Calculation of optimal parameters of the foundation for woodworking machines with large dynamic loads
Keywords:model, ground, differential equation, resonance, logarithmic decrement, optimization criterion, cost, application software
The groundwork for machines with dynamic loads should meet the calculation requirements regarding strength and suitability for regular operation and the need for occupational safety standards regarding acceptable vibration levels. In addition, fluctuations in the groundwork should not cause a harmful impact on technological processes, equipment, and devices located on the foundation or outside it.A mathematical model of foundation vibrations and a methodology for calculating the foundation parameters are presented, taking into account dynamic loads from unbalanced masses and dynamic characteristics of the ground base.The mathematical model is a solution to the differential equation of the foundation vibrations.The article refutes a number of conventional concepts regarding the body of the foundation, its base, the geometric center and the damper between the foundation and the ground.The basis for determining the vibration damping modulus is the logarithmic decrement of vibration damping.It is constant and depends on the elastic and damping properties of the soil, as well as the installation mass. The more significant the logarithmic decrement, the faster the extinction occurs. It was found that an increase in the vibration resistance coefficient allows reducing the mass of the installation with a simultaneous increase in the area of its base, so the mass acts as a limitation.It was established that to ensure vibration resistance and prevent the resonance of the foundation, the ratio of the frequency of its natural vibrations to the frequency of forced vibrations should be at least 1.5.The calculation of the optimal mass, the base area and the depth of foundation laying is carried out according to the criterion of the minimum cost of its construction.An application software has been developed for the calculation. The projection methodology for the foundation for the machine with large dynamic loads is for a two-story sawmill.
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