Analysis methods for machining fixtures with multiple point contacts

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Fixtures, Clamping force, Tolerance analysis, Finite element analysis, Stability analysis, Geometric errors

Subject Categories

Engineering | Mechanical Engineering


Workpiece geometric error, locator geometric error, clamping force, and workpiece stability are important variables in fixture design. To ensure that workpiece tolerances are met and the amount of scrap that is generated is minimized, these variables must be considered. In this dissertation, the effects of workpiece geometric error, locator geometric error and clamping error on machined features are discussed. An experimental system was then set up to measure their combined effect on the machined features. Two workpieces were used in this study. The first was a rectangular plate with a machined slot and hole. The second was a simplified workpiece similar to a real part used in an explosive device manufactured in a medium sized machine tool company was used.

Using a coordinate measuring machine, measurements were made on features on the two workpieces, a planar surface and a hole. The planar surfaces showed out-of-tolerance values for both workpieces. The holes were however within tolerance for both workpieces. This information can be used to make a decision on whether to redesign the fixture, to change the locating scheme, revise the tolerance specification or the process plan.

Two methods were developed to compute the minimum clamping force needed to maintain positive normal contact with the locators during a machining operation. The first is a relatively simple optimization problem (linear programming problem) based on a rigid body analysis of the workpiece. This problem is solved using the MATLAB optimization toolbox. The second is a nonlinear finite element model of the workpiece. This model is more accurate, but is time consuming and requires use of expensive finite element analysis software (ANSYS). The optimization model and finite element model yielded approximately the same values for the minimum clamping force needed to maintain positive normal contact with the locators during the machining operation. As expected, the finite element model gave a smaller value for the minimum clamping force. Since most machine shops do not have access to finite element software, these studies showed that the rigid body analysis can be used to estimate the minimum clamping force needed.

A linear finite element analysis procedure was used to simulate the trial and error procedure used in the machine shops to determine suitable positions for the locators and clamps for 3-2-1 fixtures. This analytical procedure enables a fixture designer to analytically determine suitable positions for the locators/clamps in 3-2-1 fixtures. It eliminates the necessity of using costly and time consuming trial and error process currently used in the shops.

Finally, two considerations for selecting a fixture based on workpiece stability were developed. In the first, the minimum eigenvalues of the fixture stiffness matrices, for the fixtures being considered, are computed. The minimum eigenvalues represent the minimum displacements at the contact points (locators and clamps). The fixture having the smallest value for the minimum eigenvalue is the best choice based on this consideration.

Since the eigenvalues are not dependant on the cutting forces, an additional consideration must also be used when selecting a fixture. The displacement of the workpiece is a function of the cutting force and the compliance of the fixture. To select from the available fixtures, a displacement measure, the largest displacement of the workpiece due to the cutting force, is computed for each fixture. Since workpiece displacements are to be as small as possible, the fixture that gives the minimum of the largest displacement of each of the fixtures is the best fixture based on this consideration. The choice of the fixture to use is often a compromise between the two considerations.


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