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Engineering Science and Technology, an International Journal 22 (2019) 346–352

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Engineering Science and Technology, an International Journal

journal homepage: www.elsevier.com/locate/jestch

Full Length Article

Design optimization of industrial robot arm to minimize redundant weight

https://doi.org/10.1016/j.jestch.2018.11.009 2215-0986/� 2018 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⇑ Corresponding author. E-mail address: [email protected] (M. Karali). URL: http://www.konya.edu.tr (M. Karali).

Peer review under responsibility of Karabuk University.

Mustafa Bugday, Mehmet Karali ⇑ Necmettin Erbakan University, Engineering and Architectural Faculty, Mechatronics Engineering Department, Konya, Turkey

a r t i c l e i n f o a b s t r a c t

Article history: Received 6 January 2018 Revised 6 November 2018 Accepted 19 November 2018 Available online 8 December 2018

Keywords: Robot arm optimization Industrial robot Finite element method (FEM)

In industrial robots, projected torque increases depending on the extending reach length and payload. This requires selection of powerful motors particularly on the second axis. Since arm rigidity becomes more important as the expected positioning precision increases, less flexible materials are used. Therefore, during operation conditions, 70% of motor’s energy is used for redundant weight. In this study, analyses conducted on five different robotic arms belong to different brands. Arm’s payload distribution in terms of region and amount is examined, alternative designs are analysed and compared with each other. Geometry and materials are changed in alternative designs. In this way, redundant weight is min- imized (without increasing the share amount) at the same positioning precision. Results of this study demonstrated a 10% decrease in inert payloads. � 2018 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC

BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction deformations formed on the robotic arm. From those studies, Kur-

Servomotors are used in industrial robots because of their pre- cise positioning control and stable structures and the cost of those motors increases in proportion with their torque. A robot with a lifting capacity between 5 and 7 kg has about 300 kg average weight. Especially the second axis motor carries 70–75% of the robot’s total weight. Considering the high acceleration of robot arms, it will be better to use a more powerful motor. Therefore, it is important to select a different material with same strength or to change the geometric structure of the same material to get a reduced motor load.

There are some other studies analyzed performance or effi- ciency of robots by employing different criteria and methods Pupaza et al. [1] reduced material by geometric changes on the sec- ond axis and conducted strength analysis. Their analysis showed that robot arm became lighter and no extra deformation occurred under the same load. In a similar study, Supriya Sahu et al. [2] con- ducted FEM analyses of loads on a robotic arm with six axis, and calculated the deformation, stress and stress values. They identi- fied the location with the maximum deformation and tried to sta- bilize the robot by implementing proper minimization techniques on those parts. In some other studies, alternative materials and arm geometries are tested by examining the stress and elastic

nool ve K. Urmila [3] by using cylinder or square segments made of steel, al-356 and aramid epoxy materials; Prasad et al. [4] by using magnesium, aliminium, zink and steel materials; Chong et al. [5] and Rueda [6] by changing material properties and geometric design of the arm, all conducted stress and deformation analyses. Results of those studies presented the proper motor and load quan- tity. While calculating the load range that the robot can securely lift, Singh et al. [7] employed analytic calculations and Chitte et al. [8] employed vibration analyses. On the other hand, Zhou et al. [9] focused on the design change by identifying the load range that a robot can securely lift to increase robot’s lifting capacity.

When the articulated robots extend their arms in full and hor- izontally as shown in Fig. 1, the torque caused by robot’s own weight is extremely high. In addition to that, when the robot is loaded at its maximum capacity, the stress on the second axis arm is increasing and it is growing closer to the rotation axis. There are other studies supporting this conclusion [10–12].

Since it would heterogeneously increase the amount of defor- mation, concentration of stress on a narrow region is an undesired situation. If those loads could be dispersed by a geometrical change, particularly on the second axis arm, deformation at the tip of the robot will be decreased. It is known that in structures with a support on one side and load on the other, conversion of rotating forces to the axial forces in the form of pull an push, increases the strength and decreases the mass [13,14]. Fig. 2 shows that when a proper channel is opened on a part, stress that concen- trated on a specific region is dispersed to different regions.

Fig. 2. The advantage of digging a hole.

Fig. 1. Articulated robot.

