Angle error compensation in wheel force transducer

Measurement 77 (2016) 203–212

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Angle error compensation in wheel force transducer Dong Wang a, Guoyu Lin a,⇑, Weigong Zhang a, Tao Jiang b a b

School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China Beijing Martial Delegate Agency, Beijing 100043, China

a r t i c l e

i n f o

Article history: Received 8 June 2015 Received in revised form 22 August 2015 Accepted 15 September 2015 Available online 21 September 2015 Keywords: Wheel force transducer Angle error Compensation algorithm Real vehicle test

a b s t r a c t Wheel force transducers (WFTs) have performance characteristics that make them attractive for applications in endurance evaluation of road vehicles, ride and handling optimization, tire development and vehicle dynamics. Since the WFT is mounted on the wheel and rotates with it, the rotational angle of the wheel is indispensable to calculate the real wheel forces. Unfortunately, an angle error caused by the steering of the vehicle will be incorporated into the measurement of the rotational angle, resulting in great error in the wheel force calculation. A new compensation algorithm is proposed in this paper to eliminate this angle error. In this algorithm, the GPS speed has been introduced to modify the measurement of the rotational angle in real time. Simulations with designed vehicle movement are carried out to demonstrate the effectiveness of the compensation algorithm. Furthermore, the results of real vehicle test show that this algorithm can be successfully used in practice to get more reasonable wheel loads. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Automobile test technology has been widely used in many fields, including the automobile manufacturing, the automobile performance test [1], the road test, etc. [2], where the wheel force is the key information for the vehicle design and test [3]. The wheel force is the result of the interaction of ground and wheel, which is necessary for improving the security and stability of the vehicle [4,5]. For example, the traction force is always used in the study on performance of the engine and brake, which is helpful to design an antilock brake system [6,7]. The positive pressure is the force of the ground on the wheel, which can be used in load spectrum analysis [8,9] so as to refine the design of suspension system [10]. Therefore, it is crucial to acquire accurate wheel force data for the development of high quality products in a reasonable time frame for car maker companies and system & component supply ⇑ Corresponding author. E-mail address: [email protected] (G. Lin). http://dx.doi.org/10.1016/j.measurement.2015.09.017 0263-2241/Ó 2015 Elsevier Ltd. All rights reserved.

companies [11]. The WFT has been designed and proven to be a cost and time effective tool for the need of wheel load data acquisition [12]. Fig. 1 shows the WFT and suitable wheel force signal processing system designed by Southeast University. As a multi-dimensional force sensor, the WFT is used to monitor wheel loads. However, differing from other multi-dimensional force sensors, the WFT is installed at the spindle of the wheel and rotates together with it during operation. Because of the rotation, the outputs of the WFT, which are in the wheel coordinate system, have to be transferred into the vehicle coordinate system in order to calculate the actual wheel loads. The rotational angle of the wheel, measured by an angle encoder, is needed to resolve the coordinate transform matrix. In practice, there are two kinds of installation for the encoders. One way is to fix the non-rotating side of the encoder on the suspension [13], and the other way is to fix the non-rotating side on the vehicle body. The two different ways make great difference if it comes to the measurement of the wheel rotational angle. Given that the non-rotating side of the

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Signal processing system WFT

Fig. 1. The first generation of the WFT designed by Southeast University.

encoder is fixed to the suspension, as shown in Fig. 2(a), the encoder is only sensitive to the rotation of the wheel. However, in certain circumstance, the non-rotating side of the encoder must be fixed on the vehicle body owing to the shortage of the installation space, as shown in Fig. 2(b). Then the encoder is not only sensitive to the wheel rotation but also to the wheel steering, which would introduce the ‘‘angle error” in the measurement of the wheel rotational angle during the vehicle steering. And the ‘‘angle error”, as will be noted in subsequent sections, might bring great error in the calculation of the wheel loads with the vehicle in motion, or even make the WFT ineffective. This problem was originally mentioned by Weiblen and Hofmann in 1998 [14], and the existence of the error in calculated wheel loads was verified experimentally by MTS tire test system [15], but unfortunately, it has not been well solved yet. Given the needs to the resolution of this pressing concern, this paper contributes to propose a new compensation algorithm that unconventionally uses the GPS speed to modify the output of the encoder. This proposed algorithm was validated by a series of numerical simulations and tested in the real vehicle experiment to evaluate effectiveness and advantage of enhancing the measurement accuracy of the WFT. The remainder of this paper is organized as follows. The principle of the WFT is given in Section 2. Section 3 elaborates the cause of the angle error and provides the solution to this problem. In Section 4, factors that could affect the

