The mathematical model for lateral stiffness of variable length conical spring

Abstract

One form of energy storage in spring is applying a bending moment and converting it into tilt at the head of the spring as strain energy. The relationship between them is the lateral stiffness of the spring. The aim is to find a mathematical equation for the lateral stiffness of the spring and the effect of the length of the spring on the behavior of stiffness. The mathematical model is created according to Castigliano’s second theorem. A simulated model of a conical spring is built using a Solid Work program. The theoretical results are compared with the mathematical model for the same conical spring. Results of both theoretical and simulated models evinced a linear behavior of lateral, while an exponential relationship between the length of the spring and the lateral stiffness is indicated. The difference between theoretical and simulated models is not exceeded 3.2%, which indicates the acceptability of results.

Implementation of Kalman filter algorithm to optimize the calculation of ultrasonic sensor distance value in Hooke law props system

“…In paper [9,10] digital distance measurement using ultrasonic sensors can be applied in Hooke's law measurement systems to produce more accurate measurements. Apply the paper concept of Hooke's Law [11][12][13][14][15] in digital measurements that can affect the calculation of the value of the spring constant, and the spring increases in length to some extent when subjected to force. The magnitude of the force applied is proportional to the increase in the length of the spring and the ratio is constant [11], as in paper [12] the longer the spring means the greater the force applied.…”

“…The magnitude of the force applied is proportional to the increase in the length of the spring and the ratio is constant [11], as in paper [12] the longer the spring means the greater the force applied. The application of varying forces to a material will affect the effect of elasticity of objects [13]. The character of the material in the paper [14] is determined by the stiffness properties of the material discussed in Young's Modulus principle.…”

“…In general, all equations that have been modified can be stated for the prediction stage shown in equations (10), and equations (11), and the correction (update) stage is shown in equations (12), equations (13), and equations (14).…”

“…The equation is to reduce the output of ultrasonic sensors in noise filtering when modifying the state transition matrix Ft = 1. The noiseless filtering output of the Kalman filter is obtained from the calculations of equation ( 12), equation (13), and equation ( 14).…”