Int J Adv Manuf Technol DOI 10.1007/s00170-016-8379-9

ORIGINAL ARTICLE

A simple general process model for vibratory finishing Stephen Wan 1 & Yu Chan Liu 2 & Keng Soon Woon 2

Received: 17 May 2015 / Accepted: 13 January 2016 # Springer-Verlag London 2016

Abstract The present work re-derives a general process model for loose abrasive processes, starting from the interpretation that, during the phase of constant stock removal (equilibrium phase), the surface roughness is actually in dynamic equilibrium about an equilibrium surface roughness, instead of the previous assumption that it tends monotonically to a limiting value. The new model better accounts for the surface roughness evolution seen in both two very different types of vibratory finishing process experiments: very aggressive roughening experimental runs versus more “subtle”, controlled ones. In fact, the original model is a special case, in which the dynamics in the equilibrium phase is highly attenuated and hence still applicable to well-controlled loose abrasive processes such as abrasive flow machining and magnetorheological finishing. Keywords Abrasive wear . Loose abrasive processes . Vibratory finishing . Surface roughness and stock removal evolution . Process model

1 Introduction The present study revisits—particularly, for the case of vibratory finishing—a process model previously derived for loose abrasive processes and effectively generalizes the original model.

* Stephen Wan [email protected]

1

Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis North, Singapore 138632, Singapore

2

Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075, Singapore

Loose abrasive processes encompass the various mass finishing techniques, of which, vibratory finishing is perhaps the most pervasive, finding applications across a wide spectrum of industries. In a typical setup, work pieces to be processed are immersed in abrasive particles in a bowl. As indicated in Fig. 1, the bowl is vibrated by rotating a central pair of eccentric fly weights, which in turn causes the abrasive particles to roll and feed round the bowl in a toroidal motion. As a result of the relative motion between the workpiece and the abrasive media, material is removed from the surface of the workpiece, and depending on the intended applications(s), the workpiece surface would either be polished (smoothened), roughened or stock material removed (for example for deburring and radiusing purposes) accordingly. A comprehensive account of vibratory finishing systems and processes can be found in the book by Gillespie [1]. Process models for vibratory finishing reported in the open literature may be broadly divided into those having a mechanistic content and those based largely on empirical approaches. An example of the latter is the empirical model of Sofronas and Taraman [2] based on experiments on various cylindrical test specimens each of which had a recess at one end of a certain height (projection height) and a lip of a certain width (projection width). The model linked three dependent variables (surface roughness, edge radius and projection width) to five independent variables (Brinell hardness, processing time, media size, vibratory frequency and projection height) for a particular test piece. By relating the cutting force power of the abrasive particles to bowl acceleration, and the mass and velocity of workpiece, Domblesky et al. [3] developed a mechanistic model that yields the total (bulk) material removal, but is silent on the evolution of surface roughness. Hashimoto [5] obtained analytical expressions for the surface roughness and stock removal evolution, based on a set of rules, the physical bases of which, however, were not

Int J Adv Manuf Technol Fig. 1 Plan and cross-sectional views showing media feed and roll directions

eccentric weights

vibratory motor

media roll direction

media feed direction

explained. Uhlmann et al. [4] developed a model that is capable of predicting surface roughness evolution, by considering how a curved fitted Abbott-Firestone profile of an asperity changes over time under an experimentally measured material removal rate. To the authors’ knowledge, to date, the only mechanistic models that encompass both surface roughness and stock removal are those derived by Hashimoto [5], which is, however, applicable only to one- or two-dimensional surfaces, and the more general model of Wan et al. [6], which was cast in terms of point variables so as to be applicable for free-form surfaces. However, in the light of certain data from an investigation on vibratory finishing by Domblesky et al. [7], and a closer reexamination of the experimental data from Hashimoto [5, 8], it was necessary to re-derive our model as follows.

It had originally been assumed, following Hashimoto [5], that the surface roughness would gradually and monotonically reach a limiting value, R∞, in the second phase. However, as indicated in Section 2.2, a physically more reasonable approach is to understand this phase as one in which the changes in surface roughness are in dynamic equilibrium—while stock is being removed at a constant rate—about an equilibrium value, RE. Thus, it is now preferred to term this phase as an equilibrium rather than a steady-state phase.