performance of the compensation algorithm have been analyzed through the numerical simulations. Section 5 presents a real vehicle test of the proposed algorithm, to further validate that the angle error caused by the vehicle steering can be practically compensated to obtain more reasonable wheel loads. Section 6 concludes the paper. 2. Principle of the WFT Data acquisition and data decoupling are two required steps for the calculation of the wheel loads. On the one hand, a rational structure design of the WFT would be of great help to collect the force data on the wheel [16]; on the other hand, with the wheel rotation, the output of the WFT and the real wheel loads would couple with each other, which makes data decoupling indispensable [17]. 2.1. Structure of the WFT A WFT is composed of elastomer [18,19] (Fig. 4(a)), electric bridge, encoder, sampling module (Fig. 4(b)), and transfer module (Fig. 2(c)) [20]. As shown in Fig. 3, the elastomer, electric bridge, encoder and sampling module are installed on the wheel and rotate with it, while transfer module is fixed on the vehicle body. First of all, the elastomer works as a sensing apparatus of the transducer, and the values of resistance strain gauges on it change with wheel loads [21]. The changes will be converted into

non-rotating side

non-rotating side

Encoder Encoder

(a)

(b) Fig. 2. Two installation methods of the WFT.

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electric bridge

elastomer

sample module

transfer module

encoder rotating part

non-rotating part

WFT

Fig. 3. The structure of the WFT.

Fig. 4. Important parts of the WFT.

differential voltage signals by the electric bridges. And the sampling module is used to sample those differential voltage signals and the encoder’s output, then package the data and send them to the transfer module wirelessly. The transfer module receives the data from sampling module and transmits them to the host computer by Ethernet, then the true wheel forces can be finally acquired from the host computer after data decoupling. 2.2. Decoupling algorithm As discussed before, it is critical to decouple the acquired data from the WFT to get the actual loads on a spinning wheel [22]. In the following sections, the vehicle body coordinate system ({oxyz}) is employed to develop the algorithm and calculate the real wheel forces, its origin o is located in the center of the wheel, the axis ox is pointing forward in the longitudinal, the axis oy is along the lateral and perpendicular to the ox axis, and the oz axis is in the vertical direction and perpendicular to the xoy plane to constitute a right-handed reference frame. This coordinate is fixed with the vehicle but not rotating with the

z’

x

z o

y o’ y’

x’ Fig. 5. Conversion of coordinate in the WFT.

wheel. Besides, a wheel coordinate system ({o0 x0 y0 z0 }) is defined to accord with the movement of the spinning wheel, which has the similar definition of ({oxyz}) as well as locates in the center of the wheel. The angular displacement of the wheel is symbolized by the angle a, as shown in Fig. 5. At the very beginning, the two coordinates coincides, and a equals to zero. When the vehicle is in motion, the wheel coordinate system rotates around the o0 y0 axis, and the transformation relation between the two coordinates is established in Eq. (1) [23].

2 3 2 32 0 3 x x cos a 0 sin a 6 7 6 76 7 1 0 54 y0 5 4y5 ¼ 4 0 z z0  sin a 0 cos a

ð1Þ

Assume that Fx (force along the ox axis) and Fz (force along the oz axis) represent the real traction force and positive pressure separately, which are defined in the vehicle body coordinate. Fx0 (force along the o0 x0 axis) and Fz0 (force along the o0 z0 axis) represent the outputs of the WFT. In its raw form, the data acquired by the WFT during vehicle motion is in the wheel coordinate and it must be processed to present the force transducer outputs in vehicle body coordinate. Based on Eq. (1), the relations between the outputs of the WFT and the real wheel forces are given in Eqs. (2) and (3)

