A comparative study of stress distribution in interference fitted assemblies

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 13, October 006, pp A comparative study of stress distribution in interference fitted assemblies Irappa Sogalad & N G Subramanya Udupa* Department of Mechanical Engineering, University BDT College of Engineering, Davangere , India Received 8 August 005; accepted 5 May 006 Interference fitted assemblies find wide engineering applications such as bearing bushes, liners in cylinder blocks and small end bush in connecting rods. The strength of any such assemblies depends on various geometric features, amount of interference and other physical conditions of the mating surfaces. This paper presents the details of analysis carried out to study the effect of different pin and bush materials, low temperature (cryogenic) treatment and geometric parameters on stress distribution at the mating surface of interference fitted assemblies. This work covers, analysis based on Lame s approach and finite element method to evaluate the principal stresses and Von Mises stresses on the performance of interference fitted assemblies. For the finite element analysis(fea), an appropriate finite element model was developed to analyse the pattern of contact stresses in interference fitted assemblies with and without low temperature effect and under varying geometric parameters such as contact length, mating diameter and amount of interference. A comparative study of both the methods has been carried out. IPC Code: G01L1/00 The reliable functioning of an interference fit depends on the correct size relationship between the mating parts of the assembly. That is, mating surfaces of the parts must fit together to fulfill the purpose for which it has been designed. By varying the sizes of two mating parts, innumerable types of fits can be obtained. Depending upon the actual limits of the hole and shaft the fits are classified into clearance fits, transition fits and interference fits. Interference fitted assemblies provide intimate contact between mating parts, intended to be held permanently as a solid component. The absence of clamping makes them compact and aesthetic in appearance. They have an excellent load bearing ability under static as well as dynamic loading conditions. These assemblies find wide engineering applications such as bearing bushes, pump impeller on shaft, small end bush in connecting rod, a crank pin in a cast iron web, liners in cylinder block, valve seats, gears, locomotive wheel on axle, stator of a fan, fitting rotors of turbines and compressors on shafts and mechanical drives and assembling of bearing races 1,. Hence, it is worth while to study the strength of the interference fitted joints. The stress distribution at the interface of interference fitted assemblies depends on various parameters such as amount of *For correspondence ( dr_ngsudupa@rediffmail.com) interference, physical dimensions, material properties, diameter and contact length, geometrical inaccuracies and surface roughness of mating members. Several investigations have been carried out to study the effect of material properties, surface finish of mating surfaces and amount of interference on load bearing ability of interference fits. Also, different methods were suggested to improve the load bearing ability of the interference fits such as glow discharge treatment of sleeves, surface hardening of pins, ageing of assemblies, surface hardening of bores, oxidation of shafts, vibro strengthening and heat treatment of mating surfaces 3-6. In this work, an attempt has been made to study the effect of pin and bush made of different materials, influence of cryogenic treatment and critical geometric features such as length of contact, mating diameter and amount of interference on stress distribution at the interface of pin and the bush of the interference fitted assembly. Geometric Modeling of Pin and Bush The size of pin and the bush are selected in such a way as to cover the actual dimensional ranges in many practical applications and details are given in Fig. 1. For the analysis, different combinations of pin and bush made of aluminium, brass and En 8 steel are considered. Selection of materials 7 in the present

