Contact Stress Analysis of Barrel Coupling

Contact Stress Analysis of Barrel Coupling

V. V. Vaidya1, A. P. Tadmalle2

Sinhgad College of Engineering, Pune, Maharashtra

Abstract The Barrel coupling is a device used to transmit torque between two rotating parts. It consists of a sleeve provided with semicircular toothing around its internal diameter and hub that is externally toothed.A series of cylindrical barrels of hardened steel are inserted in the holes formed by toothing to act as power transmission elements. This research works aims to study effect of torque transmission and radial load on contact stress in barrel coupling. Contact stress predicted by using Hertzian analytical method. Barrel coupling is modelled using CATIAV5 software. Contact stresses are predicted using Ansys software by adopting different types of contact algorithms and contact types. Frictional contact with Augmented Langrange and pure penalty gives better results of contact stresses than langrange Multiplier contact algorithm. Coupling is used transmit torque in electric overhead crane. Results obtained from Ansys is in close agreement with Hertzian analytical method.

Keywords Barrel coupling, Radial load, contact Stresses, Transmission torque, Contact algorithm

1. INTRODUCTION

   Coupling is a mechanical device used to connect two shafts together at their ends for the purpose of transmitting power. Couplings do not allow disconnection of shafts during operation, however if torque limit is exceeded beyond designed value then coupling may get disconnected during operation. Coupling can permit some degree of misalignment among the connecting shafts. By careful selection, installation and maintenance of coupling substantial saving can be made in maintenance cost.

   A Barrel coupling

   The barrel coupling consists of a sleeve provided with semicircular toothing around its internal diameter and a hub that is externally toothed as shown in fig.1.7. A series of cylindrical barrels, of hardened steel, are inserted in the holes formed by this toothing to act as power transmission element. Covers with their corresponding special seals serve to assure the perfect-tightness of the inner zone, preventing the penetration of dust and guaranteeing the continuity of the necessary lubrication. Two double-lamina elastic rings mounted on the hub, one on each side of the toothing, limit the axial displacement of the barrels. Torque is transmitted to the drums receiving flange, generally by two diametrically opposed flat driving surfaces, located at the periphery of the coupling flange, and also by means of bolts which, at the same time, serve as connection with the drum. An indicator located on the external cover which moves relative to the marks on the hub as a function of wear, permits control of internal wear of the toothing, without the need to disassemble any part of the coupling. The same indicator also serves to control the

   axial position of the sleeve relative to the hub. The convex shape of the barrels and the internal spaces of the toothing allows the oscillation of the hub relative to the sleeve compensating angular misalignments of ± 1º 30 and an axial displacement that varies between ± 3 mm and ± 8 mm.

   Fig.1 Barrel coupling

   1.Hub	6.Allen screw		11.wear grooves	limit	16.grower washer
   2.sleeve	7.Indicator		12.grease connection		17.barrel guide ring
   3.Inner cover	8.seal		13.grease overflow		18.seeger ring
   4.outer cover	9.Allen screw		14.assembly reference
   5.Barrel	10.threaded holes disassembly	for	15.barrel rings	guide

   Advantages

   1. Barrel couplings have increased contact area, radial load is better distributed hence life of coupling is increased.

   2. Due to barrel and gear profile, for a given radial load 40 % stress reduction is obtained compared to other couplings.

2. ANALYTICAL METHODOLOGY

   Analytical methodology divides into two parts; first part includes calculation of transmission torque and calculation of radial load acted on barrels. Second part includes calculation of contact stress induced due to application of torque and radial load by using Hertzian theory.

   1. Calculation of nominal transmission torque T (Nm)

   \

   1. Based on installed power

      = 9550 × × 1

      = 9550 × 1 × 1.8

      4

      T=4300 Nm

      The static pull in the drum is given by

      ( + )

      = × 2

      (60000 + 2000)

      =

      4 × 0.95

      Fp=13684.2 N

   2. Based on consumed power

   = ×

   60000

   Fig.2 Distribution of forces

   13684.2 × 4

   60000

   Stribecks equation is given by :

   = . × 1

   Pc= 0.91 Kw

   = × 9550 × 1

   = 0.91 × 9550 × 1.8

   4

   T= 3910 Nm

   B Calculation of radial load Fr

   Where Stribecks factor = 5.

