- Email: [email protected]
Design of aluminium boom and arm for an excavator
Available online at www.sciencedirect.com
Journal of Terramechanics Journal of Terramechanics 47 (2010) 201–207 www.elsevier.com/locate/jterra
Review
Design of aluminium boom and arm for an excavator Luigi Solazzi * Dipartimento di Ingegneria Meccanica e Industriale, Facolta` di Ingegneria, Universita` degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy Received 8 September 2008; received in revised form 3 March 2010; accepted 9 March 2010 Available online 28 April 2010
Abstract The aim of this work is to study the boom and the arm of an excavator in order to replace the material, which they are usually made of, with another material. In particular, the study wants to substitute the steel alloy for an aluminium alloy. This change lightens the components of the arm, allows to increase the load capacity of the bucket and so it is possible to increase the excavator productivity per hour. For this purpose many different load conditions have been studied numerically on the original excavator in order to estimate a safety factor and the deformability or flexibility of each component. These parameters have been used in order to design a new arm. The excavator which has been analyzed is composed of three elements and the load conditions assumed, in order to evaluate the stress, are five (lifting at the maximum and minimum distance from the axis of rotation, maximum load induced by hydraulic cylinders, spin of the arm of the excavator and collision with an obstacle, etc.). As regards to the safety factor and deformability in order to maintain the original value the new geometry of the arm involves an increase of the dimension and so the lightness is not correlate only to the variation of the material density. The weight of the final geometry of the aluminium arm is 1080 kg whereas the one of the steel arm is 2050 kg and consequently it has been possible to increase the capacity of bucket from 1 m3 to the 1.35 m3. With reference to the manufacturing cycle of the aluminium arm with the new pins, the price increased about € 2.500–3.000 and this aspect could be justified if we consider that the productivity per hour increased about 35%. Ó 2010 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Lifting equipment; Excavator; Design with aluminium alloy
1. Introduction The excavator examined in this work is a classical machine represented in Fig. 1. It is composed of three different arms, the power is 110 kW and the rated weight is about 21.500 kg. This machine is mainly used to demolish and move material in applications concerning civil and industrial field. Fig. 1 shows the main dimensions of the machine. Since the productivity per hour of the machine is correlated to the volumetric capacity of the bucket, the main subject of this work is to lighten the arm in order to allow to use a bigger bucket in comparison with the original one. Obviously the lightening operations concerns the arm and *
Tel.: +39 303715577; fax: +39 303702448. E-mail address: [email protected]
not the base of machine (tracked wagon) in order to not compromise the stability of the machine. This work is divided in different steps. First step is to evaluate the dimension of the each component of the arm; the second step concerns the generation of the machine cad model and the evaluation of the main load conditions which mainly stress or deform each component. Third step is to estimate the safety factors and the stiffness of the original machine (these values has been used to perform a new design of components with an aluminium alloy instead of steel alloy). According to classical mechanics theory the crosssection of the arms are designed and consequently verified by means of cad model and FEM analyses. The next step concerns the lightness of the pins and the new bucket is chosen on the base of this reduction in weight. Last step concerns the economic as regards to the lightening operations.
0022-4898/$36.00 Ó 2010 ISTVS. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jterra.2010.03.002
202
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
B
C
D
E
F
L
N
4171 1030 2720 9370 3100 450 2480 Fig. 1. Photography and main dimensions of the excavator in exam.
(a)
F=13 kN
F=13 kN
(b)
Fig. 2. First load condition: (a) initial position and (b) final position.