M. Bugday, M. Karali / Engineering Science and Technology, an International Journal 22 (2019) 346–352 347

By opening a proper channel on the second axis, this study attempts to decrease the weight through material reduction, to increase maximum strength by reducing mass inertia. Following is a list of some features distinguish this study from others;

1. Instead of designing a new robot arm, this study tries to opti- mize existing arms belong to known brands.

2. An articulated robot is analyzed by considering the motor load. 3. The chosen method to dispose the redundant weights is to

reduce the material by opening channels. Location of channels are determined with ANSYS 16.2 Shape Optimization package.

4. The force caused by the weight of disposed material is not ignored and this weight is added to the tip of the robot. When reducing material, a simulation that would not deteriorate arm’s strength and deformation values and would not increase the motor load was applied

2. Preliminary works

In order to select the proper robot model for this study, 3D models of five most preferred robots in industry were obtained

Fig. 3. Appearance of six axis robot.

Table 1 Total amount of deformation d and maximum stress ru on the robots found at FEM analy

ABB44 FANUC (45 kg) (200 kg

Steel d (base) 0,30105 2,1368 d (hole) 0,28803 2,1105 ru (base) 40,696 162,3 ru (hole) 40,32 160,7

Aluminium d (base) 0,52679 1,9242 d (hole) 0,52277 1,9316 ru (base) 32,553 141,73 ru (hole) 33,194 141,74

Epoxy d (base) 1,5239 3,2338 d (hole) 1,4439 3,2766 ru (base) 31,945 200 ru (hole) 31,828 180,91

through Solidworks. The maximum load that they can carry was applied on the sixth axis. To facilitate the job, a P force which equals to the distributed load caused by the weights of the third, the fourth, the fifth and the sixth axis and motor’s weight was calculated. As shown in Fig. 3, that P force was reduced as the F force to the second axis of the robot arm after static calculations.

The total amount of deformation was calculated for 5 different robots. For each robot, by holding the assumed maximum load conditions constant, some holes were dug on the second axis arm. Simulation was repeated after the forces that caused by weights of the excavated pieces was added to the F force. The results are presented in Table 1.

Table 1 shows comparison of robot arms before and after dig- ging the holes (maximum weights robot arms can lift are shown). In Abb44, Fanuc and Kuka robot arms holes were drilled on second axes where stress values are at minimum, in Staubli ve Abb120 robot arms holes were drilled on second axes where stress values are at maximum. Assessment of results in terms of material and holes showed that maximum stress and displacement on the sec- ond axes of Abb44 and Fanuc robot arms has decreased but maxi- mum stress and displacement on the second axes of Staubli and Abb120 robot arms has increased. For Kuka robot arm, a fluctua- tion was observed in both maximum stress and displacement val- ues. In order to identify accurate place and hole that would lower the fluctuations to the minimum, Shape Optimization module of Ansys applied to Kuka’s 3D model. Simulation results were pre- sented in Table 1.

3. Finite elements method

3.1. Mesh model

In order to measure more precise values during the mesh anal- ysis, body mesh method was employed. Three nodes triangle ele- ment is chosen as element type and element size was set as 10 mm. In Fig. 4, triangle element with three nodes was presented and formulized. The number of node was 1,056,426 and the num- ber of element was 746,142 on the robot arm. The mesh analysis is shown in Fig. 5.

u

v

� � ¼ N1 0 N2 0 N3 0

0 N1 0 N2 0 N3

� � u1 v1 u2 v2 u3 v3

8>>>>>>>>< >>>>>>>>:

9>>>>>>>>= >>>>>>>>;

ð1Þ

In this equation ‘‘u” and ‘‘v” values are displacement functions.

sis.

KUKA STAUBL ABB120 ) (6 kg) (5 kg) (4 kg)

0,028138 0,012314 0,0092191 0,0284 0,012407 0,0087651 5,1494 2,4966 2,442 4,0097 2,4247 1,8396

0,035918 0,014729 0,014337 0,039875 0,01574 0,014727 3,4193 2,0609 3,0381 2,8065 2,071 3,0816

0,097524 0,070882 0,017839 0,16775 0,078369 0,019391 3,2955 3,6083 2,4243 3,8603 3,7975 2,5067

Fig. 4. Three nodes triangle element type.

348 M. Bugday, M. Karali / Engineering Science and Technology, an International Journal 22 (2019) 346–352

u ¼ b1 þ b2x þ b3y v ¼ b4 þ b5x þ b6y ð2Þ ‘‘u” and ‘‘v” values are expressed in this form (bi (i = 1,2. . .6) con- stant coefficient).

