1、Accelerometer Principles
67 ratings | 4.01 out of 5
shift是什么意思| Print Documentgirlfriend
Overview
This tutorial is part of the National Instruments Measurement Fundamentals ries. Each tutorial in this ries will teach you a specific topic of common measurement applications by explaining theoretical concepts and providing practical examples. There are veral physical process that can be ud to develop a nsor to measure acceleration. In applications that involve flight, such as aircraft and satellites, accelerometers are bad on properties of rotating mass. In the industrial world, however, the most common design is bad on a combination of Newton's law of mass acceleration and Hooke's law of spring action.
Table of Contents
1. Spring-Mass System
2. Natural Frequency and Damping
3. Vibration Effects
4. Relevant NI Products
5. Buy the Book
Spring-Mass System
Newton's law simply states that if a mass, m, is undergoing an acceleration, a, then there must be a force F acting on the mass and given by 拉丁美洲人F = ma. Hooke's law states that if a spring of spring constant k is stretched (extended) from its equilibrium position for a distance Dx, then there must be a force acting on the spring given by F = kDx.
FIGURE 5.23 The basic spring-mass system accelerometer.
In Figure 5.23a we have a mass that is free to slide on a ba. The mass is connected to the ba by a spring that is in its unextended state and exerts no force on the mass. In Figure 5.23b, the whole asmbly is accelerated to the left, as shown. Now the spring extends in order to provide the force necessary to accelerate the mass. This condition is described by equating Newton's and Hooke's laws:
ma = kDx (5.25)
where k = spring constant in N/m
Dx = spring extension in m
m = mass in kg
a =顺利英文 acceleration in m/s2
日记用英语怎么说
Equation (5.25) allows the measurement of acceleration to be reduced to a measurement of spring extension (linear displacement) becau
If the acceleration is reverd, the same physical argument would apply, except that the spring is compresd instead of extended. Equation (5.26) still describes the relationship between spring displacement and acceleration.
The spring-mass principle applies to many common accelerometer designs. The mass that converts the acceleration to spring displacement is referred to as the test mass or i
smic mass. We e, then, that acceleration measurement reduces to linear displacement measurement; most designs differ in how this displacement measurement is made.
Natural Frequency and Damping
On clor examination of the simple principle just described, we find another characteristic of spring-mass systems that complicates the analysis. In particular, a system consisting of a spring and attached mass always exhibits oscillations at some characteristic natural frequency. Experience tells us that if we pull a mass back and then relea it (in the abnce of acceleration), it will be pulled back by the spring, overshoot the equilibrium, and oscillate back and forth. Only friction associated with the mass and ba eventually brings the mass to rest. Any displacement measuring system will respond to this oscillation as if an actual acceleration occurs. This natural frequency is given by
where fN = natural frequency in Hz 韩语我想你怎么说
k = spring constant in N/m
m = ismic mass in kg
The friction that eventually brings the mass to rest is defined by a damping coefficient , which has the units of s-1. In general, the effect of oscillation is called transient respon, described by a periodic damped signal, as shown in Figure 5.24, who equation is
XT(t) = Xoe-µt sin(2pfNt) (5.28)
where Xr(t) = transient mass position
Xo大多数英文 = peak position, initially
µ = damping coefficient
fN = natural frequency
The parameters, natural frequency, and damping coefficient in Equation (5.28) have a profound effect on the application of accelerometers.
Vibration Effects小区规划设计说明
gorgeous是什么意思
The effect of natural frequency and damping on the behavior of spring-mass accelerometers is best described in terms of an applied vibration. If the spring-mass system is expod to a vibration, then the resultant acceleration of the ba is given by Equation (5.23)
a(t) = -w2xo sin wt
If this is ud in Equation (5.25), we can show that the mass motion is given by
where all terms were previously denned and w = 2pf, with/the applied frequency.
FIGURE 5.24 A spring-mass system exhibits a natural oscillation with damping as respon to an impul input.
FIGURE 5.25 A spring-mass accelerometer has been attached to a table which is exhibiting vibration. The table peak motion is xo and the mass motion is Dx.
