Design Optimisation of Four Wheel Drive Tractor Front Axle Housing

Design Optimisation of Four Wheel Drive Tractor Front Axle Housing

Prof. Milind Ramgir SP Pune University India

Shivaji Nilakanth SP Pune University India

Idris Poonawala SP Pune University

India

Abstract Four wheel drive tractors are used for high torque demand applications in field and subjected to severe load conditions. Front axle is one of the most critical aggregate of the Tractor. Design of front axle is more important and critical in application stand point. Specific applications like front bucket, bund preparation and paddy field demand very rigid axle design. Front axle endures the most in tractor aggregate. Front axle housing has failed in field from housing shoulder location in initial proto test axles. The objective of the study is to analyse and optimise the design of the axle housing. Compare the modified design with old design for improvement. Comparison study between hand calculations, FEA and test results. Improvement of the shoulder of the axle is a major area to address the failure of the shoulder in field testing. The housing shoulder required attention during design for a fail safe operation in service. The various design formulas of mechanical elements of shafts and beam are used for design and analysis of the shoulder

Keywords MFWD- Mechanical four wheel drive, 4WD- Four wheel drive, Stress concentration factor, Axle housing, structural strength, Von misses stress, Goodman equation,

1. INTRODUCTION

   During field testing of the front axle there was a shoulder failure reported at the lower king pin bearing area. As per the analysis the design was acceptable for the given load goals and no metallurgical non-conformance was reported. This led to a data acquisition activity on the front axle which reported more severe loading than initially specified.

   The main purpose of the project is to analyze the existing design of the tractor front axle housing for service load conditions and redesign the axle housing with the updated load conditions. The existing geometry of the front axle is modified to the optimum size which suits for functional life requirements. In this analysis, the geometry of the front axle is modified and a new design is proposed. The objective of this study is to improve the existing design with a higher cross section at the spindle of the axle housing resulting in better performance of the tractor. Finite element simulation is carried out for the existing front axle. The critical location

   identified and redesigned to ensure life goals are met for the structural components.

   In this analysis, the spindle is a critical structural member and the complete load passes through the spindle. In this paper we will design the axle housing. The major advantage in using MFWD tractor is that it can deliver 10 – 15 % more power for the same fuel consumption.

2. METHODOLOGY

   The load on the axle is transferred through the lower king pin bearing. The vertical load and the tractive effort put a combined load on the axle of reversible nature. The stress in the shoulder reverses from tensile to compression in certain sections with varying severity depending on the track of the vehicle and the tire radius. The spindle and the kingpin bearing bearings support the complete load of the tractor. If the load on the spindle is within the range of 66% of the yield of the material the housing will give infinite life. In case the stress values in the spindle exceeds the 66% limit the life of the component needs to be calculated for the life and determined if sufficient life is available on the part. Similarly when the stress exceeds its ultimate tensile strength the housing will fracture.

   The process begins with preliminary analysis of failed part followed by baseline design analysis, new design of housing, stress /strain analysis, FEA approach, Experimental data collection and validation of the of the front axle housing.

   A. Process

   Failure analysis

   Analytical approach / Calculations

   FEA

   Field Test

   Comparison and improvement

3. FAILURE ANALYSIS

1. Material for axle housing,

   Material specification ductile iron, grade SAE D5506 Mechanical Properties:

   Hardness: – 187-241 BHN (MS 75 B),

   Tensile strength: – 550 N/mm^2 Yield Strength: – 380N/mm^2 Elongation: 6%

   TABLE I. INSPECTION REPORT

   #	CHARACTERI STIC	SPECIFICATION	OBSERVED
   1	GRADE – 550/6 or MS-75B Chemistry	C: 3.20 – 4.10 %	C:3.8 %
   		Mn :0.10 -1.00 %	Mn : 0.6 %
   		Si : 1.80 – 3.00 %	Si : 2.55 %
   		S : 0.005 – 0.035 %	S : 0.004 %
   		P : 0.015 – 0.10 %	P : 0.025 %
   2	Surf Hardness	187 – 255 BHN	210 BHN
   3	Tensile Strength	> 552 N/mm2	637 N/mm2
   	Yield Strength	> 379 N/mm2	430 N/mm2
   	Elongation %	> 6 %	> 8.50 %
   4	Matrix Structure	Pearlite: 80 +/-15%	57.72%
   		Ferrite : 20 +/- 15%	20.62%
   		Graphite %	21.66%
   		Nodularity > 85 %	88.30%
   5	Internal Soundness	Radiography level -II accept	ok

2. Component Geometry

   Fig.1 Housing geometry

   Fig .2 Failed housing

   Failure observed at neck of the shoulder where cross section of the housing changes. (Ref Fig. 1). It is observed that low cycle fatigue phenomenon of the failure.

