structural optimization of mini hydraulic · pdf filestructural optimization of mini hydraulic...

machine design, Vol.5(2013) No.1, ISSN 1821-1259 pp. 43-56

* Correspondence Author’s Address: Mechanical Engineering Department, U. V. Patel College of Engineering, Ganpat University, Ganpat Vidyanagar-384012, Kherva, Dist. Mehsana, State-Gujarat, India, [email protected]

Research paper

STRUCTURAL OPTIMIZATION OF MINI HYDRAULIC BACKHOE EXCAVATOR ATTACHMENT USING FEA APPROACH Bhaveshkumar P. PATEL1, * - Jagdish M. PRAJAPATI2 1 Mechanical Engineering Department, U. V. Patel College of Engineering, Ganpat University, Ganpat Vidynagar-384012, Dist. Mehsana, Gujarat,

India. 2 M. S. University of Baroda, Associate Professor, Faculty of Technology and Engineering, Vadodara - 390002, Gujarat, India.

Received (23.08.2013); Revised (11.02.2013); Accepted (13.02.2013) Abstract: Excavators are heavy duty earthmoving machines and normally used for excavation task. During the excavation operation unknown resistive forces offered by the terrain to the bucket teeth. Excessive amount of these forces adversely affected on the machine parts and may be failed during excavation operation. Design engineers have great challenge to provide the better robust design of excavator parts which can work against unpredicted forces and under worst working condition. Thus, it is very much necessary for the designers to provide not only a better design of parts having maximum reliability but also of minimum weight and cost, keeping design safe under all loading conditions. Finite Element Analysis (FEA) is the most powerful technique for strength calculations of the structures working under known load and boundary conditions. FEA approach can be applied for the structural weight optimization. This paper focuses on structural weight optimization of backhoe excavator attachment using FEA approach by trial and error method. Shape optimization also performed for weight optimization and results are compared with trial and error method which shows identical results. The FEA of the optimized model also performed and their results are verified by applying classical theory. Key words: Digging Forces, Autonomous Excavation, Resistive forces, Heaped capacity

1. INTRODUCTION In the era of globalization and tough competition the use of machines is increasing for the earth moving works, considerable attention has been focused on designing of the earth moving equipments [10]. Today hydraulic excavators are widely used in construction, mining, excavation, and forestry applications [1]. The excavator mechanism must work reliably under unpredictable working conditions. Poor strength properties of the excavator parts like boom, arm and bucket limit the life expectancy of the excavator. Therefore, excavator parts must be strong enough to cope with caustic working conditions of the excavator [8]. But in contradictory, now a day weight is major concern while designing the machine components. So for reducing the overall cost as well as for smoothing the performance of machine, optimization is needed. Structural design has always been a very interesting and creative segment in a large variety of engineering projects. Structures, of course, should be designed such that they can resist applied forces (stress constraints), and do not exceed certain deformations (displacement constraints). Moreover, structures should be economical. Theoretically, the best design is the one that satisfies the stress and displacement constraints, and results in the least cost of construction. Although there are many factors that may affect the construction cost, the first and most obvious one is the amount of material used to build the structure. Therefore, minimizing the weight of the structure is usually the goal of structural optimization [7].

There are many methods can be applied for the optimization problems like, Linear Programming (LP), Non-Linear Programming (NLP), Integer Linear Programming (ILP), and Discrete Non-Linear Programming (DNLP) and However, some newly developed techniques, known as heuristic methods, provide means of finding near optimal solutions with a reasonable number of iterations. Included in this group are Simulated Annealing, Genetic Algorithms, and Tabu Search [7]. Finite Element Analysis is the powerful technique for calculation of the strength of structure under known working load and boundary conditions [6]. Finite Element Analysis (FEA) is also one of the best powerful methods which can be applied for structural weight optimization. There are so many works done by other researchers in the field of FEA and optimization of the backhoe excavator machines which are covered in the reference paper of [2]. For our case we have adopted FEA approach for performing structural weight optimization of mini hydraulic backhoe excavator attachment using trial and error method and shape optimization method.