   P1 ,P2 ,P3 . are distributed forces

   For this model of barrel coupling there are 20 barrels.

   Total radial load 14500 N is converted into 9 forces according to stribecks equation.

   14500=1/5*20*P1

   P1=3625 N (maximum radial load acted on barrel)

   = ( (1 ) + 2 )

   = (13684.2 (1 400 ) + 7000)

   1200 2

   Fr=12267.3 N

   1. Stribecks Equation

      It is used for distribution of radial forces among barrels on lower half part of coupling. It is based on the following assumptions:

      1. The rollers are rigid and they retain their circular shape.

      2. The rollers are equally spaced.

      3. The rollers in the upper half portion not support any load. Figure 3.1.shows the forces acting on the inner race through rolling elements,that supported maximum radial load Fr.

      2 = 1(18)(32)

      2 = 3625(18)(32)

      =3362.15 N

      3 = 3625(36)(32)

      = 2637.18 N

      4 = 1(54)(32)

      4 = 3625(54)(32)

      = 1633.56 N

      5 = 1(72)(32)

      5 = 3625(72)(32)

      =622.7 N

   2. Hertz contact stress theory

   Contact between two continuous, non-conforming solids is initially a point or line. Under the action of a load the solids deform and contact area is formed According to the contact area shape (under no external load), there are point contact and line contact. It is obvious that after load applied line contact will become rectangle contact and point contact will

   be an ellipse contact area. Hertz contact stress theory allows for the prediction of the resulting contact area, contact pressure, compression of the bodies, and the induced stress in the bodies.the maximum principal stresses occurring at the surface of contact are given by Hertzian equation are following

   = (|),

   = 2(|)

   = (|)

   Maximum principle stress is given by following

   = (|)

   Where b is semi width of formed rectangular contact area is given by

   = 2

   1. Solve contact problems.

   2. Look over and analyze results.

   1. Creation of Geometry of Barrel coupling

      3D geometry moel is built in CATIA software and imported in ansys software.

      = 1

      12(1) + 12(2)

      By putting values Maximum contact stress,

      1 2

      ( 1 +

      1 2

      2 )

      Fig.3 Creation of Geometry of barrel coupling

   2. Material Selection

   = 650.8

   E. Contact stress due to Torque:

   For this application alloy steel have great advantages than

   T = ft

   × dc

   2

   others. Alloy steels have higher strength and toughness. It posses higher hardenability which has great significance in

   Tangential load = ft =80357.14 N Contact area is given by

   = × 1 ×

   Contact area for 20 barrels=20× A

   heat treatment of components and also better corrosion resistance compared to plain carbon steel. EN24 is a popular grade of through-hardening alloy steel due to its excellent machinability. EN24 is used in components such Axles,

   Contact stress=

   = = 5.655

   connecting rods, high tensile bolts, studs,power transmission slide gears, slide cams, differential shafts, pinion sleeves,

   Total contact stress = [(contact stress due to radial load)2 +

   (contact stress due to torque)2]1/2

   =[(650.8)2+ (5.655)2]1/2

   Total contact stress=650.8 mpa

   Above contact stress value is maximum contact stress corresponding to maximum radial load P1 obtained from stribecks equation.Now we obtained further contact stress value to radial load P2,P3,P4 ,P5 obtained from stribecks equation.

3. FINITE ELEMENT ANALYSIS OF BARREL COUPLING

The Finite Element Method (FEM) is a numerical approximation method. It is a method of investigating the behaviour of complex structures by breaking them down into smaller, simpler pieces. These smaller pieces of structure are called elements. The elements are connected to each other at nodes. The assembly of elements and nodes are called a finite element model. Typical surface-surface contacts analysis steps mainly include-

1. Build 3D geometry model and mesh.

2. Identify contact pairs.

3. Name target surface and contact surface.

4. Define target surface.

5. Define contact surface.

6. Set up element key options and real constants

7. Define and control rigid goals movement.

8. Apply the necessary boundary condition.

9. Define solution options and load steps.

spindle gears and compensating washers. EN24 can be further surface hardened to create components with enhanced wear resistance by induction or nitriding processing.

