Want More Precise Assembly? Use Fewer Constraints

Sept. 11, 2008
Too many constraints in a design can drive up assembly costs and diminish reliability

Exact part location and minimal clearances seem like the Holy Grail of precision mechanical systems. But insisting on the slimmest tolerances can make assembly and disassembly difficult. Assembly processes can fail because of tolerance stack-up, human error, or volumetric changes in mating parts. By thinking about assembly from the start of the design process, engineers can prevent failures and redesigns down the road.

Mechanical methods
The designer can choose from five assembly design methods: high accuracy, integrated manufacturing, adjustable, deformation, and constraint-driven design. (See box for illustrations.)

Design via the high-accuracy method means using high-precision parts and minimum clearances. Designers can get a precise final product this way. But there can be trouble with assembly and disassembly when there are slight variations in the production setting.

Higher temperatures can lead to thermal expansion, assembly lags allow corrosion to disrupt the process, and normal operations can produce debris that prevent a good fit. These problems could arise in any assembly, but the high accuracy method allows no leeway for them.

Designers can avoid some mating problems through use of the integrated manufacturing method. Here, certain manufacturing activities take place while two parts are held together. Match-drilling and other integrated processes secure an exact location and overcome tolerance problems.

However, integrated manufacturing results in the production of parts that are not interchangeable. Dedicated parts can hold back production efficiency and make it difficult to supply aftermarket spares. Integrated manufacturing design also fails to remove the sensitivity to manufacturing and operating environments.

Adjustable design methodology advocates adding adjustable mating entities between the parts being joined. The adjustable parts overcome tolerance problems and allow any two parts to be joined.

The adjusting device adds to part count and complexity, however, and the system is still subject to geometric changes caused by the environment.

The deformation design method is another option for overcoming tolerance problems. The basic idea is to give matching parts a degree of flexibility. Thin slots, living hinges, and deformable material sections are all ways to permit deformation in part mating.

The major disadvantage of this methodology is that the resulting location of the parts is unknown. And deformation may not be an option if it runs counter to the mechanical properties the assembly needs. Assemblies with deformable parts may also tolerate fewer assembly-disassembly cycles before the deformable parts fail.

The constraint-driven design (CDD) method focuses on minimizing the constraints between mating parts to reduce assembly and disassembly difficulties and ensure a reliable design. Jon Kriegel, senior development engineer at Eastman Kodak, called this idea “exact constraint design” in his 1995 Mechanical Engineering article of the same name. Gerhard Pahl and Wolfgang Beitz, suggested avoiding “double constraints” in their 1992 book Engineering Design: A Systematic Approach.

Location, location, location
Mechanical assembly locates one part in relation to another. Mathematically, a location array containing six elements, [θX, θY, θZ, X, Y, Z], links the two coordinate systems of mating parts. The first three elements represent the rotation needed to align the parts. The last three elements denote the linear motion needed to bring them together.

In CDD, each coordinate is either a constant or a statistically distributed value. The constant coordinates represent the assembly’s constraints (AC). Distributed values, marked with a line over the coordinate, are the design’s degrees of freedom (DOF). For example, a system with a location array of [θX, θY, θZ, X, Y, Z] has one DOF and five ACs.

The interfaces that join parts can be represented as mating pairs. There are several kinds of mating pairs such as plane-plane, cylinder-cylinder, and cylinder-slot.

Each can be represented as a kinematical pair having both DOFs and ACs which depend on their geometry. For example, a locating pin inserted in a hole is a cylinder-cylinder pair. The location array for this type of pair is [θX, θY, θZ, X, Y, Z], meaning it has two DOFs and four ACs.

CDD’s aim is to cut the system’s ACs to the minimum needed for error-free assembly. (See the sidebar for an illustrated example.) To do this, the designer must compare the constraints in the system as a whole with the sum of the constraints in all the mating pairs, the total pair constraints (TPC).

A TPC that is much higher than the system’s AC indicates assembly problems could be on the horizon. With the problem identified, the designer can delete mating pairs or change the pair type to cut out constraints. Altering a single interface may be enough to ease assembly and disassembly and cut sensitivity to thermal expansion, debris, and corrosion, but some systems need further massaging.

Bad vibrations
Olive Engineering applied the CDD method to a compressor assembly which was troublesome to align and seal (see cross-section above). A bracket and coupling linked the compressor to an engine. Screws snugged the compressor subassembly to the vessel flange at one end, resulting in a cantilevered load. A support on the opposite end of the subassembly, bolted through the wall of the vessel, alleviated the load and cut vibration. The support included an adjustable cylinder, a long screw, and a seal.

This design used the deformation and adjustable design methods to overcome tolerance problems. An external thread lets the cylinder move vertically until it contacts the bracket (adjustable method). The flexibility of the screw rod ensures parallelism between the seal screw and the vessel (deformation method). Despite these accommodations, human error and multiple constraints made it hard to seal the system.

The design does not need precise assembly between the compressor subassembly and the vessel as long as the seal is intact. So the ACs for the entire system should be as close to zero as possible.

An evaluation of the design’s mating pairs reveals two plane-plane matings and one cylinder-cylinder mating. Constraints in these pairs add up to 10 TPCs, the source of the assembly difficulties.

To ease the number of constraints, engineers deleted the support from under the compressor bracket. Instead, they stiffened the bracket so it could better hold the cantilevered load. That cut out two mating pairs and left only three TPCs.

Assembly problems disappeared, and operational vibrations have not returned.

Part mating design methodologies
High-accuracy design relies on precision parts and tight tolerances to exactly locate components. Integrated manufacturing designs use in-process steps like matched drilling to mate parts. Adjustable designs add mating features to overcome mismatches. Deformation design lets interfaces themselves form to the fit required. Constraint-driven design is different in that it relies on analysis and reduction of a system’s constraints to ease assembly.

Mating pair constraints
Cylinder-cylinder mating pairs are common where pins locate one part with respect to a tight-tolerance hole in the other. They only have freedom to move and rotate with respect to the Z axis. Cylinder-slot pairs have one more translational and one more rotational degree or freedom. Plane-plane pairs that form when two blocks are butted against each other have two translational and one rotational degrees of freedom.

Two blocks mated by means of two pins have six constrained coordinates (ACs) and no degrees of freedom (DOFs).

Changing one of the mating holes to a slot cuts that pair’s ACs to 2 and the TPC to 9.

Changing the pins to spheres with conical tips trims the hole’s AC from 4 to 2 and the slot’s AC from 2 to 1. The resulting TPC drops to 6, the minimum this design needs for error-free assembly.

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