How to analyze gear tolerances with a simulation tool

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Unformatted text preview: le, S1 is rigidly attached the frame. The first axis of S1 is rotational axes of pinion 1, Sf is rigidly connected with the frame. It’s common coordinate system. In the same way, the coordinate systems of bevel wheel 2 S8, S6, S4 & S2 are defined. Figure 1: Coordinate systems of gear. From S5 to S7, the nominal transformation is a rotation (2nπ/z1 with n an integer). Some deviations can be introduced in this transformation: an error on cumulative angular pitch. From S3 to S5, some deviations can be introduced: position and orientation deviations between the axis of the teeth and the hole axis. From S1 to S3, between fixed coordinate system and rotational coordinate system, rotational parameter of pinion (φ1) is introduced. From Sf to S1, some misalignments can be introduced. The matrix Mij is the homogenous coordinate transform matrix from Sj to Si. In the case of pinion 1, the matrixes are: 0 0 1 0 cos(σ (1) ) sin(σ (1) ) M57= 0 − sin(σ (1) ) cos(σ (1) ) 0 0 0 0 0 ; 0 1 cos(e2) 0 M35= sin(e2) 0 0 − sin(e2) TR1 1 0 TR 2 0 cos(e2) TR3 0 0 1 258 0 0 1 0 cos(φ ) sin(φ ) 1 1 M13(φ1)= 0 − sin(φ1 ) cos(φ1 ) 0 0 0 0 0 ; 0 1 J. Bruyere et al. cos(∆) − sin(...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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