The Mechanics of the Spiral Spring
When working with the English watch master Thomas Thompin in 1678, Robert Hook (1635–1703) observed that when an elastic body is subjected to stress, its dimension or shape changes in proportion to the applied stress over a range of stresses. On the basis
- PDF / 1,241,503 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 6 Downloads / 225 Views
The Mechanics of the Spiral Spring
When working with the English watch master Thomas Thompin in 1678, Robert Hook (1635–1703) observed that when an elastic body is subjected to stress, its dimension or shape changes in proportion to the applied stress over a range of stresses. On the basis of his experiments with springs, stretching wires and coils, he discovered a relationship between the force and the extension of the spring. This is the so-called Hooke’s law which states that strain, the relative change in dimension, is proportional to stress. If the stress applied to a body goes beyond a certain value known as the elastic limit, the body does not return to its original state once the stress is removed. In other words, the Hooke’s law applies only in the region below the elastic limit. Mathematically, Hooke’s law has the following form: F ¼ kx
ð4:1Þ
where, F is the applied force, k is the spring constant and x is displacement. Since then, more than three hundred years has passed, now the Hooke’s law is taught in every elementary school in the world. Nowadays, springs are used everywhere, including, of course, the mechanical watch and clock. This chapter is devoted to the spring: its mechanics and applications in the mechanical watch movements.
4.1 A Historical Review of Spiral Springs, Hairspring and Main Springs The mechanical watch movement has two springs: the hairspring and the mainspring. They are both spiral springs and extremely important. The hairspring is a fine spiral spring, usually assembled onto the balance wheel to form a harmonic
R. Du and L. Xie, The Mechanics of Mechanical Watches and Clocks, History of Mechanism and Machine Science 21, DOI: 10.1007/978-3-642-29308-5_4, Ó Springer-Verlag Berlin Heidelberg 2013
89
90
4 The Mechanics of the Spiral Spring
Fig. 4.1 Hairspring and its assembly
Balance wheel Hairspring
Collet Hairspring Assembly
Hairspring
oscillator, whose resonant period is a constant. It is a part of the ‘‘brain’’ of the mechanical watch movement (the escapement). The mainspring is a spiral torsion spring of metal ribbon that provides power for the mechanical watch movement. It can be considered as the ‘‘heart’’ of the mechanical watch movement. As shown in Fig. 4.1, the hairspring is a fine metal wire with a rectangular cross-section that is coiled around itself in the form of an Archimedean spiral. Note that it has a ‘‘tail’’ for the assembly. The hairspring is assembled onto the balance wheel by a collet. Together they form a harmonic oscillator, where the hairspring provides the linear restoring force that reverses the motion of the balance wheel so it oscillates back and forth. As discussed in the previous section, the motion of the balance wheel is approximately a simple harmonic motion, i.e., a sinusoidal motion with a constant period. The stiffness of the hairspring can be approximately expressed as follows: k0 ¼
E h t3 12L
ð4:2Þ
where k0 is the stiffness of the spring [Nm/rad], E the modulus of elasticity of the spring [GPa], h the height of the hairs
Data Loading...
