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The calibrated wrench method is used in the tightening of bolts in manufacturing industries in the case of a large amount of tightening work. It is important to apply a large initial clamping force to ensure tightening reliability and prevent self-loosening, fatigue breakage, and so forth. In this method, the clamping force of bolted joints is controlled using a torque wrench. However, since the clamping force is indirectly applied by a wrench, it varies greatly in the case of a large amount of tightening in a factory. Therefore, the calibrated wrench method is not so accurate from the viewpoint of clamping force control. It is conventionally thought that the distribution of the clamping force has the shape of a rhombus. When tightening torque and clamping force are considered to be two independent random variables, the clamping force is distributed within an elliptical confidence limit. Here, we show that the distribution of equivalent stress also has an elliptical confidence limit.

To secure the reliability of bolted joints, high clamping force (axial tension) is required to prevent fatigue breakage or loosening failure, and so on. In this paper, at first, we observe the behavior of the initial clamping force decrease tendency (loosening phenomenon) obtained by tightening the bolt used in the actual machine (large forklift) during operation. Based on our previous research, there is a strong linear relationship on log-log paper of loosening phenomenon between decrease tendency of clamping force and distance travelled (or passage of time). By utilizing its properties, we show estimation method of residual clamping force such as "How much the clamping force is remaining after the tens of thousands of hours (kilometers)?" Also, a method for estimating loosening lifetime with respect to residual clamping force level is shown. Finally, we examine evaluation criteria such as "Is the residual clamping force sufficient for prevention of loosening failure?"