Bolted Joints Analysis Methods and Evaluation

Transcription

1 International OPEN ACCESS Journal O Modern Engineering Research (IJMER) Bolted Joints Analysis Methods and Evaluation G. Chaitanya 1, M. Kumara Swamy 2 1 Mechanical engineering, UCEK (A)/Jawaharlal Nehru Technological University Kakinada, INDIA) 2 Associate proessor, Mechanical engineering, UCEK (A)/Jawaharlal Nehru Technological University Kakinada, INDIA) Abstract: Calculation o accurate bolt orces is the primary requirement in many industries. All the theoretical calculations or bolt orces, includes many signiicant assumption based on idealized mechanical models. In this paper two models o lange joints were taken and analyzed orpretensionvariation due to internal temperature changes, And or theforces induced in the bolt due to the combined eect o external orces applied and internal temperature change. The results were utilized to gain insight into joint sotening that arises rom gradual, nonlinear opening o lange gap under external tension. Later these results were compared with the theoretical calculations, and our models allow relaxations or many assumptions in theoretical calculations. Keywords: Bolt orce,heel gap, joint separation load, Pretension, Prying actor. I. Introduction Industrial applications, structures are oten uses the lange joints. The main objective o lange joint design is to provide adequate joint strength and stiness and to minimize the luctuating stresses induced in the bolted joint due to the thermal loads and external loads. Bolted joints are requently analyzed using hand ormulas that include many signiicant assumptions. In this paper, we evaluate several commonly used ormulas by comparing their predictions to those o detailed inite element models. Our models allow the relaxation o many assumptions and enable a rational appraisal o these very important and widely used ormulas. In addition, the FE results provide an understanding o the mechanics, which is just as important as the ability to make accurate predictions in speciic cases. The strength o the bolted joint is determined by analysis. Once the analysis is done it is clear that whether it is reaching the requirements or not. Based on the analysis results the changes have to be done in the design to increase the strength or stiness o the joint. For the purpose o improvements to be done in the joint design, the bolt loads must be accurately calculated or the realistic design and service conditions.in this study, we analyze a bolt circle joining two langes, to predict bolt load and joint stiness or loads ranging up to the joint ailure load. Thermal expansion is included. We compare the results rom both analyses to those obtained rom commonly used ormulas Using a detailed FE analysis or testing has advantages and disadvantages. The disadvantages are that the analysis may lack, or inadequately resolve, some signiicant eect present in the real hardware. The advantages are that the boundary conditions, material properties, geometry and loads can be precisely controlled, interesting quantities that may be impractical to measure can be recovered easily, and it is less expensive to obtain the insight that comes rom observing a very large number o cases than it would be i testing were the sole approach.. This section has two purposes: 1) to assess whether popular hand-calculation ormulas or bolt and lange stiness can be used to accurately predict the bolt load change due to thermal expansion, and 2) To gain insight into the joint mechanics when loads and displacements are perectly axisymmetric, so that the lessons can be applied to the more realistic joint design shown. The second purpose is arguably the more important, because bolt load changes due to thermal expansion are oten only 1% or less o the total bolt load, which is o the order o typical pretension uncertainty. We study here a single, unconstrained joint consisting o a steel bolt-nut-washer set clamping two L shaped langes o aluminum. II. Nomenclature Most symbols used in this document are deined below. In general, material and geometric properties are subscripted or lange, b or bolt and nut, w or washer and m or the clamped members (langes and washers) as a set. IJMER ISSN: Vol. 4 Iss.12 Dec

