Fundamentally Fasteners — The One Where Loads Meet Bolts
General approaches taken to design a bolted joint and challenges faced in the process and possible solutions to overcome those challenges has been a motivation for me to write this blog. The topic is vast and I plan to put a series of blogs on “Fundamentally Fasteners” — this being the first one. Well, the above image flaunts the bold and the stark orange frame made in aluminum alloy behind transparent body panels showing a masterpiece of engineered product- Ather 450 Apex. No shabby joints — bolts holding frames together — you can see three of them there — head and shoulders above!!!
Context
All of us have grown seeing and using bolts — nuts and screws for fastening something or other, be it fixing a toy, a power supply electric board, a screw for us to hang a painting on the wall or a clock. If we look around, the usage of fasteners is huge. It wouldn’t be wrong to say that bolts and nuts are the next most important findings of the human being in the mechanical engineering stream — the first one being the wheel.
Bolt is such a simple looking stuff, just rotate it with some effort through a spanner and it results in a load worth thousands of newtons which holds or clamps things together. If one has to select a bolt and tightening torque for it — the general approach is even simpler — pick a size of bolt from the experience or check what has worked in the similar applications elsewhere and refer to a so called “standard table” which will tell how much torque to be applied for a given size of the fastener. Of course such standard tables used will be coming through years of experience of using fasteners for specific applications and failing multiple times and replacing them with higher grades, size and different tightening torque and then putting all such observations in the form of a standard table. It may have already started sounding — “yeah that’s what we do and what is wrong in it ?” If that’s the case, you have bumped into the right article. This approach may work for an application of putting a photo frame on a wall through a screw but not for anything even slightly more complex like fasteners used in automotive applications e.g. integrating chassis or frame parts or mounting an assembly or a component on chassis. Rather than a blind approach of selecting a fastener or a hit and trial method, there are way better approaches to design a bolted joint which is the motivation behind writing this article. There are challenges which also come around in such an approach and what can be the possible ways for better prediction and design of bolted joints — let’s take a look at that with a case study at the end.
Take an example of automotive applications- the two widely used methods of joining or integrating members are weld and fasteners. We know that more than 90% failures in welded structures happen near welds. Imagine replacing such welded joints with fasteners. If we use bolts instead of welds in those joints, naturally the joint in itself is subjected to similar loads as welds are subjected to, which can result in multiple failures of the bolted joints, which has to be taken care through our design approach. Before I go into the approach, what are these possible failure modes that we just talked about — that’s very important.
- Static failure of the bolt — Keep tightening the bolt, don’t stop and it will break all of a sudden at one point of time while we keep torquing it. That is static failure. If we can design a bolt which fails statically first before below mentioned failures happen, that is better. The reason being that rather than having an unpredictable failure in the field due to fatigue or loosening of the bolt, better we have it fail while assembling itself so that this doesn’t go out to see external load and end up having a failure in its service life.
- Fatigue failure of the bolt shank — In the above failure, there was no external load applied on a bolt while in real life application of an automotive there are road undulations responsible for major external loads acting on the joints as well which may lead to fatigue failure of bolt shank.
- Thread Stripping — due to preload or due to fatigue load.
- Clamp loosening or loosening of the bolted joint — this is something which holds great importance in the design of a bolted joint. A joint once loosened under external loads can also result in subsequent bolt shearing due to fatigue. While we may still think that this is truly fatigue failure due to high alternating loads, the fact in many cases remains that the loss of clamping force has resulted subsequently into higher forces on the bolt resulting in a broken bolt. The root cause in such cases is to prevent loosening of the bolt rather than undersized bolt of the bolt grade used per se.
- Plastic deformation of the stress bearing area under head, nut, washers and clamped materials.
- Other failures like cold welding etc.
Challenges
Well there has been enough research done in this field and all that hard work has been beautifully compiled in the form of guidelines or standards to design a bolted joint. One such standard is VDI 2230 , a German standard which can help us design the joint for the above mentioned failure modes.
