Tolerance Stack Up Analysis of a Bicycle Frame Welding Fixture

Figure 1. Benchmark Pro and Benchmark 1.1 bike frame welding fixtures.

The Benchmark 1.1 and Benchmark Pro (Figure 1) are prosumer and professional grade bike frame building fixtures, featuring exceptional build quality with precision CNC machined parts and easy to adjust gantries. One of the most critical geometries of each fixture is the planarity of the five mounting points between the fixture and the frame tubes. The five mounting points on the bike frame are the upper and lower head tube, the top of the seat tube, the bottom bracket, and the rear axle. The bottom bracket mounting point can be adjusted laterally as to maintain planarity with the other four mounting points so it is not considered in this analysis. To better understand the possible error in planarity of each of the mounting points, we analyzed the geometric accuracy of the center plane by performing a two-dimensional tolerance stack-up analysis. The accuracy of the center plane is different from the accuracy of the linear scales. The scales on the head tube, seat tube, and rear axle gantries are pre-calibrated with little uncertainty. The exact distance from the back of the fixture to the center plane of the frame  can vary as each component in the fixture has a manufacturing tolerance. This creates a tolerance chain that stacks at each part interface. 

There are two possible methods for calculating the tolerance stack-up: a worst-case method, and a statistical method. The worst-case analysis adds all maximum values of the associated components in the tolerance chain. While this method provides an accurate tolerance range for the center plane, it is highly unlikely that each component will be at the maximum of its specified tolerance range. The statistical approach uses a sum-of-squares of the tolerances for each component in the tolerance chain, resulting in a narrower range while maintaining very high confidence. We measured the thickness variations of all components that are not produced in-house to create more accurate tolerance ranges than provided from the manufacturer. The tolerance bands were calculated via the student’s t-distribution two-sided 98% confidence interval, and propagated through to the sum-of-squares calculation, resulting in a final bilateral tolerance of ±0.043 in (±1.092 mm) for the Benchmark 1.1 and ±0.025 in (±0.635 mm) for the Benchmark Pro. These values represent the maximum possible variation from the center plane at any of the four fixed mounting points as can be seen in Figures 2 and 3.

Figure 2. Center plane tolerance shown at head tube on Benchmark 1.1

Figure 3. Benchmark 1.1 center plane showing  possible out-of-plane shift.

The Benchmark 1.1 fixture features a large variety of components leading to more component interfaces, and therefore a longer tolerance chain when compared to the Pro. The washers used in the gantry assemblies have the greatest contribution to the stack-up analysis. The washers vary in their thickness: the tolerance range stated from the manufacturer is 0.054in – 0.074in , however, we measured a more realistic range of 0.061in – 0.065in. New washers are qualified to meet or exceed this tighter tolerance range. The variance combined with the layout of these washers can create a tilt along the gantries that shifts the position of the frame mounting points away from the center plane. The lengths of the head tube and seat tube gantries create long lever arms that cause this shift in center plane to be up to 75% of the total stack-up, depending on the mounting point. The head tube experiences the greatest potential tilt from uneven washers, while the rear axle experiences the least. The shift these washers may create was calculated with the mounting points set to the maximum travel on their gantries. For frames that are smaller than the maximum distances that the gantries support, the possible tilt from the washers will be less as the lever arms are shorter, and the possible variation (tolerance) from the center plane will be smaller than the stated value. This washer analysis along with the other measured tolerances that contribute to the stack-up explain the larger tolerance range we found for the Benchmark 1.1. 

​The Benchmark Pro uses Blanchard ground MIC6 aluminum plates throughout the fixture to reduce the variety of components and interfaces and to shorten the tolerance chain. The MIC6 plates are held to a tight tolerance range allowing for the assembly of an accurate fixture. Like the Benchmark 1.1, the components that allow for the linear motion of the gantries have the largest contribution to the tolerance stack-up. However, the gantries on the Benchmark Pro are less complicated and use high precision bearings and rails to achieve even greater accuracy of the center plane when compared to the 1.1. To account for possible manufacturing imperfections, the height of the cutouts for the rails and the depth of the pockets for the bearing standoffs are measured and shimmed to the exact dimensions. . Ring shims are added to the bearing standoff pockets to bring the assembled gantry plates into alignment and parallel with the plate behind it. Any out-of-true or out of tolerance bearings are discarded as bad bearings can cause significant tilt along a gantry reducing the accuracy of the center plane. Tightly controlling the assembly process combined with high precision manufacturing of components allows for a total planarity tolerance of ±0.025 in for the Benchmark Pro.