This work deals with the tribological performance of karanja oil trimethylolpropane ester (KOTMPE) biolubricant base oil for its probable application as automotive lubricant. The biolubricant was synthesized by transesterification of karanja oil methyl ester with trimethylolpropane (TMP) under acid catalyst. The study was made with Ducom TR30L four-ball tester at 1200 rev min −1 speed and 75 °C temperature over 60 min duration under normal loads of 15 kg and 40 kg as per ASTM D 4172-94 A and B standard test method. Principal results at two loads are given here: Coefficient of friction (CoF) 0.100 and 0.042, wear scar diameter (WSD) 0.30 mm and 0.44 mm, flash temperature parameter (FTP) 80.932 and 126.249, and thermal energy (TE) 0.054 J and 0.060 J, respectively. The study found that KOTMPE has lowest CoF than any vegetable oil, TMP ester or commercial lubricant. Similarly, the WSD was lowest among all the vegetable oil based lubricants and was at par with SAE 20W-50 and SAE 40 commercial lubricants. FTP was better compared to any vegetable oil or TMP ester. Finally, the energy efficiency of KOTMPE was better than that of other vegetable oils, TMP esters and mineral lubricants. The synthesized ester demonstrated the outstanding performance in terms of friction and wear characteristics along with high thermal stability and energy efficiency worthy of comparison with multiple lubricating products reported by different research groups in available literature during last two decades.

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Vegetable oils lack acceptable thermo-oxidative stability due to the presence of tertiary β-hydrogen in glycerol backbone of triglyceride molecule. Chemical modification methods may significantly improve the thermo-oxidative stability of vegetable oils derived biolubricants without hindering their environmentally benign characteristics. This study was aimed at evaluation of thermo-oxidative stability of non-edible karanja oil derived biolubricant base oil. The biolubricant karanja oil trimethylolpropane ester (KOTMPE) was synthesized by conventional two step transesterification process. Thermal stability of synthesized product was assessed by thermogravimetric analysis in non-isothermal mode under nitrogen atmosphere, whereas the oxidation stability was analyzed using Rancimat method. Kinetics of thermal degradation of biolubricant was also investigated by thermogravimetric analysis to obtain order of thermal degradation, activation energy and the frequency factor. The results revealed excellent thermo-oxidative stability for synthesized product at high temperatures with ample scope for further improvement by blending with appropriate additives as demanded by specific applications.

Convenient formulae for finding the sums of kth power of the first n natural numbers may be useful in some engineering applications. The formulae for k = 1, 2, and 3, are commonly found in the literature. In this paper, an attempt is made to develop a general algorithm for finding the sum for any positive integer value of k. The development of the algorithm is entirely an engineering approach, based purely on a simple geometric interpretation and does not involve any deep mathematics. This algorithm may be used to derive the formulae for different values of k. Some of the possible engineering applications of these formulae are also discussed.

The work presented deals with the viscous flow characterization of karanja oil based bio-lubricant base stock. Karanja oil trimethylolpropane ester (KOTMPE) bio-lubricant base stock was prepared from karanja oil methyl ester (KOME) and trimethylolpropane (TMP) using acidcatalyzed transesterification synthesis protocol. The viscosities were measured at 10-60 °C and 10-1000 s -1 shear rates using model HR-3 Discovery Hybrid rheometer. The viscosity-temperature interdependences at different shear rates were modeled using the Arrhenius equation. The viscosity values predicted with Arrhenius model were found in good agreement with measured values. The flow behaviour index of KOTMPE bio-lubricant stretched from 1.036 to 1.527, which suggested a gradual shift in fluid behaviour from Newtonian to non-Newtonian with increase in temperature. The study confirmed that Arrhenius equation along with Ostwald-deWaele power law could be used to predict the apparent viscosity and flow behaviour of synthesized KOTMPE bio-lubricant oil.