2. Load conditions Five different load conditions have been checked in order to establish the stress conditions in each component of the excavator arm. The first load condition concerns the levelling operation which allow to start the bucket at the maximum and minimum distance from the axle of rotation. The distance of the bucket from the surface does not change in this roto-translation (Fig. 2). The main parameters for this operation are: total length = 7000 mm, time = 4 s and
the load applied in opposite direction to the movement is 13 kN. The second and third load conditions are similar. The second concerns the lifting operation with the maximum load at the minimum distance from the axle of rotation, Fig. 3a (total length = 4300 mm, time = 7 s and force is 20 kN). The third load condition concerns the lifting operation at the maximum distance from the axle of rotation, Fig. 3b (total length = 4150 mm, time = 4 s and force is 20 kN). The fourth load condition is a usual operation which concerns the levelling in the orthogonal direction as
(a) second load condition
(b) third load condition Fig. 3. Second and third load conditions: lifting at the maxima and minima distance from axle of rotation.
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207 Fx=478kN; Fy=91.8kN
203 L=2900 mm Y X
L=675 mm
CG Boundary conditions by gap elements
F=20 kN
Fx=534kN; Fy=28.2kN
Fig. 6. Forces on the first element. Fig. 4. Four load condition.
Penetration cylinder Positioning arm Bucket cylinder Positioning cylinder Lifting cylinder Lifting arm
Connecting rods Bucket cylinder bucket
Fig. 5. Schematization of the arm.
regards to the axle of the arm. This load condition is more important in order to evaluate the torsional behaviour of the components. On the basis of the maximum hydraulic torque, assumed that the distance of the bucket is 4 m, the maximum orthogonal force is 20 kN (Fig. 4). The last load condition examined is an exceptional condition. In this case the force applied to each component of the excavator arm is the maximum force generated by the hydraulic cylinders both in tension and both in compression (lifting cylinder Fcompression 390 kN, Ftension 200 kN; positioning cylinder Fcompression 560 kN, Ftension 350 kN; penetration cylinder Fcompression 455 kN, Ftension 210 kN and bucket cylinder Fcompression 330 kN, Ftensionl 180 kN). Fig. 5 shows the components of the excavator arm and the name of each part. The data used in each load conditions have been acquired both by measuring the geometry and both by the load diagram of the excavator while the duration of each operation and the working distance have been acquired through experimental tests.
of the software used is Mecad (it has been developed by the Department of Mechanical and Industrial Engineering of the University of Brescia). This program can supply the kinematic and dynamic information in every point (and at any time of the movement) of the elements of the excavator arm. For example Fig. 6 shows the forces in the first element. The next step concerns the FEM analyses on each component in order to have both the stress state (and consequently the safety factor) and the deformability for the arm. The first results show that same elements present a very high value of the stress in localized zone. For example, in the junction zone of the plate, to fasten the pin for the hydraulic cylinder to the main structure. These observation allowed to improve the component through a local redesign, for example by means of a reduction in the stress coefficient factor. Fig. 7 shows the stress state. After this optimization the safety factor for each component, in comparison with the yield stress of the material, is about 2.5. It has been assumed that the material used to make the arm is the steel alloy S355 JO EN 10025. 4. Criteria for preliminary design of the component The evaluation of the new geometry of the arm with the different material has been studied in order to obtain at least the same safety factor and deformability of the original geometry. For this purpose each component has been studied and in particular each panel was theoretically studied applying the different actions which can stress the panel (see Fig. 8). The first step is to impose the same safety factor both for the original geometry (steel alloy) and for the new geometry (aluminium alloy) [1–5]. ryield ryield ¼ : rcr STEEL rcr ALUMINIUM 4.1. Axial force
3. Evaluation of the mechanical behaviour concerning the original geometry After having carried out the operations stated above, each load condition has been implemented in a software program in order to obtain the force (inclusive of inertia effect) for each component of the excavator arm. The name
N In this case, the axial stress is obviously ra ¼ hb and so the relationship between the thickness and the height of the panel is:
bAL hAL ¼ bSTEEL hSTEEL
ryield STEEL : ryield AL
204
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
b
Fig. 7. Stress state (Von Mises) in the first element.
h
a
Axial Stress
Bending Stress
Shear Stress
Fig. 8. Geometry of a panel and the stress state.