2. BACKGROUND OF WORK Based on the market survey and reverse engineering and authors expertise in the field of design a 3D model of mini hydraulic backhoe excavator attachment is developed using the Autodesk Inventor professional 2011. The resistive forces offered by the terrain to the bucket teeth are found by applying the fundamental knowledge of soil mechanics and McKyes and Zeng models utilized to find soil-tool interaction forces [3]. The developed

Bhaveshkumar P. Patel, Jagdish M. Prajapati: Structural Optimization of Mini Hydraulic Backhoe Excavator Attachment Using FEA Approach; Machine Design, Vol. 5(2013) No. 1, ISSN 1821-1259; pp. 43-56

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resistive forces must be less than that of the digging forces offered by the actuators. Maximum resistive forces offered by the ground for the proposed tool dimensions is 3916.7 Newton, and the breakout force calculated is 7626 Newton which is higher than the forces required to cut the soil (3916.7 Newton), thus this calculated breakout force is adequate and accepted for the job to be performed by the proposed mini backhoe excavator i.e. light duty construction work [3]. The digging force calculations carried out based on SAE standards of SAE J1179 and static force analysis performed for maximum breakout force condition considering static equilibrium. The calculated bucket curl or breakout force FB = 7626.25 Newton, and calculated arm crowd force or digging force FS = 4427.419 Newton [4]. Finite Element Analysis also performed on mini hydraulic backhoe excavator attachment for the purpose of verification of part’s strength. The results shows that the developed stresses are far less than that of the designed stress limit [5]. Therefore, there is a scope to perform weight optimization for backhoe attachment using FEA approach based on strength criterion. Here, we have consider thickness of plates as a variable and adopted trial and error method to get optimized backhoe excavator model based on standard available limiting value of plate thickness and limiting safe stress criterion. The optimized model also checked for limiting safe stress and the results verified by applying classical theory. The materials used for the different components are made from HARDOX400 [11], SAILMA 450HI [12] and IS 2062 [9]. Structural optimization is performed for the bucket, arm, boom and swing link which are covered one by one in next coming sections using ANSYS software.

3. OPTIMIZATION OF BUCKET

Fig.1. Modified bucket for optimization The Fig. 1 shows the bucket with different parts which are modified to get optimum dimensions based on available standard thickness of plates. Table 1 shows the name of the parts of the bucket which are modified to get the weight optimized model. It also shows the dimensions and total weight of the parts before modification and after modifications. The total weight of the bucket is 23.143 kg and after modification we got the optimized weight of the bucket is 17.973 kg. Therefore, we achieved 5.027 kg reduction in the weight of the bucket. Based on the known boundary conditions calculated as in reference [4], the

optimized model of bucket is analyzed to check that the optimized model is within safe limit or not.

Fig.2. Static force analysis of bucket

Fig.3. Boundary conditions for bucket

Fig.4. Maximum stresses of the optimized bucket

Fig.5. Maximum displacement of optimized bucket


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Table 1. Optimization data of the bucket

Part no. Part name Quantity

Modifications Total weight (Kg)

Thickness before

modification

Thickness after

modification

Weight before

optimization

Weight of optimized

model

1 Base plate 1 5 4 7.634 6.118

2 Side protector 2 5 4 3.898 3.118

3 Bucket top plate 1 6 4 1.311 0.903

4 Side shear plate 2 6 5 3.052 2.542

5 Bucket mounting

lug 2 10 6 2.522 1.521

6 Bucket mounting

lug bush 4 20 10 0.568 0.2608

Fig. 2 shows the static force analysis of the bucket for maximum breakout force condition. Fig. 3 shows boundary conditions applied to bucket for analysis purpose. Design stress for ductile materials,

σσ

(1)