F x ¼ F x0 cos a þ F z0 sin a

ð2Þ

F z ¼ F x0 sin a þ F z0 cos a

ð3Þ

3. Angle error compensation Since the measurement error of the rotational angle a has not been considered, Eqs. (2) and (3) are called the ‘‘ideal decoupling equations”. In actual fact, because of the restriction by the installation of the WFT, an angle error

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will be introduced with the steering of the wheel, which must be compensated to obtain real wheel loads. 3.1. The angle error model As shown in Fig. 6(a), since the non-rotating side of the encoder is fixed on the vehicle body, the output of the encoder (u) could be depicted as u = a + b, where b is the angle error caused by the wheel steering. Another coordinate system ({orxryrzr}) has been set up to calculate b. Its origin locates at the intersection of the axle and the shaft. The axis orxr is in the longitudinal to forward. The axis oryr is in the lateral, and the axis orzr is in the vertical direction. Note that in Fig. 6(b) (the abstraction of Fig. 6(a)), the triangle (A) and the circle (B) represent the fixed point of non-rotating side and rotating side of the encoder, respectively. Let the location of A be (xrf, yrf, zrf) and the distance from B to the origin or be a. If there is no steering, b equals to zero and B is just on axis oryr, and the output of the encoder could be calculated by Eq. (4). Otherwise, when the steering angle of the wheel around axis orzr is c, A stays still since it is attached to the vehicle body. In this case, B moves to B0 , and corresponding to Eq. (5), the output of the encoder (u0 ) changes with the steering. Note that in the whole processing, the wheel does not rotate, meaning the rotational angle a is constant, thus b can be resolved by Eq. (6).

zr

2

f u ¼ a ¼ arctan qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2

ð4Þ

xrf þ ðyrf  aÞ 2

2

zr

2

f ffi u0 ¼ a þ b ¼ arctan qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 r ðxf  a sin cÞ þ ðyrf  a cos cÞ2

ð5Þ

b ¼ u0  u

ð6Þ

3.2. Effect of the angle error Regarding the incorporation of the angle error b in measurement of the rotational angle, Eqs. (2) and (3) then turn

into (7) and (8), where the subscript e represent the wheel loads with angle error.

F xe ¼ F x0 cosða þ bÞ þ F z0 sinða þ bÞ

ð7Þ

F ze ¼ F x0 sinða þ bÞ þ F z0 cosða þ bÞ

ð8Þ

This change leads to errors of Fx and Fz in the vehicle body coordinate system. The relative error is gained by Eq. (9).

  DLw Lwe  Lw  100% ¼ Lw Lw

ð9Þ

‘‘Lw” is the ‘‘wheel load” (Fx, Fz) and ‘‘Lwe” signifies the ‘‘wheel load with error” (Fxe, Fze). In consideration of the involvement of the angle error b in the coordinate transformation, Eq. (9) has been adapted into Eqs. (10) and (11).

  DLwx Lwz ¼ cos b þ sin b  1 Lwx Lwx  100% x-direction

ð10Þ

  DLwz Lwx ¼ cos b  sin b  1  100% z-direction ð11Þ Lwz Lwz Fig. 7 visualizes Eqs. (10) and (11) for an angle error up to 20°, which covers most of the practical driving conditions. The parameter is the load ratio (Lwz/Lwx and Lwx/Lwz), ranging from 0 to 10. For negative error angles up to 20°, the values of relative errors have the same amount but are mirror-inverted to the line of b = 0. In Fig. 7, the load error is not only related to the angle error but also to the load ratio which is on account of Eqs. (10) and (11), and even small angle errors would result in large load errors. All of these facts highlight the necessity and significance of the angle error compensation algorithm. 3.3. Compensation algorithm In actual use of the WFT, the angle error described above is very difficult to be measured directly, due to the fact that the location of fixed point A in every vehicle is random and hard to be exactly identified in the coordinate ({orxryrzr}). Meanwhile, the indirect compensation method

zr fixed point non rotating side

A

zr

A (xrf, yrf, zrf)

knuckle

vehicle body B

or axle

yr x

encoder

r

a

xr

a

shaft

T WFT

a

wheel

or ’

B’

(a)

B

(b) Fig. 6. Installation of WFT.

yr

207

350 300 250 200 150 100 50 0 -50 -100 0

4

8 12 angl 16 20 0 e err or β (deg ree)

4

2

8

6

load ratio Lwz

10

load error z-direction (%)

load error x-direction (%)

D. Wang et al. / Measurement 77 (2016) 203–212

0 -50 -100 -150 -200 -250 -300 -350 -400 0

2

/Lwx

4

6

8 10 12 14 16 18 20

angle error β (de gree)

0

2

load

6

4

8

10

Lwz w x/

oL

rati

Fig. 7. Load error as function of angle error ß.

