Push down with one foot, then the other, again and again, until your leg
muscles scream and your lungs gasp for air.
Far from some weird torture, that's a regular ritual for thousands of Americans who use stairclimbers in fitness clubs and at home to trim down and firm up. Medical and health professionals alike agree it's a great form of exercise for anyone who isn't lucky enough to have a mountain in their back yard and the time to climb.
Engineer Pete Pasero of Precor, Bothell, WA, designs some of the most popular and sophisticated stairclimbers on the market. Fit and athletic himself, he is more concerned with cutting down the weight of the machines than shedding pounds himself.
In a special Design News Design Challenge, engineers from Parametric Technology Corp. showed him how to use software to optimize the design of Precor's Model 730E Stairclimber.
Positioned at the high end of the market, the 730E and its successor, the 731E, are popular products. But, off-shore competition is forcing Precor, as well as other companies, to cut manufacturing costs while maintaining quality. Among Precor's strategies: Cut the weight of the equipment and material costs. That's the strategy this Design Challenge targeted.
The results: An approximate 20% reduction in weight--including 2 Ĺ lbs in the handles, 3 lbs in the steps, and 5.7 lbs in the base.
With PTC's finite element analysis software Mechanica Motion, PTC engineers optimized the geometry of the linkage to reduce loads on each part. The optimization adjusted the linkage by:
Shortening the link length by 0.04 inch.
The first step. The project began with a brainstorming session at Precor's Brothell headquarters. Pasero, Precor Industrial Designer Jim Birrell, and Precor marketing representative Ellie Ballew explained the design of the existing stairclimber to PTC's Chauncy Wenner and Dave Lorengo, and Design News.
Precor engineers designed the original 730 on a board without software. Typically, they built prototypes and Precor employees would sign up to use them and rate them for wear and other stress factors. The first step in the Design Challenge was to come up with a computerized baseline design engineers could then optimize. The task fell to Wenner, who used the solid modeling capabilities of Pro/ENGINEER. The goal was to capture important dimensions such as the length of the arms and the attachment for the shocks. They determined the behavior of the climber, and reflect engineering intent. Using drawings and his own hand measurements of a 730E, Wenner assembled a geometric model in the software.
Lorengo then took over, bringing the model into Mechanica and adding joints--motion constraints between parts--to make it a mechanism model. He needed the joints to define how one part moves in respect to another. But he also needed to allow for the weight of a user. Precor typically designs its machines for a maximum user weight of 250 lbs. To get an extra safety margin, he designed the model for a 300-lb person exerting a 50-lb load on the handles.
Internal to the system, Lorengo modeled shock absorbers--the body of the climber and extension rods. He also entered data from the shock absorber manufacturer on velocity vs. resistance force. Using his own engineering judgment, he added some friction to the model at the rocker and shock. The friction accounts for stiction that the shock absorber exhibits. Next step: Sequence the loads.
Extracting data. Mechanica has a feature called "Measures," which is similar to a strip-chart recorder. "Measures" is a way to extract data, such as the velocity of a joint or the amount of force created by friction or damping loads. Lorengo wanted to detect when the step board reached bottom because at that point he would turn off the force representing weight and turn it on for the other step board. He used "Measures" to track the distance between the bottom of the stepboard and the base frame. Then, he took the load (the weight of the imaginary 300-lb user) and told the software it was only active when the measure was in a certain range.
"In effect," he says, "we're turning the weight of the user on and off depending on the position of the step board."
The result: a baseline model of the 730E. Now, the engineers could begin redesigning the stairclimber.
Joint effort. Lorengo began a series of sensitivity studies in Mechanica of attachment points of the teeter totter to the column, the length of the link between the teeter totter and stepboard, moving the attachment point between the link and the stepboard, and changing the distance between steps.
Such sensitivity studies, critical to thorough engineering optimization, are among the most important features in Mechanica. The software re-runs the simulation for multiple values of the design, changing the geometry each time so the engineering team could see the effects of the changes. Lorengo plotted each design variable vs reaction forces at the teeter totter attachment to the column. He found that by making small changes to each design variable he could get even better results. The question then became: What is the best combination to get the best results? The answer would come from optimization runs in the software.
Within Mechanica, there is one data form that asks for goals, design limits, and variables. Lorengo entered his goal, which was to minimize reaction forces where the teeter totter attaches to the vertical column. His design limits were simply that he couldn't change the travel of the step boards or the maximum height of the step boards by more than one inch. That's a negligible change for the user, but cuts in half the reaction force on where the teeter totter attaches to the column. The optimizer within Mechanica showed him the best balance. Now, he could turn his attention to each piece. Within Mechanica Structure, he optimized the handlebar, baseboard, and step frame.
Reducing stress. Mechanica Structure uses adaptive polynomial technology to compute stresses, and allows the use of Pro/ENGINEER dimensions as design variables for sensitivity studies and for optimizing Pro/ENGINEER geometry. Using Structure, Lorengo looked at the stresses in the baseline design and tried to adjust each part's geometry to get the lightest parts possible. He applied the loads from Mechanica Motion to the original Pro/ENGINEER geometry, meshed it, and solved the equations in Structure, asking the software for a 15% convergence on the stress. Generally, Mechanica users decide how good an answer they want, and Lorengo believed that 15% convergence would provide the answers he needed.
With the baseline set of stress and displacement results, he tried to decide which changes would cut the stress, or cut weight without increasing stress. He ran sensitivity studies in order to answer those questions.
His design variable was to let the beam get narrower and thinner. The dimensions in Pro/ENGINEER had captured the design intent, so he chose a dimension defining the cross section of the tube from Pro/ENGINEER and had Mechanica vary it. Mechanica sent the results back to Pro/ENGINEER, which re-generated the part and brought it back to Mechanica for further solutions. Lorengo then plotted the effect of changing the variables to see which was most beneficial. "From the designer's perspective, you can see the payback for all changes," he says.
The result was a redesign with lower weight, minimum downstream costs, and minimal effect on manufacturing since no new tooling is required.
Says Precor's Pasero: "We will definitely pay less for shipping and materials. Also, thanks to Pro/ENGINEER and Mechanica, we could bring the optimization to management and illustrate how software helps optimize design."