Tolerance Stack-Up Analysis: Two-Dimensional Stacks (...and the difference between 1D-, 2D-, and 3D-stacks)
In this step, the notion of 2D- and 3D-stacks are explored and explained.
The main point for a Robust Design Engineer is how to reduce the need for complex 3D stacks. The goal is to reinforce any design changes than can simplify calculations and documentations. The overarching design principle originates from Axiomatic Design by Nam Pyo Suh (principles originate from 1977) - Axiom 2- where the objective is to minimize as much information as possible.
Series: How to setup a tolerance stack.
Episode 5: Two-Dimensional Stacks (...and the difference between 1D-, 2D-, and 3D-stacks)
1D, 2D, and 3D
The difference between a 1D-, 2D-, and 3D-stack is summarized in the illustration.
1D: The width of the boxes and cradles are in scope.
2D: Imagine that the parts are not perfect along the y-axis. Any variation here should be included.
3D: Imagine that possible variation in the depth (z-axis) is included.
The Difference between 1D- and 2D-stack
In the example given. When changing the yellow box to a cylinder - suddenly the height of the purple and blue box starts to have an impact on the stack. Hence it becomes two-dimensional.
Dogbone Configuration Calculation
Many 2D stacks are a "dogbone" in disguise.
Clearances in two fits - in this example CLR_1 and CLR_2 - results in an angular displacement, θ.
Theta, θ, is given by:
θ = tan^(-1)( (CLR_1 + CLR_2) / dist) )
Dogbone with Gearing
The dogbone example is a matter of combining multiple fits; in this example CLR_1 and CLR_2, which are the fits between the front/back wheels and the frame.
This total clearance is multiplied by the ratio between the 'Point of Interest'-distance (x_2) and the distance between the dogbone features (x_1).
Hence, any clearance in the dogbone will experience gearing - resulting in an amplification in the 'Point of Interest'.
Example: Slotted Connections
The angular misalignment of a slotted connection is a matter of adding the clearances together (often of similar size) and divide it by the distance.
As with the dogbone configuration, this means the greater the distance the less sensitive your design with regards to angular contributions from fit clearances.
Example: Multiple Slotted Connections
Adding more parts to a tolerance stack is a matter of adding the angular contribution from the fit clearance at the given radius.
Best Practice: Increasing the Distance Between Rotational Locks
• Placing constraining features far apart = Robust Design: low angular sensitivity
• Placing constraining features with small distance = sensitive design: high angular sensitivity
Best Practice: Optimize to Simplify
Most designs can be simplified by making clear constraint features on all parts by use of Robust Design principles. In most cases this eliminates the need for 3D-stacks.
Optimization can be done with know-how from the RD8 Academy courses.
The RD8 Software can check if a design is optimized or if it can be simplified.
Make Tolerancing Easy - Talk to an Expert to get to know the RD8 Software
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