The maximum Von Misses stress is acting at the end of the mounting lugs as shown in Fig. 4, which is made up of Hardox400 material with the yield strength of 1000 MPa, by taking safety factor as 2, equation (1) yields = 227.52 MPa, [σy] = 500 MPa, this clearly indicates σVM < [σy], so the design of the optimized bucket is safe for strength. Fig. 5 shows the maximum displacements on the bucket of 2.9694 mm which is very small compare to minimum thickness of the plate used in the bucket, therefore it is safe for deflection. 4. OPTIMIZATION OF ARM The failure criterion states that the Von Misses stress σ should be less than the yield stress σ of the material by taking appropriate safety factor into consideration. This indicates for the design of a part to be safe, the condition shown in equation (1) must be satisfied [13]. The Fig. 6 shows the arm with different parts which are modified to get optimum dimensions based on available standard thickness of plates. Table 2 shows the name of the parts of the arm which are modified to get the optimized model. It also shows the dimensions and total weight of the parts before modification and after modifications. The total weight of the arm is 30.938 kg and after modification we got the optimized weight of the arm is 25.342 kg. So, we achieved 5.596 kg reduction in the weight of the arm. Based on the known boundary conditions which are calculated as provided with reference [4], the optimized model of arm is analyzed to check that the optimized model is within safe limit or not. Fig. 7 shows the static force analysis of the bucket for maximum breakout force

condition. Fig. 8 shows the boundary conditions applied to arm for the purpose of analysis. Fig. 9 shows the results of the Von Misses stresses on optimized arm assembly at the arm cylinder mounting lug and it is 229.79 MPa.

(a)

(b)

Fig.6. Modified arm for optimization


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Table 2. Optimization data of the arm


Modifications (mm) Total weight (Kg)

Thickness before

modification

Thickness after

modification

Weight before

optimization

Weight of optimized

model

1 Arm side cover 2 4 4 10.676 10.8350

2 Bucket cylinder mounting lug

2 10 8 1.19 0.9514

3 Bucket cylinder

mounting lug bush 2 10 5 0.434 0.1550

4 Arm cylinder mounting lug

2 10 8 0.7738 0.6522

5 Arm cylinder


6 Arm collar-1 1 Cylinder-10,

Collar Stiffners-5

Cylinder-5, Collar

Stiffeners -3 2.975 1.4195

7 Arm collar-2 1 Cylinder-10,

Collar Stiffeners -5

Cylinder-5, Collar

Stiffeners -3 3.6116 1.9654

8 Arm reinforcement 4 5 3 1.8007 1.2024

9 Arm stiffener 1 5 3 0.8587 0.5147

Fig.7. Static force analysis for arm

Fig.8. Boundary conditions for arm

Fig.9. Maximum stresses of the optimized arm

Fig.10. Maximum displacements of optimized arm

Bhaveshkumar P. Patel, Jagdish M. Prajapati: Structural Optimization of Mini Hydraulic Backhoe Excavator Attachment Using FEA Approach;Machine Design, Vol. 5(2013) No. 1, ISSN 1821-1259; pp. 43-56

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Table 3. Optimization data of the boom


Modifications Total weight (Kg) Dimensions

before modification

Dimensions after

modification Weight before

optimization

Weight of optimized

model Modification in thickness (mm)

1 Boom side cover 2 5 4 20.7780 16.6230

2 Arm cylinder mounting lug

2 14 8 2.4670 2.2206

3 Arm cylinder


4 Boom cylinder mounting lug

2 16 10 3.556 2.6330

5 Boom cylinder


6 Boom to arm joint

bush 2 17 14 0.3265 0.2131

7 Boom

reinforcement 4 5 3 3.9565 2.1579

8 Arm cylinder

mounting plate 1 135 131 0.9358 0.9081

9 Boom cylinder mounting plate

1 135 131 1.0309 0.9928

10 Boom top cover 1 135 131 6.2241 6.0396

11 Boom bottom

cover 1 135 131 5.7469 5.5766

Modification in

width × thickness (mm)

