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*Questions and Answers I. Multiple-choice Questions (Choose one answer from A, B, C, D given) 1 The purpose of checking the minimum oil film thickness hmin in sliding bearings is . A. Determine whether the bearing can be lubricated with fluid. B. Control the heat generation in the bearing. C. Calculate the frictional resistance inside the bearing. D. Control the pressure P2. In the various situations shown in Figure 15–2 for question 15–2, fluid dynamic lubrication may occur in the following cases. 3 Babbitt alloy is used for manufacturing. A. Single-layer metal bearing shells B. Double-layer or multi-layer metal bearing shells C. Oil-impregnated bearing shells D. Non-metallic bearing shells 4 Among the materials used for sliding bearings, it is usually only used as the surface layer material for bimetallic bearing shells. A. Cast iron B. Babbitt alloy C. Cast tin-phosphorus bronze D. Cast brass 5 The eccentricity e of a liquid-lubricated hydrodynamic radial bearing decreases as . A. An increase in the shaft speed n or an increase in the load F. B. An increase in the shaft speed n or a decrease in the load F. C. A decrease in the shaft speed n or a decrease in the load F. D. A decrease in the shaft speed n or an increase in the load F. 6 For partially liquid-lubricated sliding bearings, the verification is carried out to prevent damage to the bearings. A. Excessive wear B. Adhesion due to overheating C. Plastic deformation D. Fatigue pitting 7 When designing a hydrodynamically lubricated radial sliding bearing, if it is found that the minimum film thickness hmin is not large enough, which of the following design improvements is the most effective? A. Reduce the width-to-diameter ratio of the bearing. B. Increase the oil supply volume. C. Reduce the relative clearance. D. Increase the eccentricity. 8 In such cases, the viscosity of the lubricating oil for sliding bearings should not be set too high. A. Heavy loading B. High speed C. High operating temperature D. Withstanding variable loads or vibration shock loads 9 As the temperature rises, the viscosity of lubricating oil . A. Increase subsequently B. Remain unchanged C. Decrease subsequently D. May increase or decrease. Among the conditions necessary for hydrodynamic lubrication of sliding bearings to establish oil pressure, which one is unnecessary? A. A wedge-shaped gap is formed between the shaft journal and the bearing. B. Sufficient lubricating oil is supplied. C. There is relative sliding between the surfaces of the shaft journal and the bearing. D. The temperature of the lubricating oil does not exceed 50°C. 11 Kinematic viscosity is the ratio of dynamic viscosity to that of the lubricating oil at the same temperature. A. Mass B. Density C. Specific gravity D. Flow rate 12 The of lubricating oil is also known as absolute viscosity. A. Kinematic viscosity B. Dynamic viscosity C. Engler viscosity D. Fundamental viscosity 13 Among the various mechanical devices listed below, sliding bearings are the only suitable choice. A. Gears and shafts in medium and small reducers B. Electric motor rotors C. Shafts of railway locomotives and vehicles D. Main shafts of large hydroturbines 14. The friction condition in which two relatively sliding contact surfaces are lubricated by an adsorbed oil film is called . A. Liquid friction B. Semiliquid friction C. Mixed friction D. Boundary friction 15 The formula for calculating the minimum film thickness in a hydrodynamically lubricated radial sliding bearing is . A. B. C. D. 16 In sliding bearings, the relative clearance is an important parameter; it is the ratio to the nominal diameter. A. Radial clearance B. Diameter clearance C. Minimum oil film thickness hmin D. Eccentricity 17 In radial sliding bearings, the purpose of using tilting pads is to . A. To facilitate assembly B. To endow the bearing with automatic alignment capability C. To improve the stability of the bearing D. To increase the lubricant flow rate and reduce temperature rise. 18. The purpose of using triple-oil-wedge or multi-oil-wedge sliding bearings is to . A. Increase load capacity B. Increase the amount of lubricating oil C. Improve the stability of the bearings D. Reduce frictional heating. 19 In sliding bearings with incomplete liquid lubrication, the main purpose of limiting certain values is to prevent the bearings from… A. Excessive heating leading to bonding B. Excessive wear C. Plastic deformation occurring D. Seizure occurring. 