3. Application / loading cycle

   In a front axle the forces are applied through the rear and front Trunnion and transmitted through the housing to the kingpin bearings and to the knuckles. These forces give rise reversible stress in the shoulder spindle which leads to fatigue failure. The spindle is a critical structural member and the complete load passes through the spindle.

   The existing geometry of the front axle is modified to the optimum size which suits for functional life requirements. In this analysis, the geometry of the front axle is modified and a new design is proposed. The objective of this study is to improve the existing design with a higher cross section at the spindle of the axle housing resulting in better performance of the tractor.

4. Analytical calculations

   The section modulus is directly related to the strength of a corresponding housing. It is expressed in units of volume m3, mm3. For design, the Elastic section modulus is used, applying up to the Yield point for most metals and other common materials. The elastic modulus is denoted by Z. Now Section modulus is calculated by using following formula,

   TABLE II. MECHANICAL PROPERTIES OF HOUSING

   PARAMETER	BEFORE	AFTER
   Section ID	26 mm	26 mm
   Section OD	35 mm	40 m
   Step OD	41 mm	46 mm
   Transition radius	3 mm	3 mm
   Stress concentration factor	1.68 N	1.68 N
   Young modulus	210000 N/mm²	210000 N/mm²
   Yield of material	380 N/mm²	380 N/mm²

   Fig.3 Re-action diagram

   Vertical load is divided into the resulting components at tractor tire center line.

   By drawing Free body diagram, Shear force diagram and Bending moment diagram as like below Free body diagram and calculating the forces,

   Section modulus (Z) =

   Where, Z= Section modulus

   M = Bending Moment

   F = Ultimate tensile strength of material

5. Original Design + old Loads (18KN) on axle

For the area of the spindle we can find out using,

(1)

Fig. 4 Stress amplitude Free Body diagram

H. Endurance strength & Stress Concentration factor

Laboratory endurance strength (Se) of the materials obtain from S-N diagram are therefore corrected for actual

conditions by using correction factors,

Se = Ka x Kb x Kc x Kd x Kt x Kf x Se

Where,

Ka = Surface Correction factor

A= x (D2 – d2) (2)

= x (352-262)

= 431.18 mm2

Moment of inertia (I)

I= (D4 – d4) (3)

= (354-264)

= 51204.03 mm4

Section Modulus at lower Bearing (4)

=

=

= 2925.245 mm3

1. Original design + Revised load goals (22KN) on axle

   For the area of the spindle we can find out using, A= x (D2 – d2)

   = x (352-262)

   = 431.18 mm2

2. New Design + Revised loads (22KN) on axle

For the area of the spindle we can find out using, A= x (D2 – d2)

= x (402-262)

= 725.34 mm2

Moment of inertia (I)

I= (D4 – d4)

= (404-264)

= 103179.6 mm4

Section Modulus at lower Bearing =

=

Kb = Size Correction factor Kc = Loading factor

Kd = Temperature Correction factor

Kt = Stress concentration Correction factor Kf = Miscellaneous Correction factor

Se = Endurance Strength of material specimen under laboratory condition

Se = Endurance Strength of material Stress concentration factor

Kt= Normal Stress

Kts = For Shear Stresses Kt=

Kts=

From table A-15[8]

Size factor (Kb) from 2.79 d 51 mm So for 35 mm dia.

= (d/7.62) -0.107

= (35/7.62) -0.107

= 0.85

So for 40 mm dia.

= (d/7.62) -0.107

= (40/7.62) -0.107

= 0.837

Surface factor (Ka)

Ka=a*Sutb

Sut – Minimum tensile strength, a and b from ref Table[8]

For machined component

a = 4.51 Mpa, and b = -0.265 (it is an exponent)

Ka= 4.51 *(580) -0.265

Ka=0.8353

Loading factor Kc for bending is 1

1. Stress calculation

   Moment (Pe) = Resultant load * Load distance from flanges

   =

   = 5158.98 mm3

   =8769.3 N *116.5 mm

   = 1021627 N-mm

   TABLE III. PARAMETERS

   Dist. of Horizontal load (mm)	262.49
   Span of bearings (mm)	50.5
   coefficient	0.7
   Vertical Load (N)	9000
   Horizontal Load (N)	6300
   King pin angle (deg)	13
   Parallel component Vp (N)	8769.3
   Normal component Vn (N)	2024.6
   Check	TRUE
   Vertical load Couple (N-mm)	1021627
   SLR (mm)	376

   TABLE IV. STRESS CALCULATIONS

   Fig. 5 Stress amplitude curve [8]

   The alternating stress must then have various size, load, and stress concentration factors applied to it. This is necessary because these values are different for each loading mode. In addition, because these factors are applied to each stress they are not factored into endurance limit in the Marin equation

