Optimization and innovation processes in inglese (parte 3)

Calculate for a specific tolerances which is the manufacturing cost.

In general the companies has database where I can introduce my parameters and a

mathematical model can calculate.

Cost-tolerance curves

In this case, Chase Is used by looking for the correct coe?icients, specific to a single

machining, using a regression approach, i.e. minimizing the standard deviations. Also in this

case, an EXCEL sheet, where there are some historical or experimental processing data, is

enough for the calculation.

Procedure

It is necessary to optimize a system that allows to obtain a functional tolerance, given by the

sum of the functional tolerances of the individual components, at the minimum cost, where

the cost is the sum of the costs of the individual processes.

Processing costs

To determine the optimal machining cost, it is necessary to establish the optimal combination

of tolerances that allows the minimization of the cost with the same tolerances. Simple

optimization code such as EXCEL can be used for this purpose.

Cost Curve Tables

These tables are derived from the work done by the U.S. Army to characterize mechanical

removal processes.

WC and RSS

Another possible approach for calculating the tolerance chain is RSS (Root Square

Statistical). In this case, we do not take the most critical situation (WC precautionary

approach) but a statistical “realistic” situation.

In this case, the standard deviations of the various tolerances are assumed and combined

together to calculate the overall performance.

Complex transfer functions can also be taken into account.

If you consider the propagation of errors, it does not follow the worst possible case as we have

seen in the approach before, it rather follows the root square statistical. If I have a few

component, it’s better to use the worst-case approach, while if we have a lot of component

and complex chain it’s better to use the realistic approach (root square statistical). BUT, if you

use this you have to be sure that the tolerances you insert are right and respected by the

suppliers, but it’s unlikely that this happens. Worst case is used because we are quite aware

that the tolerances reported in on the specifications are often disattended, that’s way we

often prefer to use the worst case.

Sensitivity function

In the case of simpler products, the sensitivity function can be calculated directly.

Simplified allocation

The approach considering production costs and quality costs is substantially very complex

and time-consuming.

Therefore faster solutions are often used, even if they are less performing.

These include:

1. Proportional scaling

2. Scaling with Weight Factors the seen optimizations are complex approaches that

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most companies can not apply. To solve this issue simplified approaches have been

developed.

Tolerance chain with dimensions.

A,C and G are considered fixed because they’re standard components. I can’t change their

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tolerances the cost would increase dramatically.

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Proportional scaling

In proportional scaling, you decrease (or, rarely, increase) the tolerances of the various

features that are not locked proportionally.

To give a numerical example:

Target: o.o15 tool (Kg objective)

Current (sum of current values): 0.0245 I have to reduce the tolerances of some

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components to achieve my orj (?).

Worts case approach:

To find the proportional scaling factor, you need to set up an equation in P.

Simple approach that allows me to reach my functional objectives without considering the

optimization of costs.

Considering 2 dimensions T1 and T2, the graphical representation of the proportional method

is:

Scaling with Weight Factors

Weight factors should be assigned based on how di?icult it is to achieve a certain tolerance.

The lower the factor, the easier it will be to achieve tight tolerances in that case. As an

example, the weight values are assigned to the following dimensions:

With the scaling approach I do not obtain any economical optimization. Weight factors are

value used to give an idea of the complexity necessary to achieve the tolerance.

Also in this case it is necessary to calculate the proportional value of reduction and attribute it

to the various dimensions according to their weight. The function of the final tolerance will be:

Same as the previous one but I add a weighting factor.

In this specific case:

From the formula P= 2.32

For other values

Graphically it can be represented for a case with 2 tolerances

Scaling with RSS

Both approaches can also consider the RSS case and not just WC. Only the function changes

to find the proportional scaling, which in the general case is:

For pure proportional scaling, the weights are considered to be unitary. To find P you need to

solve a 2 degree equation.

nd

Calculate tolerance values for dimensions B, D, E, F using proportional scaling considering

the final tolerance calculation with RSS.

Proportional 3D case

In the case of 2D or 3D tolerance, the problem becomes more complicated only in the

calculation phase of the tolerance chain, the optimization phase remains unchanged. In this

case, however, the sensitives of the individual tolerances to the final tolerance must be taken

into account.

The vector loop method allows you to create the chain of tolerances from the component

drawing. The chain is built by creating vectors that start for the significant design dimensions

of the product and for the points of contact.

