William J. Nowak

A Parametric Approach To Mirror Natural Frequency Calculations

A hybrid analytical/graphical method is presented to calculate the fundamental natural frequency of rectangular mirrors mounted at 3 points. A NASTRAN assisted parametric approach was used to calculate the characteristic roots of the plate vibration equation for mirrors with aspect ratios ranging from 1.0 x 1.0 to 10.0 x 1.0. Also considered were simply supported boundary conditions at three mirror corner points or at two corner points on one edge and one point along the opposite edge. Experimental varification within 6.0% was achieved for the extreme case tested with approximately a +2.0% average experimental error overall.

Dynamic modeling and analysis of spinning polygon assemblies used in xerographic laser printers

This paper describes the application of the finite element method to calculate the dynamic response of a spinning polygon, motor, and motor housing used in xerographic printers. Initially, different levels of model sophistication were evaluated showing convergence to a representative model. Using the converged model, the dynamic response of the polygon mirror was evaluated from the effects of base excitation. Frequency correlation in the 0 to 1000 hertz range was demonstrated to be better than 10% when compared to a dynamic modal test. Mechanical gain correlation at the fundamental rotor resonance was of the same order as the modal test with amplitude variations attributed to the assumed damping of the model, and differences between empirical and analytical response locations. Conclusions and recommendations on future work are also cited.

Development of a precision high-speed flying spot position detector

The theory design and performance of a fast precision flying spot laser scanner position detector are described. Using Fourier analysis a sampling requirement has been derived that assures sufficient information is contained in the samples of the flying spot profile for accurate calculation of its centroid. The derivation shows that for accurate geometric moment determination sampling can be done at a rate lower than that required by the Whittaker-Shannon sampling theorem which applies to complete reconstruction ofthe distribution. A formula for the calculation of moments from the samples is given. A numerical analysis is performed to quantify the accuracy of the calculated first moment for non-ideal sampling conditions. The theory is applied to a laser beam position detector taking into account the irradiance profile the sampling aperture the number of samples required quantization and noise. The predicted performance is compared with experimental results. 1.

Parametric study of spinning polygon mirror deformations

This paper investigates the radial growth and facet surface distortion of spinning polygon mirrors used in xerographic laser printers. The general purpose finite element code MSC/NASTRAN is first validated with a closed form analysis of spinning disks and then used to predict the radial growth of a polygon as a function of facet number. Successive finite element calculations of facet surface distortion are then completed on polygons made of 6061 aluminum, ranging from 5 to 18 facets, 1.0 to 3.0 inches in inscribed radii, and 5 to 30 krpm in rotational speed. Using the data from these calculations, a series of parametric curves are developed plotting maximum surface irregularity vs. facet number for various inscribed radii and rotational speeds. Using these curves, an example calculation is detailed so future determination of radial and facet deformations under rotational loads is more readily available to the engineer. The paper also includes a spatial representation of deformed facet shape as a function of facet number, for a polygon with an inscribed radius of 1.5 inches and an operating speed of 30 krpm. Also discussed is the effect of center hole size on surface deformation for the 12 facet case.