On tightening bolted joints, the calibrated wrench method is used in manufacturing industries for a large amount of tightening work. It is important to give high initial axial tension in respect of tightening reliability, self-loosening prevention, the prevention from fatigue breakage, etc. In this method the axial tension of a bolt is controlled by grasping the wrench torque. However, since the axial tension grasp of this method is indirect, it varies greatly in lot of tightening. Therefore, the calibrated wrench method is not so accurate from the viewpoint of axial tension control.

Turn-of-nut method, torque gradient control method and plastic-region tightening, etc. are developed as the methods of getting high initial axial tension with sufficient accuracy. But the calibrated wrench method is still widely used because of the simple tool and easy standardization.

In this paper, the statistical distribution of the magnitude of the combined stress (equivalent stress) by shear strain energy criterion in bolted joint, which are tightened by the calibrated wrench method is formulated. Tightening torque and equivalent stress coefficients are considered to be two independent random variables. We show that the equivalent stress obtained by those products is distributed in a confidence limit ellipse. It is thought that distribution of this kind is conventionally varied in a rhombus. However, this proposed method shows that the distribution is varied inside the confidence limit ellipse.

Now, when considering the permitted limit for working load stress on a bolted joint, ellipse-like variation has big margin to yield point than the shape of a conventional rhombus. Using this feature, we show that higher tightening target torque value can be set than before by this method. Finally, this research established the analysis and calculating routine for the optimum tightening torque on bolted joints.

The merit and effect of this proposed method are as follows.

1) The optimum tightening torque can be raised by about 13% than conventional method by using the experimental thread characteristic values in this research.

2) In a large amount of tightening work, the axial tension distribution (tightening coefficient Q) and distribution of equivalent stress (tightening stress coefficient S) are presumed. The predicted value of the distribution of the Q is about 1.73, which has the 20% improvement effect compared to the conventional method. Also the distribution of the S is about 1.58, which has the similar improvement effect of 18%.

As a rapid calculation, the nomograph of the optimum tightening torque can be obtained by combining the tightening torque and axial tension (axial stress) as well as the distribution of equivalent stress with dimensionless data of screw shape and strength. The example of nomograph on metric coarse screw is shown.

In order to maintain the tightening reliability in bolted joints, standardization of the tightening work in a production site is very important. We think that this method is useful for establishment of the job standard (technical engineering standard).

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