Angle error compensation in wheel force transducer
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 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 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.
Section snippets
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].
Angle error compensation
Since the measurement error of the rotational angle α has not been considered, Eqs. (2), (3) are called the “ideal decoupling equations”. In actual fact, because of the restriction by the installation of the WFT, an angle error will be introduced with the steering of the wheel, which must be compensated to obtain real wheel loads.
Numerical simulations
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.
Real vehicle test
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
Conclusions
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
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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