Design of Shrink Fit for Low Temperature Rotating Turbine Components

Design of Shrink Fit for Low Temperature Rotating Turbine Components

1. Gopalakrishnan1, Maneesh Batrani, Jatinder Mohan, Naveen Chandra Bhatt, Mukesh K Verma

   Steam Turbine Engineering, Bharat Heavy Electricals Limited, Haridwar, Uttarakhand, India

   Abstract – Key aspect to designing any turbine component is to ensure its mechanical integrity. Steam turbine rotor mechanical integrity has traditionally been and still is a concern for Original Equipment Manufacturers (OEMs) across the globe due to their catastrophic nature of failure [1]. Any joint in rotating components always present a great risk for integrity of rotating machinery. One such joint is shrink-fit in rotating components. Many steam turbine rotors of earlier designs especially impulse or low reaction bladed rotors had shrink fit discs fitted onto them. Though shrink fit joints are less employed these days, they are still relevant.

   This paper discusses the shrink fit design philosophy for rotating components operating at room temperature. Design philosophy includes identification of loads, safety factor, evaluation of stresses and interference etc. Turbine bladed discs, gear wheel etc. are not regular cylindrical shapes, hence employability of classical formulations have limitations. Additional analysis using Finite Element Method is required to substantiate the design. The methodology is validated in design of one rotor having such shrunk on components.

   Keywords: Shrink fit, interference, turbine, rotation, ANSYS

   1. INTRODUCTION

      Shrink fit is a semi-permanent joint between the shaft and hub. Outer element of the shrink fit joint is hereby referred to as Hub and inner element of the shrink fit joint is referred to as Shaft, please refer to Fig. 1.

      Shrink fit is achieved by assembling a cylindrical hub onto a shaft (shaft outer diameter is higher than the inner diameter of hub) either by pressing it in place (or) using differential thermal techniques [2]. An interfacial pressure is generated due to the local elastic deformation due to interference. The state of stress induced between interfacing cylinders is similar to that of an externally (or) internally pressurized pressure vessel and is governed by Lames equation.

      Fig. 1, Schematic of Interference Fit Joint

      The case of shrink fit in rotating discs with large diameters is slightly different. These discs with large diameter are subjected to high centrifugal force, resulting in reduction in interference between shaft and hub diameters at the interface due to centrifugal action. Stresses induced due to rotation are also a cause of concern along with interfacial stresses due to interference. Hence, additional care from the designer is required for deciding the interference tolerance, please refer to Fig. 2.

      Fig. 2, Rotating turbine wheel and hub of varying geometric shapes

   2. DESIGN CONSIDERATIONS FOR SHRINK FIT

      JOINT

      Designing a shrink fit joint for rotating discs primarily involves following aspects:

      Interference required to overcome this torsional loading [3] would be given by,

      = P * [ R *(1- ) + R * (Ro2+R2 + )] (2)

      • Torque transmission requirement and differential growth between shaft and hub due to centrifugal load. This

        T T ES

        Where,

        s EH

        Ro2-R2 H

        determines the Minimum Interference Condition

      • Stress in the joint at assembly condition as well as operating condition due to centrifugal loads would decide the Maximum Interference Condition"

      • Shaft/Hub material being used

      A designer would then integrate these requirements and define an interference tolerance. Shaft and hub materials can differ or be the same depending upon requirement. This needs to be taken care appropriately in the classical formulations.

      Differential growth due to thermal loads are not significant in low temperature turbine rotors. However, these are relevant for high temperature turbine rotors. But, they

      T = Minimum interference required for overcoming torsional load

      PT = Interference pressure corresponding to FT Es = Youngs Modulus of Shaft

      R = Nominal radius at interface

      S = Poisson ratio of shaft

      EH = Youngs Modulus of Hub R0 = Outer radius of Hub

      H = Poisson ratio of Hub

      1. Radial growth due to rotation:

         For a hollow disc at any radii, radial growth due to centrifugal loads [4] is given by the relation below:

         affect the design of shrink-fit joint only in case material of

         = [(

         2r *

         (3+)*(1-)

         2 2

         (1+v)r r

         ) * (r2+r2+ o i –

         (1+)

         r2)] (3)

         shaft and hub are different.

         Deformations induced due to centrifugal loading is function of square of rotational speed, hence joint can loosen up in case of inadequate interference resulting in adverse consequences.

   3. DESIGN METHODOLOGY

      As discussed earlier, the joint has two limiting (or) bounding conditions:

      • Minimum Interference Condition: a joint should not open up under the operating conditions due to lack of interference

      • Maximum Interference Condition: Material of Hub/Shaft should be able to withstand the interference stress during assembly. During operation, the joint should be able to withstand stress due to rotation and pressure stresses due to remaining interference

      1. Minimum Interference Condition

         This condition ensures that there is no slippage in the joint. A loose joint may result in slippage of hub onto shaft and loose its intended purpose. Minimum interference condition would overcome differential radial growth between shaft and hub due to centrifugal loading and slip due to torsional loading during operation. Following methodology is to be followed to address this concern: –

         1) Interference to overcome torque requirement:

         Friction force (FT) generated in the joint to overcome operating condition torque, is given as;

         T = R × FT (1)

         Where,

         T = Torque to be transmitted by the joint during operation R = Nominal radius at interface

         FT = Force

         E 8 o (1-)r2 (3+)

         = Radial growth of rotating disc (shaft/hub)

         = Density of rotating disc (shaft/hub)

         = Angular Velocity

         r = At any radius where growth needs to be estimated

         r0 = Outer Radius of rotating disc (shaft/hub) ri = Inner Radius of rotating disc (shaft/hub) = Poisson ratio of rotating disc (shaft/hub)

         E = Youngs modulus of rotating disc (shaft/hub)

         Using the above formula, the radial growth of inner element

         – shaft S and outer element – Hub H are calculated at maximum expected over speed condition at the nominal radius.