2 P bolt = bolt orce, P ini = pretension given to the bolt, P sep = separation load o the joint, Φ = joint stiness ratio, P ini = initial pretension given to the bolt, ΔP = change in the pretension, k = stiness, δ = change in length, T = Change in the temperature, pyr = Prying orce α = coeicient o thermal expansion l = length, A = cross section area, E = young s modulus, θ =compression rustumhal-angle, d = diameter o the bolt, e b =hole edge distance, D = maximum diameter ocompression rustum III. Loads on the Bolted joint A bolted joint is an assembly o bolt, nut, washers and langes. In order to get the adequate joint strength pretension is to be applied on the bolt. Pretension compresses the washers, and langes up to some extent. At the same time the pretension causes an elongation in the bolt. Pretension load is applied to the connection by stretching the astener to a certain torque value. Torque is the turning moment o astener or nut. Due to the many variables associated with the torque, a saety actor is calculated in determining torque value which will produce a pretension load lower than the yield point o that astener. Torque meter can be used to measure bolt tension. High pretension tension helps to keep joint tight, and increases the strength o a joint, and generates riction between parts to resist shear and improves the atigue resistance o bolted connections. Generally 75% o proo strength is applied as the pretension. As a rule o thumb, the pretension should exceed the maximum load by 15% or so. A realistic bolted joint, is subjected to thermal loads, external tensile or compressive orces. Bolted joints may be exposed to temperature changes o hundreds o degrees, as well as external loads. A change in temperature ater astener installation can induce signiicant stress when the bolt has a dierent coeicient o thermal expansion rom the langes. The design considered here is bolt, nut and washers set made o structural steel, joining two langes, the langes were mounted or welded on shells circumerence. However, irst, the basic stiness relationships between the astener and the clamped material must be understood. The oset distance rom the bolt centerline to the shell creates prying that obscures these basic relationships. External applied or constraint loads transmitted to the joint through the shells act at a distance rom the bolt circle, tending to pry open the langes rather than directly liting them o one another. Even i the external load is aligned with the bolt axis using a itting, the langes will peel apart instead o gapping all at once, unless the itting and langes are unusually rigid relative to the bolt. IV. Theoretical ormulae Most o theoretical analysis starts rom an equation (1) o the orm P bolt = ΦP ext + P ini + ΔP (1) From the above equation (1) in the absence o external load the change in bolt length (in the grip) is equal to the sum o change in the lengths o washers and langes. This leads to δ b = α b l b T + l b P (2) E b A b δ = α l T l P (3) E A δ w = α w l w T l w P (4) E w A w From the equation (2), (3) and (4) δ b = δ w + δ On solving the above P = (2α l +2α w l w α b l b ) T l b E b A b +2 l (5) +2 l w E A E A w w IJMER ISSN: Vol. 4 Iss.12 Dec

3 In the equation (1) Φ is the joint stiness ratio. For the calculation o the stiness several methods were proposed till now. Out o that we use two methods those are: 4.1 Method (1) This method is rom mechanical design textbook o Shigley: I) Stiness o any member (2) is: k = AE (6) l II) Stiness o a member in a bolted joint based on simple approach using ixed cone angle is (2) k = πe dtanθ ln (l tanθ +D d)(d+d) (l tanθ +D+d)(D d) (7) Using the equations (3) and (4) A = πl dtanθ 2ln (l tanθ +D d)(d+d) (l tanθ +D+d)(D d) (8) 4.2. Method (2) This method is that o Juvinall, this is also based on compression rustum A = π [ 3d b tan 3 2 db 2 ] (9) 4 k = πe 4l [ 3d b 2 tan db 2 ] (1) The equation (1) is applicable when the line o action o orces coincides with the axis o the bolt. In this work the external load acting on the langes. The line o action o orces is not coinciding with the axis o the bolt. Some prying is induced in the joint. For this purpose we modiy the equation (1) by inserting the prying actor in the equation. Prying actor is a multiplier on the bolt orce due to the oset bolt centerline. P bolt = Φ pry P ext + P ini + ΔP = k b k b + k + 2 k b k pyr = k t w 2 +w b e b (12) pry P ext + P ini + ΔP (11) In actual joint, joint separation occurs gradually as the langes peel apart starting at the heel. But in the theoretical calculations separation occurs at all once. P sep = (P ini + ΔP)(k b + k + 2 k b k ) k w (13) pyr (k + 2 k b k ) k w Once the theoretical value o bolt orce reaches the P sep, thus the bolt orce is k P bolt = b k b + k + 2 k b k pry P ext + P ini + ΔP, P ext P sep k w P bolt = pry P ext,p ext P sep (14) V. Flange joint model Actual bolted joints are many in types; here we are taking one common type o joint design is a lange connection between two cylindrical shells or housing. There are numbers on the circumerence o cylinder in a cylindrical shell assembly. For the Figure (1): two dimensional model o lange joint assembly. IJMER ISSN: Vol. 4 Iss.12 Dec

