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We establish a robust algorithm to analyze the influence of system uncertainties on the transmission error of a spur gear pair under 2D simplification. The algorithm provides a way of generating smooth cutter profiles with machining uncertainties and measuring the thermal deformation through the uncertainties in material properties. Then, it produces realizations of gear tooth profiles based on the analytical method for accuracy and computational efficiency. Numerical investigations show the statistical analysis on the tooth contact analysis by comparing steel and plastic gears. It is worthwhile remarking that the plastic gear is susceptible to the geometric error caused by thermal deformation. Moreover, although the impact of thermal deformation on steel gear may seem slim, it can have a noticeable influence when it exists with mechanical uncertainties together. [ABSTRACT FROM AUTHOR]

We establish a robust algorithm to analyze the influence of system uncertainties on the transmission error of a spur gear pair under 2D simplification. The algorithm provides a way of generating smooth cutter profiles with machining uncertainties and measuring the thermal deformation through the uncertainties in material properties. Then, it produces realizations of gear tooth profiles based on the analytical method for accuracy and computational efficiency. Numerical investigations show the statistical analysis on the tooth contact analysis by comparing steel and plastic gears. It is worthwhile remarking that the plastic gear is susceptible to the geometric error caused by thermal deformation. Moreover, although the impact of thermal deformation on steel gear may seem slim, it can have a noticeable influence when it exists with mechanical uncertainties together.

BACKGROUND: Versa HD linear accelerators (linacs) are used for stereotactic radiosurgery treatment. However, the mechanical accuracy of such systems remains a concern. OBJECTIVE: The purpose of this study was to evaluate the accuracy of an Elekta Versa HD linac. METHODS: We performed measurements with a ball bearing phantom to calculate the rotational isocenter radii of the linac's gantry, collimator, and table, and determine the relative locations of those isocenters. We evaluated the accuracy of the cone-beam computed tomography (CBCT) guidance with a film-embedding head phantom and circular cone-collimated radiation beams. We also performed dosimetric simulations to study the effects of the linac mechanical uncertainties on non-coplanar cone arc delivery. RESULTS: The mechanical uncertainty of the linac gantry rotation was 0.78 mm in radius, whereas that of the collimator and the table was <0.1 mm and 0.33 mm, respectively. The axes of rotation of the collimator and the table were coinciding with and 0.13 mm away from the gantry isocenter, respectively. Experiments with test plans demonstrated the limited dosimetric consequences on the circular arc delivery given the aforementioned mechanical uncertainties. End-to-end measurements determined that the uncertainty of the CBCT guidance was≤1 mm in each direction with respect to the reference CT image. CONCLUSIONS: In arc delivery, the mechanical uncertainties associated with the gantry and the table do not require remarkable increases in geometric margins. If large enough, the residual setup errors following CBCT guidance will dominate the overall dosimetric consequence. Therefore, the Versa HD linac is a valid system for stereotactic radiosurgery using non-coplanar arc delivery. [ABSTRACT FROM AUTHOR]

• The uncertainty of both the rock abrasiveness and TBM operational parameters were summarized. • A probabilistic analysis was performed to investigate the failure of the cutter and cutter group. • The uncertainty in geological and technical factors significantly influences the cutter group failure. • A design chart is proposed to estimate the potential failure of the cutter. TBM disc cutters used in a long-distance tunneling particularly in cutting through hard rock would undergo substantial and intense wear. The cutting efficiency may greatly reduce and potentially facing complete suspension if the worn-out cutters were not ascertained in a timely manner. Due to the uncertainty of both geological and technical factors, it is undoubtedly arduous to predict the failure of the disc cutter. In this study, the rock abrasiveness and strength properties of 267 rock specimens, including 9 different rock types were investigated. The uncertainty characteristics of the rock abrasiveness and TBM operational parameters were summarized based on the collected data. The rock abrasiveness, compressive strength, tensile strength, TBM advancing rate and rotation speed of the cutter head were considered as random variables in this study. A probabilistic analysis was performed to investigate the cutter failure and cutters group failure in hard rock excavation. The results show variability in the geological and technical factors withhold an important influence on the cutter failure, in particular on the cutters group failure. It is therefore essential to analyze the performance of the cutter wear in the probabilistic framework to avoid overestimation of the cutters' lifespan. Lastly, a reliability design chart is proposed for the adoption in the industries to estimate the potential failure of the cutter. [ABSTRACT FROM AUTHOR]