjects: differential equations; digging; excavator; force of hydraulic cylinder; force of resistance to digging; ladle; mass of soil; mathematical model; soil; volume bucket
• ISSN: 2071-7296; 2658-5626
• DOI: 10.26518/2071-7296-2021-18-6-688-698

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.