Overview

The Rocket Team uses bolts as its standard method of fastening the motor. This page will provide information on bolt torque, bolt shear stress, and bolt thread engagement calculations. 

Motor Case Bolt Torque Specifications

Grade 8 Steel Fasteners

In order for a fastener to perform its job, it must be appropriately pre-loaded. All fasteners shall have an installation torque called out on their assembly document. To determine the appropriate torque for a fastener, a specific value may be determined or a value my be used from the reference tables below.

All calculations are for non-lubricated, non-galvanized fasteners.

This will provide an example on how to calculate the optimal bolt torque, using calculations for the bolt torque specification of the Hermes 3 motor case.

While the upper table provides more general information, this section will provide more specific calculations.

Max Tensile Load

First we must calculate the maximum tensile load of the bolts being used. This is the measurement of the maximum amount of tension force the bolt can withstand before it fractures.  In the case of Hermes 3, we are using 5/16-18 by 5/8" Grade 8 Steel Bolts. 

The equation for this is:

P = St x As

P = maximum tensile load or clamp load (lbs,. N)

St = tensile strength (psi, MPA)

As = tensile stress area (sq. in, sq. mm)

Using the following spreadsheet, we find that the tensile stress area of our Bolts in inches squared is 0.052. The tensile strength of our material (which in this case is Grade 8 Steel), is approximately 150000 lbs/in^2.

From this we can calculate our maximum tensile load:

P = 0.052 x 150000 == 7800 lbs 

This is the maximum load, however we cannot use this value for calculating our torque specification, because a factor of safety is necessary.  The standard for this is around 75% of the calculated maximum tensile load.  When a safety factor is added, the new value is:

F (optimal clamp load) = 0.75 x 7800 == 5850 lbs

K Value, or the Nut Factor

In the equation for calculating torque, which is T = K x d x F, the value K is the most variable of the values.  While d (the nominal diameter) and F (the clamp force) have very simple calculations to acquire their values, K is much more complex. 

In simple terms, K can be thought of as a measurement of anything that increases or decreases friction between the threads of the nut. A more in depth description of K and its factors can be found in this guide on fasteners. In this wiki page, we will just provide more basic estimations of the K value needed.

The bolts we are using are non-plated black finish, so the K value we will use for this calculation of the torque will be 0.20

Side Note: One reason we do not used zinc-plated bolts is because zinc becomes a gas at 300 degrees C, and our rocket burns at around 2800 degrees C. 

Torque Calculation

Now that we have our tensile load value, as well as our K factor value, the optimal torque can be calculated. 

The equation for torque, as mentioned previously, is:

T = K x d x F

K = Nut Factor

d = nominal diameter of the bolt (in,. mm)

F = tensile load (lbs., N)

For our bolts the diameter is 5/16 of an inch, or 0.3125 inches. So our calculation is:

T = 0.2 x 0.3125 x 5850 == 365.625 in/lbs

365.625/12 == 30.5 ft/lbs

30.5 ft/lbs is now our final value for the optimal torque. This is necessary to guarantee that the bolt is not too loose (which would cause our seal to not be as strong), or too tight (which would deform our bolts and potentially damage the material being clamped). 

Motor Case Bolt Shear Stress Calculation

When building a motor with a radially bolted case, you must make sure that your bolts will be able to stand up to the forces applied to them. To demonstrate this, we will look at the Phoenix booster as an example. 

Calculated Booster Max Booster Pressure = 826 psi

Forward Closure Inner Area = 10 in^2

Number of Bolts = 24

First, we must calculate the force on the forward closure due to this pressure.

F = P*A

F = 826*10 = 8260 lbs

This force is assumed to be perfectly distributed among each bolt, so the force on each bolt is:

8260/24 = 344.16 lbs

Our bolt is under a single shear, which looks like the reference diagram below. In order to evaluate the shear stress, we need to use the equation on the right. Our bolts have a diameter of 1/4 of an inch. 

F = 344.16 lbs

D = 0.25 in

T = (4*344.16)/(pi*0.25^2) = 7,011.17 psi

That is the tensile load that each bolt experiences, so now we must compare it to the max shear rating of the bolt. The bolts we use are here: https://www.mcmaster.com/91253A537/. Using the specs here, we can calculate:

Actual Shear = 7011.17 psi

Max Shear =  120000 psi

Factor of Safety  = 120000/7011.17 = 17.12