12 Boom stiffeners 4 135 × 5 131 × 3 3.6087 2.1021 Modification in length (mm)

13 Boom collar 1 155 145 2.2847 2.1376 Now, yield strength of the material of mounting lug made up from HARDOX400 is 1000 MPa, by taking safety factor as 2, equation (1) yields [σ ] = 500 MPa and σ = 229.79 MPa (Fig. 9), so σ [σ ] and this indicates that the design of the optimized arm is safe for strength. Fig. 10 shows the maximum displacement on arm is 0.37072 mm at bucket-arm joint end which is very small compare to minimum thickness of the plate used in the arm; therefore it is safe for deflection. 5. OPTIMIZATION OF BOOM The Fig. 11 shows the boom with different parts which are modified to get optimum dimensions based on available standard thickness of plates. Table 3 shows the name of the parts of the boom which are modified to get the optimized model. It also shows the dimensions and total weight of the parts before modification and after modifications. The total weight of the boom is 51.605 kg and after modification we got the optimized weight of the boom is 41.997 kg. So, we achieved 9.608 kg reduction in the weight of the boom. Fig. 12 shows the static force analysis of the boom for maximum breakout force condition. Fig. 13 shows the boundary conditions applied to boom for the purpose of analysis.

(a)

(b)

Fig. 11. Modified boom for optimization


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Fig.12. Static force analysis for arm

Fig.13. Boundary conditions for boom

Fig.14. Maximum stresses of the optimized boom

Fig.15. Maximum displacements of optimized boom

Fig. 14 shows the results of the Von Misses stresses on optimized boom assembly in which the maximum Von

Misses stresses is acting on the mounting lug and it is 287.11 MPa. Mounting lug is made from HARDOX400 and its yield strength is 1000 MPa, by taking safety factor as 2, equation (1) yields [σ ] = 500 MPa and σ = 287.11 MPa, so σ [σ ] and this indicates that the design of the optimized boom is safe for strength. Fig. 15 shows the maximum displacement in the boom reported is 2.4149 mm at the boom cylinder mounting lug which is very less compare to minimum thickness of the plate used in the boom; therefore it is safe for deflection. 6. OPTIMIZATION OF SWING LINK

Fig.16. Modification of swing link for optimization The Fig. 16 shown the thicknesses of swing link which are modified to get optimum dimensions. Table 4 shows thickness before modification and thickness after modification. The total weight of the swing link is 177.41 kg and after modification we got the optimized weight of the swing link is 127.01 kg. So, we achieved 50.4 kg reduction in the weight of the swing link. Fig. 17 shows the static force analysis of the swing link for maximum breakout force condition. Fig. 18 shows the boundary conditions applied to swing link for the purpose of analysis. Table 4. Optimization data of the swing link

Sr. no.

Thickness

Thickness before

optimization (mm)

Thickness after

optimization (mm)

1 t1 50 40

2 t2 50 40

3 t3 40 40

4 t4 50 40

5 t5 50 40

6 t6 75 35

7 t7 20 15 8 t8 30 14

Fig. 19 shows the results of the maximum Von Misses stresses acting on the cylinder mounting lug of optimized swing link of 157.85 MPa. Cylinder mounting lug made from HARDOX400 and its yield strength is of 1000 MPa. The safety factor is taken as 2.


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Fig.17. Static force analysis of swing link

Fig.18. Boundary conditions for swing link

Fig.19. Maximum Von Misses stresses of optimized swing link

Fig.20. Maximum displacements of optimized swing link

Equation (1) yields [σ ] = 500 MPa, and σ = 157.52 MPa, so σ [σ ] and this indicates that the design of the swing link is safe for strength. Fig. 20 shows the maximum displacement in the swing link reported is 0.18208 mm at the boom to swing link joint which is very less compare to minimum thickness of the plate used in the swing link; therefore it is safe for deflection.

