tailieunhanh - Rotating Machinery Vibration 2011 Part 8

Tham khảo tài liệu 'rotating machinery vibration 2011 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Bearing and Seal Rotor Dynamics 155 a y Ay 0 0 y-displacement perturbation about equilibrium a y AÁ 0 A-velocity perturbation about equilibrium a y 0 Ay y-velocity perturbation about equilibrium . Perturbation Sizes Because of the highly nonlinear nature of Eqs. 6 special care must be taken when computing the numerically evaluated partial derivatives in Eqs. 4 . That is each of the displacement and velocity perturbations Aa Ay Ai Ay must be an appropriate value . not too large and not too small for the particular equilibrium condition to ensure reliable results. This point is apparently not adequately appreciated by some who have developed computer codes to perform the calculations implicit in Eqs. 4 . The author s approach while possibly not original is explained as follows. For the sake of explanation it is assumed that the individual computations are accurate to eight significant digits. The basic approach is to program for automatic adjustment of each perturbation size based on the number of digits of agreement between unperturbed and perturbed force components. This approach is quite versatile and can be calibrated for any specific application involving the computation of derivatives by numerical differences. The author has found the following guidelines to work well. If the difference between the unperturbed and perturbed force components originates between the third and the fifth digit the perturbation size is accepted. If the difference invades the first three digits then the particular perturbation is reduced by dividing it by 10. If the difference originates beyond the first five digits then the particular perturbation is increased by multiplying it by 10. In this manner the displacement and velocity force derivatives are tangent not secant gradients and are accurate to at least three significant digits. This is enumerated by the following. F a y 0 0 X 10 unperturbed force component 7ỷ A y 0 0 AF b-Ịbs X 10 .