Test and Measurements conference 2016 DESIGN AND DEVELOPMENT OF FREE FALL ABSOLUTE GRAVITY MEASURING SYSTEM USING PNEUMATIC ACTUATORS Author: T Mokobodi Supervisor: Prof N Theron Co-authors: Oelof Kruger, F Hungwe National Metrology institute of South Africa Private Bag X34, Lynnwood Ridge, 0040, South Africa Email: dmokobodi@nmisa.org Phone: +27 12 841 3057 Academic Institution: Department of Mechanical and Aeronautical Engineering Abstract Gravitational force and acceleration measurement devises have been in continuous development with the objective to improve the method for realizations of the gravitational acceleration measurand accurately. The accuracy requirements from the field of metrology, geodesy, geophysics and mineral exploration led to these developments. In metrology, knowledge of gravitational acceleration is required in force and pressure calibrations which are linked to SI base units. Redefinition of SI base unit of kilogram also requires accurate measurements of gravitational acceleration, which is tied to the standard SI units of length and time. Length and time measurement must be achieved with error of 10-9 or less to comply with the requirements in metrology. Experiments are performed using free fall gravimeter using 633 nm wavelength He-Ne laser with the Michelson (improved) interferometer setup to achieve these requirements. This paper discusses the method of direct free fall gravimeter designed and developed at the National Metrology Institute of South Africa using a simplified launching and capturing mechanism in the rotating vacuum chamber. Numerical simulations and signal processing method along with their results are discussed. The results of initial prototype are presented and discussed along with projected system improvements in working toward fully functional system, the average error of the prototype is found to be 5 parts in 10 4. Keywords: Gravitational acceleration, Pneumatics, Chirp signal, Signal processing, traceability, light intensity 1 Introduction Gravimeters are the equipment used to measure gravitational acceleration g or gravitational force F g. They are categorized in two groups based on how they achieve measurements, these are: absolute and relative gravimeters [1]. Absolute gravimeters uses the International System (SI) base units of length and time standard to define the derived SI unit of acceleration (units in m/s 2 ) and relative gravimeters uses spring force balance to measure the gravitational force (N) [2]. The absolute gravimeters consist of pendulum and free fall types, and relative gravimeters consist of spring and superconducting types [3]. Many fields of scientific researches requires knowledge of gravitational acceleration or force to undertake their mandates, and in metrology the absolute measurements of gravitational acceleration are used because of the direct traceability to the SI base units, while in geophysics and geodesy relative measurements are preferred as the interest of these 1
fields deals with comparison of gravitational value from location to location and the changes in gravitational value [4]. The methods of absolute gravimeters are evaluated on the bases of the accuracy and uncertainty measurements. The free fall gravimeters are adopted for development in metrology due to their improved measurement accuracy [5]. The pendulum gravity meters measures were limited to accuracy of 10-4 m/s 2 and free fall gravimeter measures with accuracy of 10-9 m/s 2 ( and still in improvement) [6]. National Metrology Institute of South Africa (NMISA) falls under the branch of metrology, and absolute gravitational acceleration measurements are required to enable the fulfillment of the institution s mandate in the calibration of force and pressure measurement equipment, and in kilogram redefinition project. 2 Free fall gravimeters In free fall gravimeter methods, a test mass is allowed to undergo free falling motion in the direction of gravitational plumb line, and the position and time coordinates of the test mass are measured during trajectory period [7]. These measurements are performed using the principles of light interference, in which He-Ne with wavelength of 633 nm red laser is used to measure length travelled by the test mass [8] [9]. These types of gravimeters consist of four major components which enables their functionality, these are: vacuum chamber, test mass, interferometer and isolation system. The vacuum chamber is used to create a vacuum space to reduce or eliminate the effect of the air resistance on the test mass, that is the test mass is launched inside the vacuum chamber. Measurements are performed by laser interferometer (Michelson interferometer). The Michelson interferometer has an optical setup which the interference of light is achieved by division of amplitude principles [10] [11]. The basic setup of the Michelson interferometer is shown in Figure 2-1. Figure 2-1: Basic optical setup of Michelson Interferometer In the setup of Figure 2-1 the beam splitter is used to divide the beam incident from the laser head into two equal parts (50/50 beam splitter) one beam travels to the reference mirror and one travels to the measuring mirror. Both the mirrors reflect the beams back to the beam splitter, the two beams are superimposed and interference takes place, the resulting interference beam is directed to the photo detector which enables the measurements of length. The