Step 1: Drive the vehicle in a straight line to get qev0, and let qwv = qev0; Step 2: Drive the vehicle in random route and measure qev in real time; Step 3: If: qev = qwv then go to Step 4, Else: modify the output of the encoder to satisfy qev = qwv, and then go to Step 4; Step 4: Calculate the wheel force, and then go back to Step 2.

speed is shown in Fig. 8, the solid line and the dotted line represent the vehicle speed and the wheel rotational speed, respectively, here, qwv = 1.317. The steering speed of the wheel is shown in Fig. 9(a). The steering angle, showing as the solid line in Fig. 9(b), can be obtained by calculating the integral of the curve in Fig. 9(a). And according to Eqs. (4)–(6), the consequent changes of the encoder’s output can be computed, goes as the dotted line in Fig. 9(b). Here, (xrf, yrf, zrf) = (0.35 (m), 0.05 (m), 0.70 (m)) and a = 0.40 (m), these parameters are set to approximate the real case of installing the WFT on a compact car. In accordance with the vehicle speed and the steering style depicted above, the route of the vehicle is shown in Fig. 10(a). Fig. 10(b) shows that when the vehicle moves in straight line, qwv equals to qev, and qwv changes when the vehicle make turns. Also, the real loads on the wheel are assumed as Fz = 21 kN and Fx = 3 kN for the positive pressure is much bigger than the traction force practically. Without the compensation algorithm, the wheel loads calculated by the WFT are far away from the real loads owing to the existence of the angle error, as shown in Fig. 11. Especially for Fx, the bigger the load ratio (Lwz/Lwx) is, the greater error of calculated wheel load would it bring in.

Numerical simulations are carried out to examine the performance of the proposed angle error compensation algorithm. The simulations consist of two segments. In Section 4.1, it is intended to establish an environment for testing the algorithm by a careful design of the vehicle trajectory. Section 4.2 analyzes the impact of sampling rate and sensor accuracy on the compensation algorithm so as to guide the future sensor selection. 4.1. Design of simulation environment In this paper, the vehicle runs for 40 s, including acceleration phases and constant speed phases. The vehicle

(m/s)

4. Numerical simulations

10

12

8

9.6

6

7.2

4

4.8

(o/s)

is much easier and feasible. It is known that the rotational speed of the wheel is proportional to the speed of the vehicle with the wheel on the ground, no matter whether it is steering. That is to say, the ratio qwv (qwv = vw/vv, where, vw is the rotational speed of the wheel and vv is the vehicle speed) is a constant. For determining qwv, vv can be conveniently derived from GPS, while vw cannot be measured directly. Comparing with vw, ve (the rotational speed of the encoder) is able to be calculated by the derivative of the encoder’s output easily. vw can be replaced with ve if the vehicle moves straight because in this situation, the encoder and the wheel undoubtedly have the same rotational speed, i.e. qev (qev = ve/vv) equals to qwv. However, if the vehicle makes turns, the rotational speed of the encoder is either faster or slower than the rotational speed of the wheel, in this case, qev does not equal to qwv. So, if qwv is obtained, the output of the encoder can be modified real-timely to satisfy the relation qev = qwv, and the angle error is able to be eliminated in this way. The specific approach follows the steps below.

Vehicle Speed Wheel Rotational Speed

2

0

0

10

20

30

t (s) Fig. 8. Speed of vehicle and wheel.

