Actual Value Definitions – ASME Y14.5.1M1994 Standard
In the last article we saw that tolerance zones are defined in the Y14.5M1994 standard for Dimensioning and Tolerancing, but actual values are defined in the Y14.5.1M1994 standard for Mathematical Definition of Dimensioning and Tolerancing Principles. These actual values are of great interest in inspection, when we need to report numerical data for geometric characteristics.
The following are tolerance zone definitions for some of the simpler geometric characteristics, and their corresponding actual value definitions:
GEOMETRIC CHARACTERISTIC 
TOLERANCE ZONE DEFINITION (ASME Y14.5M1994) 
ACTUAL VALUE DEFINITION (ASME Y14.5.1M1994) 
Cylindricity 
Two coaxial cylinders separated by the specified Cylindricity tolerance 
Smallest Cylindricity tolerance to which the surface will conform 
Flatness 
Two parallel planes separated by the specified Flatness tolerance 
Smallest Flatness tolerance to which the surface will conform 
Angularity (planar surface) 
Two parallel planes separated by the Orientation tolerance, which are oriented to the datum(s) 
Smallest Perpendicularity tolerance to which the surface will conform 
Angularity (axis) 
Cylinder whose diameter is equal to the Perpendicularity tolerance, which is oriented to the datum(s) 
Smallest Perpendicularity tolerance to which the surface will conform 
Position RFS (Axis) 
Cylinder whose diameter is the Position tolerance, oriented and located to the datum(s) 
Smallest Position tolerance zone to which the axis will conform 
Total Runout (cylindrical surface) 
Two coaxial cylinders separated by the Total Runout tolerance, oriented and located to the datum axis 
Smallest Total Runout tolerance to which the surface will conform 
Underlying Concept
The underlying concept for these actual value definitions is that the actual value is the smallest tolerance to which the feature will conform. This can be thought of as expanding or contracting the tolerance zone until it just barely contains the controlled feature component, while respecting any constraints that the zone is subject to.
Optimization within Constraints
Finding the smallest tolerance to which the feature will conform brings in the concept of optimization within constraints. Depending on the geometric characteristic, tolerance zones are subject to different constraints on their magnitude, orientation and location. For more information in this, refer to the previous article “Determining the Constraints on a Tolerance zone”. Any degree of freedom that is left unconstrained in the tolerance zone definition must be optimized when finding the actual value, in order to find the smallest tolerance to which the feature will conform.
The following table breaks down these degrees of freedom for the examples discussed above:

ACTUAL VALUE DEFINITION (RESTATEMENT) 
ORIENTATION CONSTRAINT 
LOCATION CONSTRAINT 
MAGNITUDE CONSTRAINT 
Cylindricity 
Distance between closest two coaxial cylinders that the surface conforms to 
Unconstrained (must optimize) 
Unconstrained (must optimize) 
Unconstrained (must optimize) 
Flatness 
Distance between closest two parallel planes that the surface conforms to 
Unconstrained (must optimize) 
Unconstrained (must optimize) 
N/A 
Angularity (planar surface) 
Distance between closest two parallel planes that the surface conforms to, that are oriented to the datum(s) 
Constrained 
Unconstrained (must optimize) 
N/A 
Angularity (axis) 
Diameter of smallest cylinder that the axis conforms to, that is oriented to the datum(s) 
Constrained 
Unconstrained (must optimize) 
N/A 
Position RFS (Axis) 
Diameter of smallest cylinder that the axis conforms to, that is oriented and located to the datum(s) 
Constrained 
Constrained 
N/A 
Total Runout (cylindrical surface) 
Distance between closest two coaxial cylinders that the surface conforms to, that is oriented and located to the datum axis 
Constrained 
Constrained 
Unconstrained (must optimize) 
Challenges for CMM Inspection
Optimization of the open degrees of freedom in the above simple examples is relatively straightforward, and most CMM software is able to handle it easily. Other examples, however, can introduce more complex constraint situations. These include:
· Elementbased characteristics (e.g. Circularity, Straightness, Circular Runout, Angularity with the EACH ELEMENT annotation)
· Position tolerances on patterns of features
· Composite Position (tolerance zones for lower segment are not located to the datums and must be optimized)
· Mixed groups of features linked by the Rule of Simultaneous Requirements
The optimizations required to calculate the smallest tolerance to which the feature will conform can become extremely complex in the above examples, and most CMM software does not fully deal with them. In some cases, the Y14.5.1M1994 standard did not provide a definition for the actual values (e.g. Simultaneous Requirements).
Upcoming articles will examine some of these more complex cases.