If there are buckling phenomena, the critical stress is: 2 p2 D b a ra inst ¼ ; þ a b h b2 where D¼
E h3 ; 12 ð1 v2 Þ
represents the stiffness of the panel; in this case the relationship between the geometric dimensions of the panel is: E b2 þ a2 ryield AL h2 ¼ 1 v2 a b3 AL ryield STEEL E b2 þ a2 2 h ; 1 v2 a b3 STEEL if only the thickness of the plane can be changed, the expression becomes: hAL
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ryield AL ESTEEL ð1 v2 ÞAL : ¼ hSTEEL ryield STEEL EAL ð1 v2 ÞSTEEL
4.2. Bending moment The stress induced by this action is: Mf rf ¼ 1 3 ; bh 6 and so the relationship between the thicknesses is: ryield STEEL : b3AL hAL ¼ b3STEEL hSTEEL ryield AL In case of buckling phenomena, the critical stress is: 2 p2 D 2b a 1 rf inst ¼ þ ; 2 a 2b 1 a=2 hb where a is the ratio between the maximum tensile stress and the maximum compression stress; in this case, the relationship between the geometric dimensions of the panel is the same of the conditions of load stated above. 4.3. Shear load The maximum shear stress in the panel is: s¼
3 T ; 2 hb
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
205
and so the relationship between the thickness and the height of the panel is: syield STEEL ; bAL hAL ¼ bAL hSTEEL syield AL
Table 1 Main properties of the material used in the original and the optimized geometry. Material
rR (MPa)
ryield (MPa)
A%
if we consider that the ratio between the shear yield stress syield and the yield stress ryield is equal for different materials, the final relation coincides with the relationship of the geometric dimensions in the axial load. If there are buckling phenomena, the critical stress is:
Aluminium 6101_T6 UNI9006/2 S 355 JO EN 10025
221
193
15
67,000
2.7
510
355
22
210,000
7.8
2 2
9 ð1 þ b Þ p2 D ; 2 32 b h b3
5. Final geometry of the arm
where a b¼b ; b and so sinst ¼ k
p2 D ; b2 h
therefore the correlation between the geometric dimensions of the panel is: 1 1 b2 E syield STEEL E 2 h ; ¼ syield AL 1 v2 1 v2 h2 AL
STEEL
if the height b does not change the relationship is:
hAL
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi syield AL ESTEEL ð1 v2 ÞAL : ¼ hSTEEL syield STEEL EAL ð1 v2 ÞSTEEL
4.4. Bending The classical relation to evaluate the bending in a panel is: y 00 ¼ j
q (kg/dm3)
b3AL hAL EAL ¼ b3STEEL hSTEEL ESTEEL :
M j: EJ
where M is the moment, and J is the moment of inertia of the cross-section, the relationship which correlates the geometric dimensions of the panel is:
On the basis of the relationships state above between the geometry of the steel alloy panel and the geometry of the aluminium alloy panel, for each component of the arm has been developed a new cross-section. With this cross-sections (Fig. 9) it has been numerically modeled the whole element of the arm. The consequent step is to perform the FEM analyses in order to verify both the safety factor and the flexibility of the component as regards to the original value. This last operation has been repeated iteratively until the goal has been achieved. The final geometry of the component presents a reduction in weight of about 50%. The aluminium alloy chosen for the new arm is 6061 T6. The criteria adopted for this choice are the mechanical properties (in particular the yield stress) and the costs. Table 1 shows the mechanical properties for steel and aluminium alloy. Other important elements are the pins which connect the arms between them and these ones with the hydraulic cylinders. These components have a small weight in comparison with the weight of the arm; nevertheless in order to minimize the weight it is possible to improve also these components. The main pins have a 80-mm-diameter and the material is a high resistance steel alloy: the length varies from 720 mm to 180 mm and the weight from 10 kg to 35 kg. The optimization may be performed in two ways: the first is to use an aluminium alloy and the second to perform a hollow section [6,7]. The first choice is impossible because
25⇒25
590⇒625
A 15⇒20
sinst ¼
E (MPa)
A’ 410⇒415 Fig. 9. Final geometry (mm) of the first element.
