Precision Engineering 33 (2009) 99–106 Contents lists available at ScienceDirect Precision Engineering journal homepage: www.elsevier.com/locate/precision Modelling of fluid continuum considering 3D surface parameters in hydraulic assemblies P. Saravanakumar, K.K. Manesh, M. Singaperumal ∗ , B. Ramamoorthy Department of Mechanical Engineering, IIT Madras, Chennai 600 036, Tamil Nadu, India article info Article history: Received 13 July 2006 Received in revised form 16 March 2007 Accepted 1 April 2008 Available online 4 May 2008 Keywords: Surface metrology 3D surface modelling Friction Hydraulic assemblies Birmingham parameters abstract Friction in servo hydraulic assemblies reduces the response characteristics of the system. The friction is influenced by various factors including the geometry (form and surface errors) of the sliding surfaces. In this work, functionally significant 3D surface parameters from the Birmingham parameters are investi- gated for reduced friction. A 3D surface modelling approach is presented using random process modelling as the basis. An exponential decay areal autocorrelation function is used to model the grinding and hon- ing processes which are commonly employed for the manufacture of the hydraulic assemblies. Honed surface is modelled with the crosshatches of appropriate angle. Method of surface modelling is vali- dated using the data obtained through measurements on a practical surface. Different surface maps with varying surface parameters of the ground and honed surfaces are generated. The fluid continuum gap geometries of the hydraulic assemblies are modelled using these surface maps as envelopes. Pressure dis- tribution, velocity and viscous friction force are used as measurands of the frictional characteristics. Using computational fluid dynamics (CFD) approach, these measurands are evaluated for different functionally significant Birmingham parameters. Based on further analysis, negative skewness, lower kurtosis values, higher valley fluid retention index were found to have lower frictional characteristics. © 2008 Elsevier Inc. All rights reserved. 1. Introduction Electro hydraulic servo systems (EHSS) have wide applications in power and motion transmission devices due to their high power density coupled with controllability. The performance of the EHSS (based on quickness of response, positioning accuracy, energy loss, etc.,) is affected by friction in the mating parts of the assemblies such as spool valves and actuator piston. This friction is a function of load, which acts on the assemblies, viscous drag of the fluid, gap geometry, form error and surface topography of the machined component. To reduce the friction due to form and surface errors, preci- sion components used in EHSS are given with stringent tolerances, hence difficult to manufacture and lead to higher production cost. Components cannot be machined to geometric perfection. They have form and surface errors that lead to varying gap geometry between the sliding parts in the hydraulic assembly and contribute to the friction. Few attempts were reported on the influence of form errors in hydraulic assemblies [1–4]; but no efforts have been made ∗ Corresponding author. Tel.: +91 4422574678; fax: +91 4422570509. E-mail addresses: saravanaiitm@gmail.com (P. Saravanakumar), maneshkk@gmail.com (K.K. Manesh), msingam@iitm.ac.in (M. Singaperumal), ramoo@iitm.ac.in (B. Ramamoorthy). so far to study the influence of 3D surface topography parameters except R a [1]. This work is an attempt to study the influence of func- tionally significant 3D surface topography parameters particularly for reduced friction in EHSS and other hydraulic assemblies such that its performance can be improved. 1.1. Lubrication between the sliding surfaces In EHSS assemblies where the radial clearances commonly ranges from 5 to 10 m and roughness value (R a ) of the order of 0.5–0.6 m forming the lubrication film parameter greater than 5. Thus, hydrodynamic lubrication characteristics are the major con- tributing factor for friction reduction [5]. 2. Need for 3D surface topography studies in hydraulic systems Surface topography can contribute to good fluid retention prop- erty along with the chemical property and other physical metrology parameters like hardness, residual stress, etc., of the material [6]. Surface asperities or imperfections puncture the lubricant film, cre- ating metal-to-metal contact; hence can act as a source of friction and wear. Despite the use of lubricant, a surface with good lubricant retention property must be implemented. Honing operation that 0141-6359/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2008.04.003