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8/11/2019 2006 Int Ansys Conf 349
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The Dynamic Tightening of a Bolted JointPaul Copeland
Engineering Methods, Inc.
Michael Oliver, Ph.D.
Mercer Engineering Research Center
Abstract
In an assembly that contains threaded fasteners, the nut or bolt needs to be physically tightened to a specifictorque. This is usually performed with a torque gun operating at a specific speed to drive the fastener to the
final torque target. This type of tightening process is considered dynamic in the fastener community. The
act of dynamically tightening a fastener creates tension in a bolt, clamp-load in the jointed members, and a
complex set of shear stresses in the under-head region as well as in the engaged portion of the threads ofthe fastener. FEA models of fasteners are usually created without these internal and external threads
(without a helical thread path). The clamp-load is then created in the FEA joint with the aide of pre-tension
elements and not through the application of a physical torque. Analysis conducted with the aide of thesepre-tension elements thus needs to be considered static. These elements not only fail to produce the
actual shear stresses, but also do not accurately depict the deflection and plastic deformation in both the
bearing surface and engaged threads of the fastener when non-linear material properties are used. A new
type of bolted joint model has been developed which allows for the dynamic tightening of a bolt into a
threaded through-hole using non-linear material models and a helical thread path. This model was patternedafter an actual joint created in a test laboratory. The thread and under-head coefficients of friction were
measured from the actual joint and were then used as inputs for the new model. Comparison of the clamp-
load results from the model and the actual joint showed a 0.15% difference when 50 deg of rotation was
applied to both the actual and FEA bolts. The average plastic deformation on the bearing surface of thejoint from the model matched that of the actual joint, 0.003 mm. The pretension model showed no evidence
of plastic deformation on the bearing surface however.
Introduction
The use of FEA software to determine the resultant forces on an assembled bolted joint has been becomeincreasingly popular in recent years. Users of FEA code determine the affects of cyclic, thermal, and
shear/axial loading on an assembly with one or more fasteners (screw or a nut and bolt) that secure an
assembly together. However, the clamp-load or pre-tension in the joint had to be created prior to anyexternal load being placed onto this joint. There are several means of creating the clamp-load. 1) A beam
element is created, which represents the distribution of the clamp-load through the assembled jointed
members (basically a spot weld). 2) An actual bolt is modeled, but does not contain threads. The shank ofthe bolt is attached to the jointed members either through the use of contacts or Boolean operations. Clamp-
load is created with the use of pre-tension elements. 3) An actual bolt is modeled complete with non-helical
threads. These non-helical threads are also modeled into the jointed members or into the associated nut.Clamp-load in the joint is also created with the aide of pre-tension elements.
The advantages of using the above methods are low computation time. However, there is one rather largeassumption with these methods; the shear forces and resulting deflection created in both the bearing surface
and in the threads of the joint, as a direct result of the torquing the fastener to a targeted torque, arenegligible. The purpose of this paper was to demonstrate that this assumption is neither accurate nor
prudent through the use of a new FEA bolted joint model which dynamically tightened a bolt into athreaded through hole. A comparison was made of this new model with that of model using pre-tension
elements. Additionally, both models contained internal and external helical threads.
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Creating the Dynamic Model
The bolted joint discussed in this paper was patterned from an actual bolted joint created in a Fastener
Laboratory. The joint consisted of a bolt and a nut-block, as shown in Figure 1. The bolt was ground from
an ISO 10.9 property class steel material, with a hardness of approximately 36HRC. The nut-block was
machined from a single piece of 6061-T6 aluminum. The external thread of the bolt was M10 x 1.5 mm6g6g while the internal thread was M10 x 1.5 mm 6H6H. The number/letter combination for each thread
created the maximum and minimum form limits; major diameter, pitch diameter, and minor diameter perASME/ANSI B1.13M (Reference 1). The diameters for both the internal and external threads were set at
their nominal conditions, midway between the maximum and minimum values.
Another nut-block was machined similar to that of Figure 1. However, the machining was carried further to
allow the bearing surface and the threaded section of the nut-block to be separated from the through-hole as
seen in Figure 2. The bearing surface or washer and the loose nut were then placed into a torque/tension
load-cell to measure the thread and under-head coefficient of friction (CoF) values. This load-cell measures
both clamp-load as well as the under-head torque developed through the act of tightening a fastener. Aschematic of a typical load-cell is shown in Figure 3.