206
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
Table 2 Comparison of the total weight of the arm. Element
Weight (kg) original geometry
Weight (kg) optimized geometry
Difference in percentage compared to the original geometry (%)
Elements of the arm Pins Bucket (filled)
2050 335 2150
1080 195 2785
47.3 41.8 +29.5
770 kg 800 kg
480 kg
2050 kg
solution). This value is, obviously correlated to the velocity, or rather to the rapidity of the rotation of the assembly made up of the arm and the bucket. With these constraints it is possible to increase the capacity of the bucket from 1 m3 to 1.35 m3. The weight of the 1 m3 bucket is about 650 kg while the weight of 1.35 m3 is about 760 kg. If we consider that the material density is about 1500 kg/m3, in the original geometry the total weight to be moved is 2150 kg and in the optimized geometry the final weight is about 2800 kg. The Table 2 compares the total weight for the original and the final geometry. 7. Conclusions
390 kg
420 kg
270 kg 2785 kg
Fig. 10. Different weights of the elements of the excavator arm.
in this case the diameter of the pin is very big and the reduction in weight is very small (these options generate many technological problems). If we use pins with hollow circular section, there is a significant reduction in the total weight of the pins. The new geometry is obtained by evaluating the maximum bending and shear load acting on the pins and imposing the same safety factor. In particular the final external diameter for the big pin is about 110 mm and the inner diameter is about 75 mm: in this case the weight of the pins varies from 8 kg to 25 kg. Fig. 10 shows different weight concerning the two solutions for the components of the arm. 6. Volumetric capacity of the bucket On the basis of the solutions stated above, in order to reduce the weight of the arm it is possible to increase either the capacity of the bucket or the length of the single component of the arm. The new capacity of the bucket has been chosen considering that the hydraulic system does not change and so, for instance, the maximum load from the hydraulic cylinder and the maximum torque at the tower are the same which are present in the original geometry. Another important variable for the choice of the bucket is the total moment of inertia at the tower (evaluated at the maximum distance of the bucket from the axis of rotation, this variable do not change compared to the original
This work shows the results concerning the lightening of the excavator with the goal to increase the volumetric capacity of the bucket. In particular the first step concerns the study of the excavator geometry with reference to the different load conditions. These results (with the theoretical formulae) can be used in order to design a new geometry for elements of the excavator structure with an aluminium alloy instead of steel alloy. As regards to the original geometry the result of this optimization is an arm 50% lighter. Optimizing also the weight of the pins it is possible to increase the capacity of the bucket from 1 m3 to 1.35 m3 and so to increase the productivity per hour of the excavator. We think that the process can be extended to other elements like the hydraulic cylinders whose weight is not negligible at all. If we consider the economic aspect, the increase in the cost of about € 2.500–3500 may be accepted if we take into consideration that the total weight of the arm is reduced of about 50% and the capacity of the bucket increased of about 30%. We think that these results may be obtained in the different types of excavators. Acknowledgment The author would like to thank the mechanical engineer Mr. Morabito Andrea (BS-ITALY) for his kind and valuable collaboration in this work. References [1] Progettazione strutturale con l’alluminio, Edimet (Brescia) vol. I e II; 2001. [2] Davis JR. Aluminum and aluminum alloys. ASM specialty handbook; 1996.
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207 [3] Bloom F, Coffin D. Handbook of thin plate buckling and post buckling. Chapman & Hall; 2001. [4] Sae fatigue design handbook. 400 Commonwealth Drive, 3rd ed. Warrendale (PA, USA): Society of Automotive Engineers Inc.; 1997.
207
[5] Timoshenko SP, Gere J. Theory of elastic stability. McGraw-Hill; 1988. [6] Murray GT. Introduction to engineering materials: behavior, properties, and selection. Marcel Dekker Inc.; 1993. [7] Davis JR. Aluminum and aluminum alloys, ASM specialty handbook; 1993.
