14^th March is ‘Pi Day’. This is due to the resemblance the date has to the figure Pi to two decimal places – 3.14 –  when written in the format month/day as it is in the USA – along with American Samoa, Guam, Japan, Cayman Islands, Federated States of Micronesia, Ghana, Kenya, Marshall Islands, Northern Mariana Islands, Panama, Philippines, Puerto Rico, Togo, the Virgin Islands and Canada!

The christening of 14^th March as Pi Day was decided by US physicist Larry Shaw – who is now affectionately referred to as “Prince of Pi” as a result. Larry worked at the Exploratorium museum in San Francisco, California which showcases science, technology and art exhibitions.

When talking with his colleagues about mathematical constants, Larry thought of linking Pi with the date 3.14 (14^th March in the USA). His co-workers encouraged the idea and began to celebrate the day by eating pies – this caught on and resulted in the whole museum holding the event each year until the museum moved in 2013. Shaw felt Pi Day made maths more fun and accessible for children around the world.

Larry was hired in 1972 by founder and director Dr Frank Oppenheimer, who told him for his job title, “You can put down anything you want except ‘director’”! While there, Larry designed and built many exhibits and worked to encourage visitors to understand what STEAM meant (Science, Technology, Engineering, Art and Maths – now commonly referred to as STEM).

The date is celebrated in various ways across the world – including baking competitions and challenges to memorise as many of the infinite digits following the decimal point as they can! The year 2015 was particularly poignant for Pi Day, as the date read 3.14.15 – the first five digits of Pi! Similarly, 1:59 pm is often heralded as the exact time for celebration, so it becomes 3.14159.

We decided to celebrate by ordering plenty of pies from our local butcher Drake & Macefield for the JB Springs team’s lunch and creating a pie Pi!

Maths in Manufacturing

Maths is one of the building blocks of engineering and manufacturing, providing calculations upon which many theories and concepts are built. These are just a few of the aspects of spring manufacturing reliant on the application of mathematics:

• Measurements, including: wire diameter, inner diameter, outer diameter, number of coils, free length, solid length, loads, etc.
• Spring deflection – this is how a spring responds to applied force i.e. compression, extension, torque and is calculated using Hooke’s Law – F = ks where F – applied force, k = spring constant/rate and s = spring deflection (displacement of length). The equation must be rearranged to s = F/k to find the deflection.
• Spring constant – this refers to the measurement of stiffness/strength within a spring. To calculate this, Hooke’s Law must be rearranged to k = F/s. For torsion springs, the equation k = P*M//Deg must be used where: P = Force exerted by spring, M = Moment arm, Deg = Deflection and k = Spring constant.
• Spring load – this is the amount of force being applied at the desired loaded height and is calculated using Hooke’s Law rearranged to k(s) = F.
• Spring index – the correlation between the mean spring diameter and wire diameter. This correlation determines the spring strength and the coil tightness and is calculated using the equation I = D / d where I = Index, D = Mean diameter and d = wire diameter.
• Spring rate – this is the constant force required to move an inch/millimetre of distance/deform the spring – calculated using a rearrangement of the above formula for spring load – k = L / T – where k = rate, L = load and T = travel.For more advanced mathematicians, there are also these two formulas:
• Elastic limit – the maximum force which can be applied to a material before plastic deformation occurs. This is calculated through working out the elastic potential energy using the equation Pe = ½ke² – where Pe = elastic potential energy, k = spring constant and e = extension in length.
• Compression spring constant equation – this is k = Gd⁴/8D³n and is used to calculate the properties of a spring where k = constant/spring rate, G = modulus of rigidity, of spring material, d = wire diameter, n = number of active coils and D = mean coil diameter.

Maths is ingrained and invaluable within manufacturing. At JB Springs, we apply a variety of calculations and equations such as those mentioned above throughout the spring production process in order to ensure accuracy and efficiency. We also employ Statistical Process Control (SPC), part of which is calculating the Cp and Cpk (process capability index) to measure the extent to which a process can repeatedly produce springs to the specifications set by the customer.

To discover more about our work manufacturing springs and wireform, visit our other webpages. If you’d like to find out more about the principles behind spring design and production, have a look at our other Springtelligence blog posts.