Linearization of multibody frictional contact problems

Non-Linear Dynamic Response of a Spur Gear Pair: Modelling and Experimental Comparisons

“…This problem can be solved with linear programming methods [10]. The results are then used to determine the displacement x from equations (14), (10), and (12). The contact forces p can also be used in the combined surface integral/"nite-element solution to calculate tooth de#ections and stresses near the tooth contact zone.…”

“…The approach is particularly valuable for multi-body, multi-mesh systems such as epicyclic gears where mesh modelling in discrete dynamic models is especially di$cult. Additional features that result from the "nite element approach are that coupling to #exible shafts, bearings, and housings can be handled naturally, gear geometry errors and tooth-to-tooth variability can be easily analyzed, elastic deformations of the gear bodies are modelled, friction at the tooth surface can be included in the contact analysis [10], and pro"le modi"cations of magnitudes used in practice are modelled by the rede"nition of the tooth surface without remeshing. This last point is true because local tooth deformations near the surface are handled by an analytical model near the inner region of Figure 3; small pro"le modi"cations a!ect A JMA?J in equation (17) and not the "nite element matrices in equation (6).…”

“…This problem can be solved with linear programming methods [10]. The results are then used to determine the displacement x from equations (14), (10), and (12).…”

“…The "nite element formulation is unique in its combination of detailed contact modelling between the elastic teeth [10] with a combined surface integral/"nite element solution [11] to e$ciently capture tooth deformations and loads with a relatively coarse mesh. Details are available in the references and a short description of the surface integral/"nite element solution is given in reference [9].…”

Influence of Carrier and Gear Manufacturing Errors on the Static Load Sharing Behavior of Planetary Gear Sets

“…Only the most critical features of this model will be summarized here as the details of this model can be found in Refs. (15), (16) and two recent applications (13), (14) . The deformation of the planetary system under load is modeled using a combination of finite element and surface integral techniques.…”