A novel eccentric lapping machine for finishing advanced ceramic balls

Advanced ceramic balls are used extensively in hybrid precision ball bearings and show advantages in high speed, high temperature, high load and hostile environment. Finishing these balls with high quality, good efficiency and low cost is critical to their widespread application. A brief review of the methods for finishing ceramic balls is presented. The design of a novel eccentric lapping machine for finishing advanced ceramic balls is described. The kinematics of eccentric lapping is analysed and discussed, the symbolic expressions for the ball spin angular speed, omega (b), ball spin angle, beta, and ball circulation angular speed, omega (c), are derived and numerical solutions are plotted. Two kinds of hot isostatically pressed (HIPed) silicon nitride ball blanks (13.25-13.50 mm in diameter) were lapped and polished to 12.700 mm using this machine. A maximum material removal rate of 68 mum/h was achieved at the lapping step, which is much higher than by the traditional concentric lapping method. The polished ball surface roughness, R-a, value is 0.003 mum, and the ball roundness is 0.08-0.09 mum, which is above grade 5 and close to grade 3 of the precision bearing ball specification. This machine can be used as a prototype to develop a larger-scale machine for production

Comparison of 4-ball and 5-ball rolling contact fatigue tests on lubricated Si3N4/steel contact

Accelerated four-ball and five-ball rolling tests were performed on HIPed Si3N4 ball samples (rough lapped with surface roughness value Ra0.08 μm and Rq0.118 μm) in fully lubricated condition. The contact load and the stress cycles per minute for four-ball rolling and five-ball rolling tests were maintained the same. The rolling track appearances of five-ball tests reveal severe sliding occurred. In one case, the opposite arc cracks were generated all over the two sides of the rolling track, and this could not be explained by simplified kinematics model. The failure mechanisms were discussed, which suggest the sliding on the two sides of the track was in the opposite direction

The effects of lapping load in finishing advanced ceramic balls on a novel eccentric lapping machine

HIPed (Hot Isostatically Pressed) silicon nitride ball blanks were lapped from diameter 13.255 mm to diameter 12.7 mm by a novel eccentric lapping machine. A maximum material removal rate of 68 μm/hour has been achieved under a nominal lapping load of 43 N/ball. It was found that the material removal rate was increasing almost linearly with the lapping load within this load range. When the lapping load was higher than 43 N/ball, the material removal rate started to drop and the lapped ball roundness error started to increase. At the highest nominal lapping load of 107 N/ball, surface and subsurface damages were found on the lapped balls. Because of eccentric loading effect, the actual load on individual ball could be 25~28% higher than the nominal lapping load. The surface residual stresses of lapped balls under different lapping loads were measured, and it was found that the lapping load had less effect than previous HIP process. Rolling contact fatigue tests were conducted on balls lapped at nominal loads of 43N/ball and 107 N/ball. No failure occurred on the ball lapped at 43 N/ball after 138 million stress cycles. Ball lapped at 107 N/ball was failed after 13.3 million stress cycles with a shallow spall with flat bottom inside. This research suggests that the lapping load for advanced ceramic balls in conventional concentric lapping could be doubled from 20N/ball to 40 N/ball without degrading the surface quality of lapped balls

The influence of heterogenous porosity on silicon nitride/steel wear in lubricated rolling contact

Heterogeneous porosity is detected on the surface and subsurface of hot isostatically pressed (HIPed) silicon nitride spherical rolling elements. The extent of the localised porosity accounts for an area of 6% of the rolling element surface and 4% of the material volume. An experimental investigation using a rotary tribometer is described to compare the lubricated rolling wear mechanisms and performance of HIPed silicon nitride with heterogeneous porosity defect in contact with steel. A brief review of previous investigations is presented. Localised porosity detection using white and violet light microscopy with post-test evaluation is described. Discussions, micro-hardness measurements and scanning electron microscopy illustrations are presented. Critical localised porosity size is evaluated from experimental results

Parameter optimization by Taguchi Methods for finishing advanced ceramic balls using a novel eccentric lapping machine

The final finishing process of advanced ceramic balls used in hybrid precision bearings constitutes two-thirds of the total manufacturing cost, and hence effective and economic finishing methods and processes are critical to their widespread application. A novel eccentric lapping machine is designed and manufactured. Hot isostatically pressed silicon nitride ball blanks (diameter 13.25 mm) are used to investigate the feasibility of accelerating the ball finishing process while maintaining high surface quality. Taguchi methods are used during the first step of finishing to optimize lapping parameters; the L9 (3(4)) four-parameter, three-level orthogonal array is used to design the experiment. Experimental results reveal that this novel eccentric lapping method is very promising; a material removal rate of 40 mum/h is achievable. The optimum lapping condition is found to be high speed, high load and high paste concentration with 60 mum diamond particles. The analysis of variance shows that the most significant lapping parameter is lapping load, which accounts for 50 per cent of the total, followed by lapping speed (31 per cent); the particle size and paste concentration only account for 12 per cent and 7 per cent respectively. A comparison with previous lapping experiments and the mechanism of material removal are also discussed briefly

The polishing process of advanced ceramic balls using a novel eccentric lapping machine

The finishing process of advanced ceramic balls can be divided into two steps. The first step is lapping in which most of the stock from the ball is removed at a higher material removal rate. The second step is polishing in which the required ball surface roughness, roundness, dimensional and geometric accuracy are achieved. In polishing, the abrasive particle size is ≤ 1 μm, and the load and speed are lower than lapping. A novel eccentric lapping machine is used for polishing HIPed (Hot Isostatically Pressed) silicon nitride balls. In the initial polishing stage, the polishing load is demonstrated most influential in the reduction of surface roughness value Ra. However, in the later polishing stages, the erosive process played a major role in the further reduction of Ra, although the high roughness peaks cannot be removed by erosive process alone. Experimental results also show that in order to achieve desired surface roughness value, the initial surface quality of the upper plate should be reasonably high, and deep scratches should be avoided to leave on the ball surface in previous lapping process. The best polishing results achieved were surface roughness values of Ra of 0.003 μm and rms (Rq) of 0.004 μm, ball roundness of 0.08~0.09 μm. This proves the novel eccentric lapping machine is suitable for polishing advanced ceramic balls as well

Distance colouring without one cycle length

We consider distance colourings in graphs of maximum degree at most $d$ and how excluding one fixed cycle length $\ell$ affects the number of colours required as $d\to\infty$. For vertex-colouring and $t\ge 1$, if any two distinct vertices connected by a path of at most $t$ edges are required to be coloured differently, then a reduction by a logarithmic (in $d$) factor against the trivial bound $O(d^t)$ can be obtained by excluding an odd cycle length $\ell \ge 3t$ if $t$ is odd or by excluding an even cycle length $\ell \ge 2t+2$. For edge-colouring and $t\ge 2$, if any two distinct edges connected by a path of fewer than $t$ edges are required to be coloured differently, then excluding an even cycle length $\ell \ge 2t$ is sufficient for a logarithmic factor reduction. For $t\ge 2$, neither of the above statements are possible for other parity combinations of $\ell$ and $t$. These results can be considered extensions of results due to Johansson (1996) and Mahdian (2000), and are related to open problems of Alon and Mohar (2002) and Kaiser and Kang (2014).Comment: 14 pages, 1 figur