Elasto-Plastic Thermal Stress Analysis of Clearance Fit in Turbocharger’s Swing Valve Assembly by Estimating Displacement Distribution

Elasto-Plastic Thermal Stress Analysis of Clearance Fit in Turbocharger’s Swing Valve Assembly by Estimating Displacement Distribution

Ramanandan.H.S (1)a, Sudev.L.J (2)b

Abstract

Newly developed turbocharger Swing valve assembly (arm and bush) has to be tested to study the product life cycle and to know the satisfactory working throughout entire duty cycle. The turbine housing consists of swing valve assembly used to bypass the exhaust gas directly to atmosphere whenever not required. This assembly consists of two types of fits. Interference fit between turbine housing and bush and clearance fit between bush and arm. But, it is expensive and requires more time to carry out experimental study and measurements can be made only at the limited number of time stations. So, Finite element method is considered as a standard approach which is economical avoiding frequent experimental studies to find the performance of turbochargers. This paper deals with structural analysis of turbochargers swing valve assembly where displacement distributions are plotted for both minimum and maximum clearance cases due to thermal loads acting b/w bush and turbine housing. Meshed turbocharger and swing valve assembly model is imported to ANSYS for solving and preprocessing and given run for structural analysis. Finally radial distortion v/s sector angle graph is plotted.

1. Introduction

   A Turbocharger is an air compressor used for forced-induction of an engine. The purpose of a turbocharger is to increase the mass of air entering the engine to create more power. However, a turbocharger differs in that the compressor is powered by a turbine driven by the engine's own exhaust gases. The turbine housing consists of swing valve assembly used to bypass the exhaust gas directly to atmosphere whenever not required. This assembly consists of two types of fits. Interference fit between turbine housing and bush and Clearance fit between bush and arm which must work satisfactorily throughout the entire duty cycle for proper working of turbocharger. The swing valve assembly is exposed to high temperature exhaust gases and hence two types of valve fits experience thermo- mechanical loadings. Thus it is important to study the

   change in behavior of two types of fits throughout the entire duty cycle. It is difficult to analyze such complex thermo-mechanical loading using analytical methods. Finite element method is widely used for such studies.

   Niccolo Baldanzini [1], presents general approach for designing interference-fit joints constituted of elastic-plastic components. The theory has been successfully validated by a result comparison with finite element models. Y. Zhang et.al.[2], presents interference-fits in ring gear-wheel connections showing the application of the "finite element method (FEM) for the three-dimensional stress analysis of interference fitted connections giving more complete and accurate results than the traditional method. K. Satish Kumar et.al.[3], showed rigorous elastic-plastic finite element analysis of joints subjected to cyclic loading. The results of the study are a useful input for the estimation of the fatigue life of joints. Albert Konter [4], presents the general overview of contact analysis using FEM and comparison of contact analysis in finite element (F E) software tool. S. Sen et.al.[5] presents general stress calculations in interference-fit designs estimated using conventional equations.. During heating and cooling the transient conduction heat transfer state was considered. Adnan O¨ zel et.al. [6], presents idea to calculate stresses and deformations in the shrink-fitted hubshaft joint for various fit forms and been analysed using FEM. M. Ast, et.al.[9] reviews the FEM contact analysis of a hydraulic pre stressed coupling and of a gear-shaft connection. Even the highly nonlinear transition from static to sliding friction has been analyzed.

   The literature survey revealed that less number of papers are available on Elasto-plastic thermal stress analysis for turbochargers and particularly for swing valve assemblies. Only general studies are performed to study the interference fit using analytical formulation approach and few Finite element (FE) method using 2D contact elements. Still no systematic approaches have been carried out to ascertain the effects of thermo-mechanical distortion and displacement studies in the interface regions of fits.

   So there is a need to develop a Finite element method that gives the accurate results for clearance fit studies subjected to thermo-mechanical loading.

   The present study is focused on analyzing clearance fit and estimating displacement distributions at various time stations across duty cycle of a swing valve assembly in open position of waste gate poppet valve using FEM.

