NANO-BEARING THE DESIGN OF A NEW TYPE OF AIR BEARING WITH FLEXURE STRUCTURE (2).doc

chinese journal of mechanical engineering 12 vol. 20, no. 5, 2007ko pui hang du ruxuinstitute of precision engineering,the chinese university of hong kong,shatin, n. i, hong kong, chinanano-bearing: the design of a new type of air bearing with flexure structure*abstract: a new type of air bearing with flexure structure is introduced. the new bearing is designed for precision mechanical engineering devices such as mechanical watch movement. the new design uses the flexure structure to provide 3d damping to absorb shocks from all directions. two designs are presented: one has 12 t-shape slots in the radian direction while the other has 8 spiral slots in the radian direction. both designs have flexure mountings on the axial directions. based on the finite element analysis (fea), the new bearing can reduce the vibration (displacement) by as much as 8.37% and hence, can better protect the shafts. key words: precision engineering bearing flexures structure finite element analysis0 introductionprecision engineering devices often have small shafts supported by air bearings. for these shafts, even a small vibration may cause the shaft pounding against the bearing resulting in significant damage. to solve this problem, various designs have been developed. for example, a classical design developed by breguet over one hundred years ago is to use a two-piece jewel bearing. while this method is effective, it has two limitations. first, the jewels are expensive. second, it introduces additional assembly errors.the other design is the flexible air bearing. various studies of flexible air bearing can be found in the literature. examples include flexible rotor-bearings system12, flexible supports with gyroscopic effect3, flexible rotor system on flexible suspensions used in high speed rotors for jet engines and turbopumps for space vehicles4r studies also include the effects of bearing support flexibility on rotor stability and unbalance response51, rotor imbalance and misalignment in flexibly mounted machines or flexible rotating machine671. modeling and simulation have become an important tool for the study. recent reports include the numerical and experimental study on the effects of the bearing support flexibility on the rptor dynamics81, air-bearing spacecraft simulators91, and foundation model of flexible rotating machines0.this paper presents a new design based on flexure structure. flexure is a mechanical structure that uses the elastic deformation of the material to work as a joint or a damper, delivering energy and motion from specified input ports to output ports. this compliant mechanism has some intrinsic advantages. first, it can be manufactured without much difficulty. second, it is lightweight. third, it can reduce the assembly errors. moreover, it provides the necessary damping to protect the shaft. these merits have made the flexures mechanism being used in many applications such as in mems, minimally invasive surgery instruments, and mechanical watches. for example, flexure mechanism achieves precision opening motion of the micro grippers. some interferometric instruments use flexure elements in high-accuracy linear guiding mechanism for closed-loop control in corner cube mechanism (ccm)12. also, flexure structures are found in carbon fiber mi-crorobotic mechanisms13, ultra-precision beam steering with nanopositioning mechanism14, or application in robotic hands1. moreover, flexures are applied to compliant mechanisms, such asselected from proceedings of the 7th international conference on frontiers of design and manufacturing (icfdm2006). this project is partially supported by the research grant from the hong kong walch manufacturers association, the federation of hong kong watch trade and industry and hong kong innovation and technology commission, china (no. its/001/05). received october 14, 2006; received in revised form may 25, 2007; accepted may 28, 2007diaphragm flexure for precision compliant mechanisms16, active high-accuracy and large bandwidth mechanism171.the new design is an air bearing with flexure that provides 3d damping. the rest of the paper is organized as follows: section 1 presents the design. section 2 contains the finite element analysis (fea) model simulation results. finally, section 3 includes the conclusions and future work.1 design of the nano-bearingwe proposed two different designs: one has 8 spiral slots in the radian direction, while the other has 12 t-shape slots in the radian direction, as discussed in section 1.1 and section 1.2 respectively. both designs have the same flexure mountings