エンジン補器駆動システム成立性の決め手となる最大張力，弦振動，鳴き等の問題の殆どはシステムの固有振動数とCR回転変動周波数との共振に起因している．本発表では固有振動数を求める固有値解析法，共振時に弦振動、鳴きの発生するスパン，プーリの予測法，及びこれ等手法の適用例について報告する．

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In this paper, under such various conditions as shapes and rubber hardnesses of contact wheels, grinding speeds and settings of cut, the tension acting upon the abrasive belt by means of detecting the electrical signal from a strain gauge passed on the inside of abrasive belt is researched experimentally. Moreover, by using the relation between the tension and depth of cut ratio, it is clarified that a selection method from both the shape of the contact wheel and the most suitable ratio of the effective depth of cut to setting of cut under the various grinding conditions are obtained. The main results obtained are follows. (1) It is impossible to get the shape of the contact wheel which has the most suitable ratio of the effective depth of cut to setting cut from the relation between depth of cut and tangential or normal force acting upon the contact wheel in grinding. However, it makes possible to decide the range between the effective maximum and minimum depth of cut ratio by using the tension and suitable shape of the contact wheel can also be obtained from the effective range mentioned above. (2) Considering the relation between the surface roughness of workpiece and the land height of the contact wheel, the surface finish comes to be bad in the contact wheel giving the suitable depth of cut ratio. However, the shape of the con-tact wheel which has the most effective surface roughness and depth of cut ratio must be decided by this method.

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In order to prevent timing belt jumping, which often occurs under high loads, a practical jumping torque prediction formula was studied and the following results were obtained. (1) Jumping occurs when the amount of belt elongation on the tight side span due to the increase in load after the slack side tension becomes zero is equal to the amount of belt elongation due to the belt lifting on the pulley when the lifting reaches the belt tooth height in the whole wrapping area. A jumping torque prediction formula was derived based on this mechanism. The prediction formula includes parameters such as pulley diameter, span length, wrapping angle, belt tooth height, belt extensional rigidity, initial tension, and belt speed. (2) To compensate for the difference between the basic theory of frictional transmission applied in the prediction formula and the actual phenomenon, four correction factors were introduced for the amount of belt elongation caused by the belt lifting, etc., and physical properties of belt teeth. This makes it possible to predict the jumping torque of not only the driven pulley but also the driving pulley, and to expand the application range and improve the prediction accuracy. (3) The four correction factors were obtained by running tests using curvilinear profile S8M type belt, but it was shown that they are also applicable to a trapezoidal profile L type belt. (4) Jumping tests at rest with the driven pulley shaft fixed were conducted, and it was confirmed that the jumping torque of the driving pulley at running was about twice that of the driven pulley, and almost equal to that of the driving and driven pulleys at rest.

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This paper presents an analytical method by which dynamic characteristics are clarified in a toothed belt system. In the belt system, variable tension and initial static tension act on the belt to transmit variable torque. The analysis assumes that variable tension is smaller than initial tension, and that the action of the former does not affect deformation caused by the latter. The dynamics of a meshing belt appeared through two different but related types of characteristics. One is static deformation, and the other dynamic response. The model used for analyzing the meshing belt is determined from the deformation and response in one tooth of the meshing belt. A method for calculating the elemental constants of the model is also shown. Dynamic characteristics were calculated for a simple belt system by using the model mentioned above for the meshing part of the belt. In the experiments, deformation and response were measured during meshing with plural teeth, and frequency characteristics were measured for the simple system. The computed and experimental results agreed fairly well. It was clarified that the analytical method is suitable for deducing the dynamic characteristics of a toothed belt system.

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正八角形加工物の一つの角を取り出して,加工物が正八角形から円になってゆく過程を立体的に示したのが図10である.図10は研削速度が1880m/min,切込み速度が10μm/sec,コンタクトホイルの硬度がDro 40で研削した加工物を形状測定装置で研削時間30秒ごとに測定した結果である.円孤の部分が研削面であり,研削時間の経過とともに円孤が長くなることから研削時間の経過とともに研削面が長くなり,研削時間が300秒になると加工物の全周面が研削されることがわかる.図7,図8に示された実測による研削時間と研削深さ,単位時間当りの研削深さとの関係は図3,図4に示された理論計算から求められた研削時間と研削深さ,単位時間当りの研削深さとの関係とよく一致している.研削速度を1880m/min,切込み速度を5μm/secとして研削加工を行なった実験値による研削時間と単位時間当りの研削深さとの関係を示した図8の曲線からKの値を求めると,Dro 40とDro 80のコンタクトホイルを使用した場合にはKの値が0.04～0.05の範囲にあると考えられる.また,コンタクトホイルの硬いものを使用して研削した場合にKの値が大きくなる.このKの値は円筒形加工物を円筒研削した場合とほぼ同じである.このことから,取りしろが変動する加工物も取りしろの変動がない円筒形加工物と同じように円筒研削ができ,円筒形加工物を円筒研削したときに求められるKの値を用いて,正八角形加工物が円筒研削されて円形になる過程を理論計算することができた.そこで正八角形加工物が円形になるサイクルタイムを理論計算から求めた.
加工物の最後に研削される部分(図1のB点)における単位時間当りの研削深さについて考えると,(10)式でθ=0とおけば,v_e=v_s[1-exp{-K(t-R₀/v_s×0.0761)}](13)となる.これを一次おくれの要素とみなして,正八角形加工物が円形になるサイクルタイムを時定数の考え方で表わす.
Tを時定数とし,(13)式でv_e=0.63v_s,t=Tとすると,
T=0.994/K+0.0761×R₀/v_sとなる.
(14)式においてv_s=5,10,20,40μm/secとして係数Kと時定数丁との関係を示したのが図11である.図11より切込み速度が増すとサイクルタイムは短かくなり,特に切込み速度が5～10μm/secと比較的低速度のときにその効果は大きく現われる.今回の実験範囲はv_s=5,10μm/sec,K=0.04～0.05であり,この範囲ではコンタクトホイルの硬さがサイクルタイムに及ぼす影響がほとんど見られない.
また,回式の0.0761×R₀は加工物の形状によって決まる値で山の高さを表わしており,加工物が正八角形以外の形状であるときにも加工物の山の高さを知ることができれば,(14)式により作業のサイクルタイムが計算できる.
なお,理論計算と実験結果をまとめるとっぎのようになる.
(1)取りしろが変動する加工物を研削するときも,円形加工物を研削するときと同じように研削でき,工具と加工物との問に飛び跳ねなどの現象が見られない.
(2)本研究でたてた理論式によって計算した結果と実験結果とがよく一致しており,この実験では砥粒先端角,被削材の降伏応力などによって決まる係数K_Gとコンタクトホイルのばね定数K_wとの積である係数Kが0.04～0.05の範囲にあった.これは円筒形加工物を研摩によって円筒研削したときの値とほぼ等しくなった.また理論式により作業のサイクルタイムが計算できた.

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