Engineering a safer bounce

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Springfree redesigns the backyard trampoline with optimization solutions from SIMULIA

Springfree redesigns the backyard trampoline with optimization solutions from SIMULIA.

Springfree redesigns the backyard trampoline with optimization solutions from SIMULIA.

Ask a kid if they like trampolines and their eyes are sure to light up with joy. But ask some parents and you may get an entirely different response. This is because some 90,000 children are still injured on traditional trampolines every year in the United States alone.

How can the fun go wrong? In a number of ways, thanks to the unavoidable laws of physics. The elasticity that provides a traditional trampoline’s exciting bounce comes from metal springs that connect the mat to the frame. The springs store potential energy when the mat is compressed by the person’s weight, releasing that energy back to thrust the fabric upwards and the bouncer high into the air. A jumper who lands off-center may be projected sideways and can miss the mat, hit the rim or springs, or fall through the gap between them. Even if there’s safety netting, it’s often connected to hard metal support bars or is strung too loose to control a hurtling body. Both netting and mat stitching may be weakened by exposure to sunlight.

A safer trampoline

Dr. Keith Alexander, an associate professor of engineering at Canterbury University, New Zealand, felt there had to be a safer way to enjoy the trampoline. “I always believed that, as an engineer, I should be doing things that benefit people,” he says. When his wife nixed his plans to buy a conventional trampoline for his daughter Katie out of safety concerns, he decided to build a better one.

Analyzing “reams of data,” Dr Alexander determined that there were three main impact zones in the classic trampoline design (which dates to the 1930s) that needed to be arranged so the user wouldn’t impact them: the springs connecting the bounce mat to the frame, the metal frame itself and, of course, the ground.

Many prototypes later (starting from 1989) Dr Alexander arrived at his final, innovative solution: move the frame below the jumping surface, create a soft edge to the mat, and surround the whole thing with tensioned, ultraviolet-resistant netting that would bounce users back towards the center if they went off-kilter. The result was the Springfree™ Trampoline, first produced in 2003 and currently selling at a rate of some 40,000 per year around the globe. The Springfree has proven itself significantly safer than traditional trampolines. Several studies demonstrate a reduction in equipment-related injuries of between 30 percent and 80 percent.

High-tech cleats

Yet it’s what you don’t see in the Springfree that’s most unique: the high-tech cleats under the mat’s edge—60 or more per trampoline, depending on the model. Made from fiberglass-reinforced polypropylene and shaped like a wide letter ‘T’, these have a rounded, midline socket into which the balled top of each fiberglass support rod fits. The lower ends of the rods connect to the metal base of the trampoline.

The cleat, which is inserted into a reinforced pocket in the mat, harnesses the downward tension of each jump, ensuring that the ball at the top of the rod stays wedged into the socket as it moves up and down.

Once the Springfree was commercialized, word about its benefits began to spread. Parent- and safety-association awards followed, sales bounced upwards and production swung into high gear. The company’s New Zealand-based injection molding supplier, Action Plastics, was kept busy manufacturing cleats at a rate that has now reached some 2.5 million units per year. As the molding tool used to manufacture the cleat drew near the end of its lifetime in 2013, “we had some pretty significant inducements to build a new tool and we realized it was a great time to look at optimizing and improving the cleat component,” says Hamish McIntyre, engineering manager at Springfree New Zealand Ltd. “Because the cleat was so complex in terms of loading and mechanical properties we decided we needed an engineering consultant to help us out. We located Matrix Applied Computing, through a Ministry of Science and Innovation expert search program, and selected them based on their advanced capabilities.”

Realistic simulation

Of particular interest to Mr McIntyre was Matrix’s familiarity with realistic simulation using Abaqus finite element analysis (FEA) software from SIMULIA, the Dassault Systèmes’ 3DEXPERIENCE application. “I had worked closely with FEA teams at Airbus in the U.K. and knew how powerful Abaqus was,” he says.

“The fact that Matrix used Abaqus was one of the things that drew me to them because I’d seen the software in action on advanced aircraft design.”

As Guido Quesada, CAE design engineer at Matrix, recalls, “We were already familiar with Springfree trampolines and knew it was a very technical product. Sometimes a potential customer calls with some funny toy or crazy idea that’s hard to take seriously. This was definitely not the case with Springfree. From the start, we knew we had a significant challenge with this cleat design project.”

There were two main drivers of the challenge, according to Mr McIntyre: “We wanted to improve the strength, the ultimate load capability, of the cleat. And we didn’t want to introduce significant additional cost into the component. The quantity we buy each year is expanding along with our sales growth. Just a couple cents less for materials per cleat ends up as a significant cost savings. We saw this as an opportunity to tweak the component and get the most out of it.”

