The effect of the lead error on the load distribution and no-load drag torque in a double-nut ball screw

In a ball screw mechanism, the lead error is not only the key parameter to evaluate the precision, but also an important parameter to determine the load distribution. In this paper, a model is proposed to predict the load distribution related to the lead errors. The mechanical analysis of a double-nut ball screw is conducted to investigate the effect of the lead errors on the balls’ contact deformations and contact angles. Based on the Hertz contact theory, the equations to predict the preload and no-load drag torque are established, and the amplitude of the preload is obtained when the rotational speed is low. To verify the model, various experiments are conducted to measure the lead errors and the no-load drag torques of the ball screw by changing the screws with different accuracy levels. The experimental results show that the preload and no-load drag torque rise when the lead error increases in a double-nut ball screw. Besides, the relative errors between the experimental value and the theoretical value are less than 10%. This proves that the model can predict the preload and the no-load drag torque influenced by the lead error well, which is beneficial to the design of the double-nut ball screw for a certain preload.

Effects of supraspinal feedback on human gait: rhythmic auditory distortion

Background Different types of sound cues have been used to adapt the human gait rhythm. We investigated whether young healthy volunteers followed subliminal metronome rhythm changes during gait. Methods Twenty-two healthy adults walked at constant speed on a treadmill following a metronome sound cue (period 566 msec). The metronome rhythm was then either increased or decreased, without informing the subjects, at 1 msec increments or decrements to reach, respectively, a low (596 msec) or a high frequency (536 msec) plateaus. After 30 steps at one of these isochronous conditions, the rhythm returned to the original period with decrements or increments of 1 msec. Motion data were recorded with an optical measurement system to determine footfall. The relative phase between sound cue (stimulus) and foot contact (response) were compared. Results Gait was entrained to the rhythmic auditory stimulus and subjects subconsciously adapted the step time and length to maintain treadmill speed, while following the rhythm changes. In most cases there was a lead error: the foot contact occurred before the sound cue. The mean error or the absolute mean relative phase increased during the isochronous high (536 msec) or low frequencies (596 msec). Conclusion These results showed that the gait period is strongly “entrained” with the first metronome rhythm while subjects still followed metronome changes with larger error. This suggests two processes: one slow-adapting, supraspinal oscillator with persistence that predicts the foot contact to occur ahead of the stimulus, and a second fast process linked to sensory inputs that adapts to the mismatch between peripheral sensory input (foot contact) and supraspinal sensory input (auditory rhythm).