2. Methodology

   FEM model of arm bush and turbine is generated using HYPERMESH. Two types of elements namely TETRA elements for region away from study(turbine housing) and HEXA elements are created in interface region of turbine housing, bush and arm for displacement study and to create contact elements[1-2]. Meshed model is checked for any free edges, T- connection, and min. angle of element is greater than 15degree. Editing the element size in stress concentration or sensitive area elements is refined to increase the density of elements and quality of elements is checked. FE model is prepared with 1131302 elements and 593851 nodes as shown below in fig (1) and fig (2) respectively.

   Fig.1 Arm and Swing Assembly

   Fig.2 Turbine Housing and Bush Assembly

   Fig.2 Turbine Housing and Bush Assembly

   The position of the arm and bush are as shown in fig.3(a).Seven circles of nodes are prepared in Bushing (B), named as station C1 to station C7, & correspondingly seven circles are mapped on arm(A), named as station C1 to station C7 to find clearance of mapped nodes. To find the radial clearance mapped nodes shown below in fig 3(b).

   B A

   Fig.3 (a) Arm and swing assembly with clearance region

   Fig.3 (a) Nodal circles in interface region of clearance fit

   Arm and bush assembly is analyzed for both minimum (min.) and maximum (max.) clearance conditions (i.e. case 1 & 2) under thermal loads. Excel solver is developed to find the radius of nodal circles and angular position of each node using coordinate values of each nodes of a nodal circle with respect to defined coordinate system. Radial gap(radius) between adjacent nodes of Arm & bush elements is processed using excel post processing from deformed coordinates at various angular locations (Angular position of each node is calculated by finding which quadrate node is located then using Trigonometry function tan inverse y to x ratio is found) for all the stations of nodal circles defined. Radial distortion of axis is incorporated accordingly at each nodal circle.

   1. Transient thermal analysis

      Material properties are applied on FE model with element type SOLID 87 for tetra element and SOLID 90 for hexa element to obtain temperature distribution plots. Transient thermal analysis saved as .rth file (resulting temperature) in excels post processor as input for further analysis. Considering the material properties as shown below in table (1).

      Table 1. Material properties of each component used in analysis.

      .

      Component name	Material no
      Turbine housing	IDM5365
      Bushing	IDM608
      Arm, rivet & poppet valve	IDM6027

      All material properties are non linear varying with temperature and time due to confidential, properties are not disclosed in detail. Turbine housing undergoes engine cyclic operations and considering one cyclic of operation include one heating phase and one cooling phase for worst condition graph below shown in fig(4) for worst possible temperature (758 to 80 deg) condition turbine housing is used.

      The table (2) shows the thermal boundary condition like convection coefficient and bulk temperature for all components of turbine housing and inlet region during heating conditions. External surface component is thermally loaded due to turbocharger working conditions and engine environment both during heating conditions. Inlet and inlet region component allows exhaust gases to enter into the turbine which is having higher convective coefficient and bulk temperature.

      Fig.4.Duty cycle used in for analysis. (Source; Honeywell turbochargers)

      Table.2. Thermal boundary conditions on different components for BFV ON condition. (Source; Honeywell turbochargers)

   2. Elasto-Plastic Thermal Stress Analysis Performed For Whole Assembly

      After transient thermal analysis meshed model is

      	HTC (W/m2°C)	Bulk Temperature (°C)
      DC_INLET	271	713
      BFV_INLET	499	758
      INLET & INLET REGION	683	754
      GATE_ZONE	683	754
      A_SURF	114	569
      WHEEL_CONT	379	623
      OUTLET_SURF	410	579
      EXT_SURF	50	80

      imported to ANSYS to change element type for structural analysis Solid 92 for tetra element and Solid 95 for hexa element. Applying mechanical boundary conditions whole assembly is analyzed for both min. and max.clearence conditions (i.e. case 1 & 2). Mechanical boundary conditions applied as all normal displacements, one node in UX & two nodes in UY directions in plane displacements are arrested on turbine housing flange as shown below in fig(5). At all temperature and time points the results of from the results file of thermal analysis (.rth) and applies them as body loads.