2 398 INDIAN J. ENG. MATER. SCI., OCTOBER 006 Poisson s ratio and modulus of elasticity of pin and bush respectively. The contact stress at the interface of joints for a pair of pin and bush made of same material is given by σ Eδ = 4b l 1 b c () Fig. 1 Dimensions (mm) of (a) bush and (b) pin study is based on: (i) mechanical properties such as high resistance to wear and corrosion and strength, (ii) commonly used bearing/bushing material, (iii) stress withstanding capacity (steel, brass and aluminium can be used as high, medium and low withstanding stress applications respectively), (iv) weight of the material. Based on the requirement like light, medium and heavy the appropriate material is chosen, and (v) cost and availability of the material. Further, the selection of material combination is decided based on the strength of materials. Hence, aluminium, brass and steel are considered based on their relatively low, medium and high strength in terms of hardness and modulus of elasticity. Accordingly, when the assembly involves only steel parts (pin and bush) it gives high strength combination. On the other hand when the assembly involves only aluminium parts (pin and bush) a low strength combination is obtained. In order to get a medium strength, hybrid assembly using two different metals is adopted. Methodology Analysis based on Lame s criterion The stress distribution at the joint surface of an interference fitted assembly can be assessed on the basis of Lame s equation. The contact stress at the interface of joint is given by σ l = 1 γ b Ep p 1 + E b δ c c + b b + γ b (1) where, σ l is Lame s stress in N mm -, δ is the absolute interference, b is the mating radius(d/), c is the outside radius (D/) of bush, γ p, γ b, E p and E b are the and σ r = σ 1, where σ r is the radial stress at the mating surface 8. Analysis based on FEM To investigate the stresses produced at the interface of a joint finite element analysis has been used. The model considered for the analysis is symmetric in respect of geometry and loading, a -D axi-symmetric model was analysed using NISA finite element analysis package. The geometric features of the pairs used in the analysis are shown in Fig. 1. Stress distribution at the contact surface is of main concern and the analysis was carried out on the assumption that the materials are homogeneous and isotropic in nature. The pin and bush were modeled using eight noded quadrilateral shell elements and contact between the pin and bush was modeled using D/AXI GAP elements. The appropriate material properties such as modulus of elasticity and Poisson s ratio, were incorporated in the analysis. To take the benefit of the symmetry of the problem one half of the model was considered. Figure shows the arrangement of nodes/elements of a finite element model used in the analysis of stress. Finite element grids at the joint surface are supposed to be in a node to node contact state. With respect to symmetry of loading, the displacement was given to nodes of the elements in radial direction in such a manner that they end up with the required interference along the whole length of the bush at the contact zone and appropriate boundary conditions were applied against axial movement and contact stress due to interference is obtained. The results presented in this paper refer to the condition of static structural analysis. The various parameters considered in the analysis are material, length of contact (l), mating diameter (d), outside diameter of bush (D) and amount of interference (δ) on stress distribution at the interface of pin and bush of the interference fitted assembly.

3 SOGALAD & UDUPA: INTERFERENCE FITTED ASSEMBLIES 399 Fig. Arrangement of nodes/elements in (a) pin and (b) bush, for FEA Results and Discussion Stress distribution pattern Figure 3 shows the fringe pattern of first principal stress (σ 1 ) and Von-Mises stress (σ v ) distribution in a brass pin-brass bush with 5 µm interference. Similar stress distributions were observed in cases of pairs made of different materials also, with only the magnitudes of the stresses varying. The stress pattern shows that stresses are symmetrically distributed along the contact length and maximum stress intensity is observed at both the edges of the joint. The stresses gave rise to set of fringes which originate at points of maximum stress and vary with the magnitude of the displacement. Fringes are bands of constant stress and each fringe represents a relative stress with respect to neighbouring fringe. Stress gradient is maximum at the interface of the joint and gradually decreases along the thickness of pin and bush. Figure 4 shows the distribution of first principal stresses (σ i ) along the contact length A-B of a joint as determined by the finite element analysis. The plots show the stresses produced for cases of pairs made of different