A compound pendulum for thrust measurement of micro-Newton thruster

Abstract

A thrust stand is developed for testing micro-Newton level thrusters on the ground. The stand is composed of a compound pendulum that is symmetrically suspended by two thin beryllium copper strips, and it is precisely calibrated by gravity. The stiffness of the stand can be adjusted in 3 orders of magnitude by a counterweight. When the stiffness is larger than 1 Nm/rad, the stand demonstrates a fast response to thrust. The measured range of the stand reaches 1000 μN, and the noise is less than 0.1 μN/[Formula: see text] within 1 mHz–1 Hz. To calibrate the resolution of the stand, an electrostatic force is applied to the stand with an actuator. The equivalent thrust is determined to be 0.09 μN with a standard uncertainty of 0.02 μN. Using the stand, a micro-Newton colloid thruster is tested. The output of the colloid thruster changes with the applied voltage as 0.015(1) μN/V. When changing the voltage by 50 V, the change in thrust is measured to be 0.7 μN with a standard uncertainty of 0.1 μN.

Study of the Extremely Low-Frequency Noise Characteristics of a Micro-Thrust Measurement Platform

“…The MTMP core structure discussed in this paper is similar to two symmetrically arranged single-degree-of-freedom gravity pendulums. Figure 2 shows the schematic diagram of the gravity pendulum, which constitutes a typical second-order system whose mathematical equations can be described as follows [15]:…”

“…where I and θ represent the rotational inertia and angular change value of the pendulum rod, respectively; K represents the angular stiffness of the pendulum; λ is the damping factor of the system; and τ is the applied torque. When the thrust force is applied to the pendulum, the external thrust force can be introduced into the above-mentioned mathematical model, which is obtained [15]:…”

“…The Laser Interferometer Space Antenna (LISA) team designed a pendulum structure micro-thrust measurement device with a thrust test range of up to 1 mN, a resolution that can reach 0.1 mN, and a background noise in 0.01 Hz to 1 Hz that can be less than 0.1 µN/ √ Hz, and it was tested employing the cold gas thruster and field emission electric thruster [14]. Hao Xu of the Huazhong University of Science and Technology studied a micro-thrust measurement device belonging to the composite pendulum with a measurement range of 1000 mN, and a noise of less than 0.1 µN/ √ Hz in the range of 0.01 Hz to 1 Hz [15]. Chao Yang of the Institute of Mechanics, CAS, developed a torsion pendulum-type micro-thrust measurement device with a thrust range of 0 µN to 400 µN and a resolution of 0.1 mN, and the background noise power spectral density at 0.01 Hz to 1 Hz is better than 0.1 µN/ √ Hz.…”

Microgravity Decoupling in Torsion Pendulum for Enhanced Micro-Newton Thrust Measurement

“…Therefore, it is necessary to design a mechanism that amplifies the reference tilt angle, which can not only resolve the weak changes in thrust but also provide a good reference for the platform tilt and the direction of the gravitational field. Figure 7 shows a reference tilt amplification mechanism designed based on the inverted pendulum principle [19,20]. For the inclined inverted pendulum, considering only the balance between gravity and elasticity, the equation can be written as:…”

An Improved Analytical Model of a Thrust Stand with a Flexure Hinge Structure Considering Stiffness Drift and Rotation Center Offset

“…Stefano et al use flexure hinges with symmetrical semicircular notches to connect the "tilt plate" to a rigid block [27]. Xu et al choose a beryllium copper strip hinge as the rotating mechanism with a length of only 1 mm to avoid uncertainty in the position of the rotating axis [28]. Nevertheless, almost all thrust stand designers utilize only an equivalent spring with constant K to characterize the flexure hinge in their analytical models, and few have investigated the mechanical properties of the hinge as operating conditions change.…”