7. OPTIMIZATION OF BACLHOE

ASSEMBLY

Fig.21. Boundary conditions for backhoe assembly

Fig.22. Maximum Von Misses stresses in optimized backhoe assembly

Fig. 21 shows the boundary conditions applied to the backhoe assembly for the purpose to carry out FE analysis. Fig. 22 shows the maximum Von Misses stresses produced at the mounting lugs in the backhoe attachment assembly of 227.64 MPa. Mounting lugs are made from Hardox400 with the yield strength of 1000 MPa, by taking safety factor as 2, equation (1) yields σ = 227.64 MPa, [σ ] = 500 MPa,

this clearly indicates σ [σ ], so the stresses produced

in the assembly of the backhoe are within the safe limits and the design is safe for strength.


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8. STRESS ANALYSIS OF OPTIMIZED BACKHOE PARTS WITH CONSIDERATION OF WELDING

Fig.23. Maximum Von Misses stresses of bucket with welding

Fig.24. Maximum Von Misses stresses of arm with welding

Fig.25. Maximum Von Misses stresses of boom with welding

Fig.26. Maximum Von Misses stresses of swing link with welding

Fig.27. Maximum Von Misses stresses of backhoe assembly with welding

As seen in Fig. 23 to Fig. 27 maximum Von Mises stresses developed in the mounting lugs and all mounting lugs are made from HARDOX400 having yielding strength of 1000 MPa. The developed stresses are very less compare to the safe stress [σ ] = 500 MPa, with the

factor of safety is 2. Therefore the design of all the backhoe parts and assembly is safe for strength. 9. SHAPE OPTIMIZATION In this section shape optimization of backhoe excavator parts is carried out with the help of shape optimization tool of ANSYS. In the earlier section optimization is carried out by changing variable parameter that is thickness of plates. In this section results of shape optimization shows the area which can be remove from the part by changing the geometry of the part, it also shows that how much weight can be reduced from the particular part, so that the results obtained from shape optimization will be compared with the obtained results by changing parameter (thickness) based on trial and error method performed in previous section. The material of the parts, loading conditions and constraints (i.e. boundary conditions), and meshing of all the parts remain same as covered in previous all sections. 9.1. Shape optimization of bucket Here, results of ANSYS shape optimization tool is shown in the Fig. 28, it shows the area from which we have to remove material to reduce the weight of the bucket but it is not possible to change the geometry of the bucket. Because if we change the geometry then it will lose its basic functionality and will reduced in the capacity of the bucket. So instead of changing the geometry of bucket, we have changed the parameter (i.e. thickness) to reduced the weight same as taken in the earlier section. Here, the optimized weight obtained from the shape optimization is 17.722 kg and optimized weight achieved by trial and error method (i.e. by changing thickness) is 17.973 kg, so both results are very close to each other.


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(a)

(b)

Fig. 28. Results of shape optimization for bucket

9.2. Shape optimization of arm

(a)

(b)

Fig.29. Results of shape optimization for arm

Fig. 29 shows the results of shape optimization of arm. From Fig. 29 we can see that the material can be removed from the arm coloured in red. Here the optimized weight of the arm achieved by shape optimization is 25.888 kg and optimized weight achieved by trial and error method (i.e. by changing thickness) is 25.342 kg, so both results are very close to each other.

9.3. Shape optimization of boom

(a)

(b)

Fig. 30. Results of shape optimization for boom

Fig. 30 shows the result of shape optimization of boom. From Fig. 30 we can see that the material can be remove from the boom coloured in red. Here, the optimized weight of the boom obtained from shape optimization is 42.126 kg and optimized weight achieved by trial and error method (i.e. by changing thickness) is 41.979 kg, so both results are very close to each other. 9.4. Shape optimization of swing link Here, results of shape optimization are shown in the Fig. 31 for swing link, it shows the area from which we can remove material to reduce the weight of the swing link in red colour. Here, the optimized weight obtained from shape optimization is 118.24 kg and optimized weight achieved by trial and error method (i.e. by changing thickness) is 127.01 kg. The result indicates smaller differences in weight of swing link, obtained by both the


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methods. Here, we have gone through the weight of 127.01 kg of swing link because, the swing link carry the entire weight of the all other parts of the backhoe excavator attachment.

