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Energy Procedía 68 (2015) 463 - 470

2nd International Conference on Sustainable Energy Engineering and Application, ICSEEA 2014

Measuring geometric and kinematic properties to design steering axis to angle turn of the electric golf car

Muhammad Khristamtoa*, Achmad Praptijantoa, Sunarto Kalega

aResearch Centre for Electrical Power and Mechatronics, Indonesian Institute of Sciences, Komplek LIPI Jl. Sangkuriang, Gedung 20, Lantai 2, Dago, Coblong, Bandung, Jawa Barat 40135, Indonesia

Abstract

The electric golf cart of LIPI is designed traditionally without calculating geometric and kinematic properties of it steering layout. Furthermore, it resulting less quality of handling and make it less safe to operate. The kinematics calculation of steering linkages has been explained by Ackerman. So, this paper's purpose is to calculate and make recommendation for electric golf cart of LIPI as a solution for improving the handling quality. The result is that maximum turning angle of the car is limited by 30° and the car has R at 372 cm. This is an ideal value according to Ackerman calculation.

© 2015TheAuthors.Published by ElsevierLtd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Scientific Committee of ICSEEA 2014

Keywords:Ackerman; steering knuckle distance; steering angle; tires turn angle; steering linkage

1. Introduction

The steering system is a mechanism on a vehicle that serves to regulate the direction of the vehicle by means of deflecting the front wheels [1, 2]. In the development of the rear wheel alignments to help turn or even as a primary regulator at turns also exist. In the steering system there are three main parts that are the steering column, steering gear and steering linkage [3-6].Steering column consists of the main shaft and the steering column tube. Steering column mounted to the body via breakaway bracket, so that the impact occurred the steering column can be detached easily. To reduce the transfer of road shock, at the main steering shaft universal joint paired. Steering gear

* Corresponding author. Tel.: +62-815-7361-6613 E-mail address:muha138@lipi.go.id

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Scientific Committee of ICSEEA 2014

doi: 10.1016/j.egypro.2015.03.278

serves to steer the front wheels and increase the moment with reducing their gear so that the steering becomes lighter [7-10]. Type of steering gear that is widely used today is the type of rack & pinion and recirculating ball. Rack & pinion type usage due to a simple and lightweight construction allows for construction vehicles was low. While the use of recirculating ball because he wanted to benefit big moment that driving is relatively mild. In addition, the use of recirculating ball as well as more resistant to heavy loads and more resistant to wear and vibration damping properties better. In turn besides the damping vibration in the car and reduce the shock on the road there is an important aspect in the move the front wheel [4, 11-15]. That is where the conditions require that the wheel when turning the wheel right and left wheels are not moving with the same angle. It is possible to avoid wheel slip or slide that led to unsafe conditions on the vehicle. The condition is called asymmetric Ackerman on vehicle conditions [4, 14, 15].

Many automotive companies create systems and methods in order to get perfection Ackerman conditions. Either by using a mechanical or electrical system by using the vehicle. Mechanical technology uses hydraulic power or so-called Hydraulic Power Steering (HPS) to facilitate vehicle in turn and electronic technologies is usually called Electric Power Steering (EPS). EPS was created to replace the old system that is Hydraulic Power Steering (HPS), this adds to the comfort in driving. In this paper we focus on electric golf LIPI was use manual steering for turn. The length of body electric golf car LIPI is not symmetrical between the right and left side as well as front and rear width. According that the electric golf car LIPI was unsafe and endangers passenger.

The kinematic dynamic method used solves the turn electrical car problem. In kinematic dynamic have several formula and theory, one of them was trapezoidal steering mechanism, that has been used for more than 100 years [16]. A correct condition for Ackerman or kinematic steering needed when the turning speed of vehicle is slow. While the turning speeds of vehicle fast, the significant lateral is needed. Furthermore, the loads on the inner wheels lower than the outer wheels. Tire performance curves show that the increasing wheel load, less slip angle is required to reach the peak of the lateral force.

2. Kinematic dynamic analysis

In the four-wheel steering system, there is a condition when the front wheels turn left or to right a condition in which the right and left wheels forming the same angle or both wheels to form a different angle from the corner of the wheel only. This condition is called Parallel conditions, Ackerman and Reverse conditions. However, the most favorable conditions to turn on the four-wheeled vehicle is Ackerman conditions as shown in Figure 1, because the

Fig. 1. By increasing the speed at a turn, parallel or reverse steering is needed instead of Ackerman steering.