2.4

0 40

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D. Wang et al. / Measurement 77 (2016) 203–212 4

20

30

15

20

10

10

5

0

0

0

(o)

-2

( o)

steering speed ( o/s)

2

40

-4 -6

-10

Wheel Steering Angle Output of The Encoder

-10

-8

0

10

20

30

-20

40

0

10

-5

20

t (s)

t (s)

(a)

(b)

-10 40

30

Fig. 9. Steering of the vehicle.

1.325 ρwv ρev

straight

left turn

1.32

ratio

right turn

1.315

1.31

0

10

20

30

40

t (s)

(a)

(b) Fig. 10. Route of vehicle and the angle error.

4.2. Investigation of the factors of the compensation algorithm

Fx 10 5

Wheel Loads (kN)

As a matter of fact, different sensors vary in sampling rate and accuracy, both of which play roles in the system performance. Taking our research for example, the sampling rate of encoder is much higher than that of GPS, thus the output of the encoder cannot be modified at every sampling point of the encoder. At the same time, the accuracy of the encoder and GPS would also affect the result of the compensation algorithm. In this section, the impacts of the sensor accuracy and the GPS sampling rate on the proposed compensation algorithm will be tested under three separate scenarios. In scenario 1, the influence of the accuracy of the encoder will be first analyzed. Secondly, the wheel load errors with different GPS sampling rate will be simulated in scenario 2. Thirdly, scenario 3 is intended to show the wheel load errors caused by different speed measuring precision of GPS.

0 -5

Real Loads Calculated Loads

0

10

20

30

40

30

40

Fz 22 21 20 19

0

10

20

t (s) Fig. 11. The wheel loads with the angle error.

4.2.1. Scenario 1: the accuracy of the encoder In this scenario, the accuracy and sampling rate of GPS are set to 0.05 m/s and 10 Hz, respectively, so that the accuracy of the encoder is the only variable. As it is

believed that the accuracy of the encoder is dependent on its output digits. The common digits of encoders are 8 bits, 12 bits and 16 bits, corresponding to the accuracies

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D. Wang et al. / Measurement 77 (2016) 203–212

Fx 0.5

0.4

0

0.2

-1 -1.5

0

5

10

15

20

25

30

35

40

Fz

0.1 0.05

wheel load errors (kN)

wheel load errors (kN)

-0.5

0

Fx

0 -0.2 -0.4

0

5

10

15

20

25

30

35

40

Fz

0.04 0.02

5 Hz

10 Hz

20 Hz

0 -0.02

-0.05 -0.1

8 bits

0

5

10

15

20

12 bits

25

30

-0.04

16 bits

35

-0.06

40

-0.08

t (s)

0

5

10

15

20

25

30

35

40

t (s)

Fig. 12. Wheel load errors with different accuracy encoders.

Fig. 13. Wheel load errors with GPSs of different sampling rate.

of 1.4°, 0.088° and 0.0055°. Fig. 12 shows the load errors with different encoders, and Table 1 shows the statistics of the wheel load errors. From Fig. 12, we can see that the 12 bits encoder can truly reduce the maximum error of the wheel loads in comparison with the 8 bits encoder. However, the maximum error does not keep decreasing with increasing accuracy of the encoder. For instance, the wheel load errors curve of the 12 bits encoder almost coincides with the wheel load errors curve of the 16 bits encoder. This phenomenon has also been verified by the statistical properties in Table 1. Besides, seen in Table 1, the variations of the error variance follow the trend of the maximum error, while the mean error remains about the same under different encoders. That is to say, it is limited to reduce the error of calculated wheel loads by the usage of higher accuracy encoders. Since a 12 bits encoder is enough for our research, there is no necessity to pay high price for the 16 bits or even more accurate encoders.