While calculation steps to prevent static failures are simpler and can be taken care of very well by accounting variation in Preload (clamping load) wrt. applied torque, challenges come with external loads acting in transverse and axial direction of the bolts. These varying external loads can lead to fatigue failure of the bolt, the loss of clamping load or preload hence loosening of the entire joint and stripping of the threads or shank fatigue due to subsequent high fatigue loads. Loosening prevention and fatigue can also be accounted for through some design calculations as mentioned in such standards.
If there is a standard available then what is the challenge I am talking about. Same happened with me as well. All these standards have methodologies of predicting the failures for given load input. So if we know the load and moment inputs to the joints our job is done but do we know these load inputs? Now you’d be thinking- that’s not an easy job. The thought process was if we can generate external load history or a random load on a joint then we can use techniques of cycle counting like rainflow etc. and can work on the fatigue part of it. Similarly if we know the maximum loads and moments acting on the bolted joint from the load history then we can take care of the slipping failure as well. So this force and moment time history is very important. Next task is how do we get the forces and moments on a bolted joint. This particular challenge of generating force and moment on a joint is the sole focus of this first blog in this series of “Fundamentally Fasteners”. Next blog will be on analyzing these forces and moments and using the same for design calculations.
We know the complications in measuring the load history that too on a two wheeler. In a four wheeler one can at least put wheel force transducers and measure wheel axle moments and forces but unfortunately we don’t have that liberty in two wheeler applications because we don’t get benefit of high sprung mass versus considerably low unsprung mass (wheel assembly mass) benefit in two wheeler applications as we have in four wheeler applications. WFTs are quite heavy and putting these transducers change the unsprung mass of the vehicle substantially changing the dynamic characteristics of the vehicle and hence end up in making it a different vehicle altogether and not the one on which we intended to take measurement.
I work in both the structural design and simulations & testing world — that helped me realize the need of the structural design world to design a bolted joint for which FEA models can be used. Given these measurements constraints and complexities when it comes to two wheeler applications, it makes more sense to use finite element methods and multibody simulation methods at system and vehicle level to get these loads and moments inputs.
In this blog I am going to take an example of a system level component which can be assumed to be mounted on the chassis of a vehicle through bolted joints. There are standard random signal excitations that are adopted in industry to evaluate the vibration fatigue at system level or we can also generate one for our systems by acquiring the road load data and squeezing the cycle to accelerate the fatigue behavior by maintaining the fatigue damage content across frequency range of interest and maintaining extreme or shock responses in accelerated fatigue random input to close to what system would see in its service life. Such accelerated PSDs are available with popularly known units g2/Hz against frequency band. This is a good case to start with as bolt failures are one of the most common failures observed in such accelerated vibration fatigue.
Now coming to our problem statement of getting input loads and moments at the bolted joints. Aforementioned accelerated PSDs can be converted to transient acceleration history or simply put an acceleration on the vibration shaker base and record the acceleration versus time for a couple of minutes. Fundamentally, if we do PSD of this signal we’ll get the same PSD that has been given as input to the shaker to control the input excitation. We can very well use this random signal in the form of acceleration vs time input or it can be further converted to displacement vs time input through some careful postprocessing of the signal and then make a transient response model (dynamics accounted for in this model — not just statics) using finite element methods and this model can produce the bolt loads and moments. Transient response models are necessary here for two reasons, the first being, we need a time history of loads on joints and the second being to account for the dynamics characteristics in the response which is greatly impacted by the resonance- of the system subjected to the test , its damping properties which is frequency dependent as well.
A Case Study
Image given below depicts one such case where a part(tubular structure) with enough overhang is mounted on a rigid base using two bolts. The mounting orientations are important here- axis of Bolt 1 is aligned in the vertical direction (along gravity) to the input load excitations while the other bolt is in the transverse direction to the vertical i.e. Bolt 2 axis being in the lateral direction. The vertical and lateral orientation of the system mentioned above can be assumed to be similar to that of a two wheeler. In a two wheeler, maximum forces will be witnessed in vertical direction i.e. along Bolt1 axis in this case and transverse direction of Bolt 2. Such transverse orientation of the bolts are prone to loosening and subsequent bolt failures as mentioned earlier.