      Fig.5. Structural boundary condition for whole assembly

      Elemental nodal stresses, elemental displacements from time point from 0 to 825seconds (s) are found. Finally result file .rst is generated used for post processing.

3. Results and Discussions

   1. Transient thermal analysis

      Temperature plots are taken for steady state heating and cooling conditions. full and sections views are plotted, Temperature variation is 431 C ~751C during heating condition shown in fig.6(a) and fig.6(b). Temperature variation is 127C ~408C during cooling condition shown in fig.7 (a) and fig.7 (b). Nodal temperatures are saved in .rth file for applying as body loads.

      Fig.6 (a) Temperature Distribution at End of heating of bush (650s)

      Fig.6 (b) Temperature Distribution at End of heating of arm (650s)

      Following results are derived from the plots.

      1. At the end of heating phase arm and bush end surfaces are exposed to maximum temperature

         i.e. 751.813C and 590.17C respectively showing decreasing temperature trend towards top surface.

      2. At the end of heating phase arm and bush top surface are exposed to minimum temperature

      i.e. 514.072C and 511.336C respectively.

      In arm and bush, end surface is exposed to higher temperature and heat is transferring in conduction modes from inside of turbine housing to external atmosphere as shown in the temperature distribution plots.

      Fig.7 (a) Temperature Distribution at End of cooling of bush (825s)

      Fig.7 (b) Temperature Distribution at End of cooling of arm (825s)

      Following results are derived from plots.

      1. At the end of cooling phase arm and bush end surfaces are exposed to maximum temperature i.e.350.419C and 309.71C respectively showing decreasing temperature trend towards top surface.

      2. At the end of cooling phase arm and bush top surface are exposed to minimum temperature

      i.e. 127.109C and 228.296C respectively.

   2. Elasto-Plastic Thermal Stress Analysis Performed For Whole Assembly

Results are obtained in terms of radial distortion plotted for minimum and maximum circles (case 1 & 2) at significant time stations are obtained as follows. Using Pythagoras theorem find the radius of each nodes of nodal circles. Angular position of each node is calculated by finding which quadrate node is located then using Trigonometry function tan inverse y to x

ratio is found. To find the radial gap between arm

Radial gap Vs Sector angle between ARM-BUSH for Min Clr Time 650 Sec.

0.02

C 1 ARM-BUSH

C 2 ARM-BUSH

C 3 ARM-BUSH

C 1 ARM-BUSH

C 2 ARM-BUSH

C 3 ARM-BUSH

0.015

C 4 ARM-BUSH

C 5 ARM-BUSH

C 6 ARM-BUSH

C 7 ARM-BUSH

C 4 ARM-BUSH

C 5 ARM-BUSH

C 6 ARM-BUSH

C 7 ARM-BUSH

0.01

0.005

ector

ector

De

De

0

Radial Gap (MM)

Radial Gap (MM)

external surfaces and bush internal surface seven pair of nodal circles is introduced. Displacement of these

-200

S -100 Angle (

0 g.)

100 200

or Min Clr.

200

or Min Clr.

200

Radial Gap (MM)

Radial Gap (MM)

nodes are processed in the excel solver to find the variation in the radial gap. Initially all circles are in straight line. The first significant circle observed at 180 seconds at which deformation is plotted as in fig.6 (a) and fig.6 (b) below.

Fig.6(a) radial gap v/s sector angle ARM-BUSH for min.circle at 180 s.

Radial gap Vs Sector angle between ARM-BUSH for Max Clr. Time 180 Sec.

Radial gap Vs Sector angle between ARM-BUSH for Max Clr. Time 180 Sec.

Fig.7 (a) radial gap v/s sector angle ARM-BUSH for min.circle at 650 s.

Radial gap Vs Sector angle between ARM-BUSH for Time Max Clr 650 Sec.

0.1

0.095

0.09

0.085

0.08

-200 -100 0 100 200

Sector Angle ( Deg.)

Radial gap Vs Sector angle between ARM-BUSH for Time Max Clr 650 Sec.

0.1

0.095

0.09

0.085

0.08

-200 -100 0 100 200

Sector Angle ( Deg.)