20 Among the materials listed below, which one is a bearing alloy (Babbitt alloy)? A. 20CrMnTi B. 38CrMnMo C. ZSnSb11Cu6 D. ZCuSn10P1 21 Compared to rolling bearings, which of the following is not an advantage of sliding bearings? A. Small radial dimensions. B. Small clearance, high rotational precision. C. Smooth operation with low noise. D. Suitable for high-speed operations. If the diameter of a radial sliding bearing is doubled, while the length-to-diameter ratio remains unchanged and the load stays the same, then the pressure on the bearing becomes times the original value. A. 2 B. 1/2 C. 1/4 D. 4 If the diameter of a radial sliding bearing is doubled, while the length-to-diameter ratio remains unchanged and the load as well as the rotational speed stay the same, then the value of the bearing becomes times the original value. A. 2 B. 1/2 C. 4 D. 1/4 II. Fill-in-the-blank questions 24. The specific pressure is checked for lubricated sliding bearings with imperfect lubrication in order to avoid ； The verification value is used to prevent that. 25 When designing dynamically lubricated sliding bearings, if the relative clearance is reduced, the load-carrying capacity of the bearing will ； Rotation accuracy will ； The calorific value will be . 26 The viscosity of a fluid, which is its ability to resist deformation, represents the magnitude within the fluid. 27 The oiliness of lubricating oil refers to its ability to adhere to metal surfaces. 28 The main factors affecting the viscosity of lubricating oil are and . 29 The typical friction states between two friction surfaces are , and . 30 In hydrodynamically lubricated sliding bearings, the relationship between the dynamic viscosity and kinematic viscosity of the lubricating oil is given by . (It is necessary to indicate the meaning of each symbol in the formula.) 31 In screw drives, the nuts; in sliding bearing bushings, and in worm drives, the worm gears are often made of bronze, mainly in order to improve performance. 32 The verification formulas for the operating capacity of imperfectly lubricated sliding bearings are , and . 33 The necessary conditions for achieving hydrodynamic lubrication are _, _, _. 34 The main failure modes of partially liquid-lubricated sliding bearings are, and the formulas to be checked during design are, , . 35 The lubricating function of sliding bearings is to reduce friction and increase efficiency; the oil grooves in the bearing shells should be located in the areas subject to load. 36 The necessary conditions for the formation of hydrodynamic lubrication are 1, 2, and 3, while the sufficient condition is . 37 Radial sliding bearings with incomplete liquid lubrication are subjected to conditional calculations based on their possible failure modes. 38 For sliding bearings with a relatively large outer diameter (>1.5), in order to avoid \"edge contact\" of the bearing due to shaft deflection, which can lead to premature wear of the bearing, such bearings can be used. 39 The load-carrying capacity coefficient of sliding bearings increases as the eccentricity increases; correspondingly, the minimum oil film thickness hmin also increases as the eccentricity increases. 40 In the one-dimensional Reynolds lubrication equation, its viscosity refers to the viscosity of the lubricant. 41 When selecting the lubricating oil for sliding bearings, for liquid-lubricated bearings, the main factor to consider is the properties of the lubricating oil; for partially liquid-lubricated bearings, it is the other properties of the lubricating oil that are important. III. Essay Question 42: When designing a hydrodynamically lubricated sliding bearing, what conditions must be met to ensure its proper operation? 43 Describe the formation process of the oil film in a radial dynamic pressure sliding bearing. 44 The one-dimensional Reynolds equation for hydrodynamic lubrication explains the necessary conditions for the establishment of hydrodynamic lubrication. 45 How does the size of the relative clearance in hydrodynamically lubricated sliding bearings affect the bearing capacity, temperature rise, and operating precision of these bearings? 