Journal of Terramechanics Journal of Terramechanics 47 (2010) 201–207 www.elsevier.com/locate/jterra
Review
Design of aluminium boom and arm for an excavator Luigi Solazzi * Dipartimento di Ingegneria Meccanica e Industriale, Facolta` di Ingegneria, Universita` degli Studi di Brescia, Via Branze 38, 25123 Brescia, Italy Received 8 September 2008; received in revised form 3 March 2010; accepted 9 March 2010 Available online 28 April 2010
Abstract The aim of this work is to study the boom and the arm of an excavator in order to replace the material, which they are usually made of, with another material. In particular, the study wants to substitute the steel alloy for an aluminium alloy. This change lightens the components of the arm, allows to increase the load capacity of the bucket and so it is possible to increase the excavator productivity per hour. For this purpose many different load conditions have been studied numerically on the original excavator in order to estimate a safety factor and the deformability or flexibility of each component. These parameters have been used in order to design a new arm. The excavator which has been analyzed is composed of three elements and the load conditions assumed, in order to evaluate the stress, are five (lifting at the maximum and minimum distance from the axis of rotation, maximum load induced by hydraulic cylinders, spin of the arm of the excavator and collision with an obstacle, etc.). As regards to the safety factor and deformability in order to maintain the original value the new geometry of the arm involves an increase of the dimension and so the lightness is not correlate only to the variation of the material density. The weight of the final geometry of the aluminium arm is 1080 kg whereas the one of the steel arm is 2050 kg and consequently it has been possible to increase the capacity of bucket from 1 m3 to the 1.35 m3. With reference to the manufacturing cycle of the aluminium arm with the new pins, the price increased about € 2.500–3.000 and this aspect could be justified if we consider that the productivity per hour increased about 35%. Ó 2010 ISTVS. Published by Elsevier Ltd. All rights reserved. Keywords: Lifting equipment; Excavator; Design with aluminium alloy
1. Introduction The excavator examined in this work is a classical machine represented in Fig. 1. It is composed of three different arms, the power is 110 kW and the rated weight is about 21.500 kg. This machine is mainly used to demolish and move material in applications concerning civil and industrial field. Fig. 1 shows the main dimensions of the machine. Since the productivity per hour of the machine is correlated to the volumetric capacity of the bucket, the main subject of this work is to lighten the arm in order to allow to use a bigger bucket in comparison with the original one. Obviously the lightening operations concerns the arm and *
Tel.: +39 303715577; fax: +39 303702448. E-mail address: [email protected]
not the base of machine (tracked wagon) in order to not compromise the stability of the machine. This work is divided in different steps. First step is to evaluate the dimension of the each component of the arm; the second step concerns the generation of the machine cad model and the evaluation of the main load conditions which mainly stress or deform each component. Third step is to estimate the safety factors and the stiffness of the original machine (these values has been used to perform a new design of components with an aluminium alloy instead of steel alloy). According to classical mechanics theory the crosssection of the arms are designed and consequently verified by means of cad model and FEM analyses. The next step concerns the lightness of the pins and the new bucket is chosen on the base of this reduction in weight. Last step concerns the economic as regards to the lightening operations.
0022-4898/$36.00 Ó 2010 ISTVS. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jterra.2010.03.002
202
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
B
C
D
E
F
L
N
4171 1030 2720 9370 3100 450 2480 Fig. 1. Photography and main dimensions of the excavator in exam.
(a)
F=13 kN
F=13 kN
(b)
Fig. 2. First load condition: (a) initial position and (b) final position.
2. Load conditions Five different load conditions have been checked in order to establish the stress conditions in each component of the excavator arm. The first load condition concerns the levelling operation which allow to start the bucket at the maximum and minimum distance from the axle of rotation. The distance of the bucket from the surface does not change in this roto-translation (Fig. 2). The main parameters for this operation are: total length = 7000 mm, time = 4 s and
the load applied in opposite direction to the movement is 13 kN. The second and third load conditions are similar. The second concerns the lifting operation with the maximum load at the minimum distance from the axle of rotation, Fig. 3a (total length = 4300 mm, time = 7 s and force is 20 kN). The third load condition concerns the lifting operation at the maximum distance from the axle of rotation, Fig. 3b (total length = 4150 mm, time = 4 s and force is 20 kN). The fourth load condition is a usual operation which concerns the levelling in the orthogonal direction as
(a) second load condition
(b) third load condition Fig. 3. Second and third load conditions: lifting at the maxima and minima distance from axle of rotation.