         The classical formulation for radial growth of shaft (or) hub is based on rotating disc formulation. It is important to note that the radial growth of solid and hollow shafts would be different. However, it is observed that the difference is practically negligible and hence, these formulations can be safely used.

         3) Minimum Interference:

         Minimum interference condition is estimated using s, T

         and H are determined as follows:

         minimum = [(H-S)+T] (4)

         The above interference must be achieved at the assembly condition to avoid loosening of joint in operation under combined action of centrifugal and torsional loads. An appropriate safety factor may be employed to increase the value, if needed.

         After determination of minimum interference as per above, designer should include manufacturing tolerance upon the nominal shaft/ub diameter. The maximum interference should be evaluated with the help of specified tolerances.

      2. Maximum Interference Condition

         Maximum interference is important from strength point of view and hence, may affect selection of material. The Hub is highly stressed component of the joint compared to shaft. It can fail due to:

         1. Stress beyond limits during assembly due to interference pressure

         2. Stress beyond limits during operation due to remaining interfacial pressure and rotational loads

            Maximum principal stresses have been considered for mechanical strength analysis in this paper. However, it depends upon the designer to choose the appropriate failure criterion.

            If the above stresses are beyond the material strength limits, then material selection needs to be relooked or the shrink fit parameters need to be redesigned if possible to bring stress within allowable limits.

            1. Stress due to interfacial pressure in hub during assembly/operation:

               Hub is a hollow thick cylinder subjected to internal pressure. Hoop stress at the hub inner diameter due to assembly condition/operating condition interfacial pressure is calculated using the equation below [3]:

               Stresses at assembly and operating condition should be within material limits with appropriate factor of safety.

   4. FINITE ELEMENT ANALYSIS AND ITS

      IMPORTANCE

      As discussed before, classical formulations have their own set of limitations. Hence, finite element analysis of shrink fit assembly would give designer additional information about the joint behavior and its integrity. Here, we discuss finite element analysis using ANSYSTM software to further validate the integrity of shrink fit design. Outcome of the finite element analysis depends on:

      • Quality of mesh (including refinement)

      • Interface definition using contact settings [5]. (Selection of contact and target component (shaft or hub) is designers prerogative. However, in present work, shaft is used as contact and hub is taken as target surface)

      Surface to Surface contact pair definition was used to define the interference between shrink fit components, please refer to Fig. 3

      r2 r2

      Hoop stress at hub inner diameter = P* i * (1+ 0)

      r2-r2 r2

      Where,

      0 i i

      (5)

      Fig. 3, Surface to Surface Contact Definition

      P = Interfacial pressure at the time of assembly to achieve minimum or remaining interfacial pressure at operating condition

      r0 = Outer radius of Hub ri = Inner radius of Hub

      1. Stress due to rotation in hub during operation

      Hoop stress due to rotation [4] at hub inner radius is given by

      The amount of physical interference between the hub and the shaft is defined through contact surface offset as in Fig. 4 below:

      H2 *[(3+

      )r2+ (1-

      )r2] (6)

      4

      Where,

      H 0 H i

      H	=	Density of Hub material
      H	=	Poisson ratio of Hub
      	=	Angular velocity of Hub
      r0	=	Outer Radius of Hub
      ri	=	Inner Radius of Hub

      Fig. 4, Interference definition

      After defining the contact assembly, the analysis is performed in two stages. In the first stage, the interference due to minimum interference condition is simulated. In the second stage, centrifugal loading in the form of global angular velocity is applied along with appropriate boundary condition.

      Based on requirement different over speed conditions are simulated to check for exact speed at which the joint disintegrates i.e. loosen up. Parameters that are used to check for joint integrity include contact status and contact pressure

      Fig. 5, Contact Status of the shrink fit joint

      Contact status from the finite element software is just a qualitative indicator of the condition of the joint. However the contact pressure is a quantifiable term, please refer Fig. 5

      The contact pressure should match with Interference pressure (please refer equation 2) during assembly condition and the remaining interference pressure at operating condition within acceptable margin of error Fig. 6.

      Fig. 6, Contact Pressure at running condition

      End effects (or) localized stress raisers can also be observed from the finite element model unlike the classical formulation in relevant cases.

   5. APPLICATION OF DESIGN PROCESS IN A

      RECENT PROJECT

      For a recent project, a shrink fit joint had to be designed for a low pressure steam turbine rotor in which a starting motor gear had to be shrink fitted. Through the above established process this recent project was handled.

      Fig. 7, Gear shrunk on over a turbine coupling

      Post design, the rotor was also over speed tested successfully at factory works, please refer Fig. 7

   6. CONCLUSION:

      Methodology for design of shrink fit joints for rotating components has been described. Calculations using classical formulations and validation using finite element software (ANSYSTM) has been shared. A case of successful implementation of the procedure to design a shrink fit joint for a low pressure steam turbine rotor is also presented.

   7. REFERENCES:

1. Nitta A, Kobayashi H , Burst of Steam Turbine Rotor in Fossil Power plant; http://www.sozogaku.com/fkd/en/cfen/CB1031027.html

2. Jack A. Collins, Henry Busby, George Staab; Mechanical design of machine elements and machines A failure prevention perspective; Wiley Publication; 2010

3. J Edward Pope; Rules of Thumb for Mechanical Engineers;

   Gulf Publishing Company; 1997

4. EJ Hearn; Mechanics of Materials 2; Butterworth Heinemann publication; 2001

5. ANSYSTM 17.0; Help manual