Study of Stress Sources and Critical Stress Combinations for the Input Shaft of a Longitudinally Mounted Four Speed Automotive Automatic Transmission Model ()
1. Introduction
In study of stress sources and critical stress combinations of the input shaft for the present longitudinally mounted four speed automotive automatic transmissions, which they are resulting in failure. It is common to focus on the main loads acting on the spline part of the input shaft which are forces due to the turbine torque and turbine weight, and also focus on the loads acting on the solid part of the input shaft which are forces due to the planetary set torque (the maximum set torque is occurred at the brake set is applied) and the planetary set weight respectively [1].
Turbine forces are transmitted to the input shaft through the spline part. For the simplest calculations it is assumed that the turbine transmits force and torque to the spline part of the shaft at the middle of its width, and study the stressed-strained is based on the corresponding cross-section. Although, actually, turbine force of interaction between the turbine hub and the spline shaft part is distributed along the length of the turbine hub. Also, the planetary set force is distributed along the bearing of the set.
Forces on the input shaft for the mentioned longitudinal mounted four speed automatic transmission induce stresses which are of torsional, bending, shearing, and axial nature. In studies of stressed-strained states of the input shaft resulting in fatigue failure, it is common to forces on the input shaft induce stresses which are of a torsional, bending, shearing, and axial nature. focus primarily on torsion phenomena. In so doing, torsional shear stresses are considered for the most part. The effect of axial forces is usually not significant and can be omitted.
2. Basic Concepts
The longitudinally four speed automatic transmission Figure 1 input shaft is flowed the torque converter turbine torque to a simple planetary gear set. The turbine torque is varied according to the variation of the pump torque. The turbine torque variation has two categories. The first one is given at low torque converter speed ratio
. Where, the ratio of the turbine and pump torques is given by the Equation [2]:
The second stage is occurred when the torque converter lock-up clutch is activated (at the design point), the turbine and pump are connected to the engine output. The angular velocity and torque of turbine are expressed as follows [3]:
.
The resistant torque of the planetary gear set for the turbine torque has two values. One value occurs when the DC clutch is applied Figure 2 and its value is:
.
The other value is occurred when the ODB brake is applied Figure 3 and the input shaft resistance torque is become:
.
The turbine torque (TT) transmits through a spline part on the input shaft Figure 4 effect on the whole shaft until the carrier bearing. The spline part of the shaft affected manly torsion moment (no bending).
Diagrams of bending moment Mb, caused by turbine weight (W1) and first planetary gear set (W2), and shear force (Fs), are shown in Figure 5.
Hence, the diagrams of contact forces from torsion 
are shown in Figure 6(a). Diagram of torsional moment
, caused by contact forces from torsion is shown in Figure 7. For any tooth since 
and 
are
Figure 1. A longitudinally mounted four speed automotive automatic transmission model [3,4].
(a) (b)
Figure 2. Input shaft model with dc clutch (a) Side view; (b) Plan view.
(a) (b)
Figure 3. Input shaft model with ODB brake (a) Side view; (b) Plan view.