Mechanical Engineering Design Notes

Design Contents

Preliminary Matters
Design Methodology
..brain storming
..evaluation matrix
Statistical Considerations
..variability in materials
..variability in dimensions
..variability in loading
..preferred sizes
Design Factor
Introduction to Failure
Failure Theories
Application of von Mises
..criterion in 2 D

Stress Concentration
..and notch sensitivity
Failure Under Combined Loading
..combined bending and torsion
Failure Under Cyclic Loading
..fracture mechanics
Instability - Buckling
Concentrically Loaded Strut
..slender columns
..Euler formula
..effective length
..short and intermediate columns
Eccentrically Loaded Strut
.. theory
Shock Loading

Statistical Considerations

1. Introduction
Variability in materials, in manufacturing processes and in expected loads is inevitable and needs to be considered during the design process.

2. Variability in materials
Only a small number of metals have been extensively tested to provide statistical information about the spread of their properties. In the majority of cases the properties have a normal or 'Gaussian' distribution which can be defined by the mean and the standard deviation. However work on a titanium alloy revealed a highly skewed distribution of tensile strengths.

E values of different samples of the medium carbon SAE 4340 steel were found to vary by + or - 3%.

The UTS of samples from finished rolled SAE 1020 structural steel was found to have a standard deviation of 3% of the mean UTS.

By exerting close control over rolling / annealing schedules or over tempering temperatures, tailoring processing to individual 'heats' - tolerance bands can be reduced somewhat - but at additional costs.

3. Variability in component size
Similar considerations apply when producing parts to a specific size. Generally by choosing an additional process, accuracy can be improved - but at a rapidly increasing cost.

It is therefore important that the widest tolerance band that is acceptable is specified to keep cost down and it is essential that the equipment used for the manufacture of products has the necessary capability to produce components within the specified tolerance band.

4. Variability in loading
Virtually all products designed by mechanical engineers will be subjected to fluctuating loads. In cases where the load is fluctuating in a regular sinusoidal manner, the mean stress and stress range in the component can be calculated and checked with a modified Goodman diagram. Problems arise when loads are of a statistical nature, eg wind, wave and vehicle suspension loads, being three common ones. Over the past 30 years the automotive industry has spent a lot of time and money recording and analysing vehicle suspension loads with the result that they now have a good idea of the different load spectra that different types of vehicle suspensions (and consequently the vehicle structures and their occupants) will face. Where this data is not available, estimates need to be made. The data or estimates are then converted into equivalent numbers of cycles of specified amplitude. The cumulative fatigue damage that these stress cycles cause can then be assessed with the Palmgren - Miner theory (Miner's rule). This can be written as:

(n1/N1) + (n2/N2) +..+ (ni/Ni) = C

where n is the number of cycles of a particular stress applied and N is the life corresponding to that stress. The constant C is usually in the range 0.7 to 2.2 and a value of 1 is often used.

David J Grieve, Revised: 25th January 2014, 19th February 2010, 31st January 2010, 21st July 2004, Original: September 1998.

Standardisation and Preferred Sizes

Design is a creative activity which naturally leads to diversity. If this is allowed to increase unchecked then difficulties will inevitably arise when it comes to purchasing and carrying stocks of components or spare parts. To prevent uncontrolled growth in variety, there have been standards, or preferred sizes for a long time and designers are encouraged to use these wherever possible. (In ancient Rome, standard pipe sizes were used for water supplies).

Preferred sizes are based on geometric series of numbers, three series designated the R5, R10 and R20 are used and described in ISO 3 - 1973. These series are based on the 5th, 10th and 20th root of 10 and are sometimes referred to as Renard Numbers:

R5 1 1.60 2.5 ....
R10 1 1.25 1.60 2.00 2.5 ....
R20 1 1.12 1.25 1.40 1.60 1.80 2.00 2.24 2.5 ....

Where sizes are given in mm, the following list shows preferred values:

0.05, 0.06, 0.08, 0.10, 0.12, 0.16, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.0, 1.1, 1.2, 1.4, 1.5, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 8.0, 9.0, 10, 11, 12, 14, 16, 18, 20, 22, 25, 28, 30, 32, 35, 40, 45, 50, 60, 80, 100, 120, 140, 160, 180, 200, 250, 300.

It should be noted that even where a manufacturers catalogue lists a range of sizes, this does not mean they are all available for quick delivery. Items in regular demand will normally be quickly delivered, but items that are only bought infrequently, may have long delivery times, and this should always be checked where you are working to a tight timescale.

David Grieve, 18th October 1999.

Updated: 26th January 2014.

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