Tweaking the cleat

And so the tweaking began, starting with some good old-fashioned field research. Both Matrix principal engineering analyst Don Campbell and Mr Quesada took informal walks around their neighborhoods, watching people jumping on Springfree trampolines in order to visualize what was happening to the cleats as the mats went up and down and the rods bent in tandem. Then it was back into the physical testing

lab, where a device was built to apply the load from a rod to the center of a cleat, supporting it at the sides like the socket would. SolidWorks (also from Dassault Systèmes) CAD models were made of the rod and cleat components set up in the testing apparatus. The CAD models were meshed with Abaqus FEA, and data captured through the physical tests served as input for the computer simulations that predicted how changes in cleat geometry would affect strength and durability.

“Right from the outset we worked closely with our moldmaker [Sean Dryer of Action Plastics] to ensure that what we came up with was manufacturable,” says Mr McIntyre. Matrix imported Moldflow software results into their Abaqus models to incorporate the effects of the orientation of the glass-fibers in the cleat. (The material is stronger in the direction that most fibers lie, so the fibers need to be aligned as much as possible with the most critical stresses.) Also important was to take into account the residual stress from the manufacturing process itself (mainly the result of the surface of the cleat part cooling faster than the core).

Solving manufacturing constraints

As subsequent design options were proposed and evaluated, “one of the most significant challenges was not what Springfree was asking of us but the manufacturing constraints we had on what changes we could make to the part,” says Mr Quesada. As Matrix focused on identifying the optimal geometry for the new cleat design, they considered a variety of analytical pathways before arriving at a workflow that would move them more quickly through the optimization process. Using Abaqus to help them understand the nonlinear interplay between structure, material, loading and stress, they were ultimately able to create simplified analogies which established an accurate relationship between geometric changes, stiffness and strength through fundamental deformation modes such as bending and twisting.

“Of course different sizes and abilities of trampoline users would produce different load levels,” says Mr Quesada. “SIMULIA’s solutions were particularly helpful in providing us with a nonlinear simulation framework so we could create a very realistic representation of the most important load conditions. Abaqus/CAE just made things better by providing an excellent graphical environment for all our needs, enabling edits and tweaks to the input files whenever necessary. This builds a lot of confidence when using the tool. It helped us come up with the most cost-efficient way to provide the best possible answer to our customer in terms of a good design.”

“Before we worked with Matrix to use realistic simulation it was very much a trial-and-error process based almost solely on geometry, manufacturability and physical prototyping, which involved a huge turnaround time,” says Mr McIntyre. “Compared to what we did before I would say we are now light years ahead of where we were.” The final cleat design the team arrived at uses slightly less material overall and has two ribs added on one side, to provide extra support where needed and to distribute stresses more evenly. It’s now appearing in new Springfree trampolines worldwide.

Optimising cleat configuration

After the redesign project was complete, Mr Quesada took a further look at the final cleat geometry using SIMULIA’s Abaqus Topology Optimization Modeling (ATOM) tool, which automatically finds the optimum configuration (weight as well as shape) of a component while confirming performance with FEA to ensure strength and durability targets are met.

“Our previous workflow, involving detailed CAD modeling, mold simulations, nonlinear simulation and simplified modal analysis was ultimately highly successful,” he says. “But when we applied ATOM to the same design, the process became much faster and effective with automatic exploration of the optimal geometry. I was very surprised to see that ATOM helped spot features I didn’t think of, including a third rib. It also saved us a lot of CAD work since the ATOM procedure uses the same reference geometry during each optimization round.”

He shared his new insights with Springfree; with the two-rib version already in production, a new, four-rib design, which enhances the automated optimization by putting in additional engineering and design judgment, is being considered for the next generation of trampolines.

A “next generation” is probably inevitable, given that Springfree inventor Alexander still has a few trampolines sitting in his backyard, “possibly waiting for grandchildren.” All three of his own kids are out of the house and his daughter Katie, for whom he designed the original, is now married.

Matrix Applied Computing CAE design engineer Guido Quesada shows how they identified the optimal geometry for the new cleat design

Above: Matrix Applied Computing CAE design engineer Guido Quesada shows how they identified the optimal geometry for the new cleat design.

Closeup of the innovative support structure of a Springfree trampoline shows how white rods connect via cleats to the upper, soft-edged jumping surface. Lower end of rods attach to the secure metal frame that sits on the ground.

Above: Closeup of the innovative support structure of a Springfree trampoline shows how white rods connect via cleats to the upper, soft-edged jumping surface. Lower end of rods attach to the secure metal frame that sits on the ground.

The evolution of the Springfree cleat, as photographed by inventor Keith Alexander.

Above: The evolution of the Springfree cleat, as photographed by inventor Keith Alexander. At far right is Dr Alexander’s early version of the newest cleat that he turned over to Matrix Applied Computing for design optimization with SIMULIA solutions.

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