Modeling Multi-Bolted Systems Jerome Montgomery

Siemens Power Generation Abstract Modeling a single bolt in a finite element analysis raises questions of how much complexity to include. But, modeling a system of bolts adds more considerations. The first and foremost consideration is the bolt type to be used in the finite element model (Line, Hybrid, Solid, etc.). This is determined by the analyst resource limitations. Then one must consider system level pre-load and load redistribution. This paper looks at how these and other considerations must be taken into account when modeling multi-bolted systems. It also includes the discussion of bolt pre-stress relaxation and flange stiffness effects in load redistribution. This will be done while exploring bolting features in release 10.0 of ANSYS.

Introduction The finite element method has been used to simulate real world stress behavior of complex models that is tedious to calculate by hand. This is especially true when it is desired to know the stress behavior in a bolted system.

A paper presented during ANSYS 2002 World Users Conference [1] discussed different techniques used to model bolts. This paper focuses on discussing multi-bolted systems and the additional requirements for modeling multi-bolted systems. An example of a multi-bolted system is shown in Figure 1, consisting of four bolts and one dowel stud. Figure 2 shows a cross-sectional view where one of the bolts can be seen.

Figure 1. Multi-Bolted Casing

Figure 2. Cylinder Section

There are many details that can be included in an analysis. The discussions in this paper will not include thread effects and some other detail level considerations in bolting. The most important consideration of clamping and load transfer will be modeled.

Bolt modeling in the finite element method started as beams. Analysts were creative in that many used the spider beam approach. This was where one beam represented the stud and a series of beams represented the head. That series of beams where connected circumferentially to the spot face. Pre-stress was performed using a change in temperature approach to shrink the bolt, because initial strain was not an early capability included in the beam element. Further development in beam elements resulted in the link element which included initial strain capability. Two link elements that enhanced bolt modeling capability were the nonlinear spring link and the compression only / tension only link. Further enhancements went beyond the beam element to solid elements. Here the initial strain was created by splitting the bolt at a location of the stud, initially displacing the two segments towards each other to create the effects of the preload. The two segments are essentially sewn together via constraint equations. This is the most realistic simulation to date. Contact behavior along neighboring bolt surfaces (flange) makes this an even more realistic simulation. The increased number of elements generated by solid bolt models has been minimized by improvements in meshers and solver speed.

Bolt Modeling Types Before we get into the bolt system, we must first define parameters that distinguish a bolt. Some bolts are screwed into the bottom flange (standard bolt). In these bolts there is no nut, just the head and the stud (Figure 2). In other systems the bolt goes through the top and bottom flange. These are called through bolts, as shown in Figure 3.

Figure 3. Bolt Labels

Standard Bolts In the standard bolt, attaching the stud to the bottom flange hole must be considered. For a line element (representing the stud), the end node would be coupled circle of nodes from the bottom flange hole. For a solid element stud representation, the base of the stud element circle can share the same surface as the connecting circle of the bottom flange hole. Sharing the sides of the bottom flange threaded hole is at the discretion of the analyst. The threaded hole surfaces were shared in the analyses performed for this paper. Specifically, in Figure 2 the bottom cylindrical segment of the bolt is bonded to the flange.

Through Bolts In the through bolt, the head, and the nut are typically modeled the same.

Six Bolt Modeling Simulations Determination of using a standard or through bolt is determined by the system geometry. But the bolt simulation type is determined by the analyst. Six of the more common bolt simulations, in order of complexity, are:

No Bolt (pretension applied to bolt head surface area), Figure 4.

Coupled Bolt (line element for stud and coupled nodes for head and nut), Figure 5.

RBE Bolt (line element for stud and rigid body elements for head and nut), Figure 6.

Spider Bolt (line elements for stud, head and nut), Figure 7.

Hybrid Bolt (line element for stud and solid elements for head and nut), Figure 8.

Solid Bolt (solid elements for stud, head, and nut), Figure 9.

Figure 4. No Bolt

Figure 5. Coupled Bolt

Figure 6. RBE

Figure 7. Spider

Figure 8. Hybrid

Figure 9. Solid

The analyst must choose the bolt simulation type based on the application and limits (including computer resources, time to complete the task, etc.). The analyst must understand the trade-offs of using one

simulation type over another. Therefore, the judgment on which simulation type to use is based on what is the desired simulation detail to be captured.

This paper will focus on the standard solid bolt.

Modeling Considerations When simulating bolts, there are certain bolt behaviors that must be accounted for in the finite element model. Pretension and contact were discussed in a previous paper [1], along with accounting for bolt going into shear (the transverse direction). Additional considerations include bolt pretension relaxation, bolt pretension sequencing, and bolt to flange interaction.