Many companies in the world to create technology that allows vehicles to turn Ackerman perfect condition. But some are still using standard modeling system is the basis of all calculations Ackerman [16], that is:

cot So — cotSi = y (1)

where, Si is the steering angle of the inner wheel, and steering wheel angle So is the outside. Inner and outer wheel is defined based on the turning angle centered at O (see Figure 2). while w is the width of the car, and l is the length of the car.

Fig. 2. A front-wheel-steering vehicle and steer angles of the inner and outer wheels.

At the time of the vehicle should turn round the centre circle of radius R, which aims to determine how widespread the vehicle when turning or twisting. The shorter the radius R then the shorter or more narrow the distance needed to turn and rotate, but the length of the radius R, the more wide or wider spacing is needed to turn

and rotate the vehicle [16].

R = + 12 Coi2s (2)

= Ja[T~PCot% (3)

R2 = V«2 + l2Cot280 (4) where S is the average of the cot steering angle inside and outside. a was the width of the car.

~ cot So+cot Si

cot S = ----(5)

R2 = al + (6)

Cot S = Si (7)

= i(cot Si + cotSo) (8)

Resulting in a formula:

RMax = VCRMin + w)2 + (I + g¥ (9)

Therefore, the space required for spinning is a circle with a width R, which serves as the geometry of the vehicle. g distance front axle to the front of the vehicle. Thus requiring the formula:

AR = RMax - RMin (10)

= VC RMin + W)2+ (I + 5)2 - flMin (11)

Trapezoidal steering mechanism is a calculation that has been used for over 100 years. Rmax is the outer angle and Rmin is the inner angle for vehicle. In such a mechanism, there are two characteristic parameters, namely the angle p and the long arm offset d. It is used to describe the inner and outer steer angles Si and So. The relationship between the inside and outside steering angle trapezoidal formulated in a single unit [16], that is:

Sin(fi + Si) + Sin ( P — So) = -+ /(-- 2SinP)2 - (cos(P - So)- Cos (P + Si))2 (12)

To prove this equation, can be used triangle ABC, so that when formulated can be written:

(w - 2d sin p )2 = (w-d sinQS + Si)- d sin( p - So))2 + (d cos(fi - So) - d cos(P + Si ))2 (13) 3. Results and discussion 3.1. The angle and length of buffer

Electric golf car LIPI have the right length (L1) 176 cm, the length of the left (L2) 178 cm, width of the top (T2) 111 cm and a width of bottom (T1) 118.7 cm. Because the length of the car between the right and left of different sizes this calculation make midline from the car 177 cm and does not hit or interfere with other systems of the golf car. Graph angle is proportional to the length of the material can be seen in the picture. The smaller the angle the larger the lengths d are to be possessed by the connection. And the greater the angle, the smaller the length d is to be possessed connections. It is possible that this LIPI Electric Golf car can be a good turn without endangering shift at each wheel.

Form the Equation 2 and refer to the maximum angle turn at LIPI Electric Golf car an angle of 30°, presented turn angle diameter, Si and So shown in Table 1. The restrictions at maximum angle turn 30° because of the difference between the front and rear and the length of the right and left.

Table 1. Turn angle diameter, Si and So.

Angle Diameter Si So S

1° 998.6 1 1.0 1.0

2° 707.7 2 2.0 2.0

3° 539.1 3 2.9 3.0

4° 429.0 4 3.8 3.9

5° 351.5 5 4.7 4.9

6° 293.9 6 5.6 5.8

7° 249 7 6.5 6.7

8° 214.1 8 7.4 7.7

9° 185.2 9 8.2 8.6

10° 161.2 10 9.0 9.5

11° 140.9 11 9.8 10.4

12° 123.5 12 10.6 11.3

13° 108.3 13 11.4 12.1

14° 95.1 14 12.2 13.0

15° 83.3 15 12.9 13.9

16° 72.8 16 13.7 14.7

17° 63.3 17 14.4 15.6

18° 54.7 18 15.1 16.4

19° 46.9 19 15.8 17.3

20° 39.7 20 16.5 18.1

21° 33.0 21 17.2 18.9

22° 26.8 22 17.9 19.7

23° 21.0 23 18.5 20.5

24° 15.6 24 19.2 21.3

25° 10.5 25 19.8 22.1

26° 5.6 26 20.5 22.9

27° 1.0 27 21.1 23.7

28° -3.4 28 21.7 24.5

29° -7.6 29 22.4 25.3

30° -11.7 30 23.0 26.1

Fig. 3 (a) show that between angle 0 and 10 the difference was not visible at Si and So angle, but upper 10 degree, the Si and So distance very clearly presented. While S is the average angle of Si and So. the calculation turn angle in figure 3a similiar at Si and So with the Ackerman graph [16] in Fig. 3 (b). From the result, the safety and comfort electric car can be achieved.