46 There is a hydrodynamically lubricated single oil wedge sliding bearing. When operating under two different external loads, its eccentricities are respectively , and . Determine under which condition the bearing is subjected to a greater external load. What measures can be considered to improve the load-carrying capacity of this bearing? (It is assumed that the journal diameter and rotational speed cannot be changed.) ) 47 What calculations are required for partially liquid-lubricated sliding bearings? What do they each mean? 48 To ensure that sliding bearings have a high load-carrying capacity, where should the oil grooves be located? 49 What is the bearing load capacity coefficient Cp? Does a high Cp value indicate that the bearing can withstand a greater load? 50 What are the different friction states of sliding bearings? What are their main differences? 51 What are the main failure modes of sliding bearings? 52 What is the impact of the relative clearance on the bearing’s load-carrying capacity? During design, if the calculated min value is too low or the temperature rise is too high, how should the value be adjusted? 53 When designing hydrodynamically lubricated radial sliding bearings, how should the parameters be adjusted for design when the minimum film thickness min is not reliable? IV. Analytical Calculation Problems 54: For a certain radial sliding bearing, the width-to-diameter ratio of the bearing is , the nominal diameters of the shaft journal and the bearing bush are mm, the relative clearance of the bearing is , and the ten-point average heights of the surface irregularities on the shaft journal and the bearing bush are respectively , and . Under the operating conditions of a radial load F and a shaft journal speed v, with an eccentricity of , liquid dynamic lubrication can be established. With all other conditions unchanged, determine: (1) What is the minimum oil film thickness of the bearing when the journal speed is increased to ? (2) When the journal speed is reduced to , can this bearing achieve a hydrodynamic lubrication state? Note: ① Formula for calculating the load capacity coefficient Cp; ② Values of the load capacity coefficient Cp are given in the table below: 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95. Corresponding Cp values: 1.25, 3.15, 2.81, 1.929, 2.469, 3.372, 4.808, 7.772, 17.18. It relates to a radial sliding bearing of a certain rotor: the radial load on the bearing, the width-to-diameter ratio of the bearing, the rotational speed of the shaft journal, the direction of the load being constant, stable operating conditions, the relative clearance of the bearing (where v is the circumferential velocity of the shaft journal, in m/s), the surface roughness of the shaft journal and the bearing bush, the material properties of the bearing bush, and the viscosity of the oil. (1) Determine the journal diameter when designed for mixed lubrication (incomplete liquid lubrication). (2) Round the journal diameter obtained in (1) to the nearest value where the units digit is 0 or 5. Under the conditions given in the problem, can this bearing achieve a state of liquid lubrication? 56 There is a sliding bearing, with a shaft journal diameter of , a width-to-diameter ratio of , a measured diameter clearance of , a rotational speed of , a radial load of , a dynamic viscosity of the lubricating oil of , and average heights of surface irregularities on the shaft journal and bearing shell of respectively. Can this bearing achieve a hydrodynamic lubrication state? If this cannot be achieved, what parameters can be changed while keeping the bearing dimensions unchanged in order to achieve hydrodynamic lubrication? And calculate one of the parameters. Note: The 57 unit features a sliding bearing. The nominal diameters of the shaft journal and the bearing bush are known to be , with a diameter clearance of . The bearing width is , the radial load is , the shaft’s rotational speed is , and the ten-point average heights of the surface micro-irregularities on the shaft journal and the bearing bush surfaces are respectively and . Find: (1) What should be the dynamic viscosity of the lubricating oil when this bearing is in a hydrodynamic lubrication state? (2) If both the radial load and the diameter clearance are increased by 20%, with all other conditions remaining unchanged, can this bearing achieve a hydrodynamic lubrication state? Note: ① Refer to the formula; ② The load capacity coefficient is shown in the table below ( ): 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. Cp: 0.391, 0.589, 0.853, 1.253, 1.929, 3.372, 7.772, 58. As shown in Figure 