Technical Analysis

Mechanical

Steering Column Gear FEA

The gears used to transfer torque between the steering column and the layshaft were tested using a finite element analysis. The model parameters were set in SolidWorks. The material was set to PET, the inside face of the gear was fixed, and a force of 100 pounds was applied on a single gear tooth at the pressure angle of 20 degrees. These parameters are to represent a worst case scenario in which a single tooth of the gear must take the whole load. The test force value was derived from an estimate that the max torque a driver would exert on the wheel is about 6 pound-feet. The static simulation was run and provided the plot results below. With these results, one of the goals was to identify the maximum bending stress experienced by the tooth. As shown by the stress profile diagram at the base of the tooth, the maximum bending stress occurs at the bottom left corner since the normal stress increases its magnitude as they are in the same direction. Therefore, the probe tool was used to select that point on the stress, strain, and FOS plots. The reason this is not the maximum stress location on the FEA stress plot is because there is a stress concentration at the point of application of the force. With this in mind, the maximum bending stress calculated by the FEA was 4234 psi which resulted in a factor of safety of 1.949. The gear was also successful in all other aspects as shown. Even with the stress concentration at the point of application, the minimum factor of safety was 1.1 which shows that these gears will not fail in this worst case scenario.

Steering Column Gear Hand Calculations​

To check the FEA results, the maximum bending stress within the gear tooth was calculated using the Lewis Equation. The calculations reported a maximum bending stress of 4233 psi which is nearly equal to the FEA result of 4234 psi. This proves that the FEA results are accurate.

Pinion Keyway Analysis

The pinion shaft needs to transmit the torque from the motor to the pinion gear. This is done by using a square key and a keyway cut into the pinion gear and the pinion shaft. This analysis was used to select the appropriate size key for the shaft and ensure that neither the pinion shaft or pinion gear would yield at the keyway from the torque being transmitted. An 1/8" square key will be used to transmit the torque to the pinion gear. Next was to find the force on the key based on the torque in the shaft and the shaft radius. After that we found the factor of safety by comparing the yield strength of the 1020 cold rolled pinion gear to the shear stress on the face of the key. For the pinion gear we found that the factor of safety was 1.855. We then repeated the factor of safety calculation but instead used the yield strength of the 4140 pinion shaft and we found that the factor of safety for that pinion shaft is 1.959. Both of these factors of safety are acceptable and show that the key will not yield with the torque from the motor. 

Electrical

ADC Quantization Error

When the analog signal from the potentiometers that determine the position of the steering column is quantized, there is a potential for error. This error is due to the finite resolution of the Analog to Digital Converter (ADC). The ADC has 10 bits, which equates to 1024 discrete steps that the analog signal must be mapped to. Since the voltage range of the analog signal is 5 V, this leads to each step being 4.883 mV. Mechanically, the design calls for the column to rotate two full rotations. The potentiometer has three turns, so 2/3 of the ADC range is usable, which translates to each step covering 0.018 rad. If the physical position of the column is directly in between two of these steps, the error is at a maximum, since the ADC "rounds" the value. The maximum potential error was found to be 0.073%.

Voltage Drop in Wires

The voltage drop in the wires was analyzed to ensure that adequate power is delivered to the motor. The voltage drop is proportional to the current flowing through the wire, so the analysis was computed at 13A, which was the current measured via a clamp meter when the motor stalls at the end of the rack range of motion. A target of < 3% voltage drop was set for the combined positive and negative wires, which were measured at about 8' each, for a total of 16'. Since the motor is a DC motor, only the resistance of the wires must be considered, reactance can be ignored. The resistance was obtained from a reference table. The first analysis was conducted with 16 AWG wire, which resulted in a voltage drop of 3.527%. The analysis was then conducted again, but this time upsizing to 12 AWG wire, which due to the lower resistance had a voltage drop of only 1.413%.