Joining - Bolts

Mechanical Engineering Design Notes


1. Introduction
Springs are widely used in engineering to exert a force. In many critical applications, vehicle suspension springs and engine valve springs, they are subjected to rapid changes in length and their mass must be kept as low as possible to minimise undesirable dynamic effects. This inevitably means that such springs are working at high stress levels which has implications concerning the choice of materials and manufacturing processes. This section will concentrate on coil springs working in compression, dealing with design, stress analysis, choice of materials and manufacturing processes.

2. Forces Acting
The loads in the wire can be deduced from the FBD shown at right and are equal to a force F parallel to the spring axis (acting transverse to the wire axis) and a torque T = FD/2, about the axis of the wire. Both of these generate shear stress in the wire.

3. Curvature Effect
As the wire is coiled, the rotation of the wire on the inner side of the coil occurs over a shorter distance than rotation at the outer side of the coil. This means the shear stress in the wire at the inner side of the coil must be greater than that at the outside of the coil. This also means that the centre of rotation of the wire must be displaced away from the wire axis towards the centre of the coil, although the actual displacement is quite small.

Two factors have been proposed to include the effects of both the curvature and the transverse shear.

When fatigue is likely (or the spring material must be considered to be brittle) is used as a stress concentration factor. Normally in fatigue calculations the stress concentration factor would be corrected to because of notch sensitivity, but for high strength steels the notch sensitivity is close to 1, so the full value of Kc (or KB or Kw in some procedures) is used.

4. Equations Used in Design
The relationship between load and deflection is given by:

Design methods used to make use of nomographs, however spreadsheets are now used. The Society of Automotive Engineers (SAE) publish a 'Spring Design Manual' that contains information about design and design methodology, reliability and materials.

Normally a design will start with some constraints about space available, governing D, required spring rate, limits of motion, availability of wire diameter, material, maximum allowable stress when the spring is 'solid'. Some iterations will probably be needed to reach the best solution. Fatigue testing is commonly carried out on new designs of springs destined for critical applications.

5. Materials and Manufacture
'Music wire', AISI 1085 steel is used in diameters up to 3 mm for the highest quality springs.

For diameters up to 12 mm AISI 1065 may be used in the hardened and tempered condition or cold drawn.

For larger wire diameter, or for highly stressed applications, low alloy steels containing chrome - vanadium, chrome - silicon and silicon - manganese, hot rolled, hardened and tempered (to 50 to 53 Rc hardness, equivalent to about 1600 to 1700 MPa UTS) are used.

For most spring materials increasing the wire diameter reduces the UTS, and if the UTS is plotted against the wire diameter on semi - log graph paper, the line is often nearly straight for many of the metals used for springs.

Research suggests that the yield shear stress of most metals lies in the range of 0.35 to 0.55 times the UTS, in the absence of specific information, a value of 0.5 times the UTS can be used for hardened and tempered carbon and low alloy steels.

The fatigue strength of springs can be increased by cold setting and particularly by shot peening, which can increase the fatigue strength by as much as 50%. Both processes are routinely carried out on highly loaded automotive suspension springs.

6. New Spring Material and Manufacture for Luxury Watches

Mechanical pocket watches and wristwatches have traditionally been driven by a leaf spring, which is the barrel spring or main spring, wound inside a barrel drum. The external part of the spring presses against the inside wall of the drum and one end is fastened to the drum. The inner end of the spring is fastened to a barrel arbor. By keeping the drum fixed and rotating the barrel arbor, the spring is wound around the arbor and potential (strain) energy is accumulated in the spring.

Because the dimensions of the spring and the drum are limited by the small volume available in watches, the mechanical energy stored in the barrel is also limited. The power reserve of the watch, that is, the running time of the watch at rest, without user interaction, depends on this stored energy. In most cases, the power reserve of a watch is about 48 hours.

If the density of energy storage (the stored energy to volume ratio) can be maximized, the power reserve of the watch is also increased. This is why Ulysse Nardin initiated the development of a barrel spring made of composite materials giving an elastic limit and impact resistance far superior to the best steels known.