(a)

(b)

Fig.31. Results of shape optimization for swing link 10. VERIFICATION OF STRESS ANALYSIS

USING CLASSICAL THEORY In this section the stresses produced in the optimized model of backhoe excavator performed using ANSYS software is verified with the stresses produced at the same section in the part of excavator by classical method. The classical theory applied to heavy duty backhoe excavator to verify the developed stresses by Reena Trivedi [14]. Von Mises theory is applicable for ductile material whereas the maximum principle stress theory is normally applicable for brittle material, but in the present case for validation of stress results of Von Mises, the maximum principle stress theory is applied because the shear stresses developed in the backhoe parts are very less compare to its design shear stresses and it is the case of bending and twisting stresses.

Let, σ = Bending stress, N/mm2 σ = Axial stress, N/mm2 σ = Combined stress, N/mm2 τ = Shear stress, N/mm2 J = Polar moment of inertia of arm, mm3

The bucket having the complex shape and size therefore not considered for the application of classical theory. Here, arm is taken for the verification of the results of optimized model which are obtained from the FE analysis. For arm, a section plane A-A taken at 452 mm from pivot A3, which is arbitrarily selected and shown in the Fig. 32. The calculations are made based on classical theory. It is the case of bending and twisting together. Since, the corner tooth is in action it will cause twisting. The cross section of the arm taken for study at section A-A is shown in the Fig. 33. Force analysis at section A-A shown in Fig. 34 for arm.

Fig.32. Section plane A-A in the front view section at of the arm

Fig.33. Details of arm section plane A-A

Fig.34. Forces acting at the arm section

Angle of force at A3 with horizontal axis is θ = 8.27°

Angle of force at A12 with horizontal axis is θ = 98.29°


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Force acting at point A3 is R = 22423 Newton Force acting at point A12 is R = 7783.7 Newton Distance from neutral axis to the outer fiber, y = 92.5 mm Cross section area of arm, CS = 2352 mm2

Perpendicular distance between A3 pivot and centre of section, L = 65 mm

Perpendicular distance between A12 pivot and centre of section, L = 319 mm Taking moment about point (centre of cross section of arm), we get Bending moment, BM R L R L BM = 3940495.3 N.mm Let, I = moment of inertia about X axis for hollow rectangular cross-section of arm = 11364144 mm4 Bending stresses can be calculated using the following formula,

σ

(2)

σ = 32.074 MPa Force acting in X direction, F = 21066.71 N Force acting in Y direction, F = 10927.65 N Axial stress, σ F CS⁄ (3) σ = 8.956 MPa Shear stress, τ F CS⁄ (4) τ = 4.646 MPa Combined stress, σ σ σ (5) σ = 8.956 + 32.074 = 41.03 MPa Twisting moment, TM halfwidthofbucket FD (6) TM = 2085711 N.mm Where, Width of bucket = 547 mm FD = Maximum digging force in Newton FD = 7626 Newton Polar moment of inertia, J = 2 b d t mm3 (7) J = 2 × 185 × 117 × 4 J = 173160 mm3 Shear stress due to twisting, τ TM J⁄ (8) τ 12.045 N/mm2 Mean stress, σ

σ σ (9)