Constructing the two equations of the components of the vector loop (loop indicates that it is

closed) we have:

Solving the second

From here it is possible to calculate the sensitivity of the various tolerances on phi.

Sc has the highest sensitivity: means that tolerance has a higher impact respect to the other.

The final RSS and WC tolerance are therefore as follows:

While the formula to be used to calculate the coe?icient P in the WC case is, considering the

spheres (c) from the catalog:

Now calculate the optimized value of the tolerances using the RSS proportional method.

However, it is always good to consider the technology used for the production of the

components/features as it is necessary to verify that the limits of the process are not

exceeded. In that case, it is necessary to integrate again by changing the technological

process. Choice of materials

Material selection

The choice of materials is a crucial decision for the proper functioning and cost-e?ective

manufacturability of any product. The designer is always faced with the challenge of finding a

compromise between the required functionalities and the costs needed to achieve them.

While sometimes it is easy to select a specific material that ensures the desired performance

at a low cost, it is not uncommon for there to be a significant conflict between the two.

In any case, it is essential to keep in mind that the goal is not to minimize the cost of the

material itself, but rather to minimize the overall cost, making it as low as possible. This

includes the purchase price, processing cost, assembly, maintenance, and disposal costs,

among others. Therefore, in the long term, the material with the lowest purchase price is not

necessarily the one with the lowest overall cost. Materials must always be chosen with

economic considerations in mind, since the cheapest material is not necessarily the

preferable one. The total cost of purchasing, manufacturing, and servicing must be

minimized.

In advanced mechanical design, the cost of materials can account for up to 50% of the total

product cost. Hence, the material must be selected in such a way that the functional

characteristics are ensured at the minimum total cost. Nowadays, especially thanks to the

push driven by Design for Manufacturing (DFM), designers have access to a wide variety of

metallic and non-metallic materials, some of which are specifically developed for certain

applications. DFM has introduced a strong focus on cost and on the selection of materials, an

aspect that was not as emphasized in the past.

Non-metallic materials have also begun to spread widely, mainly due to economic analyses

and the growing importance of cost optimization. This list of materials is continuously

expanding, including new plastics and new composite materials. A summary of the various

materials is shown in the figure:

Ceramic material: fragile, temperature resistance.

Glass: is a strange material, liquid in very high viscosity. Glass is considered a solid from an

engineer point of view, but instead is liquid with high viscosity.

Artificial polymers: are engineering materials (thermoplastic, thermosetting, elastomers).

Elastomers are sometimes thermoplastic and thermosetting, so there is not a big di?erence

between them.

General rules for choosing the material

- Use of commercial formats: you can switch from initial material to a standard format.

Important to start on something that is already available on the market.

- Use of commercial compositions: use of the most common composition of the

material that is available on the market. Its price is going to be higher.

- Use of pre-finished materials.

- Use of materials with high machinability: consider the processing cost. Large

batches production, cheaper solution.

- Maximize material utilization and reduce waste.

Finishing and tolerances

The tolerances of cold-worked materials (drawn, rolled) are generally better than thos of hot-

worked materials:

Tol +- 0.06 mm roughness from 0.8m to 3m.

Even tighter tolerance values can be achieved for plates and bars:

Tol +- 0.025mm.

For non-metallic materials, there are high tolerances due to the greater elasticity of the

material (glass, carbon and ceramics are excluded).

I have to select a cold working materials or hot working materials. The di?erence is about cost

and tolerance:

- Hot working materials: very high speed, tolerances not so good (construction building),

very fast production process, simple equipment with a very long life.

- Cold working materials: tight tolerance (example drawing, stamping), you have a better

accuracy, control of the dimension and an higher cost. Higher cost and higher

performances.

Cold worker is more expensive and hot worker cheaper. There is a di?erence of the

mechanical characteristics. Cold worker material has a higher strength if I use a more

expensive material. There is not a general rule. In some cases, is more convenient to use cold

worker and sometimes other. It depends on all possible costs.

The question raised by Design for Manufacturing (DFM) regarding the integrability of product

components has led to reflections on which characteristics of a component are truly

essential and cannot be compromised. It is therefore necessary to identify the required

properties of the material and assess whether similar materials can provide the same

performance at a lower total cost. The tolerances of cold-worked materials are generally<