cap, 3d_mount, on the axial directions, which is described in section 1.3. the designs are drafted using a cad software system solid-work.1.1 design 1: spiral slots along the radian directionthis design is shown in fig. 1. the bearing is made of 1 mm thick stainless steel and the diameter of the hole is 1 mm as well. to provide the damping along the radian direction of the bearing, it has 8 spiral slots with each pairs slots being 45 apart. the width of the slot is 0.1 mm and the length is approximately 8.80 mm.fig. 1 illustration of spiral shape nano-bearing design1.2design 2: t-shape slots along the radian directionthe second design is shown in fig. 2. the size and the materials are the same as design 1. though, it consists of 12 t-shape slots along the radian direction, each slot is 30 apart. the angle between the slots is 30. the dimension of the slot is shown in fig. 2, with parameter a being calculated using: a * af(slots_ number) = 360 *p(% rating). for a bearing with 12 slots with 60% circumference rating, a = 360*60%/12 = 18. in calculating the length of the slot d, it is assumed that the total length of slot is the same as the spiral design. this results in d = 0.44 mm and leading outer radius r0 = 1.04 mm.1.3modeling of the bearing mounting cap: 3d_mountas shown in fig. 3, the bearing cap is 0.5 mm thick circular disk formed by the revolution of a cross section. the cross sectionchinese journal of mechanical engineering 13*fig. 2 illustration of the t-shape nano-bearing designis made of three 0.4 mm diameter circular notch, which forms a flexure for providing damping in the axial direction of the bearing. note that the cross section can be considered as a 4-bar linkage , where the compliance is achieved by the flexure structure.fig. 3 illustration of the bearing mounting cap1.4modeling of bearing assemblythe bearing assembly includes a shaft and a pair of bsar-ings(fig. 4). the shaft is 10 mm long, with 0.99 mm diameter. in other words, the gap between the bearing and the shaft is 0.01 zxd. the flexure-bearing system is aimed at preventing the shaft being pounding against the bearings during an impact. for simplicity, it is assumed that screw mounting effect can be omitted in the fea.fig. 4 bearing assembly with exploded view2 fea model and simulation results2.1 fea modelthe fea simulation is carried out using a commercial cae software system algor. the temperature is set at 26.67 c, with no thermal variation. the material is stainless steel (aisi 302) cold-rolled. the weight of the whole bearing system is 20 g. thus, the gravitation force is mg = 20 * 9.8/1 000 = 0.196 n. this force is equivalent to the bearing being freely dropped above the ground vertically.assuming that initial velocity v0 = 0 and final velocity vf = 0, and neglecting air resistance; furthermore, assuming there is no kinetic energy loss in elastic collision. then, by conservation of energy, kinetic energy + potential energy = constant, or l/2wv2 + mgh = 1/2wv2 + mg(0). by simple calculation, it follows that v = yj2gh = 6.26 m/s. assuming the bearing is being dropped 2 m from the ground and the impact time is ts = 1 ms, then, the impact force is f= ma = m (vf- v)/s = -125.28 n.we wish to see if the new bearings are capable of reducing the deformation of the bearing when it is being dropped onto theground. fig. 5 illustrates its physical significance: the bearing being dropped onto the ground is equivalent to a point force applying onto the bearing. as a result, the bearing deforms and the deformation at the center hole is measured by dr. note that the negative value would imply a reduction in radius, while the positive are imply an increase in radius.impactbearing before impactimpactbearing after impactfig. s deformation definition d, for bearing analysis2.2the impact force on the bearingfig. 6 shows a typical simulation result: fig. 6a shows the fea model, in which a point force is applied onto the bearing simulating the bearing being dropped and hit the ground from the side. fig. 6b shows the bearing deformation near the center hole from the tea. note that if the deformation is large enough (larger than tiv- bearing / shaft assembly tolerance), the bearing will assert a large force onto the shaft. in worst cases, the shaft may even break.