Stack effect or chimney effect is the movement of air into and out of buildings, chimneys, flue-gas stacks, or other containers, resulting from air buoyancy.Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The result is either a positive or negative buoyancy force. The greater the thermal difference and the height of the. The stack effect happens, when warm air moves or flow upwards in the building. In summer, the warm air rises because it is lighter than cold air. So when it rises, it escapes out of the upper levels of the building through ventilation openings, windows or leakages.
Tolerance Stack up is the permutation of inadequacy (or, flaws) of an assembly part design which directly affects the manufacturability of a part. Knowing the complications involved in assembling a part, tolerance stackup analysis anticipates the impact on total tolerance of a part based on assembly challenges and (preliminary) fluctuating tolerance of component.
Is the perfect fit, perfect enough? Tolerance Stackup Analysis answers this integral manufacturing question and anticipates design execution demand much in advance. Widely practiced across mechanical domain, tolerance stackup analysis quantifies the impact of gathered variations qualified by requirements (tolerances and dimensions) designated by assembly.
Often defined in engineering drawings, tolerances and dimensions of an assembly part often requires precise tolerance stackups. Worst Case and Statistical Analysis (Root Sum Square/Root Mean Square) are widely used methodologies for Tolerance Stackup Analysis which resorts to validation in single or double direction. While the former calculates the maximal and minimal distance between two parts or attributes (based on worst cases), the latter intersects arithmetic and statistical methodologies to achieve similar objective.
Tolerance Stack up Methodology
To perform tolerance stackup analysis, there are two methods which are very common in the industry:
Worst Case, and
Root Sum Square (RSS)
Worst Case Method
Worst Case method calculates the impact of shift in single (or, multiple) tolerance on the entire assembly. Popular for its simplistic nature, this method is based on the assumption that every dimension in the assembly chain would be manufactured at its maximum and minimum allowable value. Further, it is assumed that each deviation has adverse combination irrespective of its uncertainty. It is as simple as adding up the tolerances of the entire assembly chain, which is termed as linear sum.
Following are commonly used signs in worst case method-
Accumulated Tolerance = (ΔY)
n = Number of constituent dimensions in the dimension chain
d i = Tolerance associated with the ith dimension.
Effect Stack 1 0 24
While it gives user the ease of calculating tolerance stackup analysis, this approach is only applicable when-
(a) The volume of production is very small
(b) 100 per cent acceptance is required
(c) The number of constituent dimensions in assembly is very small
Calculation
A worst-case tolerance analysis method is simple arithmetic (that’s right… just addition and subtraction), so let’s start there.
Say, we have an assembly of four thick plates like below:
The above diagram depicts the tolerance and thickness of quadruple plates. Herein, the dimension and tolerance value needs to be found. In order to achieve this, the following steps need to be followed-
Calculate the lower specification limit (LSL) size for each of the plates like below:
For Plate 1:
LSL= 27-0.4 = 26.6
For Plate 2:
LSL= 15-0.3 = 14.7
Effect Stack 1 0 20
For Plate 3:
LSL= 15-0.3 = 14.7
For Plate 4:
LSL= 15-0.5 = 14.5
On summing up the LSL thickness values of all plates, one would get the LSL thickness of the entire assembly as shown below:
TL= 26.6 +14.7 + 14.7 + 14.5 = 70.5
(TL = Total LSL thickness values)
Calculate the upper specification limit (USL) size for each of plate in the following manner:
So by worst case method one gets the overall dimension (X) of the assembly as:
X = 72 ± 1.5
Assembly tolerance stack-up analysis is used for calculating the tolerance value of the overall assembly (or a gap in the assembly) from the tolerance values of the individual components. The worst case method of the stack up analysis is the simplest.
Root Sum Square (RSS)
Unlike the previous method, Root Sum Square (RSS) assumes the certainty of tolerance estimate and the arrangement of tolerances being considered. This statistical method of calculating tolerance stack-up analysis denotes total tolerance as mentioned below-
Where,
n = Number of constituent dimensions in the dimension chain
d i = Tolerance associated with the ith dimension.
Contrasting the method mentioned afore, this methodology can be used in cases where-
(a) Volume of production is very high
(b) Finite rejection of the product assembly is acceptable
(c) The number of constituent dimensions in the loop is sufficiently large
Calculations
The root sum square (RSS) method works on a statistical approach. It assumes that most of the components fall to the mid of the tolerance zone rather than at the extreme ends.
The aim of the assembly tolerance stack up analysis is to find out the overall thickness (X) of the assembly with tolerance. We have the thickness and the tolerance values of all the plates (plate-1, 2, 3 and 4).
Calculate the nominal thickness of the whole assembly as below:
X = 15 + 15 + 15 + 27 = 72
Find the Standard Deviation (σ) of each components tolerance as below:
σplate1 = 0.4/3 = 0.133
σplate-2 = 0.3/3 = 0.1
σplate-3 = 0.3/3 = 0.1
σplate-4 = 0.5/3 = 0.167
Find out the standard deviation of the tolerance zone of the assembly like below:
Find out the tolerance zone of the assembly like below:
T = σassembly * 3= 0.256*3= 0.768
So, the thickness dimension (X) with the tolerance zone of assembly would be:
X = 72 ± 0.768
The root sum square or RSS or statistical tolerance stack up method is useful for tolerance stack up analysis of an assembly having a large numbers of components.
Best Tolerance Stackup Analysis Method
Effect Stack 1 0 2 0
The fast paced manufacturing sector often highlights the best (and, the worst) of both methodology. While worst case method is always deemed simple, root sum square method often guarantees extra exact results. In the course of weighing the benefit of each methodology, the fact remains unchanged-variation and its impact.
In such times, tolerance stackup analysis should be able to cater to the need of achieving accuracy at minimal cost. Irrespective of the method used, optimization in both existing and new design need to be ensured. Such should be the analysis that user should be able to troubleshoot right in the initial stage, be able to contemplate on alternate design idea…all this to meet the final production goal.
Effect Stack 1 0 25
Benefits of Tolerance Stackup Analysis
Reduces the rework resulting into cost reduction
Optimized use of resources at disposal
Sure fit which reduces the span of design-to-manufacture
Anticipate demand in advance
Knowing the cost and performance impact on the final assembled part