This video examines a simple engineering design tolerance analysis using Tolcap. It demonstrates an equation to calculate the tolerance of a stack. The example shows the sort of questions designers and manufacturers need to address during tolerance analysis to ensure the design will be sound and capable.

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## Transcript

### Tolcap Example

This presentation shows you how to analyse a design with Tolcap; how to do it, when and why.

### Tolcap Example Objectives

The simplified example sets out to show how to analyse the components of a design using Tolcap and how to calculate a stack tolerance. But it also shows when to use Tolcap (which will turn out to be as early in the design stage as possible), and how Tolcap raises questions about the design - questions you need to address with your supplier to ensure you have a sound design.

### Tolcap Example - a ‘Camera’

Here's the example: It's a ‘camera’ of some sort and it has three components – a heatsink, a body and a lens. The table also shows the dimensions and first cut tolerances in the ‘stack’ that defines the image distance in the camera.

The heatsink dimension 3 +/- 0.05mm is the height of a raised platform for a photodiode array that is connected to a surrounding printed circuit board.

The body which is 12mm long +/- 0.01mm just spaces the lens from the photodiode array. The lens is injection moulded PMMA. The front part of the lens from the mounting shoulder is 7 +/- 0.1mm.

### Camera Tolerance Stack

Accepting the assigned tolerances, the distance from the front of the lens to the ‘image’ on the heat sink is 22+/- 0.16 – worst case. We may ‘root-sum-square’ the tolerances and say the stack dimension is 22 +/- 0.11225mm (call it - 22 +/- 0.11) - but is ‘root-sum-square’ valid and meaningful? Anyway, are the component tolerances achievable? Let's use Tolcap to estimate Cpk for the assigned tolerances.

### Camera Heatsink Analysis

- Open Tolcap and log in

To analyse the heatsink:

- Select ‘Casting’ and ‘Pressure Die Casting for Copper Alloys’
- Enter the dimension 3 and the tolerance +/- 0.05
- and click ‘Calculate’

There is no ‘Mp Wizard’ shown, because the map is specific to the material. There is no modification needed from the ‘Gp’ or ‘Vp Wizard’: even so, Cpk is estimated at 0.69 – an unacceptably low answer.

To find the capable tolerance:

- Click on the ‘Cpk’ tab
- Change the target Cpk to 1.33
- and click ‘Calculate’

- The tolerance needed to achieve Cpk = 1.33 is +/- 0.082mm.

Next analyse the Body.

### Camera Body Analysis

To analyse the Body:

- Select ‘Machining’ and ‘Turning and Boring’
- Click the ‘Tolerance’ tab
- Enter the dimension 12 and tolerance 0.01
- and click ‘Calculate’

The predicted Cpk is 1.64, but next we:

- Click the ‘Mp Wizard’...and the drop down arrow, ...and select Copper
- Then click ‘Update Chart’

The predicted Cpk falls to 1.4

- ....and next click the ‘Gp Wizard’.
- Specify one additional set-up operation and
- and click ‘Update Chart’
- Select ‘Plastic Injection Moulding’
- and ‘Injection / Compression PETP, PF, PMMA.....’, - the material we are using
- Click the ‘Tolerance’ tab
- Enter the dimension 7
- and tolerance 0.1 .
- Click ‘Calculate’
- Click ‘Update Chart’
- Click the ‘Vp Wizard’
- Select ‘Yes’ in answer to the last question and
- Click ‘Update Chart’
- Click ‘Calculate’

The Body starts as a casting to save material, so it has to be turned round at some point in the machining process. So:

The predicted Cpk is 1.29 .. Which is close enough to 1.33 to be considered an acceptable design.

### Camera Lens Analysis

For the Camera Lens:

- Cpk is 2.34 so far ... next:

- Click the ‘Gp Wizard’

...the characteristic is across the parting line, (which it wasn't on the heatsink) and

The predicted Cpk falls to 1.22 ... next

Does the need for optical properties impose any limitations on material flow etc? I don't know? Let's admit ignorance here and:

... The predicted Cpk is 0.66.

To find a tolerance that gives an acceptable Cpk select the Cpk tab and set target Cpk to 1.33:

... and find the tolerance should be +/- 0.160mm.

### Camera Design - Capable Tolerances

So now we have Cpk = 1.33 capable tolerances:
The Heatsink 0.082, the Body +/- 0.01 and the Lens 0.160.
Now with capable tolerances, the distance from the front of the lens to the ‘image’ on
the heatsink is 22 +/- 0.25mm (0.252 exactly).
The ‘root-sum-square’ of the tolerances is 0.180.
Using the formula derived for Cpk = 1.33 tolerances, which is
t_{stack} is 3/11 of the sum of the tolerances plus 8/11 of the ‘root-sum-square’ of the
tolerances, we get t_{stack} coming to 0.2.

### Camera Example: Discussion

This design is presented to illustrate how to use Tolcap and how to calculate a stack tolerance. That said it also serves to highlight when to use Tolcap and how it can improve the design process. The example is presented as a diagram: just to show that Tolcap is best used early in the design process, before a drawing commits you to some concept. Don't just look at the Cpk values or tolerances you get from Tolcap: Look at the processes you selected and the answers you gave in the wizards ... these can steer your design and your project.

### Lens Discussion 1

Take the Lens for example: We wondered whether the requirement for optical properties affects process capability. We didn't know so assumed it did. We need to find the real answer to the question, so we should ask the supplier. Don't ask whether they think it does or doesn't – ask for an explanation – and vitally for evidence that it does not. Have they made similar lenses before? Don't they have process capability data on them we can use for comparison? If the optical requirement doesn't in fact affect process capability, we can go back to the analysis and reduce the tolerance.

### Lens Discussion 2

Is dimensioning to the front of the lens avoidable - is it even appropriate? If it is necessary, consider mounting the lens inside the body onto the front face, so that the dimension is on one side of the die.

But look at the optical equations: the thickness of the lens will have an effect on its focal length, but maybe the shape should be adjusted so the lens is convex on both faces. Maybe the optical centre could be brought in line with the mounting feature? Maybe rather than include the lens in the stack it is better to review optics and their sensitivity to dimensional variation.

### Heat Sink Discussion

On the Heat Sink the design assumes a raw casting will be satisfactory. It may be necessary to machine the casting to ‘clean up’ the faces or to achieve tighter tolerances if it is necessary to improve the stack tolerance.

### Body Discussion

On the Body, the capable tolerance is an order of magnitude smaller than for the other components in the stack. This may be an opportunity for cost reduction. Do we need to machine the casting? Is there an alternative process to produce the part?

### Tolcap Example Objectives

We hope this example has demonstrated:

- How to analyse a design using Tolcap

- and how to calculate a stack tolerance.

- Also when to use Tolcap - as early in the design stage as you possibly can.

- How Tolcap raises questions about the design - questions you need to address with your
supplier to ensure you have a sound design, and questions to pose about your design

- and tasks to incorporate into the design project.

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