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Tolerance Analysis of Assemblies Using Kinematically-Derived Sensitivities

Paul Faerber, Motorola Corp
Presented by Jeff Dabling, Brigham Young University 
Presented June 15, 2000 at the ADCATS 2000 Conference

By applying an analogy between variation and kinematics, tolerance analysis can be performed on mechanisms and static assemblies using commercially available kinematics software.

To estimate tolerance accumulation in a static assembly requires the calculation of the tolerance sensitivity of critical assembly features to each source of dimensional variation in the assembly. A Root-Sum-Squares expression may then be formulated to predict the variance and percent rejects to expect in production.

An analogy between tolerance analysis and velocity analysis is described which enables the calculation of the sensitivities in closed form using a kinematic model and classical kinematic analysis. The Jacobian matrix of the kinematic analysis will be identical to the tolerance sensitivity matrix if the kinematic model is modified to include dimensional variation and if the kinematic variables are defined correctly.

To analyze accumulation in a mechanism, rather than a static assembly, requires that this procedure be repeated in multiple positions, since the sensitivities change with the position geometry. Commercial kinematics software is ideally suited for the task of calculating multiple positions of a mechanism, but it does not allow for dimensional variations.

A set of variational model elements is presented, which may be added to a kinematic model, resulting in an “equivalent variational mechanism” (EVM), which includes dimensional variations as kinematic inputs. Demonstration of this method using the commercially available software ADAMS is presented. 

Bio  (Paul Faerber)  BS, MS ME BYU 1999
Mechanical Design engineer at Motorola, Energy Systems Group.  Currently involved in designing the mechanical components of desk top chargers for Motorola cellular phones.

 

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