5–58, it is given that the relative motion speed between the two plates is >>> ； Load >>>, viscosity of the oil between the plates. Analyze: For question 5—58, Figure (1), in which situations can a pressure oil film be formed? And explain the necessary and sufficient conditions for establishing a hydrodynamic lubricating film. (2) In which case is the oil film thickness the greatest? In which case is the oil film pressure the greatest? (3) In Figure (c), if is reduced while all other conditions remain unchanged, what changes will occur in the oil film pressure and the oil film thickness? (4) In Figure (c), if is reduced while all other conditions remain unchanged, what changes will occur in the oil film pressure and the oil film thickness? 59 Try to fill in the table below with the trends in the values of relevant parameters during the design of hydrodynamic lubricated sliding bearings (use representative symbols: increase↑ ； Decrease ↓: Uncertain? ). Parameter: Minimum oil film thickness (min/mm), eccentricity, radial load, oil supply rate Q/(m3/s), bearing temperature rise. When the width-to-diameter ratio increases, when the oil viscosity increases, when the relative clearance increases, and when the shaft speed increases: 60. Analyze the four friction pairs shown in Figures 5–60; identify which of these friction pairs cannot generate an oil film pressure between their friction surfaces, and explain why (It is the relative velocity; the oil has a certain viscosity.) ) Question 5—60, Figure 61: When the dynamic viscosity of the oil and the velocity v are high enough, determine whether it is possible for the slider shown in Question 5—61, Figure to establish a dynamic pressure oil film. A. Possible B. Impossible C. Not necessarily Question 5—61 Illustrated solution 1. There is a radial sliding bearing in a centrifugal pump. Given: the journal diameter d = 60 mm, the shaft speed n = 1500 rpm, the radial load on the bearing F = 2600 N, and the bearing material is ZCuSn5Pb5Zn5. Try to verify whether this bearing is usable based on the calculation method for imperfectly lubricated bearings If it is not available, how should it be improved? (Based on the shaft’s strength, the journal diameter must not be less than 48 mm.) Key points for solving the problem: (1) Based on the given information that ZCuSn5Pb5Zn5, it can be found that =8MPa, =3m/s, and =12MPa·m/s. (2) Using the known data, a width-to-diameter ratio of l/d = 1 is selected; it can be seen that υ does not meet the requirements, while both p and pυ do. Therefore, the following two solutions are considered for improvement ； (1) Without changing the material, only reduce the journal diameter to decrease the speed υ. Taking d as the minimum allowable diameter of 48 mm, the requirement is still not met; therefore this solution is not viable, and the material must be changed. (2) Modified material: Bearing alloy ZCbSb15Sn5Cu3Cd2 was poured onto the copper alloy bearing bushings; the values obtained were =5MPa, =8m/s, and =5MPa·m/s. After calculation, with d=50mm and l=42mm, it can be concluded that a copper alloy bearing bush can be used to cast the ZCbSb15Sn5Cu3Cd2 bearing alloy, where the shaft diameter is d=50mm and the bearing width is l=42mm. 2. As shown in the figure, there are two liquid-lubricated sliding bearings of the same size, with identical operating conditions and structural parameters (relative clearance Ψ, dynamic viscosity, speed, journal diameter d, bearing width l). Which bearing has a larger relative eccentricity? Which bearing bears the larger radial load F? Which bearing has a higher oil consumption Q? Which bearing generates the most heat? Hint: The load capacity coefficient and the fuel consumption coefficient. As can be seen from the graphs, the minimum film thickness in Figure a and Figure b is different. There is a relationship between these values, as well as between them and the eccentricity (relative eccentricity) and the relative clearance (where e is the eccentricity distance and is the radial clearance, with = R – r). The radial load that a hydrodynamic bearing can withstand is given by the following formula: where CP is the load capacity coefficient, and is the dynamic viscosity of the lubricating oil. For dynamic pressure bearings with l/d≤1.0 and ≤0.75, the following conclusions can be drawn: (1) The smaller the value, the larger the value; that is, as shown in Figure a, the relative