Figure 2 Drawing of the machining of a nut-block to create thenut and washer required to measure the thread andunder-head CoF values.
Figure 1 Drawing of bolted joint created in the laboratoryconsisting of a M10 x 1.5 mm bolt and a nut-block.
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The governing equation of torque, from either the ISO 16047 (Reference 2) or the DIN 946 (Reference 3)
specifications, indicate that the torque applied to a joint is equal to the sum of the under-head torque andthread torque as seen in Equation 1.
thdundApplied TTT += 1
Equations 2 and 3 show the relationship between the thread torque and thread CoF as well as under-head
torque and under-head CoF. Here P is the clamp-load, pitch is the pitch of the thread, dmis the nominal
diameter of the thread, and Dkmis the average between the through-hole diameter of the nut-block and thediameter of the bolt flange.
m
thd
thdd
pitchP
T
578.0
159.0
= 2
=
km
undund
PD
T2 3
A Teflon based lubricant was applied to the under-head region and threads of the bolt. The bolt was then
inserted against the aluminum washer and then into the load-cell. The aluminum nut was then rotated ontothe threads of the bolt. The bolt was tightened to torque of 45 Nm with an electric torque gun. The
developed clamp-load and both the thread and under-head CoF were then plotted versus the time of data
acquisition, Figure 4. Note how the CoF values are a function of the clamp-load and that the two frictional
values are different from each other. Additionally, the under-head CoF is lower than that of the thread CoF.
Data was obtained from the graph at a clamp-load value of 28 kN (0.148 for the thread CoF and 0.051 forthe under-head CoF).
The same bolt was then inserted into the actual aluminum nut-block of Figure 1. An ultrasonic piezoelectric
sensor was added to the end of the bolt to measure the amount of clamp-load developed in the joint due tothe application of torque. The Teflon lubricant was again added to the thread and under-head region. The
bolt was then torqued to 52 Nm with the aide of an electric toque gun rotating at 100 rpm. Data was
Figure 3 Drawing of a typical torque/tension load-cell configuration.
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obtained from the resulting curve at an angle of 50 deg of rotation from the onset of clamp-load, Figure 5.
The clamp-load measured at this amount of rotation was found to be 38,630 N. The bolt was removed from
the nut-block and the maximum amount of plastic deformation on the bearing surface was measured to be
approximately 0.003 mm.
Figure 4 Graph of the clamp-load, and thread and under-headCoF plotted versus time of acquisition.
Clamp-Load
Thread CoF
Under-Head CoF
Figure 5 Graph of the clamp-load and applied torque plotted versusangle of rotation for the actual joint. The angle betweenPoints a1 and a2 is 50 deg
Torque
Clamp-Load
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Development of the Dynamic Model
The FEA model was created using ANSYS Mechanical v10.1. The profiles of both the internal and external
threads were established first. The internal threads were defined by five key points and the external by six.
These points represent the intersection of lines and curves comprising the shape of threads as per equations
established by ANSI/ASME 1.13M (Reference 1) specification and were calculated for the M10 x 1.5thread profiles. The locations of these points for both the internal and external threads are shown in Figure
5. Here, Points A to E are for the internal threads and 1 to 6 for the external threads.
The flank surfaces of the threads were created using the major and minor diameters of both internal and
external threads. Initially, the angular extent of these surfaces along the path of the helix was 45. Onceestablished, they were then copied and stacked on top of each other to create a seamless thread helix. Both
sets of threads were then truncated both at the top and bottom ends, Figure 6. This thread truncation
(machining) is representative of what occurs in an actual joint, especially in the nut or internal threads.
The nut-block was created by first adding the internal threads to the inner surface of a hollow cylinder. The
resulting solid was a 12 mm long nut with 1.5 mm pitch threads to provide an eight thread engagement.This internal threaded solid was then glued to an 18 mm long square block with 11 mm diameter hole to
form the nut-block (matching the drawing from Figure 1). Note that the internal threads were created
separately from the nut-block so that the three solids could be meshed at different mesh density; higherdensity in the threads where the critical analysis was required, and lower mesh density in the nut-block,
where the analysis results were less critical.