The springs have a silicon core produced on monocrystalline silicon wafers. The surface of this silicon core is then coated with a layer of polycrystalline diamond. Compared with steel, silicon and diamond exhibit less fatigue. Moreover, a main spring created using this technique can be expected to have much greater stiffness, stored energy capacity, and resilience. For given dimensions, it is now thought possible to double the power reserve. This may be beneficial for small watches, especially ladies watches, in which the volume available for the barrel is limited.

Another advantage is obtained by using silicon deep etching technology, a photolithographic process which makes it possible to produce complex geometries. Research is under way at Ulysse Nardin to produce a barrel spring with a variable turn width that transmits constant torque. If the torque transmitted to the gear train is constant, the amplitude of the balance oscillation will also be constant. This eliminates the anisochronism related to balance amplitudes, which enables the running precision of the watch to be optimized.

The watch designs require the production of several springs that are more than half a metre long on a silicon wafer that is limited to a diameter of 6 inches (15.4 cm). This limits the dimensions of the free spring (preform), which means that a preform that is compatible with the tiling of the springs on the wafer must be selected, while imposing a varying thickness along the spring to obtain constant torque. To meet this challenge, Ulysse Nardin called upon Claude Bourgeois, who developed a modeling and optimization tool based on Maple.

First applications of silicon in watchmaking
Silicon is a very hard material that does not wear easily. It has a low friction coefficient and low density, and higher precision can be achieved in the production of complex parts by silicon machining techniques than with steel. The first applications of silicon were fixed or moving non-deforming parts, such as bearings, escapement parts, pinions, and escape wheels.

The elasticity of silicon was then also put to use, at the heart of the watch, in the spiral spring associated with the balance. To compensate for the high intrinsic thermoelastic drift of silicon, which is incompatible with accurate timekeeping, Claude Bourgeois and a team at the CSEM recommended thermal oxidation of the surface to compensate for the drift. Today, Ulysse Nardin, in partnership with Sigatec, is using this technology to produce its own thermally compensated silicon spiral springs. Sigtec, a company based in Sion, Switzerland, provides the capability to manufacture silicon parts on an industrial scale.

These new applications required new modeling tools, which were still not widespread in traditional watchmaking, to model, analyze, and optimize these new types of active structures. Maple was used to model and optimize the oxidized silicon sprung balance resonator. The developed model combined the thermal drift up to third order and the anisotropy of silicon. differential equations that characterized the springs at large displacements were integrated, while taking into account the deviation from the isochronism of the resonator at different balance amplitudes. The shape of the terminal curve of the spiral spring, which enabled the isochronism deviations to be controlled, was then optimized by a convergent iterative calculation, varying the appropriate geometrical parameters.

Maple makes it easy to identify the critical parameters related to the required function and the figures of merit of the system. It also helps to establish analytical macromodels, which are useful elements for analysis and for developing new concepts.

Ulysse Nardin Freak Caliber
The first watch to use the new barrel springs with silicon cores is the Ulysse Nardin Freak Caliber. It has a great advantage: its barrel is placed below the rest of the movement. This means that it occupies a large volume since almost the entire diameter of the watch can be allocated to it. As a result, the power reserve of this watch is more than seven days. Only one manual winding a week is necessary, by means of a grooved bezel under the watch. Another feature of this model is that the hour hand is fixed directly on the barrel drum, which is designed to rotate once every twelve hours. Also, this watch has a karrusel tourbillon, making it very precise.

The Manufacturing of silicon and diamond parts
Through its determination to innovate, the Ulysse Nardin factory today has highly sophisticated production facilities that benefit from its technological advances. Sigatec was formed as a joint venture between Ulysse Nardin and another Sion-based company called Mimotec SA, a manufacturer of nickel micro-parts. Diamaze Microtechnology SA, based in Chaux-de-Fonds, Switzerland, produces thin or thick coats of polycrystalline diamond. This is the company that coats the silicon core with diamond to produce the diamond barrel springs. A hard spring with a soft heart is possible as a result.

Other Maple applications
While employed at the CSEM, Claude Bourgeois developed many other simulation applications with Maple. These applications involved anisotropic elasticity, piezoelectricity and electromagnetism, as well as gaseous and liquid microfluidics, in particular, during the development of high-performance resonators made of quartz, then of silicon activated by AlN, and many types of MEMS sensors and actuators.

Original of section 6 from Maple website

David J Grieve. Revised 23rd March 2010. Original: 22nd March 2001

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