2 Model development The underlying mechanism of the vibratory finishing process is recognized as one of abrasive wear. Although a combination of two-body (Fig. 2a) and three-body (Fig. 2b) abrasive wear is likely to occur as illustrated in Fig. 2c, instead of one single basic mechanism, both mechanisms may be described by the wear law [9] of the form: VS ¼

kSN L H

a

ð1Þ

where VS is the steady-state wear volume; H is the hardness of the worn surface; N is the normal load acting on the worn surface; L is the relative distance slid; and kS is a wear coefficient. From here, following Queener et al. [10], it was assumed that the total abrasive wear is a combination of a steady-state (linear) portion and a transient portion. In fact, the surface roughness and stock removal evolution may be roughly divided into two phases. These are (i) a transient phase dominated by the transient portion and characterized by a sharp fall (for polishing) or rise (for roughening) in surface roughness and rapid stock removal rate over a relatively short span of process time and (ii) a phase in which the surface roughness levels are relatively flat and stock removal rate is more or less constant.

b

c Fig. 2 Schematics illustrating a two-body abrasive wear, b three-body abrasive wear, and c combination of a and b

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limiting surface roughness, R∞, with an equilibrium surface roughness, RE.

2.1 Outline of the original model To place the new model in context, the original model is briefly outlined in this section. For details of the full derivation of the original model, the reader is referred to [6] and hence they are not repeated in this note. Briefly, in developing the old model, pre-worn asperities, populating an external surface (Fig. 3a), were idealized as primitive geometrical three-dimensional shapes, volumes of revolutions generated by a full sweep of a cross-sectional profile, the height, h of which, in general, is some function of its radius of revolution, r (Fig. 3b). Then, by applying the wear law (Eq. 1) on these asperities, and relating the stock removal, hT, the current height, hp, and the pre-worn height, h0 (for which r = rb) to surface roughness values, the old model for the evolution of the surface roughness Ra and stock removal h reads: Ra ¼ ðRi −R∞ Þ⋅e−

k T pg v s H t

þ R∞


k T pg v s  h ¼ aR ⋅ðRi −R ∞ Þ⋅ 1−e− H t

ð2Þ ð3Þ

where Ri is the initial surface roughness; kT is a transient wear coefficient; pg is the point unit load per unit area or pressure; vs is the point sliding velocity; H is the hardness of the worn surface; and R∞ is the limiting value. aR is essentially a geometrical factor linking the surface roughness with the asperity height.

2.2 Transient phase (new model) As mentioned in Section 2 and reasoned in Section 2.2, instead of assuming that the surface roughness would eventually reach a limiting value, R∞, it would be physically more correct to state that the surface roughness, after a transient stage, would fluctuate about an equilibrium value, RE. Hence, the new model is obtained by replacing a

Ra ¼ ðRi −RE Þ⋅e−

k T pg vs H t




þ R∞

h ¼ aR ⋅ðRi −R E Þ⋅ 1−e−

k T pg v s H t

ð4Þ



ð5Þ

2.3 Equilibrium phase (new model) In this phase, we envisage that the surface roughness, Ra, is in dynamic equilibrium about an equilibrium surface roughness, RE. A “mental picture” of the dynamics is described as follows. Firstly, consider the case in which the surface roughness, Ra, is relatively smooth; that is the excursion, ΔRa = Ra − RE, is negative. As illustrated in Fig. 4a, asperities (peaks) indicated by red layers are generated by the removal of material, as indicated by the blue layers, forming valleys. Then, just as the valley is deepened, the top layer of an exposed asperity is also worn away (Fig. 4b). But an asperity continues to grow, as an increase of the depth of the valley exceeds that of a reduction in the height of the asperity (Fig. 4c). Finally, the asperity reaches its maximum height, that is to say the excursion, ΔRa, is at its maximum positive and the surface is at its roughest. At this stage, the tip of an asperity will be quickly removed, as illustrated in Fig. 5a. Then, just the exposed tip of the asperity is further worn away, the valley is also deepened (Fig. 5b). But the asperity continues to be more and more flat, as the reduction in the height of the asperity exceeds an increase in the depth of the valley (Fig. 5c). Then, once the surface becomes smooth again and excursion, ΔRa, reaches its maximum negative value, the cycle repeats itself. To express the above description in symbols, we again consider the situation when the excursion ΔRa has just reached its maximum negative value. In the other words, the surface is at its smoothest, it is at its greatest tendency to

Fig. 3 Schematic of a threedimensional surface, showing a normal pressure load, pg acting on a particular location, of surface area, δA, over which the media is sliding at a relative velocity, vs and populated by a number of asperities (inset) characterized as a surface roughness; and b the profile of an asperity with defining dimensions [6]

a

b

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Perhaps, the simplest way to capture the above statements is to state that the larger the excursion, ΔRa, the greater the slowing down: −