Pretension Relaxation Bolt pretension allows for clamping a joint before any external load is applied. Over time the bolts and the casing experience joint force reduction (pretension relaxation), especially joints subject to load fluctuations. Schoft, Kindersberger, and Lobl [2] investigated the joint force reduction in high current joints. But in an elastic finite element analysis, pretension relaxation is not automatically captured. It is up to the analyst to capture the relaxed pretension in load steps or by directly applying the relaxed pretension to the model. The pretension value would be the bolt relaxed pretension value obtained from a creep relaxation table or curve. This is still somewhat conservative since the casing relaxation is not included for the static analysis (it is known that the casing will also relax). An analysis that allows for the bolt and casing creep relaxation will take more time.

Whether the analyst applies the full pretension or the relaxed pretension, he must determine how to apply it to the bolt. The two common approaches are initial strain in the element or using the pretension element in ANSYS.

ANSYS pretension element was developed for the solid element, but is used on line elements also.

Pretension Sequencing In real world applications a specific order of bolt tightening is followed. This assures a completed flange closure. The analyst should be aware of this to assure that his model follows the same process. ANSYS allows for bolt pretension load step sequencing. But the user can also lock all of the bolts in a static run. It will do this in two steps. The analysis for this paper uses the static approach which locks the bolt pretension.

Bolt to Flange Interaction The bolt to flange interaction is important to the system loading. In the pretension sequencing, as the bolts are tightened, flange effects can cause a neighboring bolt to lose its original pretension. That is why in the field there are multiple tightening passes. Once all bolts are tightened they are checked to see if they carry the proper pretension. Bolts that lost the required pretension are retightened.

This same process is taken in the pretension sequencing.

Analysis Eight cases were run as shown in Table 1.

Table 1 Case # Description

1 Preload Only without Bolts

2 Preload Only with Bolts

3 Temperature Distribution without Bolts

4 Temperature Distribution with Bolts

5 Pressure Only without Bolts

6 Pressure Only with Bolts

7 Pressure plus Thermal without Bolts

8 Pressure plus Thermal with Bolts

Four cases were run without bolts (1, 3, 5, 7) and four cases were run with bolts (2, 4, 6, 8). The cases without bolts had the bolt preload added as a pressure load on the bolt hole surface. This was done to obtain a simplified model. Cases 3 and 4 were included to see the benefit of flange cooling due to the bolt.

The cases with the bolt had the bolt head and flange in bonded contact. Also, the threaded region of the bolt were in bonded contact.

Analysis Results & Discussion For the eight cases run, specific views were taken. A front view, an oblique view, a side view, and a cut-away through the middle bolt. An overview of the temperature distribution were also included. Table 2 shows the pictures associated with the cases.

Table 2 Case # Figures

1 11-15

2 16-20, 55

3 21-25

4 26-30

5 31-35

6 36-41

7 42-46

8 47-52

Table 3 is a matrix of the views for clearer cross referencing.

Table 3 CASE

VIEW 1 2 3 4 5 6 7 8

Front 11 16-17 22 27 31 36-37 42 47-48

Oblique 12 18 23 28 32 38 43 49

Side 13 19 24 29 33 39 44 50

Middle 14 55 25 30 34 40 46 51

Displacement 15 20 - - 35 41 45 52

Overview - - 21 26 - - - -

The premise of the paper is to discuss those parameters required for system bolt modeling. Several references [3], [4], [5], [6], [7], and [8], discuss the considerations in further detail. The results of the eight cases show that the influence of the bolt is significant for flange behavior. Figure 53 shows the no bolt case with pressure loads applied. The figure demonstrates that the behavior acts as a local regional stress on the bolt surface and at the horizontal joint hole. This behavior is that of a concentrated force reaction.

With the bolted model, the traditional cone-frusta is shown in Figure 54. Overlap of contact pressure is drawn in the figure. The cross lines show shared loads and the vertical line shows where three bolts share the load. The stress results show the influence of the flange geometry to the cone-frusta.

One can see this both mathematically and physically.

Mathematically the equation that represents the load applied to the flange is

Ff = (kf*P)/(kb+kf) – Fp

where,

Ff: load to keep the flange members in compression

kf: stiffness of the flange members

P: total applied load

kb: stiffness of the bolt

Fp: preload on the bolt before P is applied

With an assumption that kf=8kb, Fp=4448.22 N, and P=4893.04 N the equation 1 becomes

Ff = (kb*4893.04)/(kb+8kb) – 4448.22

Without the bolt kb=0 and the flange member load becomes Ff=Fp which means the member is not in compression.

With the bolt Ff=-98.85 N which keeps the member in compression.

Physically, the bolt included can be viewed as a local mechanism. Bolt pretension creates a bolt to flange interaction that creates first a single mechanism which causes the cone-frustum, Figure 56. In an assembly of bolts a load sharing mechanism occurs, Figure 58. In the no bolt situation the load sharing does not occur. The pressure acts independently within each hole. The load distribution is that of a cylinder, Figure 57, at best. On a more localized level the pressure around the hole creates a hole bending effect. This is more of a pinching.

