Friction and Lubrication in Mechanical Design Episode 2 Part 9 pps

430 Chapter If I Figure 11.4 quency. Correlation between speed of surface wave and dominating fre- 11.3 EFFECT OF LUBRICATION ON NOISE REDUCTION It is generally accepted that frictional noise reduction can be achieved through lubrication. This section provides a rational framework for quanti- fying the role played by the lubricating film between the rubbing surfaces in reducing the intensity of sound generated by relative motion. The hypothesis considered in this section is that frictional rubbing noise is the result of asperity penetration into the surface. The movement of the asperity therefore disturbs the surface layer and generates surface waves. The intensity of the sound can be assumed to be dependent on the depth of penetration which can in turn be assumed to be proportional to the real area Friction-Induced Sound and Vibrations 431 of contact. As discussed in Chapter 4, the real area, as well as the frictional resistance, change in an approximately linear function with the normal load. It can therefore be assumed that the real area of contact between the lubri- cated solids can be used as a quantitative indicator of the intensity of the sound generated during sliding. The roughness profile data given by McCool [ 1 I] for five different sur- face finishing processes are used to determine the input parameters for the Greenwood-Williamson microcontact model [ 121. The model is then used to compute the ratio of the real area of contact to the nominal area for the given normal load and the thickness of the lubricant film separating the surfaces. The model used for the illustration (Fig. 11.5) is represented by two rollers with radii R, = R2 = loin. subjected to a load of 2000 lb/in. The lubricant viscosity and speed are changed to produce different ratios of film thickness to surface roughness ranging from 0 to 3.0. The considered surface roughness conditions are given in Table 11.2. Figure 11,s Contact model. 432 Chapter 11 Table 1 1.2 Roughness Conditions Surface finishing rms roughness 0 Slope of the roughness process (clin.) profile 1 Fine grinding 2.74 2 Rough grinding 21.5 3 Lapping 3.92 4 Polishing 1.70 5 Shot peening 45.9 0.01471 0.090 17 0.05254 0.01 157 0.07925 This ratio of the real area of contact to the nominal area, assuming smooth surfaces, is given in Fig. 11.6. This ratio can be used to represent the change in the relative sound intensity (dB) with lubrication for the different surface finishing processes under the given load. 11.4 FRICTIONAL NOISE IN GEARS Gears are a well-known, major source of noise in machinery and equipment, and it is no surprise that gear noise has been the subject of extensive inves- Ratio of Total Contact Area to Nominal Area 0.8 I I I I I a I 1 2.0 2.5 3.0 Figure 11.6 for different roughness and lubricant film conditions. Ratio between the real area A,./& and nominal area of contact A. Friction-Induced Sound and Vibrations 433 tigations. The nature of gear noise is quite complex because of the multitude of factors that contribute to it. The survey conducted by Welbourn [ 131 and the comparative study presented by Attia [14] on gear noise revealed that the published literature on the subject did not show how friction during the mesh of the rough contacting teeth influences noise generation. A procedure for determining the effect of the different design and oper- ating parameters on frictional noise in the gear mesh is presented by Aziz and Seirig [ 151. The Greenwood asperity-based model [ 121 with Gaussian distribution of heights is utilized to evaluate the penetration of asperities in the contacting surface of the teeth. A parametric relationship is developed for relating the interpenetration of the asperities to the relative noise pres- sure level (NPL) in the lubricated and dry regimes. Numerical results are given in the following example to illustrate the effect of gear ratio, rough- ness, load, speed, and lubricant viscosity on noise. The frictional noise generated from a pair of helical involute steel gears of 5 in. (127 mm) center distance was calculated in both dry and lubricated regimes for different design and operating parameters. The teeth are stan- dard with a normal pressure angle