1. Define contact properties

   Once material properties are given to coupling in Ansys, contact elements need to define. Contact properties are given in four stages in ansys.In first stage contact class has to be defined. Generally there are two contact classes: rigid-flexible and flexible-flexible. In rigid-flexible contact, one or more of the contacting surfaces are treated as rigid. The other class flexible-flexible contact is the more common type. In this case, all contacting bodies are deformable. In second stage contact area has to be defined. , there are two groups of contact: point-surface contact and surface-surface contact. In ANSYS, the contact is generated by pair. For the point- surface contact, the `point` is contact and the `surface` is target. For surface-surface contact, both contact and target are surfaces and they have to be specified which surface is contact and which is target.

   In third stage behaviour of contact surface has to be specified. Contact surface has different types of behaviour according to different characteristics of contact. Normally there are frictional, no separation, bonded. In frictional contact, the contact body can slide on the target surface in the tangential direction. It can translate in the normal direction. This behaviour can simulate the contact opens and closes. Frictional contact is most reliable contact behaviour in analysis of barrel coupling as barrels fits in cavities of semicircular toothing of sleeve and hub where friction exists.

   In bonded contact no relative movement between each other in the rest of analysis is possible. They look like one body.In this analysis we have used first frictional contact and after that bonded and no separation contact is used for checking best possible contact. In fourth stage contact algorithm has to be specified in ansys.contact algorithms are used to solve contact problems. Pure Lagrange multiplier,pure penalty method and the Augmented Lagrangian are three contact algorithm are used to solve contact problems.In this analysis first the Augmented Lagrangian Method is used to solve contact problems with friction and after that pure penalty and langrange multiplier method is used for finding best possible combination.

2. Meshing

   In first stage of meshing element type is specified for coupling. Different element type can be given to different parts of coupling just like sleeve, hub and barrels. For barrels, hub and sleeve part solid 187 tetrahedral element type is given. Barrel surface which comes in contact with sleeve inner and hub outer surface represents contact and target surface and separate contact and target element is given to that contact faces.CONTA 174 as contact element and Targe 170 as target element is applied.

   Fig.4.Meshing

3. Setting boundary conditions and applying loads

   Total radial load 14500 N is applied on coupling and torque of 4500 Nm acted on body. the total radial load is divided according to stribecks equation and applied to barrels in lower half portion of coupling.

   Fig.5 Application of boundary and loads

4. Solution of contact stresses and deformation

   With the help of simulation contact stress and deformation obtained. Generally von misses stress can be found out and helpful in analysis. Through simulation, result of the maximal contact stress was 601.06 Mpa while the Hertzian theory value was 650.08 MPa. The comparison revealed that there was good consistency between the Hertzian theory solution and finite element solution.

   fig.6 contact stress on barrel coupling

   Fig.7 contact stress on barrels

   The above Figures 6& 7 shows the analysis results of barrel coupling. It clearly indicates that maximum stress is occurred on barrel at the contacting region. From figure we can also know that the contact area had an approximate rectangular shape in contact area. The contact stress for particular this analysis is varies 601.06 Mpa to 66.98 Mpa.In this analysis we have used frictional contact with contact algorithm as augumented langrange.after that we have changed contact algorithm pure penalty and langrane multiplier with frictional contact and solution obtained.after that we have changed types of contact such as bonded, no separation with all three algorithm and solution obtained.

   IV RESULTS AND DISCUSSION

   We have found contact stress in barrel coupling by Hertz analytical method. These contact stresses also obtained from finite element analysis. In finite element analysis different methodologies are for finding contact stress analysis. There are different types of contact such as frictional, bonded, no separation and different contact algorithms for contact detection such as pure penalty,augumented langrange,and langrange multiplier. We have made all possible combination of these types of contact along with contact algorithm to find best possible method of contact analysis in finite element analysis.

   A Comparison between contact algorithms with frictional contact

   In this frictional contact as type of contact is selected and three contact algorithm used one by in finite element analysis.

