Tolerance analysis

Chase, K. W. and Greenwood, W. H. 1988 Design Issues in Mechanical Tolerance Analysis. Manufacturing Review, 1(1), 50-59. 

Chase, K. W. and Parkinson, A. R. 1991 A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies. Research in Engineering Design, 3, 23-37. 

Chase, K. W., Gao, J. and Magleby, S. P. 1995 General 2D Tolerance Analysis of Mechanical Assemblies with Small Kinematic Adjustments. International Journal oj Design and Manufacture, 5(4), 263-274. 

Dong, Z. 1989 Automatic Tolerance Analysis and Synthesis in CAD Environment. PhD Thesis State University of NY, Buffalo, NY. 

Gerth, R. 1997 Tolerance Analysis A Tutorial of Current Practice. In Zhang, H. (ed.). Advanced Toterancing Techniques. NY Wiley Interscience. 

Korde, U. 1997 Planning for Variation in Manufacturing Processes - a process tolerance analysis software tool. SAE Technical Paper No. 970683. 

Wu, Z., Elmaraghy, W. H. and Elmaraghy, H. A. 1988 Evaluation of Cost-Tolerance Algorithms for Design Tolerance Analysis and Synthesis. Manufacturing Review, 1(3), October, 168-179. 

Thin membranes have the advantage of low area specific conductivities and more favorable back diffusion of water in comparison with thicker membranes. In the former case, this means that membranes with lower conductivity values could be tolerated. Analysis of voltage loss versus membrane thickness and specific conductivity has revealed that, if a membrane voltage loss of 25 mV at a current density 1 A cm can be tolerated, then existing materials with conductivity values similar to Nation (0.1 S cm i) could be prepared as 20-30 pm thick membranes. However, thinner membranes also typically exhibit lower mechanical strength than their thicker counterparts and can therefore fail earlier. Therefore, future materials might be suitable with just half the specific conductivity if they can be prepared into membranes of half the thickness and still possess sufficient mechanical strength. ... 

Wdrhoff K, Lambeck PV, Driessen A (1999) Design, tolerance analysis, and fabrication of silicon oxynitride based planar optical waveguides for communication devices. J Lightwave Technol 17 1401-1407... 

Designed experiments are a key tool for performing this specification translation process and helping to establish such controls. However, designed experiments are not the only tool required to accomplish this task. We will also explore other tools, such as tolerance analysis, robust design, capability studies, and Failure Modes and Effects Analysis (FMEA), to see how to combine these tools into an effective system for vahdation. 

Figure 5 Tolerance analysis when hot bar temperature = 175, dwell time = 0.5, pressure = 100, and materials temperature = 70. Abbreviations LSL, lower spec limit T, target USL, upper spec limit.

More generally, we can perform a tolerance analysis to predict how the output behaves. When all the inputs are targeted at the center of the study window. Figure 5 shows the results of a statistical tolerance analysis (HB = 175, DT = 0.5, P = 100, and MT = 70). The seal strength is estimated to have an average of 24.2 lb with a standard deviation of 2.5 lb. The defect rate is estimated to be 4.69%. 

This tolerance analysis was performed by taking the equation for the average from the response surface study and using it to derive the following equation for the seal strength standard deviation (6) ... 

While the tolerance analysis estimate will generally be the larger estimate, this will not always be the case. The tolerance analysis estimate depends on having all the sources of... 

A tolerance analysis predicts the behavior of the output for a specified set of targets for the inputs. The tolerance analysis can be repeated for different sets of targets to identify the optimal targets. In this case study, we have an observed equation for the average, and we have a predicted equation for the standard deviation. These can be used to obtain an equation for the capability index Cp. We can then maximize this equation to identify the optimal targets for the inputs. 

Table 10 shows the three competing approaches to robust design. When the equation is known, a robust tolerance analysis should be performed. When the equation is not known, designed experiments must be used and all three... 

The widths of the operating windows were selected based on the capabilities of the four critical input variables combined with the optimal targets for seal strength. To confirm that these windows are adequate, a more detailed tolerance analysis will be performed. As ranges are specified for each of the inputs, and alarms are used to detect excursions, we cannot assume the different inputs remain centered around their targets. This is particularly true for RT where one could operate at either the low end or the high end of its range for considerable periods of time. This violates one of the assumptions of statistical tolerance, so a more appropriate tolerance analysis is required. 

According to Figure 9, variation in the four critical inputs should not cause a problem if the seal strength is properly centered to start with. The variation in Figure 9 exceeds that in Figure 6, which was based on a statistical tolerance analysis. However, we are not yet done. Figure 9 assumes that the optimal set point for P is used. In actuality, there will be some error associated with selecting the set point for P. 

Cox ND. How to Perform Statistical Tolerance Analysis. Milwaukee ASQC Quality Press, 1986. 

Tolerance analysis extracting tolerance data from the design. 

Tolerance analysis process selection based on the tolerance capabilities of processes vs. the design specifications. 

Tolerance analysis comparing the tolerance specification against the tolerance capabilities of the selected tools and machine tools stacking up tolerance based on the setup and machine accuracy and setup error. 

---