equal to 25" and a helical angle equal to 31". The relation between the relative NPL and different gear ratios was determined. Figures 1 1.7 and 1 1.8 present the effect of change of load for surface contact stresses 68.9, 689, 1378, and 1722.5 MPa ( 10,000, 100,000, 200,000, and 250,OOOpsi) on the relative NPL with an average surface roughness of 0.005 mm (CLA), gear oil viscosity of 0.075 N-sec/m' (0.075 Pa-sec), and pinion speeds of 1800 and 500 rpm, respectively. The results show that the relative NPL increases with the increase of load for all gear ratios. The rate of the relative NPL decreases as gear ratio increases. When reducing the pinion speed from 1800 to 500 rpm the same trend occurs but with higher noise levels, as shown in Fig. 11.8. This could be attributed to the change in the film thickness and consequently the amount of penetration. This effect is clearly shown in Fig. 11.9 for surface contact stress 689 MPa (100,000 psi), viscosity 0.075 N-sec/m2 (0.075 Pa-sec) and surface roughness 0.005 mm. The effect of change of surface roughness at different gear ratios on the relative NPL is shown in Fig. 1 1.10 for contact stress 689 MPa (100,000 psi), pinion speed 1800 rpm, viscosity 0.075 N-sec/m2 (0.075 Pa-sec), and surface roughness 0.0015, 0.002, 0.003, and 0.005mm, respectively. As can be seen in this figure, the relative NPL increases as would be expected with the increase of surface roughness for every gear ratio since the number of aspe- rities subject to deformation is high for higher roughness and consequently the associated NPL becomes higher. The effect of change of lubricant viscosity on the relative NPL at dif- ferent gear ratios is presented in Fig. 11.1 1 for surface contact stress 689 434 Chapter I I U = 0.005 mm Contact Stress -m- 68.9 MPa -0- 689 MPa -A- 1378 MPa -F- 1722.5 MPa 0.15 - 0.10 I I I I I . I I 1 .o 1.5 2.0 2.5 3.0 3.5 Gear Ratio Figure 11.7 Effect of load change on NPL. 'l'l'l'l'l'l 1 .o 1.5 2.0 2.5 3.0 3.5 Gear Ratio Figure 11.8 Effect of load change on NPL. Friction-Induced Sound and Vibrations 5 g 0.50- - 3 0.45 1 0.40 - 0.35 - 0.30 - 435 0.50 - 0.45 - 0.40 - 0.35 - 0.30- 2 ? 0.25- a 0 K 5 0.20- 0.15 - 0.10 - 0.05 - I u-u-1-1-1 1 .o 1.5 2.0 2.5 3.0 3.5 Gear Ratio Figure 11.9 Effect of speed change on NPL. 0.00 ! I 1 I 1 I I 1 I 1 .o 1.5 2.0 2.5 3.0 3.5 Gear Ratio Figure 11.10 Effect of roughness change on NPL. 436 Chapter I I 0.40 - 0.10 1 I I I I I I I 1 .o 1.5 2.0 2.5 3.0 3.5 Gear Ratio Figure 11.1 1 Effect of viscosity change on NPL. MPa ( 100,000 psi), pinion speed 1800 rpm, surface roughness 0.005 mm and viscosities 0.075, 0.15, and 0.25 N-sec/m2 (0.075, 0.15, and 0.25 Pa-sec) respectively. It can be seen that the relative NPL decreases with the increase of viscosity. This is attributed to the increase in the film thickness, which causes a decrease in the penetration of asperities and the relative NPL. The results from all the considered examples show that, as the gear ratio increases, the relative NPL also increases. The reason is that with the increase of the gear ratio, the transmitted load is decreased for the same contact stress. Accordingly, the separation in the dry regime between the mating teeth increases and the penetration decreases. While in the presence of the lubricant, the film thickness is reduced due to the increase in gear ratio, leading to an increase of penetration of the asperities. This results in an increase in the ratio of penetration in lubricated regime to that in dry regime, which gives rise to the increase of relative NPL. It can therefore be seen that the surface roughness effect as a contribut- ing factor in the complex frictional gear noise spectrum could, to some extent, be controlled. It could be reduced by improving the surface finish of gear teeth through limiting their surface roughness to very low values, and by using lubricating oils of high viscosities. Friction-Induced Sound and Vibrations 437 Gear ratios of values greater than unity can have a significant effect on increasing the NPL even with lower values of roughness. The devel- oped procedure can be used to guide the designer in selecting the appro- priate parameters for minimizing the frictional noise for any particular application. 