4.2.2. Scenario 2: the sampling rate of GPS As it is mentioned above, the sampling rate of the GPS determines the modification frequency of the encoder’s output. The market is flooded with various GPS devices of different sampling rates, and commonly, higher sampling rate means higher price. Three typical GPS sampling rates are evaluated in this simulation, which are 5 Hz, 10 Hz and 20 Hz. Apart from that, the accuracy of GPS is set to 0.05 m/s and a 12 bits encoder is adopted. Fig. 13 shows the load errors with different sampling rate GPS,

and Table 2 shows the statistics of corresponding wheel load errors. Fig. 13 confirms decrease in the maximum error and error variance of the wheel loads with the increase in the GPS sampling rate. And similar with the results in scenario 1, different sampling rate of the GPS does not affect the mean error of the wheel loads, as shown in Table 2. Therefore, it is best to choose the GPS device with higher sampling rate as far as possible. 4.2.3. Scenario 3: the speed measuring precision of GPS The measuring precision of the GPS speed is crucial for the proposed compensation algorithm. On the one hand, it provides the reference speed to the whole system; on the other hand, the GPS speed error will accumulate to the rotational angle error, which has a great impact on the accuracy of the calculated wheel load. Thus the precision of the GPS speed should be guaranteed. The differential GPS can offer a measuring precision of the speed with 0.01 m/s in open space, but the precision drops with the reducing number of the available satellites. In this Scenario, three speed measuring precisions have been selected to perform the simulation, which are 0.02 m/s, 0.05 m/s and 0.10 m/s, the GPS sampling rate is set to 20 Hz, and the 12 bits encoder is adopted. Fig. 14 shows the load errors with different speed measuring precision GPSs, and Table 3 shows the statistics of the wheel load errors in this scenario. Fig. 14 and Table 3 imply that the GPS speed measuring precision is the key factor of the proposed algorithm,

Table 1 Statistics of the wheel load errors in scenario 1. Fx

Maximum error (kN) Mean error (kN) Error variance

Fz

8 bits

12 bits

16 bits

8 bits

12 bits

16 bits

1.2 0.048 0.048

0.63 0.049 0.013

0.63 0.048 0.012

0.098 0.013 8.6e04

0.051 0.013 2.1e04

0.05 0.013 2.1e04

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Table 2 Statistics of the wheel load errors in scenario 2. Fx

Maximum error (kN) Mean error (kN) Error variance

Fz

5 Hz

10 Hz

20 Hz

5 Hz

10 Hz

20 Hz

0.31 0.061 0.011

0.25 0.061 0.0054

0.23 0.060 0.0041

0.079 0.0090 2.3e04

0.049 0.0090 1.2e04

0.036 0.0088 8.8e05

measuring precision of speed, such as 0.02 m/s or even better, the compensation algorithm can significantly enhance the measurement accuracy of the WFT during the vehicle steering.

Fx

6 4

wheel load errors (kN)

2

5. Real vehicle test

0 -2 0

5

10

15

20

25

30

35

40

35

40

Fz

0.2 0 -0.2 -0.4 0.10 m/s

-0.6 0

5

0.05 m/s

10

20

15

0.02 m/s

25

30

t (s) Fig. 14. Wheel load errors with GPSs of different speed measuring precision.

mainly because the GPS speed is employed as the reference speed. For the GPSs with the measuring speed precision less than 0.10 m/s, the provided reference speed can hardly modify the encoder’s output, or even introduce bigger error to the system. In application of a GPS with high

In this section, a Mengshi Jeep has been chosen as the testing vehicle to evaluate performance of the angle error compensation algorithm [24]. The installation of the WFT is shown in Fig. 15, where, 1 represents the transfer module, 2 denotes the sampling module, 3 stands for the encoder, 4 symbolizes electric bridge, and 5 represents the elastomer. Both the WFT and GPS are mounted on the left front wheel. Guided by the analytical results of the numerical simulations, we adopted a 12 bits encoder in the WFT and a differential GPS with speed measuring precision of 0.03 m/s (20 Hz) to conduct the vehicle test. The vehicle path was recorded by GPS, as shown in Fig. 16, where the start is marked with a circle. The whole path can be divided into six segments. In segment I (0–9 s), the vehicle remained at rest. As shown in Fig. 18, the traction force (Fx) starts with 0, and the positive pressure (Fz) equals to a quarter weight of the whole vehicle approximatively. And in Fig. 17, qev is about zero since both the rotational speed of the encoder and the vehicle speed are zero. In segment II (9–27 s), the vehicle accelerated in a straight line.

