The dashpot

Text Box: Fig 16-9 When I first thought of including the dashpot in this chapter I thought that it belonged too far back in time to be justified now but on reflection, it is the fundamental version of modern dampers and shows us something about the characteristics of such devices. I first met the dashpot in use on a steam engine as part of the Porter governor to control the speed of the engine.  The Porter governor is shown in figure 16-9. Its function is to open and close a steam valve and so control the speed of the engine. Such valves are, and were, sensitive to the movement of the valve stem and non-linear. The valve was linked to a lever mounted on a pivot and that lever was moved by the system of weights and levers shown in the upper part of the figure. Two fly-weights were mounted on the two upper links and rotated on a spindle driven by the engine. These fly-weights swung in and out in response to changing engine speed. Their motion was stabilised by the two lower links that were attached to a collar that could move up and down and lift the dead weight. Two spigots on the main link ran in a groove in the collar and so the fly-weights lifted the lever.

 

This whole moving system could bob up and down and cause the engine speed to fluctuate and the dashpot was fitted to damp out this motion.

 

Figure 16-10  shows the essential features of the simple dashpot. There is a cylinder that is fixed somehow, a piston with a significant radial clearance and oil to fill the cylinder. In practice there would be some system of guidance to keep the piston coaxial with the cylinder.

 

Text Box: Fig 16-10 If a force  is exerted on the piston this force will produce a pressure in the oil under the piston and cause a flow through the annular gap. There must be a relationship between the force, the viscosity of the oil, the relevant dimensions and the speed of the piston.

 

In this device the oil flows between two parallel surfaces but they are two cylindrical surfaces of length  and, if  is small when compared with  the effective width  and the oil flows through an area .

 

Now, if the force  is applied suddenly, the piston will start to move and, because of the high viscosity of the oil, conditions will quickly become steady with the piston moving at a velocity . Then the work done by the force will be continuously lost to the internal energy of the oil. We now have a case of oil flowing between two parallel plates where one is moving. The expression that we have is:-

                                        

 

 and the pressure  in the oil under the piston =   then :-

                      .

 

This easily reduces to :- .

 

If  is small when compared with   we can write .

 

 

Then, once the dimensions are chosen, the speed is proportional to .

 

Text Box: Graph 16-5 Of course when a dashpot is in use the force is always changing and it is worth calculating the relationship between force and velocity for a typical case. I have taken the case where the diameter of the piston is  50 mm and the length is 30 mm with the oil having a viscosity of 0.08 kg/ms. Then, in graph 16-5 I have plotted speed against force for three values of , 1 mm, 0.5 mm and 0.25 mm.

 

Cleary, for a given oil the speed response of the dashpot is critically dependent on the value of .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

It is evident that, by a trial process, coupled to some calculation, a dashpot can be matched to an application.

 

However there is one important fact to note. Dashpots have to work in both directions and on the down travel in figure 16-10 the pressure will rise to resist any force. On the upward travel the pressure below the piston can only fall to zero absolute and, if the upward force is too great, voids will appear in the oil under the piston. Those voids will make the oil foam. One might consider capping the cylinder and fitting a seal between the cap and the piston rod. Then, if the space above the oil is filled with compressed nitrogen the dashpot will work in both directions equally well without foaming. This is the basic concept of the so-called shock absorber[1] used in vehicle suspensions.

 

In the shock absorber the piston fits tightly in the cylinder so that  is small and, instead of the oil flowing through this very narrow space round the piston a hole in made in the piston and energy is dissipated into the oil from the jet of oil produced by the hole. In this design it is easier to make the hole reproducible than the radial clearance between the piston and the cylinder.

Text Box: Fig 16-11

The most common application of the shock absorber must be in the spring suspensions of vehicles. There the shock absorber must be cheap to make, last a long time and be of a shape that suits the application. On top of this the oil must circulate so that it can be cooled to carry away the heat generated by the continual loss of energy into the oil. This leads to the complexity shown in figure 16-11.

 

The shock absorber is telescopic and a system of holes and non-return valves in both the piston and the end cap that joins the inner cylinder and the outer annular volume is designed to circulate the oil. A typical shock absorber is shown in figure 16-.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


[1] In fact it is the spring that absorb the shocks and the “ shock absorber” is the damper.