By John Wiltse
FLIR Systems, Inc.
In stabilized multi-axis gimbal systems, wire harnesses (needed to transmit power, communication, and video to and from the payload) can impart an undesirable torque to the payload. This torque couples the payload to the outer, unstabilized gimbal axes, and thus can cause line of sight jitter when the platform rotates. We us springs to cancel this wire torque and, in the ideal, results in a payload which has no wire torque coupling to the environment and thus has much lower jitter than ordinary gimbals.
Wires (for power, communications, and video) are a necessary part of any gimbal system. However, since wire harnesses have a nonzero stiffness, they necessary add a torque to the payload. This torque couples the payload to the outer (unstabilized) gimbal axes and creates line of sight jitter.
In William Hinks’ US20140265077 “Negative Spring Compensation for Elastomeric Bearing Torque” negative stiffness is used to overcome the torque inherent in elastomeric bearings. Hinks is directed towards helicopter rotor bearings, where the torque is too high to be actuated without hydraulic assist. We attempt to reduce (or even eliminate) the very low torque introduced by wiring in gimbal systems. Hinks mainly uses compression springs, such as buckled leaf springs. In this implementation, the counteracting torsional negative stiffness quickly goes nonlinear. This is acceptable for Hinks application, but for us it is critical that the counteracting torque be linear with angle, to more accurately cancel out the wire torque.
In Dijkstra, et al. US Patent 4,607,382 “Electroacoustic transducer unit with reduced resonant frequency and mechanical spring with negative spring stiffness, preferably used in such a transducer unit” magnets are used to provide a negative stiffness to isolate parts of a speaker. However, because magnets are used Dijkstra is also very nonlinear. In addition, Dijkstra deals with linear, not rotational, stiffness.
Figure 1 illustrates the various components of a gimbal. Here the inner elevation ring is attached to the outer elevation yoke through a set of fine ball bearings. The wire harness transmits power, communications, and video to and from the payload (payload is omitted for clarity). The inner elevation ring typically rotates a small amount, for example ±4°, with respect to the outer elevation yoke. The wire harnesses used to connect the gimbal to the payload can act as a torsional spring when they cross a fine axis (elevation or azimuth). They can thereby apply an oscillating torque to the payload by coupling rotations of the outer unstabilized axes to the inner stabilized axes. Since the payload is designed to be inertially stabilized (stabilized because no torques are acting on it), this can cause undesirable line of sight (LOS) jitter.
Since the outer axes (including the outer elevation yoke) are unstabilized, they can rotate with the aircraft. Assume the wire harnesses have a torsional spring rate (ozf-in/mrad). Also assume the outer axis is oscillating with a frequency f and a peak magnitude o. Then the torque applied to the payload is M1 = o**sin(2**f*t). The angular acceleration of the payload is
1̈=M1/J , or 1̈=θ∗k∗sin (2∗π∗f∗t)/J
where J is the moment of inertia of the payload. Integrating twice, 1=−θ∗k∗sin (2∗π∗f∗t)/((2∗π∗f)2∗J)
The peak-to-peak and r.m.s. motion of the inner axis become: 1−=2∗θ∗k/((2∗π∗f)2∗J) 1=0.707∗θ∗k/((2∗π∗f)2∗J)
As an example, assume J = 1 in-lbf-sec2, o = 5 mrad, =1.0 ozf-in/mrad, and f = 10 Hz. Then the rms jitter is 55 urad r.m.s.
For this reason, it is desirable to reduce or eliminate the spring torque rate contributed by the wire harnesses. Typically this is done by minimizing wire count, increasing the flexibility of the individual wires (for example, choosing a compliant insulating material) and minimizing the moment arm the force acts on.
Here we apply a spring force to counteract the torque applied by the wire harnesses. Figure 1 (rightmost) shows an example. A spring is connected to the inner ring via a linkage or stiff wire. The connection point is a distance d from the pivot point (bearing). The other end of the spring is connected to the outer yoke, also via a linkage or stiff wire. The connection point D is >> d so that the force F the spring applies is nominally parallel to the outer yoke for small relative rotation angles . When there is a relative rotation between the outer yoke and the inner ring , the force applied by a spring can be broken down into a component along the inner ring F*cos() and a component normal to the inner ring F*sin(). Using the small angle approximation, the normal force simply becomes F*. The moment applied is then –F*d*. Comparing this torque to that applied by the wire bundle, it can be seen that this will counteract the wire torque if F*d = .
Ideally, if F*d = then the jitter due to wire torque will be zero. Residual jitter will be due to nonlinear torques such as those from bearing friction. It may be necessary to tune the spring force F (for example, by using springs of different spring rates) on a unit-by-unit basis to optimize the performance.