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207 Fx=478kN; Fy=91.8kN
203 L=2900 mm Y X
L=675 mm
CG Boundary conditions by gap elements
F=20 kN
Fx=534kN; Fy=28.2kN
Fig. 6. Forces on the first element. Fig. 4. Four load condition.
Penetration cylinder Positioning arm Bucket cylinder Positioning cylinder Lifting cylinder Lifting arm
Connecting rods Bucket cylinder bucket
Fig. 5. Schematization of the arm.
regards to the axle of the arm. This load condition is more important in order to evaluate the torsional behaviour of the components. On the basis of the maximum hydraulic torque, assumed that the distance of the bucket is 4 m, the maximum orthogonal force is 20 kN (Fig. 4). The last load condition examined is an exceptional condition. In this case the force applied to each component of the excavator arm is the maximum force generated by the hydraulic cylinders both in tension and both in compression (lifting cylinder Fcompression 390 kN, Ftension 200 kN; positioning cylinder Fcompression 560 kN, Ftension 350 kN; penetration cylinder Fcompression 455 kN, Ftension 210 kN and bucket cylinder Fcompression 330 kN, Ftensionl 180 kN). Fig. 5 shows the components of the excavator arm and the name of each part. The data used in each load conditions have been acquired both by measuring the geometry and both by the load diagram of the excavator while the duration of each operation and the working distance have been acquired through experimental tests.
of the software used is Mecad (it has been developed by the Department of Mechanical and Industrial Engineering of the University of Brescia). This program can supply the kinematic and dynamic information in every point (and at any time of the movement) of the elements of the excavator arm. For example Fig. 6 shows the forces in the first element. The next step concerns the FEM analyses on each component in order to have both the stress state (and consequently the safety factor) and the deformability for the arm. The first results show that same elements present a very high value of the stress in localized zone. For example, in the junction zone of the plate, to fasten the pin for the hydraulic cylinder to the main structure. These observation allowed to improve the component through a local redesign, for example by means of a reduction in the stress coefficient factor. Fig. 7 shows the stress state. After this optimization the safety factor for each component, in comparison with the yield stress of the material, is about 2.5. It has been assumed that the material used to make the arm is the steel alloy S355 JO EN 10025. 4. Criteria for preliminary design of the component The evaluation of the new geometry of the arm with the different material has been studied in order to obtain at least the same safety factor and deformability of the original geometry. For this purpose each component has been studied and in particular each panel was theoretically studied applying the different actions which can stress the panel (see Fig. 8). The first step is to impose the same safety factor both for the original geometry (steel alloy) and for the new geometry (aluminium alloy) [1–5]. ryield ryield ¼ : rcr STEEL rcr ALUMINIUM 4.1. Axial force
3. Evaluation of the mechanical behaviour concerning the original geometry After having carried out the operations stated above, each load condition has been implemented in a software program in order to obtain the force (inclusive of inertia effect) for each component of the excavator arm. The name
N In this case, the axial stress is obviously ra ¼ hb and so the relationship between the thickness and the height of the panel is:
bAL hAL ¼ bSTEEL hSTEEL
ryield STEEL : ryield AL
204
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
b
Fig. 7. Stress state (Von Mises) in the first element.
h
a
Axial Stress
Bending Stress
Shear Stress
Fig. 8. Geometry of a panel and the stress state.