Shape functions at ‘‘x” and ‘‘y” points:

N1 ¼ 1 2A

½ðx2y3 � x3y2Þ þ ðy2 � y3Þx þ ðx3 � x2Þy� ð3Þ

N2 ¼ 1 2A

½ðx3y1 � x1y3Þ þ ðy3 � y1Þx þ ðx1 � x3Þy� ð4Þ

N3 ¼ 1 2A

½ðx1y2 � x2y1Þ þ ðy1 � y2Þx þ ðx2 � x1Þy� ð5Þ

Here ‘‘A” represents region.

A ¼ 1 2 det

1 x1 y1 1 x2 y2 1 x3 y3

2 64

3 75 ð6Þ

3.2. Static analysis

In Fig. 6 point A represents joint of first and second axes, point B represents center of gravity of second axis, point C represents joint of second and third axes, distance between C and E represents part where third, fourth, fifth and sixth axes are located. ‘‘k” represents distance between [AB], ‘‘l” represents distance between [BC], ‘‘m” and ‘‘n” represent distance between [CD] and [DE] of robot arm. ‘‘WB” shows weight of second axis and ‘‘WD” shows total weight of third, fourth, fifth and sixth axes of robot arm. ‘‘P” force repre- sents maximum weight that robot arm can lift. Since the optimiza- tion will be applied to the second axes, ‘‘P” and ‘‘WD” weights turned into an ‘‘F” force at point C and the moment resulted from force transmission applied to point C.

Formulization of conversion of ‘‘P” and ‘‘WD” weights into ‘‘F” is;X F ¼ P þ WD ð7Þ

Fig. 5. Mesh analys

F ¼ 6 � 9; 81 þ 107 � 9; 81

F ¼ 1108N

X MC ¼ P � ðm þ nÞ þ WD � m ð8Þ

M ¼ 58; 86 � 0; 7 þ 107 � 0; 3

Fig. 6. Analytic calculation.

C

MC ¼ 347; 3 N � m

The maximum weight that Kuka Kr210 industrial robot can carry is 6 kg. After static calculations, the maximum weight that the robot can lift was reduced from the sixth axis to the second axis and converted to a 1108N force. Moment as a result of force transmission in the second axis became 347,3 N�m. Fig. 7a shows the limiting values of the robot. In Fig. 7a, point A represents acceleration due to gravitation. 1108N to point B, 40N to points E, D and 347,3 N�m as a result of force transmission to point F were applied. That force (1108N) was applied to the second axis of the robot arm in ANSYS Static Structural software. The deforma- tion and stress values were calculated as 0.03444 mm and 6.4506 MPa in simulation. Maximum stress and deformation val- ues are shown in Fig. 7b and c.

3.3. Modal analysis

This analysis is conducted to identify the causes of vibrations occurred at the tip of the robot arm and the dynamic characteris- tics of the structure. Natural frequency and the mod types were identified by conducting modal analysis on the robot. Natural fre- quency is important to spot the places where resonance may hap- pen. Generally the resonance is not a desired situation for a structure. Resonance can be removed by either changing outer force frequency or by changing structure’s frequency. Solution of equation of motion belongs to a multiple degree of freedom system yields natural frequencies and shape mods. Equation of motion of an undamped system with multiple degree of freedom is;

½M� €xðtÞf g þ ½K� xðtÞf g ¼ fðtÞf g ð9Þ [M] and [K] represent mass and rigidity matrices, €xðtÞ; xðtÞ ve

fðtÞ represent momentum, displacement and force vectors. Analysis results showed that mode 1 and mode 2 were calcu-

lated as f 1 ¼ 121:75 Hz and f 2 ¼ 150:28 Hz, and the structure

is of the robot.

Fig. 8. Robot modes.

Fig. 7. Static analysis. a: Limiting values ve b: Maximum stress c: Maximum Deformation.

M. Bugday, M. Karali / Engineering Science and Technology, an International Journal 22 (2019) 346–352 349

twisted in mode 1 and deflection in mode 2. The third and the fourth modes were calculated as f 3 ¼ 323:48 Hz and f 4 ¼ 369:85 Hz, and the structure twisted in mod3 and deflection in mode4. Finally, the fifth and the sixth modes were calculated as f 5 ¼ 626:61 Hz and f 6 ¼ 774:73 Hz, and the structure twisted in both modes. These modes are depicted in Fig. 8.