Fig. 4 Generation of surface asperities in the equilibrium phase: a nascent asperities (red layers) formed by an initial removal of material (blue layers), followed by b growth of the asperities from further material removal which deepens the valleys but counteracted by removal of the exposed tips and c continual net growth as the increase of the depth of the valleys exceeds that of a reduction in the height of the asperities

roughen. At this point, we would expect to see an initial acceleration of the surface roughness. Hence, comparing the excursions, (ΔRa)t, (ΔRa)t − Δt, (ΔRa)t + Δt, at a time, t, a preceding time, t − Δt, and a subsequent time, t + Δt, respectively, we have ðΔRa ÞtþΔt > ðΔRa Þt > ðΔRa Þt−Δt and ðΔRa ÞtþΔt − ðΔRa Þt > ðΔRa Þt − ðΔRa Þt−Δt or ΔðΔRa ÞtþΔt > ΔðΔRa Þt > ΔðΔRa Þt−Δt Now, as a sharper asperity would be more rapidly worn down compared with a blunter one, we hypothesize that this would be manifested as a slowing down of the acceleration in surface roughness with time. In other words,

Δ½ΔðΔRa Þ ∝ΔRa ΔtΔt

and the simplest model is obtained by assuming a linear constant of proportionality, c so that, in the limit, Δt → 0, we have ΔRa ¼ −c

∂2 ðΔRa Þ ∂t 2

ð6Þ

Equation 4 is a linear second-order differential equation, for which the solution takes the form: n
pffiffiffiffiffiffi o ΔRa ¼ k E sin c−1 t where kE is a constant. Writing c− 1 as ω2, we have ΔRa ¼ k E sinðωt Þ

ð7Þ

where ω is recognized as the radial frequency at which the excursion, ΔRa, cycle over the equilibrium surface roughness, RE; and kE is recognized as the amplitude of the excursion, ΔRa. Conversely, once the surface roughness, Ra, has reached its greatest value with respect to the equilibrium surface roughness, RE, and the asperities are at their sharpest, we would expect a sharp initial reduction or deceleration in surface roughness. Thus, ðΔRa ÞtþΔt < ðΔRa Þt < ðΔRa Þt−Δt and

ΔðΔRa ÞtþΔt − ΔðΔRa Þt < ΔðΔRa Þt − ΔðΔRa Þt−Δt

ðΔRa ÞtþΔt − ðΔRa Þt < ðΔRa Þt − ðΔRa Þt−Δt

or

or

ΔΔðΔRa ÞtþΔt < ΔΔðΔRa Þt

ΔðΔRa ÞtþΔt < ΔðΔRa Þt < ΔðΔRa Þt−Δt Again conversely, as a smoother surface is more prone to being roughened while a rougher one is more prone to be smoothened, we hypothesize that this would be manifested as a slowing down of the deceleration in surface roughness with time: ΔΔðΔRa ÞtþΔt > ΔΔðΔRa Þt

Fig. 5 Smoothing of surface asperities in the equilibrium phase: a rapid initial removal of the tips of asperities (blue layers) resulting in smoother asperities (red layers), which b continue to be smoothened from further material of the peaks but counteracted by material in the valleys and c continual net reduction in asperity height as the reduction in the height of the peaks exceeds the increase in the depth of the valleys

Assuming that the smoothening process is symmetrical with respect to the roughening process described earlier on, Eq. 4 also applies to this process and hence to the whole equilibrium phase. The above is graphically illustrated in Fig. 6 where all values have been normalized to their maximum magnitudes, respectively, except for the process time, which has been normalized to the equilibrium period, ω.

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Fig. 6 Graphical illustration of the theoretical variation of the surface roughness excursion, ΔRa, with respect to process time, normalized to aÞ the equilibrium period, ω; together with its speed, ∂ðΔR ∂t , and acceleration

of change, ∂

2

ðΔRa Þ ∂t2

At the same time (see [6] for detailed derivation), the stock is removed according to hS ¼

k s pg v s t H

ð8Þ

2.4 Full model By combining the models for both phases, the full model is given by Ra ¼ ðRi −RE Þ⋅e−

k T pg vs H t

þ k E sinðωt Þ þ RE
k T pg v s  k s pg v s t h ¼ aR ⋅ðRi −R E Þ⋅ 1−e− H t þ H

or more compactly, after combining Eqs. 6 and 7, by   k s pg v s ∂h ∂Ra −ωk E cosðωt Þ þ ¼ −aR ⋅ ∂t H ∂t