If there are buckling phenomena, the critical stress is: 2 p2 D b a ra inst ¼ ; þ a b h b2 where D¼
E h3 ; 12 ð1 v2 Þ
represents the stiffness of the panel; in this case the relationship between the geometric dimensions of the panel is: E b2 þ a2 ryield AL h2 ¼ 1 v2 a b3 AL ryield STEEL E b2 þ a2 2 h ; 1 v2 a b3 STEEL if only the thickness of the plane can be changed, the expression becomes: hAL
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ryield AL ESTEEL ð1 v2 ÞAL : ¼ hSTEEL ryield STEEL EAL ð1 v2 ÞSTEEL
4.2. Bending moment The stress induced by this action is: Mf rf ¼ 1 3 ; bh 6 and so the relationship between the thicknesses is: ryield STEEL : b3AL hAL ¼ b3STEEL hSTEEL ryield AL In case of buckling phenomena, the critical stress is: 2 p2 D 2b a 1 rf inst ¼ þ ; 2 a 2b 1 a=2 hb where a is the ratio between the maximum tensile stress and the maximum compression stress; in this case, the relationship between the geometric dimensions of the panel is the same of the conditions of load stated above. 4.3. Shear load The maximum shear stress in the panel is: s¼
3 T ; 2 hb
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
205
and so the relationship between the thickness and the height of the panel is: syield STEEL ; bAL hAL ¼ bAL hSTEEL syield AL
Table 1 Main properties of the material used in the original and the optimized geometry. Material
rR (MPa)
ryield (MPa)
A%
if we consider that the ratio between the shear yield stress syield and the yield stress ryield is equal for different materials, the final relation coincides with the relationship of the geometric dimensions in the axial load. If there are buckling phenomena, the critical stress is:
Aluminium 6101_T6 UNI9006/2 S 355 JO EN 10025
221
193
15
67,000
2.7
510
355
22
210,000
7.8
2 2
9 ð1 þ b Þ p2 D ; 2 32 b h b3
5. Final geometry of the arm
where a b¼b ; b and so sinst ¼ k
p2 D ; b2 h
therefore the correlation between the geometric dimensions of the panel is: 1 1 b2 E syield STEEL E 2 h ; ¼ syield AL 1 v2 1 v2 h2 AL
STEEL
if the height b does not change the relationship is:
hAL
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi syield AL ESTEEL ð1 v2 ÞAL : ¼ hSTEEL syield STEEL EAL ð1 v2 ÞSTEEL
4.4. Bending The classical relation to evaluate the bending in a panel is: y 00 ¼ j
q (kg/dm3)
b3AL hAL EAL ¼ b3STEEL hSTEEL ESTEEL :
M j: EJ
where M is the moment, and J is the moment of inertia of the cross-section, the relationship which correlates the geometric dimensions of the panel is:
On the basis of the relationships state above between the geometry of the steel alloy panel and the geometry of the aluminium alloy panel, for each component of the arm has been developed a new cross-section. With this cross-sections (Fig. 9) it has been numerically modeled the whole element of the arm. The consequent step is to perform the FEM analyses in order to verify both the safety factor and the flexibility of the component as regards to the original value. This last operation has been repeated iteratively until the goal has been achieved. The final geometry of the component presents a reduction in weight of about 50%. The aluminium alloy chosen for the new arm is 6061 T6. The criteria adopted for this choice are the mechanical properties (in particular the yield stress) and the costs. Table 1 shows the mechanical properties for steel and aluminium alloy. Other important elements are the pins which connect the arms between them and these ones with the hydraulic cylinders. These components have a small weight in comparison with the weight of the arm; nevertheless in order to minimize the weight it is possible to improve also these components. The main pins have a 80-mm-diameter and the material is a high resistance steel alloy: the length varies from 720 mm to 180 mm and the weight from 10 kg to 35 kg. The optimization may be performed in two ways: the first is to use an aluminium alloy and the second to perform a hollow section [6,7]. The first choice is impossible because
25⇒25
590⇒625
A 15⇒20
sinst ¼
E (MPa)
A’ 410⇒415 Fig. 9. Final geometry (mm) of the first element.
