AGMA 11FTM08-2011 pdf free.A Comprehensive System for Predicting Assembly Variation with Potential Application to Transmission Design.
There are three main sources of variation which must be accounted for in mechanical assemblies:
1. Dimensional variations (lengths and angles)
2. Geometric, or form and feature variations (flatness, roundness, angularity, etc.)
3. Kinematic variations (small displacements between mating parts)
Dimensional and form variations are the result of variations in the manufacturing processes or raw materials used in production. Kinematic variations occur at assembly time, as small internal displacements between mating parts in response to dimensional and form variations.
The two-component assembly shown in Figure 2 and Figure 3 demonstrates the relationship between dimensional and form variations in an assembly and the small kinematic displacements which occur at assembly time. The parts are assembled by inserting the cylinder into the groove, until it makes contact with upper and lower surfaces of the groove. For each set of parts, the distance U will adjust to accommodate the current value of dimensions A, R, and 0. The assembly resultant U1 represents the nominal position of the cylinder, while U2 represents the position of the cylinder when the variations M, AR, and A0 are present. This adjustability of the assembly describes a kinematic constraint, or a closure constraint on the assembly.
It is important to distinguish between component and assembly dimensions in Figure 2. Whereas A, R, and 0 are component dimensions, subject to random process variations, distance U is not a component dimension, it is a resultant assembly dimension, which locates the point of contact. U is not a manufacturing process variable, it is a kinematic assembly variable. Variations in U can only be measured after the parts are assembled. U is a dependent variable. A, R, and 0 are the independent random variables in this assembly.
Figure 3 illustrates the same assembly with exaggerated geometric feature variations. For production parts. the contact surfaces are not really flat and the cylinder is not perfectly round. The pattern of surface waviness will differ from one part to the next. In this assembly, the cylinder makes contact on a peak of the lower contact surface, while the next assembly may make contact in a valley. Similarly, the lower surface is in contact with a lobe of the cylinder, while the next assembly may make contact between lobes.
Local surface variations such as these can propagate through an assembly and accumulate just as size variations do. Thus, in a complete assembly model all three sources of variation must be accounted for to assure realistic and accurate results.
Vector assembly models
Figure 4 shows a general 2-D vector loop. The vectors are chained tip-to-tail, representing the component dimensions which add to determine the resultant assembly dimensions. Chaining allows length variations to accumulate and propagate through the assembly. The choice of angles in the loops is significant. As shown in Figure 4, the angles are defined as the relative angle between two adjacent vectors. The use of relative angles allows rotational variation to accumulate and propagate through the model as well.
Figure 5 shows two vector loops representing a locking hub assembly. In a closed loop, one or more vector lengths or angles represent kinematic variables, which adjust to maintain loop closure. An open boo is used to describe a critical assembly gap, orientation. etc. between adjacent parts. In Figure 5, the open loop describes the Gap between the Reel and Pad: the closed loop locates the Arm as it slides in or Out to accommodate dimensional variation. In this case, to properly grip the Reel, the Gap must be negative over the full range of dimensional variations. As is often the case, the open loop depends on elements of the closed loop for its solution. In this case, RL is the result of the vector chain in the dosed loop, so the loops are coupled.AGMA 11FTM08 pdf free download.