The creation of the external threads was performed by adding the external threads to the outer surface of a
hollow cylinder. A solid cylinder was then inserted inside this threaded solid. This procedure was used to
generate the external threaded bolt so that a denser mesh could be generated in the threaded region, and a
coarser mesh in the center section of the attached solid cylinder, where critical analysis was not required.The remaining parts of the bolt such as the shank, heavy hexagonal head and flange were added to the
external-threaded cylinder. The dimensions of these volumes were calculated from the ANSI B18.2.3.4M
(Reference 4), which subsequently match those of the actual bolt used in this investigation. The volumesthat made up the bolt were then glued together to prevent rigid body motion when the model was executed.
Figure 6 Drawing of the base key point locations for both theinternal and external threads.
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The critical areas such as the flank areas of both the internal and external threads, as well as the bearingsurface of the nut-block and the flange of the bolt, were initially meshed with MESH200 elements. The
volumes, which are attached to these areas, were then meshed with SOLID186 20-node tetrahedral
elements. The remaining volumes of the bolted joint were meshed with SOLID187 10-node tetrahedral
elements.
Two contact areas were created in dynamic model; between the internal and external threads as well as
between the flange of the bolt and the bearing surface of the nut-block, Figure 8. Default contact settingwas used in both contact areas including standard initial contact. Each contact area did have its own CoF
value however, measured from the friction experiment discussed previously. The under-head of the bolt
was allowed to both rotate about the z axis as well as expand radially as the bolt was tightened against the
nut-blocks bearing surface. The external threads were allowed to also rotate about the z axis as well ascontract radially due to the elongation of the bolt. The nut-block was held fixed in the x-y-z directions but
the internal threads were allowed to expand radially as clamp-load and pressure increased due to therotation of the bolt.
A pilot node was created inside the head of the bolt as the target with the faces of the hexagonal features ofthe bolt head as the contacts. A rotation was applied to the contact surfaces using the
D,NODE,ROTZ,VALUE command.
The completed model had 291,981 elements, 423,772 nodes, and 1.27m degrees of freedom (DoF). Therewere two materials used in the model, steel and aluminum. The steel was patterned after the ISO 10.9
property class bolt material with a modulus, yield strength, tangent modulus, and Poisons Ratio of 203,403
MPa, 830 MPa, 138,526 MPa, and 0.295 respectively. The aluminum was patterned after 6061-T6 with a
modulus, yield strength, tangent modulus, and Poisons Ratio of 68,900 MPa, 46,665 MPa, 276 MPa, and
0.29 respectively. Both materials were allowed to linearly plastic deform using the BKIN rules.
Figure 7 Internal threads following flattening or truncationof the threads on top and bottom.
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Comparing the Results
The bolt in the dynamic model rotated 50 deg to create the clamp-load in the joint whereas the clamp-load
in the pre-tension model was created by applying this same clamp-load in a tensile or static manor. Even-
though the contact areas in the pre-tension model were allowed to slide in a radial manor, there was no
rotation and subsequent development of associated shear forces.
The bearing surfaces from both models were isolated and the resulting volumes were plotted with theequivalent stress, Figure 9 for the dynamic model and Figure 10 for that of the pre-tension model. Note the
difference in both the magnitude and extent of the stress between the two models. This is due to the fact
that the dynamic model is creating shear stresses and the pre-tension model is not. Recall that the yieldstress for this 6061-T6 aluminum material is 276 MPa. This indicates that the bearing surface of the
dynamic model yielded whereas the pre-tension model did not. Figures 11 and 12 shows the equivalent
plastic deformation on the bearing surfaces for the dynamic and pre-tension models, respectively. Note that
the pre-tension model showed no evidence of plastic deformation.
