Parámetros de diseño

MR fluids are the slurry of hydrocarbon oils or silicone oils and micron size ferrite particles. The ferrite particles are coated with anticoagulant for preventing them from forming lumps due to coagulation. The coating of surfactant and anticoagulant also delays the sedimentation of the ferrite particles. When un-activated by the magnetic field they behave like ordinary slurry of ferrite particles. Therefore the viscous behaviour of an MR fluid in the absence of magnetic field is like an ordinary Newtonian fluid. However, when a magnetic field is applied in the direction perpendicular to the flow the ferrite particles align along the magnetic field to form columnar structures which offer resistance to the parent fluid as it flows over them. The parent fluid tries to shear off the chains of magnetised ferrite particles and because of this, the sheared off chains of ferrite particles flow in a plug like lump. As a result of this the MR fluids show a Bingham fluid like behaviour. The shear stress developed due to the flow of parent fluid over the ferrite particles chains, results in the breaking and reformation of ferrite particle chains. This results in an increase in apparent viscosity of fluids. The magnetic fluids can be divided into following three types:

(1) Magnetorheological fluid. (2) Ferro fluids.

Out of the above magnetic fluids the behaviour of magneto-rheological fluids has already been described above. Ferro-fluids are the suspensions of nano-ferrite particles in hydrocarbon oil. These fluids exhibit an increase in viscosity under steady magnetic field in the manner similar to MR fluids, with the difference that the increase in apparent viscosity is limited to twice the viscosity of parent fluids. This is because the ferro fluids contain nano size ferrite particles so they behave like colloids and the forces due to Brownian movement are stronger than the force of the magnetic field (Bossis et al (2002)). In case of MR fluids the increase in viscosity is 5-7 times that of parent fluid. The ferro-fluids have many other interesting properties such as they show a reduction in apparent viscosity as compared to the parent fluid when subjected to oscillatory magnetic field. The energy of the applied oscillatory magnetic field gets converted into the kinetic energy of the fluid, leading to an apparent decrease in the parent viscosity.

Bi-disperse fluids are the mixture of MR and Ferro fluids and they have faster response to magnetic field as compared to MR fluids and they have a longer sedimentation time for ferrite particles as compared to MR fluids ( Bossis (2002), Ngatu and Wereley (2007)). The behaviour of all of the above types of fluids under the influence of steady magnetic field is the same. The formation of columnar structures of ferrite particles in magnetic fluids is as shown in Fig 2.1.

Fig 2.1 Behaviour of ferrite particles under the influence of magnetic field as the MR fluid flows between the two parallel plates.

MR fluids can be used in three modes of flow, (Stanway et al 1996, Boelter et al (1997), Dixon (1999) , Poynor (2001), Gregory et al (2007), Liao et al (2007),). In the valve mode the fluid flow is like a Poisueille flow. In this mode the resistance of the fluid flowing through the channel can be varied by varying the strength of the applied magnetic field. The channel in this case can be a gap between the two parallel plates or an annular gap between the two concentric cylinders, (see Fig 2.1).

In the shear mode one of the plate or cylinder is moving in the direction opposite to the flow. The MR fluid can be stationary or moving with some value of velocity. In latter case it is more appropriately called as the mixed mode operation of MR device (ref Fig 2.2).

Fig 2.2 Shear mode operation of MR device.

In the rotary devices such as clutches and brakes pure shear mode type operation of MR fluid takes place. In the squeeze mode operation of an MR device one of the parallel plate moves perpendicular to the direction of flow as shown in Fig 2.3. Since the force required to squeeze

the magnetised force is quite large therefore the squeeze mode MR device is suitable for bearing applications.

Fig 2.3 Squeeze mode operation of MR device.

2.2.2 MR devices

MR fluids can be used in various applications such as dampers, clutches, seals, bearing etc. In this work the application of MR devices shall be confined to the dampers as it is the theme of this investigation. Out of the application of above three modes the dampers use valve mode or shear mode operations. The simplest design of MR damper has a piston which has magnetic coils provided with suitable wiring arrangement for energisation. The damper is usually provided with an integral gas type restoring spring which similar in configuration to a hydraulic damper shown in Appendix –I, Fig A.13. If the damper has an integral restoring spring then it is called as twin tube damper. On the other hand if the restoring gas spring is separate then the MR dampers are usually mono-tube type construction (See Fig 2.4) (Dixon (1999), (2001), Boelter et al (1997), Gregory et al (2007), Liao et al (2007), Poynor (2001)). In this design the MR fluid flows between the cylindrical surface of the piston and the wall of the cylinder.