4. Optimization works

Although the optimization algorithm does not provide more certain and clear answers than the traditional methods, it gives an approximate result. This method has two advantages over tradi- tional methods: cost and time reductions [1]. The main objective of

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this study is to identify suitable locations to reduce material from robot arm by using ANSYS Shape Optimisation analysis. In addi- tion, different holes were dug and analyzed to identify the best geometric shape when reducing material. Fig. 9 shows best places for the holes.

Fig. 9. Shape op

Fig. 10. Sampling points

Fig. 11. Precisio

Main objective of optimization work is to reduce the loads of motors by decreasing the mass of the arm and getting smaller deformation and stress values than calculated in static analysis. Hole’s height L and radius r were inputs to ANSYS Response Surface Optimization module. The weight of robot arm, the amount of

timization.

on the design space.

n analysis.

Fig. 12. Optimizasyon sonucu a: Maximum Deformation and b: Maximum stress.

Fig. 14. Distribution of stress amounts on the curve.

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deformation and stress value were defined as outputs. The soft- ware searched for the best results by changing L and r within a pre- defined range ð�3 mmÞ.

The software made some improvements on design space by using Kriging Response Surface algorithm to accurately identify the best design domain. It solved the structure through 45 different samplings. Fig. 10 shows sampling points on the design space.

According to the precision analysis method, the hole placed on the upper side of the robot arm has greater impact on the output parameters, namely stress, deformation and robot arm mass. Fig. 11 shows the precision analysis.

Finally, Fig. 12a and b shows optimized robot arm and mini- mum amount of deformation achieved.

After the optimization the weight of the robot was reduced by 10% percent. The stress value was reduced about 23% from 6.4506 MPa to 4.9832 MPa. Finally, deformation value is reduced from 0.034444 mm to 0.012214 mm with a 65% decrease. Results showed that neither deformation nor stress values was not close to the anticipated limiting values.

5. Simulation results and discussion

A busy industrial robot can make about 10,000 cycle daily. Therefore, energy efficiency is the major concern when designing robot components. Since the diameter of robot arm decreases toward tip of the robot, the load of servomotor lightens and its energy consumption is reduced. However since the motors of the fourth, the fifth and the sixth axises are placed on the shoulder of the robot, the load of the second axis servomotor increases and bigger motors are needed. Therefore, this study analyzed stress and deformation on the second axis arm. In addition, an optimiza- tion by reducing material to increase efficiency of the robot was conducted.

Fig. 13. Maximum stress reg

Fig. 13a shows the initial distribution of stress on the robot arm. Fig. 13b shows the distribution of stress on the robot arm after the optimization.

Examination of Fig. 14 shows that the region close to the motor on the second axis has greater amount of stress. Curvilinear accu- mulation of stress would increase deformation on that region. Increase in the deformation would eventually affect the robot’s precision. Industrial robot vendors are trying to solve this problem by using thicker materials. This study achieved to reduce the max- imum stress value and motor’s load by distributing the stress on the second axis to a wider region. Fig. 14 shows base and optimized stress values.

Fig. 14 shows that the stress values decreases on regions where maximum stress values are accumulated. There are two reasons for this decrease:

ions on the second axis.

Fig. 15. Distribution of deformation amounts on the curved line.

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1. By opening channel, the stress in the regions with maximum stress values are turned into pull and push stress. As a result of that, the stress is distributed to a wider region.

2. As a result of geometric change weight is reduced.

Normally, when the weight of an arm decreased, the amount of deformation due to the load increases. However, this situation reverses depending on the location and geometry of the channel. In addition to that there is an optimum point between the wide of the channel and its contribution. Fig. 15 shows that this study improved the distribution of deformation by using Shape Optimi- sation module.

Examination of Fig. 15 shows that there is not any increase in the region with maximum deformation.

6. Conclusion

When mechanical systems working on different loads and fre- quencies are optimised in terms of energy efficiency and cost, a

partial reduction in operating costs can be achieved. Considering the limiting factors like elasticity, rigidity, and precision that are expected from mechanical systems, some costs can be ignored. However, the optimization of long-life robots not only improves the cost and efficiency but also the increases the motor’s lifetime.

This study found that in spite of the material reduction by 10% on the second axis, there was not any increase in the elastic defor- mation values; moreover, an improvement on the rigidity values of the material was observed.

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