50[deg]

34.4 22 9

w/10.5 ß = 6 dcg .--- "v.

w=2.4 m J n A m W -id

— / X

Ackerma

50[rad]

0 5 10 15 20 25 30 35 40 45 50

S/ldeg]

Fig. 3. (a). Turn angle diameter, Si and So; (b) Ackerman [16].

3.2. The length of R, R1, R2, Rmin and Rmax

The calculation of length R, R1, R2, Rmin and Rmax according to Equation 10 and 11, shown in Table 2. The maximum angle turn at LIPI Electric Golf car an angle of 30°. The theory show that the greater R create a greater turn distance.

Table. 2. The length of R, R1, Rmin and Rmax.

Angle R R1 R2 Rmin Rmax A R

1° 10,196.2 10,195.8 10,306.8 10,140.7 10,254 113.3

2° 5,124.9 5,124.1 5,235.1 5,069.4 5,184.9 115.5

3° 3,434 3,432.9 3,543.9 3,378.5 3,496.2 117.7

4° 2,588.2 2,586.7 2,697.7 2,532.7 2,652.5 119.8

5° 2,080.5 2,078.6 2,189.6 2,025 2,146.9 121.9

6° 1,741.8 1,739.5 1,850.5 1,686.3 1,810.2 123.9

7° 1,499.7 1,497 1,608 1,444.2 1,570.1 125.9

8° 1,317.9 1,314.9 1,425.9 1,262.4 1,390.3 127.9

9° 1,176.4 1,173 1,284 1,120.9 1,250.7 129.8

10° 1,063 1,059.3 1,170.3 1,007.5 1,139.2 131.7

11° 970.1 966.1 1,077.1 914.6 1,048.1 133.5

12° 892.6 888.2 999.2 837.1 972.4 135.3

13° 826.9 822.2 933.2 771.4 908.5 137.1

14° 770.5 765.4 876.4 715 853.8 138.8

15° 721.5 716.1 827.1 666 806.5 140.5

16° 678.6 672.8 783.8 623.1 765.2 142.1

17° 640.6 634.4 745.4 585.1 728.8 143.7

18° 606.7 600.2 711.2 551.2 696.6 145.3

19° 576.4 569.5 680.5 520.9 667.8 146.9

20° 529 541.8 652.8 493.5 641.9 148.4

21° 524.1 516.6 627.6 468.6 618.6 149.9

22° 501.5 493.6 604.6 446 597.4 151.4

23° 480.7 472.5 583.5 435.4 578.1 152.9

24° 461.6 453 564 406.1 560.4 154.3

25° 444 435.1 546.1 388.5 544.2 155.7

26° 427.7 418.4 529.4 372.2 529.2 157.1

27° 421.5 402.9 513.9 357 515.4 158.4

28° 398.3 388.4 299.4 342.8 502.6 159.8

29° 385.1 374.8 485.8 329.6 490.7 161.1

30° 372.7 362.1 473.1 317.2 479.6 162.4

In Table 2 show that the best R at the electric golf car was 372 cm while value of R1 refers to Equation 3 and value of R2 refer to Equation 4. Rmax is the outer angle and Rmin is the inner angle for electric cars in turn. Thus, in the calculation find the result geometri and kinematic with angle 30° electric car LIPI was safe and according category ideal.

4. Conclusion

The angle 0 and 10 the difference was not visible at Si and So angle, but upper 10 degree, the Si and So distance very clearly presented. The best R at the electric golf car was 372cm while value of R1 refer to equation 3 and value of R2 refer to equation 4. Rmax is the outer angle and Rmin is the inner angle for electric cars in turn. Thus, in the calculation find the result geometri and kinematic with angle 30° electric car LIPI was safe and according category ideal with Ackerman grap.

Acknowledgements

Thanks for Research Centre for Electrical Power and Mechatronics, Indonesian Institute of Sciences, Komplek LIPI Jl. Sangkuriang, Gedung 20, Lantai 2, Dago, Coblong, Bandung, Jawa Barat 40135, Indonesia, Yukhi Mustakim, Latief Rozaki, and Asep Nugroho.

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