Radial Bolt Calculations:

A simple Matlab script for calculating the number of bolts and margin of safety can be found below:

boltcalcs.m

How to use:

• Input the following parameters into the Matlab script per your preferences
  • Yield Stress for case material (for aluminum 6061, it's roughly 35000 psi)
  • Design chamber pressure
  • Case inner diameter
  • Case outer diameter
  • The number of bolts in a ring
  • the bolt's major diameter
  • the bolt's head diameter
• By running the script, the program will output three factors of safety 
  • relates to the compressive, shear, and tensile stress on the aluminum case as a result of the bolts
  • per our rocket team adopted standards, all three values must have a factor of safety of 2 or above (margin of safety above 1)
  • if the bolt pattern meets these requirements, it is a valid design
• Important assumptions
  • these calculations simplify the process by assuming the case of the motor is always the weakest link in the connection, the other factors being when the forward closure/nozzle carrier will break, or what pressure the bolts will shear. a similar calculation can be run for the forward closure/ nozzle carrier, just update the values to reflect the designed diameters of the connected ring (but as long as the thickness of the nozzle carrier is larger than that of the case, it should be fine). bolt shear can be calculated through a simple shear stress calculation on the cross-section of the bolts
  • The current version assumes a single bolt ring, but will be updated to include multiple rings in a future version
  • minimum edge distance between the bolt center and the edge of the case is standardized at 1.25 times the major diameter of the bolt

Common design problems:

• low compressive FoS: to enough bolt area, add more bolts or increase the major diameter
• low shear FoS: bolts too close to the edge or rings too close together
• low tensile FoS: low case cross-section area, reduce the number of bolts, decrease the major diameter, or add a ring if not possible due to compressive requirements

NOTE: this is a design tool to build the case and is NOT a substitute to a hydrostatic pressure test.  ALL PRESSURE VESSELS MUST BE HYDROSTATIC TESTED BEFORE STATIC FIRE OR LAUNCH 

Bolt Torque Calculations:

torquecalcs.m

How to use:

• Input the following parameters into the Matlab script
  • Tensile stress for bolt
  • Bolt nominal diameter
  • Torque reduction factor (based on lubricant)

• Running the script will output torque spec in lbf-in

• Important Notes
  • Assuming lubricated bolts: Use torque reduction factor to account for lubricated bolts
  • Using a dry torque value on a lubricated bolt can exceed tensile strength

Changelog

4/16/23 Updated boltcalcs.m to consider multiple rows of bolts - LW
5/05/23 Added torquecalcs.m to help determine torque spec - LW