単純化模型による研削砥石の弾性率 Elastic Moduli of Grinding Wheel Based on a Simplified Model

研削砥石の弾性率は, 研削性能及び研削理論に関係する最も重要な機械的性質である. このため研削砥石の弾性率を直接測定し, または砥石の構成要素である, 砥粒, 結合剤及び気孔の容積率の関係から求める方法等が試みられた, しかし研削砥石の組織と弾性率の関係について, 単純で効果的な説明はなされていないといえる.この報告では研削砥石の単純化モデルを考えて, このモデルから導出した弾性率の理論式を示した. すなわち研削砥石の弾性率をEとすると, 砥粒及び結合剤の, 弾性率Eg, Ebと, 砥石中の容積率Vg及びVbとの関係は次式で表される.E={1/Vg1/3・Eg+3(1-Vg1/3)2/Vb・Eb}-1この式を確かめるために, ビトリファイド研削砥石の試験片を, 砥粒率43-51%, 結合度H-Rの範囲で, WA砥石の砥粒粒度#46-#120及びGC砥石の#60, #80について作製し, 曲げ試験法で弾性率を測定して計算値と比較した. その結果それぞれの砥粒及び結合剤の容積率の組み合わせについて弾性率の良い近似が見られ, ほぼ1-8×103kgf/mm2の範囲であった. したがってこの単純化モデルによる弾性率は妥当なものと考えられる.

The elastic modulus of grinding wheel is one of the very important mechanical properties on the grinding performance and theory of grinding. To obtain this value, the direct measurements on grinding wheels or the mathematical methods from the theoretical relation among volume fractions of grains, bonds and pores that are constituents of a grinding wheel and from each elastic moduli of the constituents are tried in the past. No simple and effective explanation was, however, established between the elastic modulus and composition of grinding wheel. In this paper, a simplified structure model was contrived and from this model, was induced the theoretical formula of the elastic modulus. The elastic modulus of grinding wheel is expressed as E, elastic moduli of grains and bonds as Eg and Eb, volume fractions of abrasive grains and bonds in the grinding wheel as Vg and Vb. Then, following relation is obtained: E={1/Vg1/3Eg+3(1-Vg1/3)2/VbEb}-1To verify this formula, test specimens of vitrified grinding wheel were trial-manufactured, based on the grain percentage: 43-51%, grade (hardness): H-R, and grain size: #46-#120 of WA, #60 and #80 of GC, and the elastic moduli of specimens were measured by bending method.The specimen size is 5(thickness)×12.8(width)×120mm(length). The obtained values were compared with the calculated ones from the formula, and the results showed a good agreement in each combination of the volume fractions of grains and bonds, employing elastic modulus of WA grain Eg: 35.7×105kgf/cm2 and of vitrified bond Eb: 6.31×105kgf/cm2. The elastic moduli of specimens are in the range of 1-8×105kgf/cm2. Therefore, the values of elastic moduli from the simplified model of grinding wheel are inferred to be reasonable.