C 1 ARM-BUSH C 2 ARM-BUSH

C 3 ARM-BUSH

C 4 ARM-BUSH

C 5 ARM-BUSH

C 6 ARM-BUSH

C 7 ARM-BUSH

C 1 ARM-BUSH C 2 ARM-BUSH

C 3 ARM-BUSH

C 4 ARM-BUSH

C 5 ARM-BUSH

C 6 ARM-BUSH

C 7 ARM-BUSH

Radial Gap (MM)

Radial Gap (MM)

Fig.7 (b) radial gap v/s sector angle ARM-BUSH for max.circle at 650 s.

During steady state heating the radial gap is decreasing up to 650 Sec. nodal circles 1 & 2 having mor radial gap throughout the duty cycle compared to other nodal circles because nodal circles 1 & 2 are not displaced comparatively which is located away from the inside surface of turbine housing where hot gases flows. The nodal circle 6 & 7 are located very near to flow of exhaust gases are displaced cyclically more compared to other nodal circles throughout the duty cycle.

Radial gap Vs Sector angle between ARM-BUSH for Min Clr Time 712.5 Sec.

0.03

0.108

0.104

0.1

0.096

0.092

0.088

0.084

0.08

S-e1c0t0or Angle ( D0eg.)

0.108

0.104

0.1

0.096

0.092

0.088

0.084

0.08

S-e1c0t0or Angle ( D0eg.)

C 1 ARM-BUSH

C 1 ARM-BUSH

C 2 ARM-BUSH

C 3 ARM-BUSH

C 4 ARM-BUSH

C 5 ARM-BUSH

C 6 ARM-BUSH

C 7 ARM-BUSH

-200

C 2 ARM-BUSH

C 3 ARM-BUSH

C 4 ARM-BUSH

C 5 ARM-BUSH

C 6 ARM-BUSH

C 7 ARM-BUSH

-200

Radial Gap (MM)

Radial Gap (MM)

0.025 C 1 ARM-BUSH

C 2 ARM-BUSH

Radial Gap (MM)

Radial Gap (MM)

0.02

C 3 ARM-BUSH

0.015 C 4 ARM-BUSH

C 5 ARM-BUSH

0.01 C 6 ARM-BUSH

0.005

100

100

200

200

0

-200 -100 0 100 200

Sector Angle ( Deg.)

C 7 ARM-BUSH

Fig.6(b) radial gap v/s sector angle ARM-BUSH for max.circle at 180 s.

Fig.8 (a) radial gap v/s sector angle ARM-BUSH for min.circle at 712.5 sec.

Radial gap Vs Sector angle between ARM-BUSH for Max Clr Time 712.5 Sec.

0.1

Radial Gap (MM)

Radial Gap (MM)

0.098 C 1 ARM-BUSH

nonlinearity is characterized by "large" displacements and/or rotations. A number of material-related factors can cause your structure's stiffness to change during the course of an analysis. Nonlinear stress-strain relationships of plastic, multilinear elastic, and

0.096

0.094

C 2 ARM-BUSH

C 3 ARM-BUSH

C 4 ARM-BUSH

hyperelastic materials will cause a structure's stiffness to change at different load levels (and, typically, at

0.092 C 5 ARM-BUSH

0.09 C 6 ARM-BUSH

different temperatures). Creep, viscoplasticity, and

viscoelasticity will give rise to nonlinearities that can

0.088

0.086

-200 -100 0 100 200

Sector Angle ( Deg.)

C 7 ARM-BUSH

be time-, rate-, temperature-, and stress-related. Swelling will induce strains that can be a function of temperature, time, neutron flux level (or some analogous quantity), and stress.

Fig.8 (b) radial gap v/s sector angle ARM-BUSH for min.circle at 712.5

sec.

BUSH for Min Clr

200

BUSH for Min Clr

200

0.025

0.025

C 3 ARM-BUSH

C 3 ARM-BUSH

0.02

0.02

C 4 ARM-BUSH

C 4 ARM-BUSH

Radial Gap (MM)

Radial Gap (MM)

Radial gap increases in heating up to 750 Sec. but variation in gap is nominal in cooling cycle up to 825 Sec as shown in the below graphs fig.9(a) and fig.9(b) of both Min. and Max. clearance condition in each time stations.