We ran a transient analysis of this system with following settings:
Total time of run : 1 s
Time step : 0.00025 s (corresponds to 4000 Hz)
Modal Frequencies accounted : 0 to 500 Hz
Damping : 3% structural damping ( to start with)
Both bolts in the case study are M6 and a bolt pretension corresponding to 8 N-m is applied.
Gravity is turned on in this case.
Transient input in time domain given to the base is shown below:
PSD of the above transient input:
PSD of input acceleration shows that input signal strength after 200 Hz is negligible. Keeping this in mind modal results of up to 500 Hz were accounted for to get transient responses.
Bolt contact modeling details are given below:
Linear contact (Bonded) modeling used for the Bolt thread to the fixture.
Other contact pairs viz “Bolt head to the structural component under test contact” and “Component to Fixture “ was modeled using nonlinear contact (frictional).
Before we trust on forces and moments on the bolts, we need to validate the FEA model. For this we can monitor acceleration at any suitable location.
The top of the tube as indicated here with a red square is the response location in this case for the simple reason that it will be an antinode for the critical resonance deformation shapes( mode shapes ) in this case.
Acceleration transient response (g) for the aforementioned accelerometer:
Let’s try overlaying this acceleration response from FEA with Test results:
Clearly FEA is underpredicting as evident from the above graph. A closer look in the section marked in cyan is further shown below to get better visibility on error levels from FEA against Test data:
Fundamentally transient response error has to be related to dynamics characteristics of the system hence transfer functions of the response to input excitation reveals the differences between the FEA and Test. Acceleration response at the same location for 1g sinusoidal sweep as input excitation was captured and compared against FEA harmonic response analysis results. Comparison of the FEA and Test data is shown below.
It is evident from above graph that the critical resonance frequencies are matching very well between FEA and Test but amplitudes are different. The biggest difference observed around 130 Hz will contribute maximum to the error noticed in the correlation earlier. This particular frequency is the in-plane resonance that is shown in the section above.
It is difficult to predict damping factors upfront and use that in any analysis, and typically we go with 2% to 3% of assumed damping values for FEA. Since test data is available, we can easily compute damping at resonating frequencies using half power bandwidth method. That revealed that damping values at those frequencies were much lesser than initially used in the FEA model. Modifying the damping values as observed in the test help bridge the gap in the sinusoidal response acceleration as can be seen in the following graph. (For such a tricky situation, initially in absence of any data, it is better to have a range of damping factor that is typically observed in these structures as function of frequency and have an engineering understanding of forces for these damping ranges for bolted joint design calculations.)
As a result the acceleration response as seen in time domain also improves substantially and can be seen in the graph below.
With a very good correlation of transient acceleration response at the peak acceleration location on the component, as shown above in the graph, we can now trust the bolt forces and moments generated through the FEA on the two bolts. Well, that was the focus area of this part of the blog series.
We’ll refer to the coordinate system shown in image above for directional forces and moments on bolts. Axial forces on bolts are along the Z axis while shear forces (transverse) will be in the XY plane of the coordinate system i.e. resultant of X & Y direction forces.
Similarly, moment about Z axis will result in torsion deformation of bolt and moments about X and Y axes will cause a bending deformation of bolt.
A snippet of transient forces along X direction is shown below.
Summary
We discussed failure modes of bolted joints and the lack of methods to generate forces and moments as a challenge for any joint calculation. We took a case of vibration fatigue test cases on a dummy component, we modeled and correlated an FEA model for transient analysis. We also went deep to identify issues in models and correct the parameters for better correlation with testing results. This in turn helped generate forces and moments. In the upcoming blog, we’ll see how to use these transient data for bolt calculations to avoid certain bolt failure modes.