   Results obtained are compared to Hertz analytical method. Results are shown in Table I and figure 8

   TABLE I

   COMPARISON BETWEEN CONTACT ALGORITHMS WITH FRICTIONAL CONTACT IN FEM

   Radial Load in N	Contact stress(Mpa) by Augumented Langrange	Contact stress(Mpa) by Pure penalty	Contact stress(Mpa) by Langrange Multiplier	Hertz Analy tical Meth od
   3625	601.06	601.06	531.04	650.8
   3361.8	580.12	580.12	472.07	627
   2636.9	502.79	502.79	413.1	555.3
   1633	425.46	425.46	354.12	437
   621.99	270.8	270.8	236.18	269.8

   700

   600

   500

   conta

   augumented

   langrange

   pure penalty

   ct

   stre3s0s0

   in Mp2a00

   100

   0

   langrange

   multiplier

   Hertz analytical

   Radial load in

   400

   Fig.8 Comparison between contact algorithms with frictional contact in FEM

   Results shown in table I revealed that contact stress obtained from contact algorithm pure penalty and augumented langrange is almost same within 5% to 7% to Hertz analytical method contact stress values but langrange multiplier method obtained results deviates more than analytical method.frictional contact is with all contact algorithms. In Frictional contact the contact body can slide on the target surface in the tangential direction. The results for the augumented langrange and pure penalty algorithms are good for all problems provided they are used with surface to surface contact elements. The results for the langrange multiplier algorithms can be quite sensitive to matching of the nodes on contact region so values deviate more [10].frictional contact with pure penalty or augumented langrange nearly gives reliable solution.

   B Comparison between contact algorithms with bonded contact

   In this we have used bonded contact and contact algorithm is changed one by one. Results are obtained are shown in table II and fig.9 are compared to Hertz analytical method.In Bonded

   contact as soon as the contact is detected, then the nodes in contact are bonded in all directions and all the degrees of freedom are constrained. Not any relative movement between each other in the rest of analysis is possible. They look like one body,irrespective of loading, behaviour of other parts.

   TABLE III

   COMPARISON BETWEEN CONTACT ALGORITHMS WITH BONDED CONTACT IN FEM

   Radial Load in N	Contact stress(Mpa) by Augumented Langrange	Contact stress(Mpa) by Pure penalty	Contact stress(Mpa) by Langrange Multiplier	Hertz Analytical Method
   3625	109.72	109.72	109.72	650.8
   3361.8	97.533	97.533	97.533	627
   2636.9	85.342	85.342	85.342	555.3
   1633	73.351	73.351	73.351	437
   621.99	60.96	60.96	60.96	269.8

   700

   600

   500

   400

   co 300

   nta

   ct 200

   str

   ess 100

   pure

   penalty augumente d langrange

   in

   Mp a

   0

   Radial

   load in N

   Fig.9 Comparison between contact algorithms with bonded contact in FEM

   Results in table II and Fig.9 reveals that bonded contact gives the same result of all three contact algorithm as in bonded contact there is no relative movement among parts. Results are highly deviates more than 25% from Hertz analytical method, so results are not reliable.

   1. Comparison between contact algorithms with no seperation contact

      In this we have used no separation contact and contact algorithm is changed one by one. Results are obtained are shown in table no and graph are compared to Hertz analytical method.

      TABLE IIIII

      COMPARISON BETWEEN CONTACT ALGORITHMS WITH NO SEPERATION CONTACT IN FEM

      Radial Load in N	Contact stress(Mpa) by Augumented Langrange	Contact stress(Mpa) by Pure penalty	Contact stress( Mpa) by Langra nge Multipl ier	Hertz Analytical Method
      3625	490.78	490.78	732.81	650.8
      3361.8	436.27	436.27	651.39	627
      2636.9	381.74	381.74	569.37	555.3
      1633	327.2	327.2	488.54	437
      621.99	272.67	272.67	407.12	269.8

      800

      700

      co 600

      nta

      Hertz

      analytic al

      a

      200

      100

      0

      Radial

      3625 3361.8 2636.9 1633 621.99 load in

      N

      Augum

      ented langran ge

      str

      ess 400

      in

      Mp300

      500

      ct

      Fig.10 Comparison between contact algorithms with no seperation contact

      Results in table III and Fig.10 revealed that pure penalty and augumented langrange gives same result for no separation contact.Langrange multiplier gives more than 20%deviation to Hertz analytical method than other two contact algorithm.For 3D model pure penalty and augumented langrange gives better than langrange multiplier.

