the offset and the cone profile will be fixed and will not be as design variables therefore the only design variables for a row are the crest length lc the radial position of the center of the crest length rc and the tooth angles u03b1 and u03b2 therefore the number of design variables is 4 times of the total number of rows on a bit the second step in the optimization procedure is to define the objectives and express mathematically the objectives as function of design variables according to equation 1 the force acting on an element is proportional to the rock volume removed by that element this principle also applies to any tooth therefore the objective is to let each cone remove the same amount of rock in one bit revolution this is called volume balance or energy balance the present inventor has found that an energy balanced bit will lead to force balanced in most cases consider fig4 which shows the patterns cut by each cone on the hole bottom the first rows of all three cones have overlap and the inner rows remove the rock independently suppose the bit has a cutting depth u03b4 in one bit revolution it is not difficult to calculate the volumes removed by each row and the volume matrix may have the form where i represent the cone number and j the row number for example v 32 is the element in the volume matrix representing the rock volume removed by the second row of the third cone the elements v ij of this matrix are all functions of the design variables in reality the removed volume by each row depends not only on the above design variables but.