11.5 FRICTION-INDUCED VIBRATION AND NOISE There are numerous cases in physical systems where sound due to vibrations is developed and sustained by friction. Such cases are generally known as self-excited vibrations. They are described as such because the vibration of the system itself causes the frictional resistance to provide the necessary energy for sustaining the motion. The frequency of the vibration is therefore equal to (or close to) the natural frequency of the system. Some of the common examples of self-excited (or self-sustained) vibrations are the chat- ter vibration in machine tools and brakes, the vibration of the violin strings due to the motion of the bow and numerous other examples of mechanical systems subjected to kinetic friction. We shall now consider as an illustration the well-known case of a single- mass system vibrating in a self-excited manner under the influence of kinetic friction, Fig. 1 1.12. Assuming that p is the coefficient of kinetic friction, and N is the normal force between the mass m and the frictional wheel, the unidirectional frictional force acting on the mass will therefore be equal to pN. It is well known that the coefficient of kinetic friction is not a constant value but diminishes slightly as the velocity of relative sliding increases (see Fig. 1 1.13). If, due to some slight disturbance, the mass starts to vibrate, the frictional force pN will not remain constant but will be larger when the mass moves in the direction of the tangential velocity Vo of the wheel than when it moves opposite to it. Assuming that the velocity of the oscillation i is much smaller than the tangential velocity of the frictional wheel, the frictional force p N, which is a function of the relative velocity ( Vo - X), will therefore always be in the direction of Vo. Over a complete cycle of vibration, the frictional force will therefore produce net positive work on the mass and the amplitude of its vibration will build up. In order to study this vibration, the equation of motion can be written as: mi + ci + kx = pN = (po + ai)N (1 1.4) 438 m Chapter I I I Figure 1 1 .12 Frictional drive for self-excited vibration. Sliding Velocity Figure 1 1 .13 Coefficient of kinetic friction. Friction-Induced Sound and Vibrations 439 where c = coefficient of viscous damping a = slope of the friction curve at Vo and can be considered constant po = coefficient of kinetic friction at Vo relative velocity = for a small .U This equation can be rearranged as: m.f + (C - aN)i + kx = N (1 1.5) The term (c - aN), which represents a net damping coefficient, will deter- mine whether the vibration will be stopped or built up in a self-excited manner. If aN < c, the resultant damping term will be positive and the vibration will decay signifying the stability of the system. On the other hand, if aN > c, a negative damping term will exist and the vibration will build up as shown in Fig. 11.14a. The system in this case is unstable. It is quite clear from the previous example that a quantitative knowl- edge of the frictional force and damping functions is essential for any ana- lysis of this type of self-excited vibration. Any variation in either function due to increase in amplitude or velocity of the vibration can have consider- able effect on the vibration. 11.5.1 The Phase-Plane4 Method Because frictional forces are usually complex functions which require experi- mentally obtained information, the phase-plane4 method of analysis is particularly well suited for studies of self-excited vibration [ 101. Assume that in the previous equation the resultant function (c - aN) was not a linear function of the velocity but rather a complicated function f(x) obtained experimentally. The equation of motion is now: mjl +f(i) + kx = puN (1 1.6) This equation can be written in the S form as: i + U:(, + 6) = 0 (I 1.7) (1 1.8) [...]... 10, pp 193 -21 3 24 Anand, A., and Soom, A., “Roughness-Induced Transient Loading at a Sliding Contact During Start-up,” ASME J Tribol., Jan 198 4, Vol 106, pp 49- 53 25 Othman, M O., and Seireg, A., “A Procedure for Evaluating the Frictional Properties of Hertzian Contacts under Reciprocating Sliding Motion,” Trans ASME, J Tribol., 199 0, Vol 1 12, pp 361-364  12 Surface Coating INTRODUCTION 12. 