ANALYTICAL ESTIMATION OF THE BACK CUT AREA WHEN DEFINING THE COEFFICIENT OF USEFUL LOG SAWING

Abstract

Introduction. When optimising sawing schedule of saw log cuttings the key efficiency indicator is the yield of cut lumber. In real industrial conditions the edged board sections are formed using high-power energy-intensive equipment. However, the energy efficiency used to operate this equipment is not taken into consideration. We suggest using the coefficient of useful sawing defined as the relation of the cut boards surface area to the required sawing area depending on the place of boards in the sawing pattern and the size of sawing logs as the optimisation criteria for sawing pattern in terms of energy efficiency. In other words, the energy directly used to make the sawing board faces is considered effective, while the energy used to make only wood laths or logging slabs is considered ineffective. The coefficient of useful sawing includes the coefficients of useful sawing of board face, edges and crosscut end and allows evaluating the relative energy efficiency of the equipment involved (without taking into consideration the cutting thickness) in terms of a certain sawing pattern or otherwise, make improvements in the sawing pattern in terms it its energy efficiency, thus, reducing its energy intensity necessary to produce the sawn wood. The work aims to develop the method for definition of useful sawing coefficient for different types of boards. The paper reveals a detailed derivation of formulas enabling to calculate the surface of the external sawn face of the untrimmed board and the edge area, which should be sawn in order to gain the edged board. Based on these formulas it is possible to obtain the accu-rate value of useful sawing coefficient for any board in the sawing pattern. We took the log model as the cut paraboloid of revolution. It has been established that the value of the useful sawing coefficient depends on the size of a log and an edged board as well as on the distance between the sawn board and the log axis. In order to validate the obtained formulas the paper refers to comparative tables of analytically defined areas and graphically defined areas obtained using AutoCAD software. We argue that fine precision obtained as a result of this comparison confirms the accuracy of the suggested analytical formulas. Conclusion. Analytical calculation of the useful sawing coefficient allows accurate definition of the relative energy efficiency of sawing different boards of the sawing pattern. In addition, the algorithmic approach makes it possible to computerise calculations, which significantly eases the process. With the knowledge of the efficiency of energy use when producing different types of boards on the sawing pattern it is possible to optimise the cutting plan in order to minimise energy consumption.