8/11/2019 2006 Int Ansys Conf 349

1/14

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.

8/11/2019 2006 Int Ansys Conf 349

2/14

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.

8/11/2019 2006 Int Ansys Conf 349

3/14

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.

8/11/2019 2006 Int Ansys Conf 349

4/14

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

8/11/2019 2006 Int Ansys Conf 349

5/14

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.

8/11/2019 2006 Int Ansys Conf 349

6/14

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.

8/11/2019 2006 Int Ansys Conf 349

7/14

8/11/2019 2006 Int Ansys Conf 349

8/14

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.

8/11/2019 2006 Int Ansys Conf 349

9/14

Figure 10 Von Mises stress of the static models nut-block bearingsurface.

Figure 9 Von Mises stress of the dynamic models nut-block bearingsurface.

8/11/2019 2006 Int Ansys Conf 349

10/14

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.

8/11/2019 2006 Int Ansys Conf 349

11/14

Figure 13 Von Mises stress of the dynamic models internal threads.

Figure 14 Von Mises stress of the static models internal threads.

8/11/2019 2006 Int Ansys Conf 349

12/14

Figure 16 Von Mises plastic strain of the static models internalthreads.

Figure 15 Von Mises plastic strain of the dynamic models internalthreads.

8/11/2019 2006 Int Ansys Conf 349

13/14

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

8/11/2019 2006 Int Ansys Conf 349

14/14

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