- Introduction to acceleration sensors
I am working on my final year project which involves the use of the Nitendo Wii Nunchuk. The Wii Nunchuk operates based on a 3-axis accelerometer, a joystick and two push buttons. I carried out a small theoretical research on the accelerometer, and in this wiki page I am going to briefly explain what an accelerometer is, how it works, types of accelerometers, how to selection an accelerometer for a project requirement, and shows some applications of accelerometers.
Physically, acceleration is a vector quantity having both direction and magnitude that is defined as the rate at which an object changes its velocity with respect to time. It is a measure of how fast speed changes . An object is accelerating its velocity is changing. [1] In order to measure acceleration, an acceleration sensor called accelerometer is used. Accelerometer measures in units of g. A g is the acceleration measurement for gravity which is equal to 9.81 m/s². However, depending on altitude, this measurement can be 10 m/s² in some place. - Working principle of an accelerometer
The design of an accelerometer is based on the application of physics phenomenon. In aviation, accelerometers are based on the properties of rotating masses. In the world of industry, however, the design is based on a combination of Newton's law of mass acceleration and Hooke's law of spring action. This is the most common design applied to the making of accelerometers, and therefore, in this wiki page I will focus on explaining the accelerometer's working principle based on this combination of Newton's law and Hooke's law. Figure 1 shows a simplified spring-mass system. In figure 1a, the mass of mass m is attached to a spring at equilibrium position x0 which in turn is attached to the base. The mass can slide freely on the base. Suppose that the base friction is negligible. Figure 1b shows the mass is moving to the right by a displacement of Δx = x - x0. Since the mass is slowing down, the direction of acceleration vector is to the left. In this case, the mass is subject to the force according Newton's second law and Hooke's law.
Figure 1. A simplified spring-mass system accelerometer. [2]
Reprinted from Process Control Instrumentation Technology book
According to Newton's second law, if a mass, m, is undergoing an acceleration, a, then there must be a force, F, acting on the mass with a magnitude of F(N) = m(kg) x a(m/s²) (1)
Hooke's law states that if a spring of spring constant k is extended from its equilibrium position (x0) by a distance of Δx = x - x0 (x is the current position with reference to x0), then there must be a force acting on the spring given by F(N) = k(N/m) x Δx(m) (2) [2].
Equating equations (1) and (2) yields
m x a = k x Δx
<=> a = (k x Δx) / m (3)
where k is spring constant in N/m
Δx is the displacement in m
m is the mass in kg
a is acceleration in m/s²
Equation (3) shows the measurement of acceleration in relation to mass, spring constant and spring extension. This is equivalent to the the linear equation y = λ x where y represents acceleration a, λ = k /m being a constant, and x being the displacement of the mass. This is how the design of an accelerometer is based on. The design and types of accelerometer based on spring-mass system differ in how this displacement measurement is made, and this comes to discussion on section 3 of this wiki page. - Characteristics of spring-mass system based accelerometers
The equation (3) as a result of the analysis from figure 1 and b holds true on the assumption that there is no friction applied to the mass m. In practice, other factors have to be considered - Types of accelerometers
fdfdfdfdfdfd
fdfdfdfd
fdfdfd
fdfd - Selection of an accelerometer
fdfdfdfdfdfd
fdfdfdfd
fdfd - Applications of accelerometers
Accelerometers can measure: vibrations, shocks, tilt, impacts and motion of an object.
As a rule of thumb, in low-frequency applications (having a bandwidth on orders from 0 to 10 Hz), position and displacement measurements generally provide good accuracy. In the intermediate-frequency applications (less than 1 kHz), velocity measurement is usually favored. In measuring high-frequency motions with appreciable noise levels, acceleration measurement is preferred
...