1 In tribological... survey,“ 197 9 Conf Noise and Vibration of Engine Transmissions, Cranfield Institute of Technology, Institute of Mechanical Engineers 14 Attia, A Y., “Noise of Gears: a Comparative Study,” 198 9, Proc Int Power Transmission and Gearing Conf., Chicago, ASME, Vol 2, p 773 15 Aziz, S M A., and Seireg, A., “A Parametric Study of Frictional Noise in Gears,” Wear, 199 4, Vol 176, pp 25 -28 16 KO, P L., and Brockley,... Resulting in Noise Generation,” J Eng Indust., Feb 197 6, pp 81-86 22 Aronov, V., D’Souza, A F., Kalpakjian, S., and Shareef, I., “Interactions Among Friction, Wear, and System Stiffness - Part 2: Vibrations Induced by Dry Friction, ” ASME J Tribol Trans., Jan 198 4, Vol 106, pp 59- 64 23 Tolstoi, D M., “Significance of the Normal Degree of Freedom and Natural Vibrations in Contact Friction, ” Wear, 196 7,... Jan 198 4, Vol 106, pp 54-58 19 Brockley, C A., and KO P L., “Quasi-Harmonic Friction- Induced Vibration,” ASME J Lubr Technol Trans., Oct 197 0, pp 550-556 20 Godfrey, D., “Vibration Reduces Metal to Metal Contact and Causes an Apparent Reduction in Friction, ” Trans ASLE, Apr 196 7, Vol lO (2) pp 1 83- 1 92 21 Earles, S W E., and Lee, C K., “Instabilities Arising from the Frictional Interaction of a Pin-Disk... Measurement of Friction and Friction Induced Vibration,” ASME J Lubr Technol Trans., Oct 197 0, pp 543-5 49 17 Bell, R., and Burdekin, M., “Dynamic Behavior of Plain Slideways,” Proc Inst Mech Engrs, 196 6- 196 7, Vol 181, Part 1, No 8, pp 1 69- 184 18 Aronov, V., D’Souza, A F., Kalpakjian, S., and Shareef, I., “Interactions Among Friction Wear and Systems Stiffness Part 1: Effect of Normal Load and System Stiffness,”... determining the friction- velocity characteristic by measuring the friction force versus displacement in one cycle of a quasiharmonic friction- induced vibration using a pinon-disk apparatus They reported that their technique proved useful in reducing the effect of changes of the surface and external vibration In 198 4, Aronov [ 181 investigated the interaction between friction, wear, and vibration and. .. 199 0, pp 328 -331 10 Seireg, A., Mechanical Systems Analysis, International Textbook Co., 196 9, p 4 12 1 I McCool, J I., “Relating Profile Instrument Measurements to the Functional Performance of Rough Surfaces,” Trans ASME, J Tribol., April 198 7, Vol 1 09, pp 26 4 -27 0 12 Greenwood, J A., and Williamson, J B P., “Contact of Nominally Flat Surfaces,” Proc Roy Soc Lond Series A, 196 6, Vol 29 5, pp 300-3 19 13... measurements during one cycle of the friction- induced vibration of slideways to evaluate the frictional force as a function of the instantaneous velocity The force was calculated from the knowledge of the mass, stiffness, and damping coefficient of the vibrating system by summing the inertia, damping, and restoring forces at each increment of the friction- induced cycle In 197 0, KO and Brockley [ 161... M., and Nakai, M., “A Fundamental Study on Frictional Noise,” Bull JSME, NOV. 197 9, Vol 22 (173), pp 1665-1671 4 52 Chapter I I 8 Symmons, G., and McNulty, G., “Acoustic Output from Stick-Slip Friction, ” Wear, Dec 198 6, Vol 1 13( I), pp 79- 82 9 Othman, M O., Elkholy, A H., and Seireg, A A., “Experimental Investigation of Frictional Noise and Surface-Roughness Characteristics,” Exper Mech., Dec 199 0,... Diagnostic and Educational Challenge,” Noise Vibr Control Wldwide, Sept 198 5, Vol 16(8), pp 22 1 -22 4 5 Fielding, B., and Skorecki, J., “Identification of Mechanical Source of Noise in a Diesel Engine; Sound Emitted from the Valve Mechanism,” Proc Inst Mech Engrs, 196 6-67, Vol 181, Part I (I), pp 434446 6 Thompson, J., “Acoustic Intensity Measurements for Small Engines,” Noise Control Eng J., Sept.-Oct 19 82, . process (clin.) profile 1 Fine grinding 2. 74 2 Rough grinding 21 .5 3 Lapping 3. 92 4 Polishing 1.70 5 Shot peening 45 .9 0.01471 0. 090 17 0.0 525 4 0.01 157 0.07 92 5 This ratio of the. stiffness, and damping coefficient of the vibrating system by summing the inertia, damp- ing, and restoring forces at each increment of the friction- induced cycle. In 197 0, KO and Brockley. used to guide the designer in selecting the appro- priate parameters for minimizing the frictional noise for any particular application. 11.5 FRICTION- INDUCED VIBRATION AND NOISE There are