(b) fea simulation result (displacement near center hole) fig. 6 sample fea simulation result of the bearingtable 1 summarizes the simulation results. from table 1, following observations can be seen: first, in the impact direction x, the two new designs have less deformation. particularly, the t-shape design reduces the deformation by 1.28%, while the spiral design reduces the deformation by as much as 8.37%. this indicates that the new design will be able to provide better damping. second, in the direction y, the two new designs have large. i4.ko pui hang, et al: nano-bearing: the design of a new type of air bearing with flexure structuredeformation. fortunately, this should not affect the stability of the bearing system as they deform into the positive range.table 1 displacement of hole radius d,nmtype of slot no slot t-shapespiralin x direction -2.580 0 -2.547 0 in y direction 2.615 4 8.227 3-2.351 1 15.036 013 the impact force on the bearing capin our design, the flexure bearing cap acts as a damper. fig. 7 shows the fea models in three difficult cases. in fig. 7a, the point pressures are applied to the center of the bearing cap simulating the bearing had a direct hit. note that the pressure p is calculated byp = f/a = f/l-ns) 125.28/ti * (0.32) * 443.10 n mm2. in fig. 7b, a point force is applied to near the center of the bearing cap simulating the bearing had a sharp hit. in fig. 7c, an angled point force is applied to the bearing cap simulating an indirect sharp hit. in all the cases, the displacement of the bearing is in a scale of 1 um. this indicates that the bearing cap provides sufficient damping to protect the shaft.in order to evaluate the performance of the new design bearing cap for the whole system, three more cases are considered on the assembled system. the first case is shown in fig. 8a, where a pressure is applied to the center of the bearing cap simulating a large direct impact on the bearing. the second case is shown in fig. 8b, where an angled point force is impacted near the center of the bearing cap. finally, the third case is shown in fig. 8c, where an angled point force is impacted away the center of the bearing cap. the results show that the displacement keeps on below 10 urn, or such displacement is mainly due to the vertical z-direction, which is not critical to rotating performance. it further verifies the damping performance of the flexure structures, especially for the vertical deformation of the bearing cap (3d_mount), to protect the rotating behavior of the bearing systems. the simulation results are summarized in tables 2-4 respectively. from the tables, it is seen that in all the cases, the new designs can provide sufficient protection for the shaft as the resultant deformation will not result in a contact to the shaft. moreover, it seems that the spiral design is more sensitive to the angler impacts.zk(a)x(b)u(c)fig. 7 deformation of the bearing cap under different impact conditionsfig. 8 three cases in the fea modelchinese journal of mechanical engineering 15 urntable 2 maximum displacement in case 1bearing capt-shapespiralill!2.280 524 021 4.790 755 923 3.060 923 834 2.755 242 9875.327 643 717 2.517 650 866 2.742 754 067 2.471 297 188table 3 maximum displacement in case 2 urnbearing capt-shapespiralx-axis -axis z-axis magnitude3.530 838 717 3.207 204 428 1.895 073 044 1.693 755 5004.107 992 3.391 255 838 1.969 671 395 1.957 872 611table 4 maximum displacementin case 3 nmbearing capt-shapespiralml3.323 626 732 4.213 124 636 1.934 587 585 1.438 282 0632.086 936 569 4.642 634 023 2.055 654 165 1.676 735 4403 conclusionsthis paper presents a couple of new bearing designs. since the designs involve micro-scale flexure features, they are called the nano-bearings. based on the fea simulation, following conclusions can be drawn.(1) the new design will provide better protection for the shaft. this is mainly due to the fact that the flexure structure provides a good damping effect.(1) the spiral design seems to have better performance than the t-shape design when the impact is from the side. though, when the impact is on the bearing cap, its performanr.jj varie:-.presently, we have made a t-shape inipo-beatini; as shown hi fig. 9 and are planning to make a spiral shap tiano-bearing. we are also planning to make a test station t9 validate the proposed bearing design. finally, we are considering adding carbon nano-tube coating for better performance.fig. 9 sem photo of t-shape nano-bearingreferencesledwards s, lees a w, friswell m i. experimental identification of excitation and support parameters of a flexible rotor-bearings-foundation system from a single rundownj. j. of sound and vibration, 2000, 232(5): 963-992.2tiwari r, vyas n s. non-linear bearing stiffness parameter extraction from random response in flexible rotorbearing systemsj. j. of sound and vibration, 1997, 203(3): 389-408.3dutt j k, nakra b c. dynamics of rotor shaft system on flexible supports with gyroscopic effectsj. mechanics research 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