pin and bush materials at 5 µm interference. Similar trend was observed in all other cases. The stresses produced along the contact length were relatively constant and fringes show maximum stress at both the edges of a joint. This localized stress is due to abrupt transition from uncompressed to compressed material at discontinuity in the contact Fig. 3 Stress distribution in pin and bush (a) First principal and (b) Von-Mises length 9, leads to stress concentration at the edges of a joint. Figure 5a shows the relationship between stress concentration factor K n (ratio of maximum contact stress to the minimum contact stress obtained in the analysis) with length of contact of the bush. It reveals that length of the bush has no much effect on the stress concentration and satisfactorily agrees with the earlier results Figure 5b shows the relationship between stress concentration factor K t (ratio of contact stress obtained in the analysis to the Lame s stress) with outside diameter of the bush. As D/d increases, stresses produced on the bush decrease due to size

4 400 INDIAN J. ENG. MATER. SCI., OCTOBER 006 (a) Pattern of stress distribution along the contact length A-B of a joint (a) Variation of K n with 1/d ratio (b) Variation of stress along the contact length Fig. 4 Stress distribution along the joint surface of pin and bush effect. That is, increased D/d ratio causes enlarged thickness of the bush. This in turn results in augmented projected area resisting the contact stress on the bush. Thus, for a given interference, if D/d ratio is increased the resisting strength of the bush will go up there by reducing stress on the bush. Comparison of results Figure 6 shows the stresses produced in a different pair of pin and bush at the contact surface with 5 µm interference based on Lame s approach and finite element analysis. The stresses produced at the mating surface have been taken as the reference value for comparison. The stresses produced from finite element analysis differ slightly from that obtained through Lame s approach. Stresses produced in case of finite element analysis are about 30% more than the value obtained through Lame s approach. Because, interference fit problems are studied with Lame`s approach, which is primarily applied in the elastic range. However, there (b) Variation of K t with D/d ratio Fig. 5 Influence of K t and D/d ratio on stress concentration factor Fig. 6 Variation of stress with different pin/bush materials is a deviation from this and practically, the mating surface of pin contracts (plastically deformed) due to pressure exerted by the inner surface of the bush and inner surface of the bush expands (plastically deformed) as a result of pressure generated by pin 13.

5 SOGALAD & UDUPA: INTERFERENCE FITTED ASSEMBLIES 401 This results in strain hardening at the interface of both pin and bush. Hence, stresses obtained from FEA is larger than Lame`s approach and the trend of contact stress variation satisfactorily agrees with the Lame`s approach. It is observed that a pair of brass pin-brass bush and steel pin-steel bush can withstand higher stresses of about 1.4 times and.8 times respectively when compared to a pair of aluminium pin and aluminium bush. A pair of steel pin-steel bush can withstand about times higher stresses than that with the brass pin-brass bush pair. Further, it was observed that, the difference in stress variation with first principal stress (σ 1 ) and Von-Mises stress (σ v ) obtained using finite element analysis is negligible. Figure 7 shows the variation of contact stress with respect to different pin materials. The variation corresponding to Lame s equation and finite element analysis for the cases with different bush materials at 5 µm interference are clearly indicated. Figure 8 shows the comparison of stress variation corresponding to Lame s equation and finite element analysis with different bush materials. The trend of the variation of contact stresses agrees satisfactorily with the results obtained through Lame s approach. It is seen that a pair with different pin and bush materials produces a stronger assembly than the one with a pair made of same material having lower hardness. Table 1 shows the comparison of stress variation corresponding to Lame s approach and finite element analysis under different combinations of pin and bush materials with 5 µm interference. It is observed that: (a) (a) (b) (b) Fig. 7 Variation of stresses with different pin materials (a) Lame s approach and (b) FEA (c) Fig. 8 Comparison of stress variation with different pin/bush materials (a) aluminium, (b) brass and (c) steel