Figures 13 and 14 shows the equivalent stress on the internal threaded volume for the dynamic and pre-tension models respectively. The arrow depicts the initiation point of the helical of the thread. The
maximum pressure develops at a point where full contact of the flanks of the internal and external threads
occurs (about 45 deg from start of the thread). Note that the magnitude of the pressure is larger for thedynamic model. Figures 15 and 16 shows the equivalent plastic deformation on the internal threaded
volumes for the dynamic and pre-tension models respectively. The magnitude of the plastic deformation islarger on the dynamic model compared to that of the pre-tension model.
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Figure 10 Von Mises stress of the static models nut-block bearingsurface.
Figure 9 Von Mises stress of the dynamic models nut-block bearingsurface.
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Figure 11 Von Mises plastic strain of the static models nut-blockbearing surface.
Figure 12 Von Mises plastic strain of the dynamic models nut-blockbearing surface.
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Figure 13 Von Mises stress of the dynamic models internal threads.
Figure 14 Von Mises stress of the static models internal threads.
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Figure 16 Von Mises plastic strain of the static models internalthreads.
Figure 15 Von Mises plastic strain of the dynamic models internalthreads.
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Conclusion
A FEA model had been created that allowed for the physical tightening of a bolt to create clamp-load in a
bolted joint. This type of tightening is deemed dynamic because it mimicked the method of tightening a
fastener in reality. This new method was compared to the conventional way of establishing clamp-load in a
bolted joint via the use of pre-tension elements. This later method was deemed static because no rotationoccurred. The static and dynamic models contained internal and external threads, which allowed both to be
more realistic. The bolt was steel and the threaded through-hole nut-block was aluminum.
The following are the results of this investigation:
1. The actual joint developed 38,570N of clamp-load through a physical rotation of 50 deg.
2. The bolt of the new dynamic model was rotated 50 deg and produced 38,630 N of clamp-load.This represents a 0.15% difference between the FEA model and the actual joint it was patternedafter. The maximum amount of plastic deformation on the bearing surface of the nut-block in the
dynamic model was measured to be 0.003 mm. This matched that of the actual joint.
3. A load of 38,570 N was applied to the shank of the bolt in the static model as pre-tensionedelements. No plastic deformation on the bearing surface was evident on this pre-tension model
however.
4.
The maximum Von Mises pressure on the bearing surface of the nut-block was found to be 613MPa for the dynamic model and only 211 MPa for the static model. This represents a 66%
difference between the two pressures. The difference was due to the rotational shear forces
produced in the dynamic model, which were non-existent in the pre-tension model.
5. The maximum Von Mises pressure on the internal threads of the nut-block was found to be 830MPa for the dynamic model and 771 MPa for the static model. This represents a 7% difference
between the two pressures.
6. The maximum Von Mises plastic deformation on the internal threads of the nut-block was foundto be 0.038 mm for the dynamic model and 0.005 mm for the static model. This represents a 18%
difference between the two deformations.
Discussion
The results of the bolt rotation of the dynamic model matched that of the actual joint it was patterned after
with respect to clamp-load and plastic deformation of the bearing surface. This indicates that the dynamic
model is an excellent representation of the actual joint. The pre-tension model matched poorly to the actualjoint with respect to the bearing surface. However, the stress and plastic deformation of the internal threads
of both the dynamic and static models were not all that different. This is probably due in part to the helicalnature of the threads. For the pre-tension model, the standard contacts in the threads allowed for sliding and
slight rotation of the bolt threads on the nut threads. This same sliding/rotating action was evident in the
dynamic model, but with a larger magnitude.
Future Work
Secondary analysis could be applied to either the dynamic or static model once it has been solved. This
secondary task could be thermal cycling, the application of a shear force, or possibly a fatigue cycle. At thetime of this writing, a thermal cycle was being applied to both models to determine how well both modelsfollow the results of the actual joint. Additionally, the size of the model is being refined in order for the
solve time can be reduced as much as possible. This model is also being examined for the possibility of
incorporating the algorithm into Workbench.
References
1) ASME/ANSI B1.13M 1983 Metric Screw Threads M Profile
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2) ISO 16047 Fastener Torque/Clamp Force Testing, 2000
3) DIN 946 German Standards (CIN-Normen), Determination of Coefficient of Friction ofBolt/Nut Assemblies Under Specified Conditions, October 1991
4) ANSI B18.2.3.4M 2001 Metric Hex Flange Screws
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