Although nuts and bolts are seemingly straightforward objects, some researchers are questioning how reliably joints hold structures together under high stresses. This trustworthiness gap is spawning global efforts to create computer models good enough to increase confidence in joint mechanics.
“It’s an extremely large, nebulous problem that we cannot solve using traditional methods,” says Matthew Brake, a principal research scientist at Sandia National Laboratories in New Mexico, where he’s organized an international research institute on the subject this summer.
In response, investigators are reevaluating well-established physics they’ve since found inadequate and circumventing the overcomplexity and uncertainty of standard equations used in their models.
“Just about everything built uses joints,” adds Brake, who is secretary of the American Society of Mechanical Engineers’ (ASME) research committee on the mechanics of jointed structures. “Many things are overdesigned to ensure that failures will never occur,” he notes, perhaps including “the chair you’re sitting on.”
“What will benefit from joints research are the high-consequence areas that would have severe and costly consequences for a failure. Those include cars, airplanes, satellites, civil engineering structures and weapons.”
One example: the 2012 grounding of all Airbus 380 passenger jets after inspectors found cracks in wing joints. It cost an estimated $630 million for repairs, plus about $1.22 billion in lost revenue.
In the joint arena “there seems to be one major failure a year,” Brake says. “Luckily, most of the failures have been non-lethal, but there are a few notable exceptions.”
One of those occurred in 2009, when two turbines at a Russian hydroelectric station self-destructed, triggering a chain of events that killed 75 people and brought on widespread power failures. The cause was diagnosed as fatigue damage from turbine vibrations. Repairs took two years and cost $1.3 billion, not including the bill to clean up 40 tons of leaked oil.
Investigators at Sandia, which shares research oversight of the nation’s nuclear stockpile, have focused on an even more critical issue: the reliability of joints holding together missiles and shielding nuclear weapons. Such complex joint assemblies can be modeled for assurance, but under international rules nuclear weapons cannot be physically flight-tested. The challenge: to develop realistic simulations of how these large systems respond over a span of several minutes of operation while accounting for the effects of phenomena happening at the atomic scale over nanoseconds.
Joints modeling: A worldwide movement
Matthew Brake, a principal research scientist at Sandia National Laboratories, New Mexico, estimates that several thousand researchers worldwide are striving to improve how mechanical joints are modeled on computers.
Many work in laboratories led by 80 active members of the American Society of Mechanical Engineers’ Research Committee on the Mechanics of Jointed Structures, which Brake serves as secretary. These investigators collaborate at institutions across the world, including in the United States, Canada, the United Kingdom, Germany, Italy, France, Ireland, Belgium, Turkey, Japan, and Brazil.
They also meet at workshops and conferences to develop research initiatives and share ideas and findings. And they attend special functions such as the Nonlinear Mechanics and Dynamics Research Institute hosted at Sandia this summer. Sandia also has published a “joints handbook” as a guide to the engineering community.
In Brake’s opinion, the most important contributors in the last decade have included Daniel Segalman, who recently retired from Sandia and now is at the University of Wisconsin-Madison; Larry Bergman at the University of Illinois at Urbana-Champagne; and David Ewins at Imperial College London. Ewins, Segalman and Bergman were all instrumental in starting international joints workshops.
Other principals would include Marc Mignolet at Arizona State University; Lothar Gaul at the University of Stuttgart; David Hills and David Nowell at Oxford University; Norbert Hoffman at the University of Hamburg and Imperial College London; and Muzio Gola at the University of Torino. Some of the next generation’s research leaders would include Sandia’s Michael Starr, Wisconsin’s Matt Allen, and Dan Brown, who has been leading the research efforts at the Atomic Weapons Establishment, Sandia’s British equivalent.
Some of the international collaborators also work for other government research laboratories and for Rolls Royce, General Electric and Boeing.
Sandia research reports have shown that strongly vibrating joints can become gremlins trapped in automobile-sized cages as they try to dissipate tremendous energy by flexing, slipping, locking, knocking, deforming and even fracturing unpredictably over such minuscule times and distances.
Nuclear reentry uncertainties aside, a presentation Brake co-authored at a 2013 ASME conference noted that, in general, stiffness measurements of nominally identical bolted joint hardware can vary by as much as 25 percent, and energy dissipation measurements by up to 300 percent.
“There really is a large amount of variation in these systems,“ Brake says. “We may think we have a model for how joints behave, but this model may not have all the correct physics and thus we are neglecting effects without realizing them.”
One major shortcoming, Brake says, is the inability to accurately model friction. Another ASME presentation he coauthored in 2013 called it a ”grand challenge” for experimental and theoretical mechanics in the 21st century, even though friction has been studied since the 1600s.
The truth is that “the fundamental mechanisms behind the phenomenon of friction are poorly understood,” the presentation added. What happens when two surfaces slide against each other, heating up in the process, actually is an unclear combination of deformation, atomic bond breaking and the generation and damping of stress waves, the authors wrote.
Traditionally, researchers have attempted to model complex joint interactions with fine-mesh finite element analysis. That approximation technique uses differential equations to create three-dimensional, geometric grids divided into discrete parts interconnected at node points and spread throughout the domain being modeled. “You can think of it as taking a car and breaking it up into a whole bunch of Lego blocks,” Brake says.
But there’s a catch. For maximum accuracy, each mathematical block must be extremely small. That data density means joint systems modelers must solve an overwhelming tens-of-millions of equations for each simulation time step. Even short simulations might require millions of time steps producing trillions of equations.
So researchers are exploring Reduced Order Modeling (ROM) in a quest to “find mathematical equivalents that faithfully represents aspects important for analysis while reducing the number of equations that must be solved,” Brake says.
For instance, researchers have found that vibration frequencies above hundreds of kilohertz are too rapidly damped out of structures for proper experimental validation. Eliminating such high vibrations, which can’t be properly accounted for anyway, reduces the number of modeling equations from many millions to tens of thousands per time step, Brake says.
Another ROM tactic called “frequency-based substructuring” evaluates an entire jointed system based on how its segments vibrate instead of how each block is described mathematically. That can reduce by about three orders of magnitude the computational time needed to model jointed structures with interfaces subject to friction, a paper Brake co-wrote says.
Investigators also are trying to broaden ROMs to accommodate nonlinearities – aspects of joint behavior that are difficult or impossible to describe mathematically. Another of Brake’s 21st–century grand challenges is modeling unavoidable uncertainty in joint behavior. He thinks that will require stepping into the realm of chance and probability with tools like Monte Carlo equations.
Why the focus on modeling? To reduce the need for costly experiments, Brake says. “Building prototypes is even more expensive and time consuming than building models. If a test fails and you need to redesign something, it’s a year and a half until you can test the next iteration. By developing a predictive and efficient analysis tool, we can circumvent this lengthy process.
“Our goal is to eventually develop a model that doesn’t necessitate the biggest supercomputer for simulating these systems.”