Radial gap Vs Sector angle between ARM-

Time 825 Sec.

C 1 ARM-BUSH

Radial gap Vs Sector angle between ARM-

Time 825 Sec.

C 1 ARM-BUSH

0.03

C 2 ARM-BUSH

0.03

C 2 ARM-BUSH

0.005

0.005

C 6 ARM-BUSH

C 6 ARM-BUSH

-200

0

-10S0ector Angle ( D0eg.)

100

C 7 ARM-BUSH

-200

0

-10S0ector Angle ( D0eg.)

100

C 7 ARM-BUSH

USH for Max. Clr

200

USH for Max. Clr

200

0.015

0.01

0.015

0.01

C 5 ARM-BUSH

C 5 ARM-BUSH

0.11

0.11

C 3 ARM-BUSH

C 3 ARM-BUSH

0.1

0.09

0.1

0.09

Radial Gap (MM)

Radial Gap (MM)

Fig. 9(a) radial gap v/s sector angle between ARM-BUSH for min.circle at 825 sec.

Radial gap Vs Sector angle between ARM-B

Time 825 Sec.

C 1 ARM-BUSH

Radial gap Vs Sector angle between ARM-B

Time 825 Sec.

C 1 ARM-BUSH

0.12

C 2 ARM-BUSH

0.12

C 2 ARM-BUSH

-200

0.05

S-1e0c0tor Angle ( D0eg.)

100

C 7 ARM-BUSH

-200

0.05

S-1e0c0tor Angle ( D0eg.)

100

C 7 ARM-BUSH

C 4 ARM-BUSH

C 4 ARM-BUSH

0.08

0.08

C 5 ARM-BUSH

C 5 ARM-BUSH

0.07

0.06

0.07

0.06

C 6 ARM-BUSH

C 6 ARM-BUSH

Fig. 9(a) radial gap v/s sector angle between ARM-BUSH for max.circle at 825 sec.

Nonlinear structural behaviour arises from a number of causes: Changing status, Geometric nonlinearities and Material nonlinearities.

If a structure experiences large deformations, its changing geometric configuration can cause the structure to respond nonlinearly. Geometric

5. Conclusion

Clearance is reducing marginally in steady state heating till 650 sec & increasing in sharp heating from 712.5- 750 sec. Clearance variation is marginal during sharp cooling between 650 712.5 sec & 750 -825 Sec.

References

1. Niccolo Baldanzini, A General Formulation for Designing Interference-Fit Joints With Elastic-Plastic Components, Journal of Mechanical Design, Trans. of ASME, Vol 126, pp 737-743, (2004).

2. Y. Zhang*, B. McClain, X.D. Fang, Design of interference fits via finite element method, International Journal of Mechanical Sciences, Vol 42 (2000) pp 1835- 850, (1987).

3. K. Satish Kumar,B. Dattaguru,T. S. Ramamurthy and K.

   N. Raju S, Elasto-plastic contact stress analysis of joints subjected to cyclic loading, journal of Computers & Structures Vol 60, pp 1067-1077, (1996).

4. Albert Konter, Finite element modeling of contact phenomena in structural analysis, NAFEMS workshop, Netherlands institute of metals research.

5. S. Sen, B. Aksakal, Stress analysis of interference fitted shafthub system under transient heat transfer conditions, journal of Materials and Design, Vol 25, pp 407417 (2004).

6. Adnan O¨ zel , emsettin Temiz, Murat Demir Aydin, Sadri Sen, Stress analysis of shrink-fitted joints for various fit forms via finite element method, journal of Materials and Design, Vol 26,pp 281289 (2005).

7. MacInnes, Hugh., Turbochrgers,H.P.books, new York

8. ANSYS Inc., http://www.ansys.com.

9. M. Ast, H. R osle, R. Schenk, Finite Element Analysis of Shrink-FitShaft-Hub Connections.