method in which the length measurements are performed from detected interference fringes which these are counted is shown in Figure 2-2 and discussed processing paragraphs [12] The Michelson interferometer used in the gravimeters perform measurements of length using the intensity distribution of the interference which resulted from the beam splitter after the interference, the reference mirror is placed in a displacement vibration isolating system against seismic and human induced vibration to prevent It from any form of excitations[13]. The interference signal produced depends on the change in displacement of the measurement mirror. At the interference site, the two beams results with a signal that has variable intensity distribution as a result of moving test mass, which gives direct relationship between the phase difference of the two beams (waves) and the change in displacement of the measurement mirror [14]. The phase difference of the two signals and measurement mirror displacement relationship is shown by equation (2-1) below. (2-1) 2
( ) ( ) (2-2) Figure 2-2: Fringe signal generated and the light intensity diagram as mapped by the detector and converted into electrical signal (Voltage). Interference is observed through dark and bright light bands fringes formed at the interference site, in constructive interference a bright red band fringe is observed (maximum voltage ) and in destructive interference a dark fringe (minimum voltage ) refer to Figure 2-2. The free fall gravimeters have two general system configurations, the direct free fall, and rise and fall configuration [3]. The four major components discussed above are found in both direct, and rise and fall configuration. In the direct free fall, test mass is released in the vacuum chamber at the higher elevation from rest to undergo free fall and it is captured at a lower position. Rise and fall gravimeters releases the test mass by launching it up with initial velocity, the test mass undergoes free fall, decelerate, reaches the apex and drop back to the launching mechanism where it is captured [15] [16]. The position-time graphs of the test mass of the two configurations are shown in Figure 2-3 below with the equations of calculating gravitational acceleration for each configuration. (a) ( ), ( ) ( ), ( ), ( ) (b) Figure 2-3: Falling distance z vs. time graphs for a) Direct free fall and b) Rise and fall (2-3) In the search for high accuracies of the two configurations, both methods are comparable with uncertainty errors of few parts in 10 9 or less. At NMISA direct free fall configuration has been designed and developed with a new method of repositioning the test mass in the vacuum chamber. The design is projected to use traditional methods of displacement isolation (active isolation) and the interferometer setup. The design of the vacuum chamber is described in the next chapter. 3 NMISA DFFG-01 3.1 Design overview The NMISA DFFG-01 is the first free fall gravimeter designed within the institution. The project is aimed to form the supporting integral for force and pressure lab calibration functions and to enable local gravitational acceleration measurements required in the project of the watt balance. Watt balance is the potential method identified to be solution in the redefinition of SI base unit of mass, kilogram, which the electrical and mechanical force are balanced to enable mass measurements [17]. The vacuum chamber designed is fully pneumatic powered, test mass launching, capturing, aligning and reposition are achieved by pneumatic actuators. The design of the vacuum 3
chamber resulted with the design the symmetric double sided test mass mounted with two prisms to enhance measurements process. The design overview of NMISA DFFG-01 is shown in Figure 3-1 below 3.2 Mathematical modeling In the derivation of gravitational computation model, Newton s equations of motion are adapted to derive evaluation equations, the equation is given below (3-1) Where represent acceleration of the falling mass in the z direction and it is defined by integrating equation (3-1) above, equation (3-2) is derived, to solve the displacement of the falling objects, the equations (2-2) and (2-3) in chapter 1 can also be derived. ( ) (3-2) ( ) Figure 3-1: Vacuum chamber structure of the NMISA DFFG-01 The test mass is launched using simple pneumatic grippers, releasing the test mass with no initial resultant force in the direction of gravity plumb line, as the grippers jaws releases symmetrical in the direction perpendicular to the falling direction, and resulting with zero force applied to the test mass during instant of launch in any direction, refer to Figure 3-2 below Figure 3-2: Test mass gripper jaws The repositioning of the test mass to enable continuous gravitational measurements is performed by full 180 0 rotation of the vacuum chamber using rotating actuator indicated in Figure 3-1 [18]. The gravitational gradient term is given by the accepted value of [19]. When measurements are performed over short falling distance, the gravitational gradient is negligible, and the derived equation above is written as ( ) (3-3) 3.3 Simulations and processing The numerical simulations were performed using Matlab programming software, the simulations performed are parameterized by the equations of motions, prototype physical structures and dynamic constrains of the test mass [20]. To test the algorithms of gravitational acceleration calculation, the voltage signal of the practical ideal signal was produced with induced noise to the signal and test the algorithms used in processing. A chirp signal with linear continuous frequency gradient increasing with projectile time was generated and is it is represented by ( ) { [ ( ) ] } (3-4) The free fall gravimeters are supported by the use of electronic devises which enables signal detection, storage, digitizing and processing [21]. The interference signal produced by the interferometer is detected using photo diodes which convert the light 4