206
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207
Table 2 Comparison of the total weight of the arm. Element
Weight (kg) original geometry
Weight (kg) optimized geometry
Difference in percentage compared to the original geometry (%)
Elements of the arm Pins Bucket (filled)
2050 335 2150
1080 195 2785
47.3 41.8 +29.5
770 kg 800 kg
480 kg
2050 kg
solution). This value is, obviously correlated to the velocity, or rather to the rapidity of the rotation of the assembly made up of the arm and the bucket. With these constraints it is possible to increase the capacity of the bucket from 1 m3 to 1.35 m3. The weight of the 1 m3 bucket is about 650 kg while the weight of 1.35 m3 is about 760 kg. If we consider that the material density is about 1500 kg/m3, in the original geometry the total weight to be moved is 2150 kg and in the optimized geometry the final weight is about 2800 kg. The Table 2 compares the total weight for the original and the final geometry. 7. Conclusions
390 kg
420 kg
270 kg 2785 kg
Fig. 10. Different weights of the elements of the excavator arm.
in this case the diameter of the pin is very big and the reduction in weight is very small (these options generate many technological problems). If we use pins with hollow circular section, there is a significant reduction in the total weight of the pins. The new geometry is obtained by evaluating the maximum bending and shear load acting on the pins and imposing the same safety factor. In particular the final external diameter for the big pin is about 110 mm and the inner diameter is about 75 mm: in this case the weight of the pins varies from 8 kg to 25 kg. Fig. 10 shows different weight concerning the two solutions for the components of the arm. 6. Volumetric capacity of the bucket On the basis of the solutions stated above, in order to reduce the weight of the arm it is possible to increase either the capacity of the bucket or the length of the single component of the arm. The new capacity of the bucket has been chosen considering that the hydraulic system does not change and so, for instance, the maximum load from the hydraulic cylinder and the maximum torque at the tower are the same which are present in the original geometry. Another important variable for the choice of the bucket is the total moment of inertia at the tower (evaluated at the maximum distance of the bucket from the axis of rotation, this variable do not change compared to the original
This work shows the results concerning the lightening of the excavator with the goal to increase the volumetric capacity of the bucket. In particular the first step concerns the study of the excavator geometry with reference to the different load conditions. These results (with the theoretical formulae) can be used in order to design a new geometry for elements of the excavator structure with an aluminium alloy instead of steel alloy. As regards to the original geometry the result of this optimization is an arm 50% lighter. Optimizing also the weight of the pins it is possible to increase the capacity of the bucket from 1 m3 to 1.35 m3 and so to increase the productivity per hour of the excavator. We think that the process can be extended to other elements like the hydraulic cylinders whose weight is not negligible at all. If we consider the economic aspect, the increase in the cost of about € 2.500–3500 may be accepted if we take into consideration that the total weight of the arm is reduced of about 50% and the capacity of the bucket increased of about 30%. We think that these results may be obtained in the different types of excavators. Acknowledgment The author would like to thank the mechanical engineer Mr. Morabito Andrea (BS-ITALY) for his kind and valuable collaboration in this work. References [1] Progettazione strutturale con l’alluminio, Edimet (Brescia) vol. I e II; 2001. [2] Davis JR. Aluminum and aluminum alloys. ASM specialty handbook; 1996.
L. Solazzi / Journal of Terramechanics 47 (2010) 201–207 [3] Bloom F, Coffin D. Handbook of thin plate buckling and post buckling. Chapman & Hall; 2001. [4] Sae fatigue design handbook. 400 Commonwealth Drive, 3rd ed. Warrendale (PA, USA): Society of Automotive Engineers Inc.; 1997.
207
[5] Timoshenko SP, Gere J. Theory of elastic stability. McGraw-Hill; 1988. [6] Murray GT. Introduction to engineering materials: behavior, properties, and selection. Marcel Dekker Inc.; 1993. [7] Davis JR. Aluminum and aluminum alloys, ASM specialty handbook; 1993.