ð9Þ ð10Þ

ð11Þ

32.3 m2/s (realized by adjusting the weight of the eccentric flyweights) with offset triangular abrasive media. We could benchmark against only the surface roughness data, as the stock removal data in the transient phase was not reported. From their surface roughness time histories, plots are reproduced below and transient and equilibrium phases of the surface roughness evolution are easily identified. Modelpredicted curves generated by setting model constants listed in Table 1 were compared against the corresponding experimental plots (indicated by their legend titles as listed in Table 1) by superimposing them on the experimental plots reproduced in Figs. 7 and 8. It can be seen that the model is able to reproduce fairly well the salient features of the experimental data, in particular, the oscillation of the surface roughness about an equilibrium surface roughness. In fact, both Hashimoto’s model [5] and the original model of Wan et al. [6] would not have been able to reproduce this particular feature as both these models require the surface roughness to eventually and monotonically arrive at a single limiting value. Examining the values in Table 1, we first note that values of Ri are simply the initial surface roughness values and hence are fixed values. For Steel – 27.4 m/s2 and Steel – 32.3 m/s2 runs, the dynamic response, as reflected in the values of ω and kE would be similar (in fact, they have the same values, in this case) as the material is the same and the bowl accelerations are not too far apart. The difference in the RE values is probably due to the difference in the initial surface roughness, Ri. k p v

Interestingly, the term T Hg s has the same value. This is probably because (a) the granular flow field and, hence, the pg and vs values are similar, as, again, the bowl accelerations are not too far apart and (b) that the wear coefficient, kT, values are similar, as the material is the same. In the case of Al – 23.5 m/s2 and Brass – 23.5 m/s2 runs, although the bowl acceleration is the same, their dynamic responses would be expected to differ, as indicated by the respective values of ω and kE as the materials are different. k p v

3 Benchmarking against experimental data: results and discussion The above model was benchmarked against the experimental data reported by Hashimoto [5, 8] and Domblesky et al. [7] in order to cover both polishing and roughening cases of vibratory finishing. 3.1 Roughening process In their investigation on vibratory finishing, Domblesky et al. [7] essentially roughened the surfaces of cylinders (25.4 mm in diameter and 25.4 mm in height) made of aluminum, brass and steel for various bowl accelerations of 23.5, 27.4, and

For the same reason, the values of the term, T Hg s , are expected to differ, as the respective values of the wear coefficient, kT, and the hardness, H, would be different for different materials. Table 1 Model constant values for generating the model-predicted curves for comparison against the experimental data from Domblesky et al. [7] Experiment data legend title

Ri [μm Ra]

Al – 23.5 m/s2

25 15 40 28

Brass – 23.5 m/s2 Steel – 27.4 m/s2 Steel – 32.3 m/s2

RE [μm Ra]

k T pg vs H

ω [per h]

kE [μm Ra]

2 2 1.5 1.5

4 3 2 2

[per h] 85 58 52 47

3 2.5 2 2

Int J Adv Manuf Technol Table 2 Model constant values for generating the model-predicted curves for comparison against the experimental data from Hashimoto [8] Experiment plot legend title

Ri RE [μm Ra] [μm Ra]

k T p g vs H

ω kE [per min] [μm Ra]

[per min]

Ir = 0.053 μm Ra 0.053

0.01

0.05

0.012

0.07

Ir = 0.71 μm Ra

0.01

0.058

0.01

0.03

0.71

Hashimoto [5] reported results of three polishing experiments and one roughening experiment on steel cylindrical workpieces, with various initial surface roughnesses. For benchmarking purposes, the experimental surface roughness and stock removal plots are reproduced from his patent documents [8], rather than from his paper, as they are larger and more readable. For comparison against the surface roughness experimental data, model constants listed in Table 2 were set and the resulting theoretical curves were compared against the corresponding experimental plots (indicated by the their legend titles as listed in Table 2) reproduced in Fig. 9. We infer, from the good fit between the model-predicted curves and experimental data, that the surface roughness is, in fact, in dynamic equilibrium. In this case, the dynamics are somewhat more subtle than that in then roughening experiments of Domblesky et al. [7]. In fact, by comparing Hashimoto’s model predictions, using the same parameter values he input into his model [5], and superimposing them on the experimental data, as shown in Fig. 10, we observed that Hashimoto’s model [5] (and,