= 20515.5 MPa Maximum principal stress,

σ σ σ τ (10) σ = 41.9 MPa As per classical theory the value of maximum principal stress is 21.039 MPa. For verification of stress results obtained from classical theory applied for arm, a same section plane is taken at a same distance of 452 mm from the pivot A and stresses developed at that section plane A-A are between 32.837 MPa – 49.25 MPa and its average value is of 41.044 MPa, which indicates that the results are remains identical with the results of classical theory, as shown in Fig. 36. Fig. 35 shows the section

plane (A-A) taken for calculations and Fig. 36 shows the result of stresses produced at that section plane A-A. Now here, boom is taken for the verification of the result of optimized model which is obtained from the FE analysis. For boom, a section plane B-B taken at 440 mm from pivot A2 which is arbitrarily selected as shown in the Fig. 37. The calculations are made based on classical theory. It is the case of bending and twisting together. Since, the corner tooth is in action it will cause twisting. The cross section of the boom at section plane B-B taken for study is shown in the Fig. 38. Force analysis at section plane B-B shown in Fig. 39 for boom.

Fig.35. Section plane A-A in the arm

Fig.36. Stresses at section plane A-A from FE analysis

Fig.37. Section plane B-B in the front view of the boom

Angle of force at A with horizontal axis is θ = 18.870

Force acting at point A is R = 26432 Newton


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Distance from neutral axis to the outer fiber, y = 85 mm Cross section area of boom, CS = 2344 mm2

Perpendicular distance between A pivot and centre of section, L =142.30 mm

Fig.38. Details of boom section at section plane B-B

Fig.39. Forces acting on the right hand side of the boom section

Taking moment about point S (centre of cross section) the bending moment, BM R L (11) BM = 3761273.6 N.mm Let, I = moment of inertia about X axis for hollow rectangular cross-section of boom = 10055421.33 mm4 Bending stress,

σ

(12)

σ = 31.79 MPa Force acting in X direction, F = 50022.81 N Force acting in Y direction, F = 17097.38 N Axial stress,

σ (13)

σ = 21.34 MPa Shear stress,

τ (14)

τ = 7.29 MPa Combined stress, σ σ σ (15) = 21.34 + 31.79 σ = 53.13 MPa Twisting moment, TM halfwidthofbucket FD (16) = 2085711 N.mm Where, Width of bucket = 547 mm

FD = Maximum digging force in Newton FD = 7626 Newton Polar moment of inertia, J = 2 b d t mm3 (17) = 2 × 170 × 131 × 4 J = 178160 N.mm Shear stress due to twisting, τ TM J⁄ (18) = 11.71 MPa Mean stress, σ

σ σ (19)

= 26.565 MPa Maximum principal stress, σ σ σ τ (20) σ = 54.11 MPa

Fig.40. Section plane B-B in the boom

Fig.41. Stresses at section plane B-B from FE analysis

Fig. 40 shows the section plane B-B taken for calculations and Fig. 41 shows the results of stresses developed at section B-B getting from FE analysis performed using ANSYS. So as per classical theory the value of maximum principal stress is 54.11 MPa. For verification of stress results obtained from classical theory applied for boom, a same section plane is taken at a same distance of 440 mm from the pivot point A and stresses developed at that section plane B-B are between 41.028 MPa – 61.535 MPa and its average value is of 51.2815 MPa, Which indicates that the results are remains identical with the results of classical theory, as clearly shown in the Fig. 41.


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11. RESULTS AND DISCUSSION

Table 5. Summary of weight reduction by trial and error method (i.e. change in thickness) in different parts of excavator

Sr. no.