   Bending Moment @ corner radius
   Dist of radius point from Bearing (mm)	15	Lower Brg
   OLD DESIGN
   Bending Moment	653957	Nmm
   Section ID	26	mm
   Section OD	35	mm
   Moment of Inertia	51230	mm^4
   Stress	223	Mpa
   Size corr. Factor Kb	1.68
   Actual stress	375	Mpa
   NEW DESIGN
   Bending Moment	653957	Nmm
   Section ID	26	mm
   Section OD	40	mm
   Moment of Inertia	103232	mm^4
   Stress	127	Mpa
   Size corr. Factor Kb	1.68
   Actual stress	213	Mpa

   The no of cycle for failure are calculated by using through calculations using the following equations

   Nf = [a`/a]1/b

2. Using modified Goodman equation

   After calculating the maximum and minimum for each stresses the alternating and mean effective stresses calculated. The following equations are used.

   Mean Stress m = (max + min) / 2 (11)

   Range of Stress r = (max – min) (12)

   Stress Amplitude a = r/2 = (max – min) / 2 (13)

   Stress Ratio R = min / max (14)

   (15)

   Where a = (0.9*Sut)2 / Se

   And b = -1/3log [0.9*Sut / Se]

   Life Comparison
   Parameter	Original Design + Original loads	Original design + Revised load	New design +Revised load
   Torsion	0	0	0
   Bending	375	459	213
   Axial	0	0	0
   Alternating stress	375	459	213
   Mean stress	0	0	0
   Max stress	375	459	213
   Min Stress	-375	-459	-213
   Stress Amplitude	375	459	213
   Reversible	375	459	213
   Slope	6	6	6
   Fatigue limit	165	165	163
   Life (No of cycles)	728	216	20225
   Ultimate Stress Nmm	580	580	580
   Yield Stress N mm	380	380	380
   Endurance ratio	0.5	0.5	0.5
   Size factor Kb	0.85	0.85	0.837
   Surface Ka	0.67	0.67	0.67
   Load	1	1	1

   TABLE V. LIFE CALCULATIONS

   It is observed the life, No of cycles has increased drastically to cater the field application requirement. The design life of housing has improved by multiple times. This is because the next available suitable bearing is of dia.40 mm. so by changing the section modulus with the same material of housing the duty cycle of axle accomplished.

   Fig.6. New Housing with 40 mm diameter

   Fig.7. Optimisation geometry comparison

3. FEA analysis

   FEA analysis is carried out using Abaqus 6.13-1 with SimLAb 9.0. The results of analytical and FEA compared with each other and it is found that both correlate to each other. Tie rod, hydraulic cylinder and axle shaft are simulated with beam elements. Beam release is provided to simulate the ball joint. It was observed that panic stop and breakout are causing the maximum damage to the housing. With new design the panic stop stress 358 Mpa reduced to 300 Mpa. And loader breakout application stresses 313Mpa to 294 Mpa.

   Fig.8. Panic Stop Old housing

   Fig.9. Panic Stop New housing

   Fig.10. Enlarged view of stress damage

   Fig.11. Loader Breakout Old Housing

   Fig.12. Field testing of axle with New Housing

4. Other Options of design

   There are few more options for this design

   • Case hardening of current housing shoulder

   • Use of high tensile forged steel material

I. CONCLUSIONS

The calculated life of the housing is better in revised design with revised load goals. The section modulus change has improved the life of housing. Panic Stop and loader break out are the two critical applications that need to be withstand by the new design. It was observed that panic stop and breakout are causing the maximum damage to the housing. With new design the panic stop stress 358Mpa reduced to 300Mpa and breakout stresses 313Mpa to 294Mpa. The next bearing available to accommodate the best option to choose and opt for the application is of 40 mm. the fatigue life of the housing increased from 728 cycle to 20225 cycles. The New Housing weight is increased by 150 grams. New Axle Tested in field for loader application and found no damage to the housing. Field application data is very crucial to have robust design. Product performance has improved drastically than the required no of cycles. Close co-relation of design factors and application study decides the life of a product. Factor of safety plays vital role in applications where application data is not precise.

ACKNOWLEDGMENT

I would like to give my sincere thanks to my guide Prof.

1. Ramgir, who accepted me as his student and being a mentor for me. He offered me so much advice, patiently supervising and always guiding in right direction. I have learnt a lot from him and he is truly a dedicated mentor. His encouragement and help made me confident to fulfill my desire and overcome every difficulty I encountered. Also I would like to mention my sincere thanks to senior Mr. Idris Poonawala who guided me thru all steps of design and helped to complete the project and understand the design in detail.

   I also highly obliged to the organization and management, for giving me an opportunity to continue my education and enhance my knowledge.

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