핵심 단어: 토크; 비틀림 각도 비틀림 각도; 입자 이미지 속도계; 비틀림 강성 비틀림 강성; 심상; 토크는 엔진 설계부터 검증까지 폭넓게 사용되기 때문에 토크는 다양한 방법으로 측정되어 왔으며, 샤프트 비틀림 각도 측정은 필수적입니다. 지금까지 다양한 토크 측정 방법이 제안되어 왔으며, 본 논문에서는 시각화를 이용한 토크 측정 방법을 설명한다.
신뢰성이 높은 전통적인 토크 측정 방법은 접촉식입니다. 시각화를 통한 토크 측정 방식은 카메라를 사용하기 때문에 비접촉 방식이고 다양한 샤프트 직경에 사용할 수 있어 접촉 방식보다 활용도가 높습니다. 그러나 시각화를 통한 토크 측정 방법은 새로운 측정 방법이기 때문에 접촉 토크 측정 방법에 비해 신뢰성 평가가 미흡하다.
따라서 본 논문에서는 PIV를 이용한 가시 토크 측정 방법과 접촉 토크 측정 방법의 토크 측정 결과를 비교 분석한다. 핵심 단어: 토크; 비틀림 각도 비틀림 각도; 입자 프레임 속도; 비틀림 강성 비틀림 강성; 심상;.
Introduction
- Background
- Objectives
- Power Variable
- Torque Variable
- Torque Variable Formulation
- Shaft Torque Variable Formulation
A torque is a mechanical behavior which is created when a shaft turns in the direction of rotation. Therefore, if the rotation angle of the rotating shaft can be accurately measured, the torque can be measured with the material properties of the shaft. Thus, equation (2.4) is not sufficient to calculate the shaft torque and further formulation of the torque is required.
Before deriving the torque formula, it is important to find out the physical meaning of the twist angle in the axle system. Likewise, the arc length can be represented in relation to the radius(s) of the shaft and the torsion angle (). Using the angle information and equation (2.5), equation (2.6) can be derived, which is the equation for shear stress.
Since the integration part of equation (2.9) is 2nd moment of inertia, one can replace it with J and rearrange equation (2.9) to equation (2.10). Also, shear modulus in equation (2.10) can be related to the 2nd moment of inertia shown in equation (2.11).
Principle of Imaging Technique for Torque Measurements
Conventional Torque Measurement Systems
A piano tape is a distinctive reflective tape that allows the tachometer to read signals in steps. Using the method at the two end points of the shaft, one can determine the pulse time difference to find the rotation of the shaft. 5, the time difference allows the torsion angle to be calculated using the shaft diameter and shaft speed.
A vibrometer works in the same way as a tacho-meter; however, they are very advanced devices that can measure different vibrations on a shaft. Similar to tacho-meters that calculate the time difference to find the angle of rotation, a vibrometer also uses the time difference to calculate the angle of rotation. The disadvantage of these non-contact torque sensors is that it needs two optical sensors to calculate the rotation angle together with a calculation unit.
When the torsion angle of a shaft is desired, one must set up two optical sensors (tachometer or vibrometer) and then connect the sensors to the computing unit for data processing. The computing unit is then reconnected to the user computer for data transfer. Optical contactless torque sensors are difficult to use due to the many connections and multiple equipment.
However, non-contact type torque sensors are much more versatile than contact type sensors due to the fact that they can measure different diameters of shafts. Both contact and non-contact torque sensors have limitations on measuring torque, but the non-contact type has a more efficient measurement system. Therefore, this paper introduces a novel non-contact torque measurement system to overcome the limitations of conventional non-contact type torque sensors using an image technique torque measurement system.
Non-Contact Image Technique Based Torque Measurement
- Experimental Setup
- Experimental Procedure
- Image Technique Algorithm
In this experiment, it is important to synchronize the cameras to start recording, as a small delay from one camera would result in an incorrect torsion angle. This is problematic because as the rpm changes from 200 to 300 rpm, the torsion angle calculation becomes inconsistent. Therefore, to increase the accuracy of the torsion angle, a motor capable of supplying high frequency current is highly recommended.
Random pattern in image at 200 RPM is clearly visible, but random pattern in image at 1000 RPM is elongated. Because the PIV method used in this study measures the torsion angle by following a random pattern, the result may contain an error if the pattern is not very visible. Both the 200 RPM image on the left and the 1000 RPM image on the right show a visible random pattern with no elongated pattern.
As mentioned earlier, short exposure time is ideal for capturing visible random pattern; However, as the exposure time becomes shorter, the light received by the image sensor also becomes less. Inconsistent light intensity is not very ideal as it also creates errors in the torsion angle calculations. Then, the torsion angle calculated results using the PIV method are compared for each RPM case.
As a result, when the axis is rotated, the angle of rotation can be calculated from the displacement difference between the oscillating pattern and the position of the stored pattern. When the load is applied, two synchronized high-speed cameras capture the angle of rotation between the two positions. In this paper, to apply the PIV technique, the random axis model is applied.
As previously mentioned, PIV is used to calculate particle motion at the interrogation site. This means that particle motion is smaller than a pixel, and particle motion in the x and y directions is not visible for the cross-correlation calculation. In this paper, Equation (2.18) is used for subpixel interpolation, since the Gaussian method shows the best performance compared to the other two methods (Scarano 2002).
Experimental Results and Discussions
- Torque Transducer Measurement Results
- PIV Based Torque Measurement Results
- Measurement Results Comparison
- Relevance of Coupling Stiffness
- Revised Torsional Stiffness
- Power Results
Also, load 2 creates higher torque than load 1 since load 2 has more load on the axle than load 1. The graphs show that the left side of the axle is moving ahead of the right side of the axle. Now that the angle of rotation is derived from experiment, the torque applied to the shaft can be calculated.
According to equation (2.11), it is necessary to find torsional stiffness k, shaft length L, shear modulus of the shaft G and 2nd moment of inertia J variables. Since the material of the shaft is made of aluminum, the shear modulus is 77.2GPa or 772010MPa. Since all the unknown variables L, G and J exist, torsional stiffness can be calculated using equation (2.11).
By substituting the torsion angle and torsional stiffness into the equation, we can successfully calculate the torque. The reason for the large error in the torque magnitude is that only the torsional stiffness of the shaft is taken into account, and the torsional stiffness of the couplings in the shaft is omitted. Most shafts that are connected to motors or gears have couplings, and these couplings also have a torsional stiffness that takes into account the torsional angle in the shaft.
The shaft used in this experiment also has two couplings that connect the motor to the shaft, and the rotational stiffness of the two couplings must also be considered for accurate torque measurement. According to the highly flexible GKN STROMAG PERIFLEX VN DISC COUPLING product catalog by Stromag (2016), Stromag recommends that when calculating the torque with the coupling attached to the shaft, multiply 0.7 and 1.35 by the rotational stiffness of the coupling. Also, when the RPM is low and the load on the joint is weak, the rotational stiffness of the joint changes.
Therefore, to compensate for both cases, Stromag recommends multiplying 0.7 and 1.35 by the torsional stiffness of the attached coupling. According to EXPLANATION OF TECHNICAL DATA of Vulkan Couplings (2016) it states that in the case of low turning amplitude the torsional stiffness is "equivalent to 1.35 CTdyn". Vulkan Coupling (2016) also states that when considering temperature, the torsional stiffness is "equivalent to 0.7CTdyn".
Therefore, it is important to consider the torsional stiffness of the couplings to correctly calculate the torque on the shaft. Using the calculated results from the previous sections, the power applied to the shaft can also be calculated.
Conclusions
