Effect of Assembly Errors on Position Accuracy in a Rotary Magnetic Recording System

A rotary magnetic sensing system, which consists of a patterned ferrite-magnetic (FM) ring, a set of magnetoresistors (MRs) and a signal-processing unit for generation of position information, is commonly used in rotary stages or motors for position control. The magnetic signal for positioning can be generated by excitation coil [1], [2] or polarities [3], [4] from FM medium. The $2 ^{nd}$ method is the focus of this paper in which the alternative polarities are made through perpendicular magnetization over the FM ring; from which magnetic signals the anisotropic MR sensors can then generate position signal based on measured magnetic profile from the FM ring. Several factors that may affect overall accuracy of the rotary platform. Firstly, position accuracy is determined during pattern writing process caused by assembly errors between writing head and the FM ring in the magnetization platform. Another crucial factor for pursuing high precision magnetic sensing accuracy is the geometry tolerance such as roundness, isotropy and homogeneity of the FM ring. Besides, errors induced by assembly between the FM ring and the MRs would lead to signal distortion [5]. A MR sensor discussed in this paper consists of two sets of Wheatstone bridge; each bridge contains four MRs that are stacked in quarter period of polarity. According to the principle of MR output signal, the magnitude and magnetization angle of magnetic flux originated from patterned media would induced the resistance changes of MRs packaged in a sensor. Namely, different magnitude and magnetization angle of magnetic flux distribution can lead to different output voltages. When two sets of Wheatstone bridges are properly arranged in the moving read head, output signals can be generated in form of sine and cosine waveforms from which a Lissajous graph can be depicted for positioning feedback. With perfect sine and cosine waveforms, an ideal Lissajous graph is a perfect circle. By dividing Lissajous graph into equivalent divisions, higher resolution can be achieved. The difference between ideal and distorted Lissajous graphs can then be used to determine position error [6]. The inevitable assembly error of MR sensor in manufacturing can cause the angle between magnetization vector and magnetoresistance to vary, which directly affect the resistance value, resulting in imperfect sinusoidal output voltage, which then becomes an obstacle for increasing resolution and position accuracy. Effect of assembly errors including eccentricity I1, offset I2 from rotary platform's rotation center, and pitch, roll, yaw errors of the MR sensor read head relative to the surface of FM ring as depicted in Fig. 1 will be discussed in the context of position accuracy through a commercial available FM rotary scale. The commercial FM rotary scale has pre-magnetized 256 polarities mounted on a precision rotary platform. The assembly errors can be categorized to eccentricity between rotary stage and the FM ring and the assembly errors due to sensor itself are shown in Fig. 1(a) and Fig. 1(b), respectively. The Os and Oe represent the center point of rotary platform and rotary scale. l1 and l2 respectively represent the eccentricity between rotary platform and magnetic ring and eccentricity between sensor and rotary platform. Both experimental and analytical approaches are conducted in this study. In the experiments, this FM ring was first assembled with least eccentricity by calibrating with high-resolution digimatic indicator, leading to minimum eccentricity l1. To investigate the effects of assembly error of sensor on accuracy, the MR sensor read head was fixed on a linear precision stage, which was aligned with the centerline of rotary platform. As such, the eccentricity l2 could be known from the linear precision stage. In the analytical method, magnetic flux density distribution of the rotary scale with assembly error is obtained through 3D finite-element simulation. By putting the simulated outputs into flux density and circuit voltage equations, the output of the MR sensors in the read head can then be attained. The sensor assembly offset error discussed in this study is set from 0 mm to 0.5 mm with step of 0.1 mm, and rotational assembly error such as pitch, roll and yaw error are both ranged from 0° to 2° with step of $0.2 ^{circ}$. Fig. 2(a) shows the simulated accuracy distribution at 0.2 mm flying height over three polarities on stack lines by y offsets plot with offset of read head ranging from 0 mm to 0.5 mm. At different offset, the distribution of accuracy is found to shift to the left side as the offset is increased. The simulated accuracy errors caused by assembly error of read head including pitch, roll, and yaw errors are shown in Fig. 2(b). The result of pitch error percentile is marked on left vertical axis, whereas roll and yaw error percentiles are indicated on right vertical axis. It is found that pitch assembly error up 2° contribute more significant effect on accuracy error caused by roll and yaw assembly errors. The pitch assembly error can worsen accuracy nearly 115% relative to perfect assembly. On the other hand, degradation of accuracy caused by roll and yaw assembly errors is found only 6.4% and 3.5%, respectively relative to perfect assembly.