# Spring-like device with anisotropic k value

Is there a device that acts like a spring (i.e. $F=kx$) but the spring constant, $k$, has different values in compression and tension?

For example, if $k_c > k_t$ (where c and t refer to compression and tension), then the spring would quickly compress und a compressive force but would slowly expand under a tensile force.

I imagine you could design a hydraulic system like this with some check valves and control valves. Is there a single device that does this? Or alternatively, are there practical engineered systems that do this?

• useful search term : hysteresis. Some elastomers (rubber) have this property to a certain extent. As it involves energy loss, rapid cycling produces heat. This was used to provide both spring and damping in the Mini suspension. – Brian Drummond Feb 15 '17 at 0:02

You can get something very similar to this with belleville washers. A stack of belleville washers takes load only in compression. It has zero stiffness in tension. I cannot find any good illustrations of this on google, but what you can do is to set up two separate stacks of washers, one for each direction. In ASCII art it looks kinda like this:

|>>>>>>|<<<<<<<|

If the middle bar is moved to the left, the left stack is in compression and the right stack is in tension. Since the belleville washers have no stiffness in compression, the force on the bar is controlled only by the left stack. If you move the middle bar to the right, the right stack is in compression and the left stack is in tension. Then, to get an anisotropic spring, just put a different number (or size) of washers in the left stack versus the right.

• – Narasimham Feb 18 '17 at 19:52

One limitation is that a spring, by definition, exerts a force proportional to its displacement so once you compress it the returning force is what it is.

From your description it actually sounds like what you really want its a damper which provides a resistance proportional to the speed of movement and doesn't provide a returning force when it isn't being displaced.

You can certainly get dampers off the shelf which provide damping in one direction only which sounds like what you want this is one example picked at random : http://www.slamproof.co.uk/epages/BT3287.sf/en_GB/?ObjectPath=/Shops/BT3287/Products/%22HD22/100%22

You could also have a compression and extension dampers of different rates in parallel if you still want some damping in one direction.

• Assuming a constant mass of the system, this would give me $F=-k_v dx/dt-k_2 x$ where k_v depends on the direction of motion. I'd rather have $F=k_v x$ where that k_v depends on the direction of displacement, but I could probably work with the damped version in this case. The type of product you linked hadn't occurred to me, thanks. – ericksonla Feb 15 '17 at 17:01
• That's the path I was thinking of -- it's sort of like an air pump, where it's easy to draw air in via the valve, but then the valve closes so it's hard to push air out. – Carl Witthoft Feb 15 '17 at 19:16

Essentially a bi-modulus or bilinear characteristic? In this suggestion two strips are pinned together and one end is fixed at the other. When compressed the buckling resistance is low. In tension strip stresses in metal are high, so acts as a stiff spring.