Nomograms for the design of light weight hollow helical springs

Abstract

The helical spring is a widely used element in suspension systems. Traditionally, the springs have been wound from solid round wire. Significant weight savings can be achieved by fabricating helical springs from hollow tubing. For suspension systems, weight savings result in significant transportation fuel savings. This paper uses previously published equations to calculate the maximum shear stress and deflection of the hollow helical spring. Since the equations are complex, solving them on a computer or spreadsheet would require a trial-and-error method. As a design aid to avoid this problem, this paper gives nomograms for the design of lightweight hollow helical springs. The nomograms are graphical solutions to the maximum stress and deflection equations. Example suspension spring designs show that significant weight savings (of the order of 50% or more) can be achieved using hollow springs. Hollow springs could also be used in extreme temperature situations. Heating or cooling fluids can be circulated through the hollow spring.

Nomograms in the History and Education of Machine Mechanics

“…Considering the field of Machine Mechanics and Design over the last 30 years, we found several works on nomograms for gear train design (Esmail & Hussen, 2010;Esmail, 2013Esmail, , 2016Esmail et al, 2018); they are also still used for the design of planar (Hassaan, 2015) or spherical (Hwang & Chen, 2007;Lu, 1999) linkages, for optimizing motion laws in cams (de Freitas Avelar et al, 2021), for the analysis of the efficiency of a kinematic chain (Aleksandrov, 2011), for studying tire dynamics in a vehicle (Zotov & Balakina, 2007), and for the design of hollow springs (Bagaria et al, 2017).…”

Analytical solutions and computational nomograms for maximum pressure angle for cam mechanisms for full and half cycloidal and harmonic motion curves

“…1,[4][5][6][7][8] The use of nomograms was very common in engineering for making complex calculations quickly, but fell into disue due to increasing use of calculators and computers, 9 but had a recent resurgence in medical field due to introduction of evidence-based medicine in clinical practice [10][11][12][13] and can still be found in engineering and computing in recent publications. [14][15][16][17] The use of nomograms for educational purposes can also be very useful for students learning complex problems through fast and simple resolution methods as they can be found in current textbooks. [18][19][20][21] Varnum 22 created the first circular nomogram for maximum pressure angle on cams for cycloidal motion and constant acceleration curves.…”