ApplyingⓂin Assembly

In earlier articles, we explained howⓂnotation expands the tolerance zone of a measured feature and how a reference‑zone M‑Ring allows the datum to float within a fixture.

This article demonstrates how to solve multi‑part assembly problems when both the datum and measured features carry M‑Ring specifications.

Assembly Process (Fig. 1):

1. Align two locating pins on the upper (blue) shell with two holes on the lower (purple) shell. 

2. Connect corresponding bolt holes on both shells with bolts.
   

Objective:
Determine if bolts can be inserted smoothly after alignment under given tolerances, and predict the assembly success rate.

Conventional dimensional‑chain methods cannot handle this multi‑axis clearance problem. Here, DTAS tolerance‑analysis software with Monte Carlo simulation provides accurate, actionable results.

DTAS Multi‑Axis Through‑Hole Analysis

DTAS simulates multi‑hole assembly by virtually manufacturing parts and modeling pin float based on specified tolerances.

Process

1.Upper Shell Datum Simulation
Generate virtual upper‑shell parts according to drawing tolerances.

2.Lower Shell Datum Simulation
Generate virtual lower‑shell parts according to drawing tolerances.

3.Floating Simulation & Pass‑Rate Calculation
Apply the DTAS Floating Algorithm to simulate alignment between shells and compute both individual‑bolt and overall assembly success rates.

Upper Shell Simulation Manufacturing

Animation 2 Explained

•Locating Pins (Large Circles): The red inner circles represent the M‑Ring‑expanded tolerance zones. The pins can float within these zones, while the 160 mm center‑to‑center distance remains fixed. 

•Mounting Holes (Small Circles): Red inner circles similarly indicate compensated tolerance zones. Horizontal and vertical center distances are fixed at 100 mm and 110 mm respectively, with hole positions shifting in response to pin alignment. 

•Movement Relationship: The positions of the mounting holes dynamically adjust based on the floating of the locating pins, visually demonstrating how  Ⓜ  compensation enables flexible yet controlled assembly under tolerance variation.

Lower Housing Simulation Manufacturing

Animation 3 Explained

•Locating Holes (Large Circles):
The red inner circles represent the M‑Ring‑expanded tolerance zones, allowing positional shifts while maintaining a fixed 160 mm center distance. 

•Mounting Holes (Small Circles):
Red inner circles similarly show compensated tolerance zones, with horizontal and vertical center distances fixed at 100 mm and 110 mm respectively. Their positions shift in response to changes in the locating holes. 

•Dynamic Alignment:
The positions of the mounting holes automatically adjust based on the floating locating holes, demonstrating how   Ⓜ  enables controlled assembly flexibility under tolerance variations.

Upper and Lower Housing Assembly Simulation

Animation 4 Explained

•Lower Shell: Red circles indicate locating holes and bolt holes. 

•Upper Shell: Blue circles show locating pins and corresponding bolt holes.

The animation visualizes how pin‑hole misalignment influences bolt‑hole alignment, affecting overall assembly success.

Result (Fig. 5)
Assembly success probability: 56.82% under current tolerances.

Summary
This practical case demonstrates M‑Ring application in tolerance analysis using DTAS. The software evaluates all M‑Ring notations, calculates assembly success rate and single‑hole pass rate, and simulates production and assembly.

•Use the overall success rate to validate tolerance design. 

•If needed, the single‑hole pass rate pinpoints failure causes for targeted improvement.