6 40 INDIAN J. ENG. MATER. SCI., OCTOBER 006 (1) the contact stresses at the mating surface as computed by finite element analysis is larger than the value obtained through Lame s approach by about (i) 40% and 60% for brass pin-aluminium bush pair and steel pinaluminium. bush pair respectively, (ii) 4% and 58% for aluminium pin-brass bush pair and steel pin-brass bush pair respectively, and (iii) 10% and 19% for aluminium pin-steel bush pair and brass pin-steel bush pair respectively. () Further, the increase in contact stresses at the mating surfaces for different pin and bush materials based on finite element analysis is greater than (i) by about 14% (brass pinaluminium bush) and 40% (steel pinaluminium bush) than the aluminium pinaluminium bush pair, (ii) by about 14% (aluminium pin-brass bush) and 30% (steel pin-brass bush) than the aluminium pinaluminium. bush pair and brass pin-brass bush pair respectively, and (iii) by about 50% (aluminium pin-steel bush) and 30% (brass pin-steel bush) than the aluminium pinaluminium bush pair and brass pin-brass bush pair respectively. It is observed that a pair (pin/bush) made of different materials can withstand higher stresses because; ductile materials become stronger when they are deformed plastically by cold working. Cold working results in strain hardening which in turn increases the hardness and strength, and reduces ductility 14. Hence, the enhanced hardness and strength of the pin/bush result in greater resistance to plastic deformation at the contact surfaces of the interference fitted assemblies. Figure 9 shows the stresses produced at the contact surface under varying interferences based on Lame s equation and finite element analysis for cases with pairs (pin/bush) made of different materials, Stresses produced in case of finite element analysis are more than the value obtained using Lame s approach. Stress distribution on pin and bush At the interface of the joint the mating surface of pin contracts and inner surface of the bush expands. In other words, both the members experience a radial Table 1 Variation of stress with different bush materials Pair Bush- Pin Bush- Brass Pin Bush- Steel Pin Brass Bush- Pin Brass Bush- Brass Pin Brass Bush- Steel Pin Steel Bush- Pin Steel Bush- Brass Pin Steel Bush- Steel Pin Stress σ l (N mm - ) σ v Deviation from σ l σ v/ σ l (a) (b) Fig. 9 Stress variation with interference (a) Lame s approach and (b) FEA

7 SOGALAD & UDUPA: INTERFERENCE FITTED ASSEMBLIES 403 deformation at the joint surface. Hence, compressive stresses (σ r = σ 1 ) induce in pin and bush. The variation of stress with interference shows that stresses are symmetrically distributed along the contact length of pin and bush. Cryogenic treatment is gaining prime importance in industrial applications due to technological advances in cryogenics. The important mechanical properties are usually strength, stiffness and wear resistance which generally increase as the temperature is decreased. Hence, it has captured many industrial applications such as high temperature super conductors, cryobiology, nuclear and electrical applications, cutting tools, dies, gauges, surgical scissors, bearings, racing engines, slicers, gears and automotives. The process is a one time permanent treatment affecting the entire part not just the surface. In this work, an attempt has been made to study the effect of cryogenic treatment on stress distribution at the interface of pin and the bush of the interference fitted assembly. Figure 10 shows the comparison of stress variation with interference. The variation corresponding to Lame s equation and finite element analysis for the cases-with and without cryogenic effect are clearly indicated. The trend of the variation of contact stresses agrees satisfactorily with the results obtained through Lame s equation and assemblies with steel pin treated cryogenically can withstand higher stresses than that with untreated pins. Because, to carry out assembly of pin and bush, pin is cooled at cryogenic temperature, which causes change in material property as given in Table. The stress distribution obtained using FEA takes into account of modulus of elasticity (E) and Poisson s ratio (γ). It is observed that cryogenic treatment will have an effect on hardness and modulus of elasticity though not on Poisson s ratio. The increase in hardness of the material (steel) observed in the Table is attributable to transformation of retained austenite to martensite at cryogenic