4 Analysis purposes it is suicient to model one lange joint with careully chosen boundary conditions. Here we have taken standard M1 bolt o class 9.8, and nut with pitch 1.5mm. Flanges are o L shape. The bolt, nut and washers are made o structural steel, and langes are made o aluminum. Table (1): material properties Material E α θ Structural steel Pa / c.3 Aluminum Pa / c.33 Bolt and nut are modeled as per Metric Threads. The bolt belongs to class 9.8 the proo strength o bolt is 65 MPa, Yield strength is 72 MPa, and the tensile strength is 9 MPa. VI. Finite element analysis procedure The detailed inite element analysis or a bolted joint presented is exempliied in the ollowing phases: The irst phase is modeling the joint using CREO sotware. The model geometry was generated using the same sotware and then imported as a neutral ile in ANSYS WORKBENCH. Geometric details, such as chamers, radii o connection have only a local inluence on behavior o the structure. Figure (2): dimensions o the lange joint: t 12.7mm h n 8.4mm t w 2.8mm t ba 12.7mm w b 31.3mm h 1mm w b 31.3mm e b 15.65mm h h 6.85mm d b 1mm. Next, the prepared geometric structure is reproduced by inite elements. The inite elements are connected by nodes that make up the complete inite element mesh. Each element type contains inormation on its degree-oreedom set (e.g. translational, rotational, thermal), its material properties and its spatial orientation (1D-, 2D-, 3D-element types). The mesh was controlled in order to obtain a ine and good quality mapped mesh. The assembly had nodes and elements. In order to solve the resulting system equation, boundary and loaded conditions are speciied to make the equation solvable. These langes were given an axial load, bolt was given a pretension o N, and total joint was subjected to a thermal load 11 c. Pretension is applied in Z axis direction. The last phase is interpreting the results. IJMER ISSN: Vol. 4 Iss.12 Dec

5 Figure (3): loads and supports given on long lange joint assembly. Figure (5): loads and supports given on short lange joint assembly. VII. Results Fig.(6) shows that results were plotted or short lange assembly bolted joint. The plot is or bolt orces versus external load or an initial pretension o N. It is clear rom the plot, external load reaches near to the given pretension value, Bolt orce reaches the yield strength o bolt. Ater this bolt orces crosses the elastic limit, that is yield criteria, the joint behavior ater yielding is beyond the limitations o this study. IJMER ISSN: Vol. 4 Iss.12 Dec

6 bolt orce 8 5 Bolted Joints Analysis Methods and Evaluation short 5 external load Figure (6): bolt orce developed or external load in short lange model assembly Fig.(7) shows the results o long lange assembly. From the graph it is clear that the bolt orces increases gradually unlikely in the theoretical calculations. In the Fig.(8) the bolt orces o short and long lange were compared or the purpose o better design o joint. From the graph it is very clear that there is no much dierence in the bolt orces induced in the short and long langes. 5 bolt orce long lange 5 external orce Figure (7): bolt orce developed or external load in long lange model assembly. 8 5 bolt orce short lange long lange 5 external orce Figure (8): comparison o bolt orces developed in long and short lange assembly models. IJMER ISSN: Vol. 4 Iss.12 Dec

