Model and algorithm based on accurate realization of dwell time in magnetorheological finishing

Abstract

Classically, a dwell-time map is created with a method such as deconvolution or numerical optimization, with the input being a surface error map and influence function. This dwell-time map is the numerical optimum for minimizing residual form error, but it takes no account of machine dynamics limitations. The map is then reinterpreted as machine speeds and accelerations or decelerations in a separate operation. In this paper we consider combining the two methods in a single optimization by the use of a constrained nonlinear optimization model, which regards both the two-norm of the surface residual error and the dwell-time gradient as an objective function. This enables machine dynamic limitations to be properly considered within the scope of the optimization, reducing both residual surface error and polishing times. Further simulations are introduced to demonstrate the feasibility of the model, and the velocity map is reinterpreted from the dwell time, meeting the requirement of velocity and the limitations of accelerations or decelerations. Indeed, the model and algorithm can also apply to other computer-controlled subaperture methods.

Deterministic measurement and correction of the pad shape in full-aperture polishing processes

“…The angle increment (ϕ) and the spiral path coefficient (b) should be set properly. Dwell time at each dwell point is the product of the dwell time density at the point and the area enclosed by the point, of which the former can be obtained by various algorithms [27,28] and the later by Eq. (8).…”

Dwell-time algorithm for polishing large optics

“…Therefore, the simulation experiment is usually adopted to verify the dwell-time calculation algorithm instead of the actual one [22,23,25,32]. In references [22,23,25,32], all the initial surface errors are measured from a real part to make the simulation process closer to reality.…”

“…The velocity distribution result has been carried out as shown in Fig. 7(b) based on the method reported in references [20,25]. In the velocity distribution results, the derived velocity which is larger than the maximum velocity of the machine, will be set as 250 mm∕s, and which is smaller than the minimum velocity, will be set as 1 mm∕s.…”

“…To achieve a high-accuracy surface, calculation of the dwell-time algorithm plays a crucial role during the process. Hitherto, many algorithms to optimize the dwell time of CCOS have been studied [2,[12][13][14][15][16][17][18][19][20][21][22][23][24][25] and are mainly based on two models, which are the discrete convolution model and the linear equation model.…”

“…Shi [24] chose an iterative method of a large sparse matrix to improve efficiency and accuracy. It is beneficial for realizing the large-scale numerical calculation and enhancing the feasibility of the solution, but it may lack a good balance between time and residual error [25]. Song et al [25] combined the realization of the dwell time to solve the linear equation, which makes it as accurate as possible when realizing the dwell time.…”