Table 3 Statistics of the wheel load errors in scenario 3. Fx

Maximum error (kN) Mean error (kN) Error variance

Fz

0.10 m/s

0.05 m/s

0.02 m/s

0.10 m/s

0.05 m/s

0.02 m/s

4.9 1.3 1.8

0.32 0.04 0.013

0.22 0.02 0.0039

0.47 0.13 0.015

0.064 0.025 4.7e04

0.016 0.0034 2.8e05

4 1

2

GPS

3

WFT 5 Fig. 15. WFT assembly drawing.

D. Wang et al. / Measurement 77 (2016) 203–212 32.6469 32.6469

latitude

32.6469 32.6468 32.6467 32.6467 32.6467 32.6466

117.6898 117.69 117.6902117.6904117.6906117.6908 117.691 117.6912

longitude Fig. 16. Route of the vehicle.

15

I

II

III

IV

V

15

VI

10

5

5 GPS speed rotational speed of the encoder

0 -5

0

20

40

60

(°/s)

(m/s)

10

0

80

-5 120

100

3

ratio

2

X: 77.27 Y:: 1.283 Y

1

6. Conclusions

X:: 20.09 X Y: Y: 1.286

eev v

0

20

40

60

80

100

120

t (s) Fig. 17. The changes of the speed related parameters in real vehicle test.

10

20 whe wheel eel Loads without angle err error or compensati compensation on wheel whe eel Loads with angle err error or compensation

wheel loads (kN)

16

9 8

Fz

14

7

12

6

10

5

8

4

6

3

vehicle speed

2

4 2

1

Fx

0

0 -2

(m/s)

18

I

0

II

20

And along with the increase of the speed, qev tends to a constant (1.286), which will be assigned to qwv in the next. In segment III (27–75 s), the vehicle made successive ‘‘8 style” turns. As illustrated in Figs. 17 and 18 of this segment, the positive pressure increases yet qev decreases in left turns, for the WFT is installed on the left front wheel. After several turns, the vehicle ran straight in segment IV (75–80 s). As a result, qev converges towards qwv again, which is obvious in corresponding segment of Fig. 17. Another one and a half ‘‘8 style” turns occurred in segment V (80–108 s). Similarly with segment III, both qev and the wheel loads change with the steering of vehicle. The braking processing appeared in segment VI. This segment in Fig. 18 shows that the traction forces increase negatively in order to provide braking force for the vehicle. And because of the axle load shifting, the growing loads on the front wheels will induce the rise of the positive pressures. It’s worth noting that the dotted line in Fig. 18, lacking the compensation so that the traction force Fx stays positive during the test except for the braking phases, does not match well with the vehicle speed. In this circumstance, the obtained wheel loads are no way available for employment. What’s more, it is clearly in Fig. 18 that the wheel loads are more reasonable with the angle error compensated, and the negative traction force is effective in reducing the vehicle speed. In a word, the proposed algorithm is attested to be effective in the real vehicle test.

X: 111.5 111 Y: 1.285 1.28

0 -1

211

III

40

IV

60

80

V

VI

100

-1 120

The WFT is an important tool to obtain the wheel loads for automobile design and testing. According to its principle, the measurement accuracy of the wheel rotational angle should be guaranteed. In this paper, a new angle error compensation algorithm has been proposed to eliminate the angle error introduced by the steering of vehicle. In this algorithm, the rotational speed of the encoder has been checked with the GPS speed in real time in order to be further corrected, and such checking and correction loop make sure that the ratio between the rotational speed and GPS speed is a constant. With this approach, the measurement accuracy of the wheel loads can be greatly improved. Moreover, numerical simulations have been carried out to test the impact of the sensor sampling rate and precision on the compensation, in which the measuring precision of the GPS speed has been demonstrated to be the key factor. Furthermore, the algorithm is tested in a real vehicle experiment, and the practical results illustrate the operational effectiveness with superior accuracy of the propose algorithm.

t (s) Fig. 18. Calculated wheel loads in real vehicle test.

As the vehicle just started to move, both the rotational speed and the vehicle speed were quite small that an impulse of qev has been created, as shown in Fig. 17.

Acknowledgments This work was financed by Grant-in-aid for scientific research from Natural Science Foundation of China (Grant 51305078) and Suzhou Science and Technology Project (Grant SYG201303).

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