   2. Comparison between contacts with augumented langrange algorithm

      In this contact algorithm as augumented langrange is kept constant and contact changed with frictional, bonded and no separation. Results obtained are compared with Hertz analytical method.

      TABLE IV

      COMPARISON BETWEEN CONTACTS WITH AUGUMENTED LANGRANGE

      Radial Load in N	Contact stress(Mpa) With frictional contact	Contact stress(Mpa) With bonded contact	Contact stress(Mpa) With no separation contact	Hertz analytical method
      3625	601.06	109.72	490.8	650.8
      3361.8	580.12	97.533	436.27	627
      2636.9	502.79	85.342	381.74	555.3
      1633	425.46	73.351	327.2	437
      621.99	270.8	60.96	272.67	269.8

      Fig.11 Comparison between contacts with augumented langrange algorithm

      Results obtained in table IV and fig.11 revealed that frictional contact gives nearly same within 5% to 7% to as result to Hertz analytical method. Bonded contact and no separation contact stress values deviate more than 20% . Other contact failed to give proper results.

   3. Comparison between contacts with pure penalty algorithm In this contact algorithm as pure penalty is kept constant and contact changed with frictional, bonded and no separation. Results obtained are compared with Hertz analytical method.

      TABLE V

      Radial Load in N	Contact stress(Mpa) With frictional contact	Contact stress(Mpa) With bonded contact	Contact stress(Mpa ) With no separation contact	Hertz analytica l method
      3625	601.06	109.72	490.8	650.8
      3361.8	580.12	97.533	436.27	627
      2636.9	502.79	85.342	381.74	555.3
      1633	425.46	73.351	327.2	437
      621.99	270.8	60.96	272.67	269.8

      COMPARISON BETWEEN CONTACTS WITH PURE PENALTY

      Fig.12 Comparison between contacts with pure penalty algorithm

      Results obtained in table V and fig .12 revealed that frictional contact gives nearly same as result to Hertz analytical method. Bonded contact and no separation contact stress values deviate more. Other contact failed to give proper results.

   4. Comparison between contacts with Langrange Multiplier In this contact algorithm as Langrange multiplier is kept constant and contact changed with frictional, bonded and no separation. Results obtained are compared with Hertz analytical method.

   TABLE VI

   COMPARISON BETWEEN CONTACTS WITH LANGRANGE MULTIPLIER

   800

   700

   Hertz

   analyti

   cal Frictio

   nal

   600

   Contact

   stress in

   bonde

   d

   Mpa

   400

   300

   200

   100

   0

   3625 3361.8 2636.9 1633 621.99

   Radial

   load in N

   500

   Fig.13 Comparison between contacts with Langrange Multiplier algorithm

   Results obtained in table VI and Fig. 13 revealed that frictional contact gives nearly same and realistic result to Hertz analytical method. Bonded contact and no separation contact stress values deviate more. Other contact failed to give proper results.

   V .CONCLUSION

   Radial Load in N	Contact stress(Mpa) With frictional contact	Contact stress(Mpa) With bonded contact	Contact stress(Mpa) With no separation contact	Hertz analytical method
   3625	531.04	109.72	732.81	650.8
   3361.8	472.07	97.533	651.39	627
   2636.9	413.1	85.342	569.37	555.3
   1633	354.12	73.351	488.54	437
   621.99	236.18	60.96	407.12	269.8

   1. Contact stresses depend on contacting area between barrel and sleeve, barrel and hub

      surfaces.

   2. Contact stresses of barrel coupling are depending on pitch circle diameter of sleeve and hub, diameter of barrel, material properties of coupling.

   3. The results estimated for frictional contact with pure penalty and augmented langrange algorithm is close agreement with Hertz analytical method where as langrange multiplier predicts higher than 7% error.

   4. Frictional contact method is most effective contact than no separation and bonded contact. Bonded contact does not show significant change with contact algorithm.

VI. ACKNOWLEDGEMENT

This paper is supported by Demag cranes and components(India) pvt.ltd.Author wish to thank all staff of SCOE Pune for supporting and guiding for completion of paper.

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