Belleville Springs

Belleville springs are conical washers that rely on the curvature of the shell to provide stiffness as it is compressed.

Bi-stable: Their geometry means that belleville spring can have a bi-stable snap-through behavior. This behavior can be very useful in mechanisms that we want to fail in a stable position, like this poppet valve:

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From Fundamentals of Machine Elements by Schmid, Hamrock, and Jacobson


Hysteresis: Unlike helical springs, Belleville springs also generate friction as they deform because there is a coupled radial and axial motion at the outer and inner rim. This friction creates hysteresis in the spring’s force-deflection curve that (although it can inhibit repeatability) can also act as a damper if that is needed.

Figure 12. Isothermal load–deflection curve of the Belleville spring at T t = 323 K and subsequent thermal cycle. 

From NiTi Belleville washers: Design, manufacturing and testing, by Maletta et al.


Compact: Due to the non-linear nature of Belleville springs, it is possible to get a very large stiffness in a small volume. Additionally, Belleville springs can be stacked in series (like a bellows) to reduce their stiffness, or in parallel to increase their stiffness.


From Raymondasia

Information also taken from:

Belleville Springs

Vicsous Shaft Couplings

Most automatic car transmissions use a fluidic coupling to transmit torque. Fluidic couplings have the benefit of controlling the relative speed of two shafts with the shear forces generated in the working fluid (usually Silicone) between a set of discs and the housing. In automatic transmissions, these couplings allow one shaft to spin freely for a brief period of time while gears are changed.

In the case of extreme slip, the fluid heats up and thermally expands. This expansion pushes the discs against each other, nonlinearly increasing their ability to transfer high torques. This self help, called the hump effect, also prevents the coupling from overheating. When the fluid expands under heat, the shafts spin at nearly (if not the exact) same speed, reducing the generation of heat from shear in the fluid.

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image and concept taken from Mark’s Standard Handbook for Mechanical Engineers

Vicsous Shaft Couplings

3D Kinematic Coupling (p-set4)

Repeatable opening and closing of the sample box is important for maintaining a good seal. Kinematic couplings (KCs) are good at ensuring high repeatability, down to the quality of the surface finish in the part. Therefore, this week, I decided to make a mockup of the general shape and size of the box to gain more intuition for the project and practice making a kinematic coupling. For manufacturing simplicity, I decided to go with a 3 V-groove KC. Since the mockup was constructed out of wood, the plate holding the KC balls in place was the largest source of compliance in the structure. The KC box is imaged below.



To test the repeatability of the KC, I taped the box to the floor, taped a laser pointer to the lid, and placed a mark 488″ away from the box. Then my lab-mate removed and replaced the KC lid while I marked the position of the apparent center of the laser. Each time she replaced the lid, she pressed the laser. This introduced an error by deforming the plate on top of the KC balls. In one direction, the angular error was 0.002 radians, and int he other direction, the angular error was 0.005 radians. This happened with the press of a finger, or approximately 0.25 N. This means that the stiffness of the KC is approximately 0.02 radians/N.



However, when the laser was taped on, the force variation from pressing the button was eliminated. The resulting test was far more precise because of the consistent force. In this case, the error was at most (we were limited in accuracy by the width of the laser at that distance) 0.23″ over 488″ or 0.0005 radians.


3D Kinematic Coupling (p-set4)