temperature (lower the temperature, higher is the hardness). This phenomenon has been investigated earlier 15. When steel pin is cooled at cryogenic temperature, causes the transformation of retained austenite to freshly formed martensite, which is a hard and strong constituent and enhances the formation of fine carbides. The formed fine carbides from cryogenic treatment fill the open spaces or micro voids resulting in a much denser, coherent and sound structure of the steel. Fine carbides thus formed and (a) (b) (c) Fig. 10 Comparison of stress variation with interference (with and without cryogenic) (a) steel pin-aluminium bush, (b) steel pinbrass bush and (c) steel pin-steel bush Table Effect of cryogenic treatment Sl. No. Parameter Before cryogenic treatment Material: Steel After cryogenic treatment 1 Hardness (HB) Modulus of elasticity (N mm - 10 ) Poisson s ratio

8 404 INDIAN J. ENG. MATER. SCI., OCTOBER 006 resultant tight lattice structures are precipitated from cryogenic treatment results in increase in wear resistance and hardness 16. Hence, the enhanced hardness and wear resistance of the pin result in good dimensional stability. Further, the hardness and tensile strength are proportional to each other 17 and causes greater resistance to plastic deformation at the contact surfaces of the interference fitted assemblies. The other material property which shows improvement with cryogenic treatment in Table is modulus of elasticity E. Modulus of elasticity of steel increases marginally by about 10-15% after cryogenic treatment 18,19. Hence, assemblies with interference fit, treated cryogenically can withstand higher stresses. When the cryogenic effect was incorporated in the analysis, it was found that, stresses under cryogenic treatment are more (about 1%) than the stresses computed from the analysis of assemblies without cryogenic effect. Conclusions From the study following conclusions may be drawn: (i) Assemblies with steel pin-steel bush can withstand higher stresses than the brass pinbrass bush and aluminium pin-aluminium bush pairs and brass pin-brass bush pair can withstand higher stresses than the aluminium pinaluminium bush pair. (ii) Assemblies with pin and bush made of different materials produce a stronger assembly than the one with a pair made of same material having lower hardness. Hence, wherever interference fit with higher stresses is required, it is desirable to carry out the assembly of pin and bush made of different materials. (iii) A change in contact length of the bush, does not affect the stress distribution at the interface of the joint (i.e., stress concentration is almost constant along the contact length). (iv) The outer diameter of the bush has significant influence on stress distribution at the joint surface of bush. Because, stress concentration decreases with increase in outer diameter of the bush. (v) Stresses produced along the contact zone based on FEA differ slightly and the trend of variation of contact stresses agrees satisfactorily with the results obtained through Lame s approach. (vi) Assemblies with steel pin treated cryogenically can withstand higher stresses than that with untreated pins. References 1 Johnson Harold R, Mach Des, 53 (1) (1981) Firsov V T, Sov Eng Res, (11) (198) Ramamoorthy B & Radhakrishnan V, Proc Inst Mech Eng, 06 (199) Andreev Ya G, Russ Eng J, 58 (4) (1978) Papshev D D, Russ Eng J, 60 (10) (1980) Dobrovenskii Yu M & Manokhin V A, Russ Eng J, 58 (6) (1978) Wilcock Donald F & Richard Booster E, Bearing design and application, 1st Ed. (McGraw Hill Book Co. New York), 1957, Rothbart Harold A, Mechanical design and systems hand book, (McGraw Hill Book Co. New York), 1964, Norton Robert L, Machine design an integrated approach, nd Ed. (Pearson Education ASIA. New Delhi), 000, Weibel E E, Arbor Ann & MICH, J Appl Mech Trans ASME, APM (1934) Peterson R E & Wahl A M, J Appl Mech Trans ASME, 57 (1935) A1-A11. 1 Iosilevich G B & Lukashchuk Yu V, Russ Eng J, 59 (6) (1979) Zhang Y, McClain B & Fang X D, I J Mech Sci, 4 (000) Vanvlack Lawrence H, Elements of material science and engineering, 6th Ed. (Addison-Wesley. New York), 1989, Dieter George E, Jr, Mechanical Metallurgy, International Student Edition, (McGraw Hill Book Company. New York), 1961, Yen Pen li, Ind Heat, (1997) Callister William D Jr, Material science and engineering an introduction, 6th Ed. (John Wiley and Sons Inc, Singapore), 003, Barron Randall F, Cryogenic Systems, nd Ed. (Oxford University Press, New York), Cheng Yang Tse & Che Cheng Che Min, Appl Phys Lett, 73 (5) (1998)