hence, the original model of Wan et al. [6]) was not able to reproduce the subtle dip in the surface roughness at the process time, t = 15 min, for the Ir = 0.053 μm Ra experimental run (indicated by the red arrow). Nor could these two models explain why differences in surface roughness levels persist even at t = 180 min, as they would have predicted the surface roughness value to monotonically converge to a single limiting value. We note that the new model is able to reproduce these persisting differences for the same value of the equilibrium surface roughness, RE. Model-predicted curves for stock removal for the corresponding Ir = 0.71 μm Ra and Ir = 0.053 μm Ra experiments were generated by setting aR = 7.5 and 20, respectively, and compared against the experimental data reproduced in Fig. 11. The present model (and, hence, the original model of Wan et al. [6] as both models are identical with respect to stock removal) is able to reproduce the experimental data fairly well. Likewise, by comparing Hashimoto’s model predictions, using the same parameter values he input into his model [5], and the superimposing them on the experimental data, as shown in Fig. 12, we observed that Hashimoto’s model is able to reproduce the Ir = 0.71 μm Ra experimental data well, but under predicts the Ir = 0.053 μm Ra experimental data. We also observed that the model predictions appear to be in closer agreement with Hashimoto’s experimental data (Fig. 11) than with Domblesky’s data (Figs. 7 and 8). We surmise this is because, as mentioned above, Domblesky ‘s roughening experimental runs are much more aggressive and

Fig. 8 Comparison of model-predicted surface roughness evolution against the experimental data of roughening vibration finishing runs on steel samples, from Domblesky et al. [7]

Fig. 9 Comparison of theoretical surface roughness evolution against the experimental data from Hashimoto [8]

Fig. 7 Comparison of model-predicted surface roughness evolution against the experimental data of roughening vibration finishing runs on aluminum and brass samples, from Domblesky et al. [7]

3.2 Polishing process

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Fig. 10 Comparison of Hashimoto’s model [5] predictions for surface roughness evolution against the experimental data from Hashimoto [8]. Note that Hashimoto’s model is unable to reproduce the subtle dip in surface roughness indicated by the red arrow

extreme and hence less controlled as compared to the polishing experiments of Hashimoto. 3.3 Original model as a special case Looking at the benchmarking results in Section 3.1 and Section 3.2 together, it is clear that the dynamics of the equilibrium phase is governed by the frequency, ω, and the amplitude, kE. The larger the value of the frequency, ω, and the amplitude, kE, the more obvious of the dynamics. In fact, as the amplitude, kE → 0, as in a very controlled process, the evolution model (Eqs. 9, 10, and 11) simplifies to the original model of Wan et al. [6]: Ra ¼ ðRi −R∞ Þ⋅e−

k T pg v s H t




þ R∞ k T pg v s

ð12Þ 

h ¼ aR ⋅ðRi −R ∞ Þ⋅ 1−e− H t þ   k s pg v s ∂h ∂Ra þ ¼ −aR ⋅ ∂t H ∂t

k s pg v s t H

ð13Þ ð14Þ

where the equilibrium surface roughness, RE can now be considered as a limiting surface roughness, R∞.

Fig. 11 Comparison of model-predicted stock removal evolution against the experimental data of relatively well-controlled vibration finishing runs on steel samples, from Hashimoto [8]

Fig. 12 Comparison of Hashimoto’s model [5] predictions for stock removal evolution against the experimental data from Hashimoto [8]

In this case, the surface roughness does behave monotonically. Indeed, in their work on abrasive flow machining (AFM), a very well-controlled loose abrasive process, Wan et al. [11] found that the reduced model describes the experimental data well. It is not surprising, therefore, that Kum et al. [12] also found that the reduced model is adequate for describing surface roughness and material removal in their experiments on magnetorheological finishing (MRF) of glass. Magnetorheological finishing is an even finer process compared with abrasive flow machining. Details of AFM and MRF can be found in [13] and [14], respectively. 3.4 Application of old and new models Both the old and new models can be applied to predict the surface roughness, Ra, and stock removal, h, distribution evolution over a three-dimensional free-form surface, if the pg, the point unit load per unit area or pressure, and vs, the point sliding velocity distribution, are known and hence substituted into the model equations. To this end, Wan et al. [15] modeled and simulated the flow of vibratory finishing abrasive particles as a continuum-based granular flow, and so obtained estimates of pg, the point unit load per unit area or pressure, and vs, the point sliding velocity from the calculated granular flow field. A particularly useful application would be the prediction of changes in the geometry of a free-form surface from a prediction of the stock removal, h, distribution, especially in the case of engineering components whose performance is very sensitive to deviations from the design specifications, such aeroengine turbine and compressor blades (aeroengine aerofoils). Indeed, this idea forms the basis of the development of devices, reported in [16], for adjusting the granular flow of abrasive particles in order to control local stock removal over a critical area, for example, the leading edges of aeroengine aerofoils. In the case of the old model, the wear coefficient, kT, and the limiting surface roughness, R∞, were measured by a tribometer [17] for the particular machine setting at which