This is verified in the analysis results by the different views. The side and middle views from Table 2, show the frustum pattern in the bolted models. The frustum is changed according to the geometry changes. The front views, show the effect of the frustum over a series of bolts. The dowel stud (the longer bolt) is

Eqn 1

Eqn 2

stiffer than the other bolts and is influenced by the adjoining stiffening ring. The oblique views were generated to show the influence of the stiffening ring.

In terms of the no bolt, the results show a pinching effect at the bolt holes. Also, there is a shear slip effect due to lack of stiffness at the bolt hole. Thus, the displacement view showing an offset.

The temperature distribution was run to show the influence of bolt head temperature to help cool the flange locally. The overview plots were generated to show this.

Conclusion Including bolts in finite element models simulates real world behavior. During preliminary sizing and bolt arrangements, link elements can be used. But the final design should be based on a solid bolt simulation. However, engineering judgment must be used in deciding which simulation type to use.

Another factor that must be accounted for is flange crushing. It was not discussed since this paper focused on elastic analyses. But the reader should be aware of this as he evaluates his bolting.

Overall, making designs faster, cheaper, and more accurate is a goal we all strive to achieve.

Figure 10. Bolt Pretension

Figure 11. Preload w/o bolts, front

Figure 12. Preload w/o bolts, oblique

Figure 13. Preload w/o bolts, side

Figure 14. Preload w/o bolts, middle

Figure 15. Preload w/o bolts, displacement

Figure 16. Preloaded bolts, front1

Figure 17. Preloaded bolts, front2

Figure 18. Preloaded bolts, oblique

Figure 19. Preloaded bolts, side

Figure 20. Preloaded bolts, displacement

Figure 21. Temperature w/o bolts, overview

Figure 22. Temperature w/o bolts, front

Figure 23. Temperature w/o bolts, oblique

Figure 24. Temperature w/o bolts, side

Figure 25. Temperature w/o bolts, middle

Figure 26. Temperature bolts, overview

Figure 27. Temperature bolts, front

Figure 28. Temperature bolts, oblique

Figure 29. Temperature bolts, side

Figure 30. Temperature bolts, middle

Figure 31. Pressure Only w/o bolts, front

Figure 32. Pressure Only w/o bolts, oblique

Figure 33. Pressure Only w/o bolts, side

Figure 34. Pressure Only w/o bolts, middle

Figure 35. Pressure Only w/o bolts, displacement

Figure 36. Pressure Only bolts, front1

Figure 37. Pressure Only bolts, front2

Figure 38. Pressure Only bolts, oblique

Figure 39. Pressure Only bolts, side

Figure 40. Pressure Only bolts, mid

Figure 41. Pressure Only bolts, displacement

Figure 42. Pressure+Thermal w/o bolts, front

Figure 43. Pressure+Thermal w/o bolts, oblique

Figure 44. Pressure+Thermal w/o bolts, side

Figure 45. Pressure+Thermal w/o bolts, displacement

Figure 46. Pressure+Thermal w/o bolts, middle

Figure 47. Pressure+Thermal bolts, front1

Figure 48. Pressure+Thermal bolts, front2

Figure 49. Pressure+Thermal bolts, oblique

Figure 50. Pressure+Thermal bolts, side

Figure 51. Pressure+Thermal bolts, middle

Figure 52. Pressure+Thermal bolts, displacement

Figure 53. Concentrated Stress w/o bolts

Figure 54. Distributed Stress bolts

Figure 55. Preloaded bolts, middle

Figure 56. Cone Frusta

Figure 57. Cone Frusta System

Figure 58. No Bolt Cylinder

References 1) Montgomery, Jerome, Methods for Modeling Bolts in the Bolted Joint, 2002 ANSYS World Users

Conference.

2) Schoft, S., Kindersberger, J., and Lobl, H., Reduction of Joint Force by Creep in High Current Joints, Proceedings of the 21st Conference on Electrical Contacts 2002, Zurich, pp. 406-412.

3) T. Fukuoka, Analysis of the Tightening Process of Bolted Joint With a Tensioner Using Spring Elements, Journal of Pressure Vessel Technology, November 1994, Vol. 116, pgs. 443-448.

4) Bickford, John H., An Introduction To The Design and Behavior of Bolted Joints, 3rd edition

5) Shigley, Joseph E., Mechanical Engineering Design, McGraw-Hill, 1977, 3rd edition

6) Norton, Robert L., Machine Design – An Integrated Approach, Prentice-Hall: New Jersey, 1998, 2nd printing

7) Levinson, Irving J., Machine Design, Reston Publishing: Virginia, 1978, 1st printing

8) Spotts, M. F., Design of Machine Elements, Prentice-Hall: New Jersey, 1978, 5th edition