Page 385 - Marks Calculation for Machine Design

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CHAPTER 9
MACHINE ENERGY

9.1 INTRODUCTION

In this chapter two types of machine elements will be discussed: helical springs and fly-
wheels. Both of these machine elements either absorb or store energy, or do both, many
times in repetitive cycles. Both are very important to the machine designer. Each will be
discussed with examples in both the U.S. Customary and SI/metric system of units.
Helical springs are used in a variety of machines, from high-performance engines to
vegetable choppers. Helical springs can be large or small. Helical springs can be expen-
sive one-of-a-kind, or inexpensive mass produced. All helical springs are critical to their
specific application, therefore, their design must be appropriate for the expected operating
conditions. The discussion on helical springs will cover: (1) terminology and geometry,
(2) loads and stresses, (3) deflection, (4) spring rate, stiffness, compliance, and flexibility,
(5) work and energy, (6) series and parallel arrangements, (6) extension springs, (7) com-
pression springs, (8) stability, (9) critical frequency, and (10) fatigue loading. Along with
the discussion, which includes several algebraic developments considered important for the
understanding of the underlying principles, there are ten examples to provide the necessary
practice in using the applicable design formulas.
Flywheels have long been used as energy storage devices for rotational motion, whether
attached to the crankshaft of an automobile engine, or part of the drive system for an
industrial punch press. Just the right amount of inertia must be used in the design; too little
inertia and the system loses momentum each cycle, too much inertia and the system is
slugish. This design parameter, and others critical to a safe design, will be presented.

9.2 HELICAL SPRINGS

Springs absorb, store, and release energy, sometimes only infrequently, or over continuous
cycles. In their design, both the level of stress and the amount of deflection is important,
usually at the same time. There are many types of springs, almost too many to cover
thoroughly. However, the principles presented here are applicable to all springs.

9.2.1 Loads, Stresses, and Deflection
Helical springs are what usually comes to mind when the word springs is used. Typically,
they have circular cross sections, although other cross sections are possible, and their coils

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