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the process will be run and for the particular workpiece material. Now, in the light of the new model, the tribometer will be used to also measure the dynamic response system values (ω, kE, and RE).

2.

3. 4.

4 Conclusion 5.

We conclude this Short Communication with a summary of the salient points, as follows: &

The original model of Wan et al. [6] was re-derived based on the interpretation that, during the constant stock removal rate phase (equilibrium phase), the surface roughness, Ra, is actually in dynamic equilibrium about an equilibrium surface roughness, RE, instead of the assumption it tends monotonically to a limiting value, R∞. The new model better accounts for the evolution of the surface roughness reported for both two very different types of vibratory finishing process experiments: very aggressive roughening experimental runs versus more “subtle”, controlled ones. The new model for stock removal, h, retains the same form as the old model and reconfirms the applicability of the original model to stock removal prediction. The original model is a special case of the new model, where the dynamics of the equilibrium phase is not prominent; that is when the amplitude, kE → 0, which is the case for a well-controlled process

&

& &

6.

7. 8. 9. 10. 11.

12.

13. 14.

15.

Acknowledgments The authors gratefully acknowledge the support given by their respective institutes in the preparation of this manuscript. 16.

References 17. 1.

Gillespie LR (2006) Mass finishing handbook. Industrial Press Inc, New York

Sofronas A, Taraman S (1979) Model development and optimization of vibratory finishing process. Int J Prod Res 17(1):23–31 Domblesky J, Evans R, Cariapa V (2004) Material removal model for vibratory finishing. Int J Prod Res 42(5):1029–1041 Uhlmann E, Dethlefs A, Eulitz A (2014) Investigation into a geometry-based model for surface roughness prediction in vibratory finishing processes. Int J Adv Manuf Technol 75: 815–823 Hashimoto F (1996) Modelling and optimisation of vibratory finishing process. Annals of the CIRP 45(1):303–306 Stephen W, Yuchan L, Keng Soon W, Guan Leong T (2014) A material removal and surface roughness evolution model for loose abrasive polishing of free form surfaces. Int J of Abrasive Technology 6(4):269–285 Domblesky J, Cariapa V, Evans R (2003) Investigation of vibratory bowl finishing. Int J Prod Res 41(16):3943–3953 Patent US5873770. Vibratory finishing process. Inventor: F Hashimoto. Feb 23, 1999. Hutchings IM (1992) Tribology: friction and wear of engineering materials. Edward Arnold, London Queener CA, Smith TC, Mitchell WI (1965) Transient wear of machine parts. Wear 8:391–400 Wan S, Ang YJ, Sato T, Lim GC (2014) Process modeling and CFD simulation of two-way abrasive flow. Int J Adv Manuf Technol 71(5):1077–1086 Kum CW, Sato T, Wan S (2013) Surface roughness and material removal models for magnetorheological finishing. Int J Abrasive Technology 6(1):70–91 Rhoades L (1991) Abrasive flow machining: a case study. J Mater Process Technol 28:107–116 Kordonski WI, Golini D (1999) Fundamentals of magnetorheological fluid utilization in high precision finishing. Journal of Intelligent Material Systems and Structures 10(9): 683–689 S Wan, W S Fong and Z H Tay. Process modelling and simulation of vibratory finishing of fixtured components, Proceedings of the 10th EUSPEN (European Society for Precision Engineering and Nanotechnology) Conference, Vol 2, pp 269-273. Oral Presentation Vibratory finishing flow controls. Inventor: S Wan. Technology disclosure: IHPC - TD – FD – 2011 – 005. Institute of High Performance Computing, Singapore Vibratory finishing tribometer. Inventor: S Wan.Technology Disclosure: IHPC - TD – FD – 2011 – 008, Agency for Science and Technology, Singapore.