Tolerance stack

Tolerance stack analysis - Tolerances on components that are assembled together to achieve an overall design tolerance across an assembly can be individually analysed, their potential variability predicted and their combined effect on the overall conformance determined. The analysis can be used to optimize the design through the explorations of alternative tolerances, processes and materials with the goal of minimizing the costs of non-conformance. This topic is discussed in depth in Chapter 3. 

The initial design is analysed using CA at a component level for their combined ability to achieve the important customer requirement, this being the tolerance of 0.2 mm for the plunger displacement. Only those characteristics involved in the tolerance stack are analysed. The worst case tolerance stack model is used as directed by the customer. This model assumes that each component tolerance is at its maximum or minimum limit and that the sum of these equals the assembly tolerance, given by equation 2.16 (see Chapter 3 for a detailed discussion on tolerance stack models) ... 

The body is impact extruded from a cold forming steel. The characteristic dimension to be analysed in the tolerance stack is the base thickness of 3 mm (on a 020 mm bore) and this dimension has been assigned a tolerance of 0.02 mm. 

Following the tolerance stack through the end assembly, the bobbin dimension of 22 mm from the outside face to the back face of the magnetic pole is analysed next. This characteristic dimension does not include the tolerance on the impact extruded pole. The pole is to be moulded into the bobbin and the pole face is considered to be part of a mould related dimension. The bobbin is injection moulded using 30% filled polybutylene terephthalate (PBT). The tolerance assigned to the bobbin dimension is 0.035 mm. 

The associated cost of failure for the solenoid end assembly is calculated to be over 3 million for a product cost of 7.66 and production volume of one million units. This figure is for the tolerance stack failure mode alone as this is most important to the customer. Although the assembly variability risks are analysed, they are not taken into account in the final costs of failure. In conclusion, the process capabilities... 

Most literature tends only to focus on tolerance stack analysis when assessing the capability of assemblies. The variability of the actual assembly operations is rarely considered and does not rely solely on the tolerances accumulating throughout the assembly, but on the feasibility and inherent technical capability of the assembly... 

In general, tolerance stack models are based on either the wor.st case or statistical approaches, including those given in the references above. The worst case model (see equation 3.1) assumes that each component dimension is at its maximum or minimum limit and that the sum of these equals the assembly tolerance (initially this model was presented in Chapter 2). The tolerance stack equations are given in terms of bilateral tolerances on each component dimension, which is a common format when analysing tolerances in practice. The worst case model is ... 

The bilateral tolerance stack model including a factor for shifted component distributions is given below. It is derived by substituting equations 3.11 and 3.18 into equation 3.2. This equation is similar to that derived in Harry and Stewart (1988), but using the estimates for Cp and a target Cp for the assembly tolerance... 

In addition to understanding the statistical tolerance stack models and the FMEA process in developing a process capable solution, the designer should also address the physical assembly aspects of the tolerance stack problem. Any additional failure costs determined using CA are independent of whether the tolerances assigned to the assembly stack are capable or not. As presented in Chapter 2, the Component... 

Figure 3.9 Chart showing that capable tolerances cannot be optimized for solenoid tolerance stack design...

Figure 3.12 Chart showing optimized tolerances for solenoid tolerance stack redesign...

The inadequacy of the worst case model is evident and the statistical nature of the tolerance stack is more realistic, especially when including the effects of shifted distributions. This has also been the conclusion of some of the literature discussing tolerance stack models (Chase and Parkinson, 1991 Harry and Stewart, 1988 Wu et al., 1988). Shifting and drifting of component distributions has been said to be the chief reason for the apparent disenchantment with statistical tolerancing in manufacturing (Evans, 1975). Modern equipment is frequently composed of thousands of components, all of which interact within various tolerances. Failures often arise from a combination of drift conditions rather than the failure of a specific component. These are more difficult to predict and are therefore less likely to be foreseen by the designer (Smith, 1993). 

The inadequacy of the worst case approach to tolerance stack design compared to the statistical approach is evident, although it still appears to be popular with designers. The worst case tolerance stack model is inadequate and wasteful when the capability of each dimensional tolerance is high > 1.33). Some summarizing comments on the two main approaches are given below. 

The worst case tolerance stack approach is characterized by the following ... 

The variation of mount density is caused by the tolerance stack-up in the converter components. 

Adequate facilities should be provided for the stacking and storage of materials, spares, equipment, and other items. One of the weakest areas in bnsiness order is stacking and storage. Stacking should be neat, stable, and controlled, and no unsafe stacks should be tolerated. Stacking should only occur in anthorized areas and places. 

The quality benefits of CAD/CAM are perhaps the most underrated of all the benefits. Drawings produced by CAD/CAM systems from three-dimensional models have been shown to be of a consistently higher quality than those produced manually. Dimensions are totally defined by the geometry in the database, and as such are never incorrect. Tolerance stack-ups and other tolerance-related issues can also be calculated by the... 

O-Ring solution Less expensive. Less bulky. Marginal control in tolerance stack-up induced pressure. 

Infrared welding is much more forgiving of part tolerance stack up than radiant hot plate or laser welding it is similar to or even significantly better than vibration welding and ultrasonic welding. 

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