intensity into voltage signal. Where constructive and destructive interference bands corresponds to the high and low voltage respectively as shown in Figure 2-1 are accurately mapped. Analog to digital convertor (ADC) card is used to discretize the intensity signal to a digital signal to enable numerical computation in post processing using microcomputers. The ADC card is locked to the time (real time) standard which the signal is produced in real time. The zero crossing processing method is used to detect the zero crossing points of the intensity signal, the processing coded detects the time when the signal crosses zero voltage line, this checks the sign change of the voltage value [22]. By detecting these points accurately, using theory of interference, as shown in chapter two of this article, displacement coordinates are determined to resolution of and the resulting data consist of time and displacement coordinates after the zero crossing detection. This method is shown in Figure 3-3 below digital ADC algorithms. From these calculations, the terms of equation (3-4) are determined. Using calculated terms, equation (3-4) is used to generate the signal to be processed. The ideal pure voltage signal was also produced. The signal processing method were applied to the signal and the final computed gravitational acceleration is found to be 9.7860985 0.0000005 m/s 2, the error introduced in numerical computation of the pure generated signal is related to the number accuracy of the software. Noise was added to the ideal voltage signal to practicalize the signal and test the processing codes and the signal processing codes used in ideal voltage signal processing were used, noise magnitude added to the coded equals the collective sum of components used in the signal acquisition. The results are indicated in the table below Table 4-1: Simulation data with added noise Data parameters Parameter value [m/s 2 ] Average 9.7860985 Average total error 8.06286x10-8 Average Standard deviation 6.78607x10-7 Figure 3-3: Zero crossing signal processing method 4 Simulations results The parameters of the simulations were set to denote the parameters of the vacuum chamber. The dropping height vacuum chamber is 0.3 m, and absolute vacuum is assumed in the chamber. The equations used to set up the dynamic parameters of test mass (4-1) (4-2) The current measured gravitational acceleration value of 9.7860985 m/s 2 is used as the ideal measurand (this values is taken from force and pressure lab NMISA as measured by council of geoscience Pretoria in 1999), using equations (4-1) are (4-2), height and current gravitational acceleration value, and time of the flight is computed. The final time is divided by the sampling rate of the ADC to give the sampling points of the 5 Prototype results The NMISA DFFG-01 prototype results discussed in this paper are taken from sample size of 20 drop measurements performed in two different vacuum chamber pressures each, atmospheric pressure and 50 Pa pressure. The summary of the results are shown in tables Table 5-1 and Table 5-2 below. Table 5-1: Atmospheric pressure gravitational drops Data parameters Parameter value [m/s 2 ] Average 9.7804036 Average error 3.58x10-4 [-] Standard deviation 5.04x10-3 The vacuum pressure used was due to limitation in the pump used. 5
Table 5-2: 50 Pa vacuum pressure gravitational drops Data parameters Parameter value [m/s 2 ] Average 9.79059905 Average error 2.19x10-4 Standard deviation 2.58x10-3 The effect of the pressure is observed as the gravitational acceleration increases with low pressure in the vacuum chamber. 6 Conclusion After performing numerical simulations on data generated using Matlab, the decision to implement these numerical codes as major processing codes for the prototype was taken. As the prototype is the first design ever constructed NMISA using free fall, these will serve as primary software codes for numerical computations. The NMISA DFFG-01 is aimed to be part of the development in the support of the redefinition of kilogram project. The results discussed above are the measurements taken using the initial prototype. Looking at the results, it is observed that pressure plays a very crucial part in the direct free fall gravity meter, and future projected objectives to improve the vacuum chamber and attainable vacuum would benefit in improvement results. The current results as compared with the force lab currently used gravitational acceleration shows an error of 5 parts in 10 4, this error is aimed to be reduced in the projected continuous development of this invention. This project displays the positive results as the measurands of the drops are with 3 decimals of accuracy with what has been measured in the past. The differences will be compared in continuous development. 6
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