eccentricity is greater ； (2) The smaller the value, and the larger it is, the greater CP and F become; thus Fa > Fb, which means that graph a experiences a greater radial load ； (3) Based on the fuel consumption, the higher it is, the larger the fuel consumption coefficient CQ becomes; thus, as shown in Figure a, the fuel consumption is high ； (4) As the value increases, Q also increases; therefore, the heat generation in Figure a is less than that in Figure b. 3. A radially sliding bearing with incomplete liquid lubrication in a reducer, where the shaft is made of 45 steel and the bearing bush is made of cast bronze ZCuSn5Pb5Zn5, subjected to a radial load of F=35 kN ； Bearing journal diameter d=190mm ； Working length l=250mm ； Rotational speed n=150r/min. Conduct tests to determine whether this bearing is suitable for use. Tip: Based on the bearing bush material, it has been determined that =8MPa, =3m/s, and =12MPa·m/s. Key to solving the problem: Conduct a capacity check; therefore, this bearing is suitable for use. 4. There is an imperfectly lubricated radial sliding bearing with a diameter of d=100 mm, a width-to-diameter ratio of l/d=1, and a rotational speed of n=1200 rpm. The shaft is made of 45 steel, while the bearing is made of cast bronze ZCuSn10P1. What is the maximum radial load that this bearing can withstand? Hint: According to the available data, it has been determined that =15MPa, =10m/s, and =15MPa·m/s. Key points for solving the problem: The maximum radial load that a bearing can withstand must satisfy both of the following conditions: (1) 150,000 N; (2) = 23,875 N. Therefore, Fmax=23,875 N. 5. Try to design a hydrodynamic lubricated radial sliding bearing for a gear reducer. Given: Radial load F = 25,000 N, journal diameter d = 115 mm, speed of the light journal n = 1000 r/min. Key points for solving the problem: (1) Determine the bearing structure type – an integral structure is used, with a specified bearing angle. (2) Determine the structural parameters of the bearing – taking l/d=1, the working width of the bearing is l = l/d = 1×115 mm = 115 mm. (3) Select the material for the bearing bush – calculate the values of p and p; based on these values, the 11-6 tin-antimony bearing alloy (ZSnSb11Cu6) is chosen, with values of =25 MPa, =80 m/s, and =20 MPa·m/s. The journal is made of steel, quenched and precision-ground. (4) Select the relative clearance Ψ of the bearing and the bearing fit tolerance; determine the diameter clearance of the bearing to be mm. When selecting the bearing fit tolerance, the minimum and maximum fit clearances chosen should be close to the theoretical clearance △ of the bearing. Now, with the chosen fit being , the bore diameter of the bearing shell is D= , the diameter of the shaft journal is , the maximum clearance is , and the minimum clearance is . (5) Selection of lubricating oil: Based on the values related to the bearing, L-AN32 mechanical oil is chosen, with a dynamic viscosity of v40 = 32 cSt (32×10-6 m2/s); its density, and specific heat capacity c = 1800 J/(kg·℃). Calculate the dynamic viscosity of the lubricating oil at the average temperature tm: Taking tm = 50°C, the kinematic viscosity v50 of L-AN32 at 50°C is 19–22.6 cSt; thus, v50 is taken as 19 cSt (19×10^-6 m²/s). The dynamic viscosity is then calculated as follows: (6) Calculate the bearing’s operating capacity. Determine the load capacity coefficient of the bearing: Calculate the eccentricity: Based on the values of CP and l/d, the eccentricity is 0.652. Calculate the minimum oil film thickness ； = =With a surface roughness of 0.026 mm for the selected bearing shells and shaft journals, we have =0.026 > 2(Rz1 + Rz2) = 2 × (0.0016 + 0.0032) = 0.0096 mm. (7) Verification of bearing temperature rise and operational reliability: The coefficient of liquid friction is calculated as follows: the angular velocity of the shaft journal is 104.72 rad/s; since l/d = 1, the friction coefficient is determined accordingly. Oil supply volume: Using the bearing’s eccentricity and the width-to-diameter ratio l/d, values are obtained through table lookup and interpolation, giving CQ = 0.142; thus, the oil supply volume is =14.7×10-6 m3/s = 882 cm3/min. Bearing temperature rise: With a thermal conductivity of …°C, the temperature rise is 13.09°C. The inlet oil temperature is …°C – …°C = 43.46°C (within the range of 35–45°C), while the outlet oil temperature is …°C + …°C = 56.55°C℃