Fig 2.4 Schematic of a mono-tube damper

Thus, it is a flow and shear mode type damper or mixed mode type damper. In valve mode type dampers the MR fluids either flows through a hole in the piston which is surrounded by the coils or the piston forces the fluids through an annular gap which is surrounded by the coil as shown in Figs 2.5 and 2.6 (Dixon (1999), Kawashima et al (2001), Boelter et al (1997), Gregory et al (2007), Liao et al (2007), Poynor (2001)).

Fig 2.5 Schematic of a mono-tube valve mode type damper with flow passage embedded in the piston.

Fig 2.6 Schematic of a mono-tube valve mode type damper with bypass type flow passage.

The principle of valve mode type damper can also be used for valve application as described in Ai (2006). For enhancing the effectiveness of the valve the coils can be designed to be positioned in the annular gap so that the flow of MR fluid under the influence of magnetic field can be radial and annular. This design results in an increase in the fluid volume affected by the magnetic field. The MR fluids based valve can be modified into a more compact form and used to control the valve lift of the valve type damper described in the survey of conventional hydraulic type dampers to control the damper force spike. The schematic of such a design which, has been also referred to in Poynor (2001) is shown in Fig 2.7.

Fig 2.7 Schematic of a MR damper or valve controlled conventional valve type damper Poynor (2001).

A brief survey of all the damper designs based on study of literature such as (Dixon (1999), Boelter et al, (1997), Gregory et al (2007), Liao et al (2007), Poynor (2001)) shows that the MR dampers have been tested in speed range of 0-2m/s. However in recent times the work on MR dampers subjected to impact loading has started appearing (Wang and Li (2006), Lee and Wereley (1999), Norrsi and Ahmedian (2003), Facey et al (2005)). The study of publications on the MR dampers which were tested in the speeds in the range of 5-7 m/s show the presence of damping force spike (Wang et al (2006)). There are very few publications describing the performance of the damper behaviour at speeds above 8m/s second. This can be possibly because a large number of real life applications which require dampers to operate at speed up to 2m/s. The challenge in the development of high speed damper is the attenuation of transients which are non controllable components of the damper force. These transients appear as force spike in the force versus displacement curves for the hydraulic dampers in general and MR dampers in particular. The applications of dampers for aircraft landing gears (including UAVs)

operate at heavy loads and in the speed range of 5-7m/s (Batterbee et al (2007,1&2), Sims(2000), Peel and Bullough (1994)). The behaviour of MR dampers has been described by fluid dynamics model based on Herschel Bulkley model or Bingham plastic type non- Newtonian fluids (Kamath et al (1996)). Due to the formation and breakage of the chain ferrite particles in the MR fluids subjected to the magnetic field, MR fluids behave like Bingham fluids (nature of flow is similar to toothpaste). A generalized plot showing the variation of shear stress with the shear rate is shown in Fig 2.8. The fig 2.8 shows that the Bingham plastic behaves like a rigid body until the shear stress in the fluid is less than the initial shear stress. The yield shear stress is dependent on the strength of the magnetic field and this relationship makes the MR fluid a field controllable fluid. If the shear stress corresponding to the pressure gradient across the fluid channel exceeds the pre-yield shear stress, then the post yield shear stress is the sum of pre-yield shear stress and shear stress due to post yield viscosity.

So far, the modeling of force of an MR damper has been done by three classes of models. The first class of models is called phenomenological models. Since the MR dampers exhibit a hysteretic behavior, MR damper models of the first type use the experimental data to fit a hysteresis curve to predict the damper force as a function of velocity. The details of such model have been outlined in Wereley et al (1999), Butz and Von Stryk (2002), Mohammad et al ( 2007) and Wang and Liao (2011). In this class, also lie the phase transition models based on Falk and Kanopka (1990), Lookman et al (2003) and Wang and Liao (2011). The phase transition model for MR dampers was developed on the basis of phase transition theory which was proposed for the investigation of crystallographic phase transition in shape memory alloys (Wang and Liao (2011)). However, in Wang and Liao (2011) it is given that although the physics involved in the MR fluids is taken into account to some extent in this model but it is still a phenomenological model. The second class of models is called as sigmoid function models Wang et al (2003). In these models the force velocity relationship is obtained by fitting the sigmoid function to the experimental data. In the third class of models called as the equivalent models, the variation of force with velocity is expressed in terms of equivalent springs, variable viscous damping and friction element (Oh and Onoda (2002)). The third class of models are based on the quasi steady solution of the Navier Stokes equations using either Bingham plastic model or Herschel Bulkley model for deriving the equations for the velocity profile of MR fluid flowing through the channel, Phillips (1969), Kamath et al (1996), Lee and Wereley (1999), Norrsi and Ahmedian (2005), Facey and Rosenfeld (2005), Chooi and Oyadiji (2008), Wang and Gordaninejad (2007), Li (2000). In this work the quasi steady model will be discussed in details as present work is going to be an extension of this model.