7 The theoretical calculations method (1), and method (2), was used to ind bolt orces. Later on the results o theoretical calculations and inite element analysis were compared. The comparison is shown in the ig.(9) and ig.(1) and it was showing that the theoretical calculations estimate a sudden change in the slope o the bolt orces curve. That sudden change in the slope o the curve, which is at the joint separation load o 19 N. there is a steep increase in the curve with a slope o Where as in the inite element analysis results slope o the curve is lesser than the theoretical value. It is observed thatthe theoretical values are 1 to 2% greater than the FEM results. It is very diicult to measure the pretension applied on bolt, so there may be lot o uncertainties in applying the pretension to the bolt. I any pretension uncertainty exists in the joint, the hand calculations may over predict or lesser estimates the bolt orce. This study calculated the bolt orces with hand ormulae, or a pretension o ±25% to the actual value. At the same time inite element analysis was also conducted or a pretension o ±25% to the actual value.both inite element analysis and theoretical calculations were compared. Comparisons were shown in Fig.(11) and Fig.(12). The observations are stating that the increase in the pretension tends to overestimate the bolt orce. 9 8 bolt orce 5 short lange method1 method 2 5 external orce Figure (9): comparison o bolt orces developed in long and short lange assembly models with theoretical calculations method (1) and (2). 9 8 bolt orce 5 method1 method 2 long lange 5 external orce Figure (1): comparison o bolt orces developed in long lange assembly models with theoretical calculations method (1) and (2). From the observations it was clear that the theoretical values were giving a closer it to the inite element analysis results i the prying actor is reduced. It was shown in the Fig.(13) that a lesser prying actor value gives a closer it to the inite element analysis values. IJMER ISSN: Vol. 4 Iss.12 Dec

8 bolt orce Bolted Joints Analysis Methods and Evaluation FEA value external orce Figure (11): comparison o bolt orces developed in long lange assembly models with method 1 or the pretension value o N. bolt orce FEA value theoretical 5 external orce Figure (12): comparison o bolt orces developed in long lange assembly models with method 1 or the pretension value o 35N bolt em value theoretical 5 external orce Figure (13): comparison o theoretical values with prying actor 2 to the inite element analysis values. IJMER ISSN: Vol. 4 Iss.12 Dec

9 VIII. Conclusions 1) Theoretical calculations shows that the initial pretension applied is not having any eect on the calculation o change in the pretension due to the temperature change. 2) It is clear rom the results plot; increase in the pretension increases the amount o overestimate o bolt orces. 3) Length o the lange does not have any eect on the bolt orce estimation either in theoretical calculations or in the inite element analysis results. 4) Decreasing in the prying actor in the theoretical calculations gives a closer it to the theoretical and experimental values. 5) Stiness o the total joint is based on the initial geometry in the theoretical approach. But when the joint starts separating stiness decreases with increase in the heel gap. 6) Because there are many assumptions in the theoretical calculations, theoretical calculations are overestimating the results up to 1-2% o actual values, or the complicated design o lange joints. REFERENCES [1]. Mechanical engineering design Shigley. [2]. Mechanics o materials Punmiabc. [3]. Anonymous, \Space Shuttle: Criteria or Pretensioned Bolts," Tech. Rep. NSTS 837 Rev. A, NASA, Houston, [4]. An Evaluation o Common Analysis Methods or Bolted Joints in Launch Vehicles 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conerence<BR>18 th,12-15 April 21, Orlando, Florida. [5]. FINITE ELEMENT ANALYSIS OF BOLTED JOINT Iuliana PISCAN, Nicolae PREDINCEA, Nicolae POP [6]. Engineering Fundamentals o Threaded Fastener Design and Analysis RS Technologies, a Division o PCB Load & Torque, Inc. [7]. Juvinall, R. C. and Marshek, K. M., Fundamentals o Machine Component Design, Wiley, 2 IJMER ISSN: Vol. 4 Iss.12 Dec