Name of the part

Weight before optimization

(Kg)

Weight after

optimization (Kg)

Reduction in weight

1 Bucket 23 17.973 5.027 2 Arm 30.938 25.342 5.596 3 Boom 51.605 41.979 9.608

4 Swing link

177.41 127.01 50.4

Total weight 70.631

Table 5 shows the weight of the all parts before optimization and weight of the all parts after optimization, table shows the total reduction in the weight by trial and error method (i.e. change in thickness) is 70.631 kg. The FEA of the backhoe parts with the maximum breakout configuration is carried out for optimized model based on boundary conditions as calculated in chapter 7 are presented in this chapter. The maximum Von Mises stresses acting on bucket, arm, boom and swing link are 227.52 MPa, 229.79 MPa, 287.11 MPa and 157.85 MPa and the yield strength of these parts are 1000 Mpa, 450 Mpa, 1000 Mpa and 450 Mpa respectively, and by taking safety factor = 2 all the parts are found to be safe. The stress analysis of whole assembly is also carriedout and the stress produced are within the safe limit. Table 6 shows the comparison of sresses produced in the model without and with considering welding. Comparison shows that the backhoe model with welding having reduced stresses, so it is clear that the welding improves the strength of the parts.

Table 6. Comparision of stresses produced in the optimized model with and without welding

Sr. no. Name of

parts

Maximum Von Mises stress produced (MPa)

Optimized model

without welding

Optimized model with

welding

1 Bucket 227.52 206.45 2 Arm 229.79 221.01 3 Boom 287.11 277.84 4 Swing link 157.52 155.98

5 Backhoe assembly

227.64 223.45

Table 7 shows the comparison of optimized weight achieved by trial and error method (i.e. reduction in thickness) and shape optimization achieved by ANSYS tool, which shows that the results are very close to each other and results from trial and error method are acceptable. The stresses produced in the optimized model by performing FE analysis using ANSYS software is also verified with the stresses obtained by applying classical theory and the results obtained from both the methods are identical.

Table 7. Comparision of optimized weight obtained by trial and error method and shape optimization

Sr. no.

Name of parts

Weight before

optimiz-ation (Kg)

Weight after optimization

(Kg) % Variatio

n in results by both methods

Trial and error

method (i.e. by

changing thickness)

Shape optimiza

-tion (i.e. by

changing geometr

y)1 Bucket 23 17.973 17.722 1.39

2 Arm 30.938 25.342 25.888 2.10

3 Boom 51.605 41.979 42.126 0.34

4 Swing Link

177.41 127.01 118.24 6.90

Total Weight 282.953 212.304 203.976 3.92

12. CONCLUSIONS FE analysis of backhoe parts shows that the parts with welding provide higher strength. Structural weight optimization carried out by trial and error method shows the total reduction in weight is of 70.649 kg (24.96%) and weight reduced by applying shape optimization is of 78.977 kg (27.91%). Comparison shows that the variations in results of individual parts are very less and total variation in result is of only 3.93% which reflect that the results of structural weight optimization performed by trial and error method are accurate and acceptable. The differences in results of the Von Mises stresses and the classical theory are very less and we can say that the results are identical and acceptable. REFERENCES [1] BHAVESHKUMAR P. PATEL, DR. J. M.

PRAJAPATI, Soil-Tool Interaction as a Review for Digging Operation of Mini Hydraulic Excavator, International Journal of Engineering Science and Technology, Vol. 3 No. 2, February 2011, pp 894-901.

[2] BHAVESHKUMAR P. PATEL AND J. M. PRAJAPATI, A Review on FEA and Optimization of Backhoe Attachment in Hydraulic Excavator, IACSIT International Journal of Engineering and Technology, Vol. 3, No. 5, October 2011, pp 505 –511.

[3] BHAVESHKUMAR P. PATEL, DR. J. M. PRAJAPATI AND BHARGAV J. GADHVI, An Excavation Force Calculations and Applications: An Analytical Approach, International Journal of Engineering Science and Technology, Vol. 3, No. 5, May 2011, pp 3831-3837.

[4] BHAVESHKUMAR P. PATEL AND J. M. PRAJAPATI, Evaluation of Bucket Capacity, Digging Force Calculations and Static Force Analysis of Mini Hydraulic Backhoe Excavator, MACHINE DESIGN – The Journal of Faculty of Technical Sciences, Vol.4, No.1, 2012, pp 59-66.

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