Learn how to apply interference fit in a Simcenter 3D contact solution. Take advantage of interference fit to improve fatigue margins for a lug joint.
- High cycle fatigue failure of joints
- Capturing contact behavior for an interference fit
- Analysis time constraints
- Improved fatigue margins
- Use of Simcenter contact settings to easily model interference
- Take advantage of Simcenter solution 401 to efficiently solve the nonlinear contact problem
Pin-Lug Joint w/ Interference Fit
Pin-lug joints are common. So common in fact that we already have a blog post dedicated to one: https://www.m4-engineering.com/simcenter-3d-analysis-of-a-pinned-lug. In this blog post, we will pick up this same geometry and take it one step further by incorporating an interference fit into the joint.
Why model an interference fit in a lug joint? One concern in loaded joints is fatigue behavior. Even though joints may be able to statically carry the limit and ultimate load requirements, they may still be subject to long-term fatigue failure. Fatigue is the weakening of materials when subjected to cyclic loads. The cyclic loads result in progressive structural damage. If not considered carefully, fatigue can result in abrupt and catastrophic failure of structural components, sometimes with fatal consequences, as in the Eschede train derailment, where fatigue loads in the train wheels resulted in derailment and 101 deaths.
Metal fatigue failure results in Eschede train derailment
In order to consider the effects of interference fit, we will use the following lug geometry.
Lug geometry for interference fit analysis
The model consists of three lugs and a single pin arranged as shown below. All components are modeled as PH13-8Mo steel with properties obtained from MMPDS. A hex-dominant mesh was created. Glued contact was applied between the pin and the two upper (red) lugs. A contact condition was modeled between the lower (green) lug and the pin. The upper lugs were fixed at the faces shown (123456 DOF) away from the lug hole. The lower lug was allowed to translate along the vertical axis (Y), while all other DOFs were fixed. A load of 12500 lbf was applied to the lower lug face.
Lug geometry arrangement (three lugs and a single pin) and resulting mesh
In order to simplify the nonlinear solution, the contact settings for the pin-lug contact were modified to set the initial gap/penetration to zero. In addition to this, an offset equal to 0.001 inches was added to the contact. This makes it easy to incorporate an interference fit into the model without too much effort. It also simplifies the contact solution and prevents us from having to create geometry with interference. A neat feature of Simcenter is the ability to define parameters in either unit system. Notice that the offset is defined in mm, although just as easily it could have been defined in inches.
Resulting contact settings – set initial gap / penetration to zero, and add offset
Results: No Interference
So now the fun part: let’s look at some results. To start, let’s look at the stress in the lug when no interference is applied.
Max principal stress in lug with no interference applied
In our case the minimum stress is the stress in the unloaded configuration, 0 ksi.
The maximum stress, as seen in the contour plot, is 151 ksi.
To determine the fatigue damage, we will use the data that is readily available in MMPDS, reproduced below.
MMPDS fatigue data for PH13-8Mo
For simplicity, the nominal curve will be used for damage calculation. In other words, statistical knockdowns, surface treatment, temperature, etc. will be ignored.
Using the equivalent stress equation provided in MMPDS, we can compute the damage caused by this fatigue cycle. For our purposes, the required number of cycles is one million.
R = Smin ⁄ Smax = 0
Seq = Smax ( 1 – R )0.64 = 151 ( 1 – 0 )0.64 = 151 ksi
log ( Nf ) = 16.32 – 5.75 log ( 151 – 92.6 ) = 6.16
Nf = 106.16 = 1,455,822 cycles
D = N⁄Nf = ( 1,000,000 ) ⁄ ( 1,455,882 ) = 0.687
Results: With Interference
Now let’s consider the results with interference applied. First let’s look at the stresses when the interference stress is applied with no external load.
Max principal stress of lug under interference load only
The max principal stress at the center of the hole face is 88 ksi. We can compare this to a hand calculation. The pressure applied by the interference can be found as follows:
p = ( Eδr ⁄ 2R )[ 1 – R2⁄r02 ] = ( 28000 * 0.001 ) ⁄ ( 0.375 ) [ 1 – ( 0.18752 ) ⁄ ( 0.5182 ) ] = 64.9 ksi
σ = p ( r02 + R2 ) ⁄ ( r02 – R2 ) = 64.9 ( 0.5182 + 0.18752 ) ⁄ ( 0.5182 + 0.18752 ) = 84.4 ksi
This is a difference of 4%, which is acceptable. Now we can look at the results for the step with load applied.
Max principal stress, interference and applied load
Notice that the peak stress is lower than in the previous analysis. The interference fit enforces contact along the full lug hole face which redistributes the load. This results in less ovalization of the hole and thus lower stresses.
Now we can use this data to compute the fatigue damage.
R = Smin ⁄ Smax = 88 ⁄ 147 = 0.6
Seq = Smax ( 1 – R )0.64 = 147 ( 1 – 0.6 )0.64 = 93.6 ksi
log ( Nf ) = 16.32 – 5.75 log ( 93.6 – 92.6 ) = 16.32
Nf = 1016.32 = infinite cycles
D = N⁄Nf = 0.000
The damage is considerably smaller than 0.687. By using an interference fit, a tensile load is induced in the lug. This added tensile load decreases the maximum stress slightly, but more importantly increases the minimum stress significantly. This increases the mean stress in fatigue cycling but greatly decreases the alternating stress. This in turn increases the reversal ratio, R (minimum stress to maximum stress). The combination of these effects results in a significant improvement in fatigue life for the component.
Fatigue can be extremely detrimental to structures and can lead to catastrophic failures, including fatalities. Fatigue depends on many factors. Some of the important ones are the applied stresses. By using interference fit in a joint, the reversal ratio can be increased, thus increasing the allowable fatigue cycles. Simcenter 3D was leveraged to do a simple analysis to show the beneficial effect of interference fit. Incorporating this into the model was quick and no convergence or modeling issues were encountered.
Written by Vitaliy Rezekulov
Vitaliy Rezekulov is a Senior Engineer with a background in structural analysis. He has worked on some interesting linear and nonlinear problems. Outside of work he enjoys spending time with his family and friends.