Andrew Biehl

 The objective of this project is to develop a method for determining the nut factor of a bolted joint using the finite element method.

 The torque-tension equation is used to calculate the installation torque, T, necessary to achieve the desired preload in a fastener, P. The installation torque is calculated by multiplying the desired preload by the nominal diameter of the fastener, d, and the nut factor, k.

 The nut factor is an experimentally determined fudge factor representing all of the variables that affect preload.  A single-bolt torque-tension test, such as depicted below, is typically used to obtain the nut factor.

 In order to determine the nut factor, representative testing of a single fastener joint may be performed.  However, the multi-fastener joint for which the data is intended to be used will include variables not considered in the test.  More accurate testing of an exact replica of the multi-fastener design joint may be necessary, in order to determine the average nut factor of the joint and its distribution about the mean.  A significant drawback to the testing of a multi- fastener joint is the cost involved.

 It is hypothesized in this study that finite element analysis can be used in place of testing, in order to determine the nut factor for a multi-fastener bolted joint.

 Assume a specific multi-fastener joint design.  Obtain torque-tension test data from a test of a single- fastener joint with primary characteristics corresponding to the design joint.  Build and analyze a finite element model of the single- fastener test joint.  Use comparison of the FEA results with the test data in order to validate the method.  Build and analyze a finite element model of the multi- fastener design joint. Individually vary several parameters to determine their affect on nut factor.

 Test data was obtained from the torque-tension testing of an M12 fastener, nut and washer lubricated with Lubrisilk synthetic grease.

 Thirty-three total tests were performed under varying conditions.  Five tests were performed with a new fastener, nut and washer used for each test, under constant conditions, and with grease applied to the fasteners just prior to the test. Nut factor and coefficient of friction data from these five tests are summarized below: Test No. Coefficient of Friction Nut Factor K Average

 The configurations of the as-tested bolted joint and the modeled bolted joint are compared below.  All of the clamped members are consolidated into a single rectangular block in the modeled joint (simplifies the model, is not expected to affect results)

 Single-Fastener FEM is shown below:

 Mesh is significantly refined in the threads, as this is the region of the most complex contact behavior

 Fastener and nut are separated into several components connected via tie constraints.  Contact is specified in normal and tangential directions between all applicable surfaces.

 A fixed boundary condition is applied to a section of one side of the clamped plate, representing the fixed support in the test joint.  A roller boundary condition is applied to the OD of the fastener head.  A multi-point constraint is used to rotate the nut. ◦ A prescribed rotation is applied to the control node of the MPC. A rotation is used instead of an applied moment, because prescribed rotations/displacements are inherently more stable than applied moments/loads for non-linear analyses.  A second multi-point constraint is used to restrict movement of the washer.

 In order to show that the model is behaving as generally would be expected, a plot of the von Mises stress acting through a cross- section of the model is shown below.  Peak stresses occur in the root of the threads.

 The plots on the next slide also demonstrate that the general behavior of the model is consistent with what would be expected.  The plots display the contact stress distribution on the clamped plate under the head of the fastener and under the washer.  As would be expected, the peak stress occurs at the edge of the hole.  Also as would be expected, the washer effectively spreads out the load, resulting in a lower peak stress than under the head of the fastener.

Peak Contact Stress = MPa Peak Contact Stress = MPa Contact Stress Under Fastener Head Contact Stress Under Washer

 Torque-tension results from the analysis are shown below. The nut factor is calculated to be There is a 4.5% difference between the analysis results and the test results, which is considered to be reasonable.

 A convergence analysis was performed to ensure mesh adequacy. Number of Nodes Number of Elements Average Shank Stress Percent Change Nut Factor Percent Change

 Four bolt flanged joint analyzed with and without part imperfections.

 Von Mises stress acting through a cross-section of the assembly is shown below. The stress distribution in and around each fastener is nearly identical to the distribution for the single-fastener model.

 The next slide shows the torque-tension relationship for each of the four bolts in the model with part imperfections modeled.  The torque-tension relationship is also shown for the bolts in the model without imperfections (the data for all four bolts was nearly identical)

 Re-write several sections  Formatting  Discuss results  Write conclusion