Drive System Sizing

In general, it is suggested to limit the maximum load "L_max" of the HSD143 series drives to 7000 lbs, the HSD184 series drives to 12000 lbs, and the HSD276 series drives to 20000 lbs. However, the rate at which the maximum load must be accelerated may further limit these drives. If it is determined that the limitations of the standard products must be exceeded, contact TranTek for information about larger diameter drives.

To establish the minimum screw diameter required for an application, use the following formulas to perform a series of calculations. Assuming a horizontal drive system with a solid nut, guide rail frictions of 10%, and an acceleration/deceleration profile of 25%, these formulas will assist you in determining which drive system series to consider. The parameters that must be evaluated are defined as follows:

To avoid overstressing the epoxy composite, thread pressures should be below 100 PSI. Ideally, systems should be designed so that thread pressures remain below 75 PSI, which will yield increased system life.

The preceding formulas are based on single screw drive systems, which have solid nuts. If index length considerations or critical speed limitations (see next page) necessitate the use of a multiple screw drive, the results of the solid thread pressure calculations must be increased by multiplying them with the appropriate surface area ratio factor (as shown in the table below). These factors are the result of dividing the surface area of a drive series’ solid nut by the surface area of its respective split nut.

Note: there is no split nut/multiple screw option available for the HSD143 series, 1-7/16" diameter, drives.

After determining which drive system meets your load, distance, and index speed requirements, confirm that the critical speed of the drive screw is sufficient. If the critical speed of a single screw configuration is to low, consider changing to one of the multiple screw configurations. If such a change is necessary, be sure to multiply the solid-nut-thread-pressure results by the surface area ratio factor, as shown in the table above.

As previously stated, thread pressure should remain below 100 PSI, and preferably be kept below 75 PSI.

Critical Speed
Rotating screws have a natural frequency known as the critical speed that varies with their length, diameter, straightness and mounting configuration. Increasing rotational speed will eventually cause this harmonic to create damaging vibrations throughout a drive system. TranTek drives are minimally affected due to high lead angles that convert modest rotational speeds to significant linear speeds. Furthermore, straightening processes are performed on TranTek drive screws during journal machining.

If the critical speed threshold of a single screw system is too small to perform a desired task, TranTek offers standard drive systems that utilize multiple screw segments; providing higher critical speed ratings for a given index length. Rather than increasing the screw diameter, as with ball screw drives, these unique systems join multiple screws together and support them with standoffs that allow the nut to pass right over.

The graph below illustrates how the use of standoffs yields higher critical speeds for given index lengths of drive screws (in this case, the 2.75" diameter HSD276 Series). For convenience, these critical speed thresholds have been converted to linear travel rates of inches per second. These rates include an 80% safety factor that should be respected to avoid costly re-designs, and to allow for subtle speed adjustments after installation.

To calculate the critical rpm for a TranTek drive, use S.H. Weaver's formula for evenly distributed loads with an 80% safety factor (as shown below). Refer to the following table for the appropriate minor diameter "d", end fixity factor "F_ef", and the correct unsupported screw length "L_u". Determining the critical index speed in inches per second is done by multiplying the critical rpm by the screw's lead and dividing by 60 sec/min.

Note: The required index speed (ips) for a drive system with a 25% Acc/Dec profile is 4 D_max ÷ 3T_min.

Life Expectancy
DriTran drives initially have .002” to .005” of axial lash. The nut’s epoxy composite wears at a linear rate over time, and by itself causes no damage to the screw. Drive life is defined as the time it takes for the axial lash to reach a predetermined value (typically .030”). Drive life expectancy calculations are good estimates, provided care will be taken to properly lubricate and shield the system.

To approximate the life of a DriTran nut, use one of the following formulas to perform one calculation for every move of an operation, being careful to use the correct formula for the drive series of interest. Each result "Cy_m" is the number of cycles a drive will last under the conditions of a particular move. To obtain the total drive life expectancy in terms of cycles, perform the summing operation defined on the next page.

Assuming a properly lubricated horizontal drive system with a solid nut, guide rail frictions of 10%, and an acceleration/deceleration profile of 25%, use these formulas to estimate how long the composite will take to reach .030” of axial lash. The parameters that must be evaluated are defined as follows:

When using a multiple screw drive system, the results of all life calculations must be decreased by dividing them with the appropriate surface area ratio factor (as shown in the table below). These factors are the result of dividing the surface area of a drive series’ solid nut by the surface area of its respective split nut.

Note: there is no split nut/multiple screw option available for the HSD143 series, 1-7/16” diameter, drives.

Summing Calculation:

To obtain a total life expectancy "Life" for any drive, invert each result "Cy_m" obtained for each move of the motion profile, add them all together, and then invert the result, as follows:

where "n" represents the last move.

Since the result of the calculation for "Life" is in terms of cycles, it must be divided by cycles per shift, shifts per day, and days per year to determine how many years the drive should last.

Life calculations of a correctly sized drive screw are typically 4 to 5 years. In any case, these predictions allow nut replacement schedules and preventative maintenance programs to be quickly and accurately established.

Sizing and Life Assistance
Since every application has unique characteristics, accurate life predictions are often difficult to perform with simple formulas. If you need assistance with drive sizing or life expectancy calculations because your drive will be in a peculiar situation; perhaps on an incline or with time constraints that require extreme acceleration; TranTek is able to accurately determine the life of a DriTran drive system for you. All parameters such as environment, load, index time, transfer distance, acceleration/deceleration profile, screw/nut friction, guide rail friction, and angle of inclination must be considered for each move of a motion profile.

If you are not comfortable or satisfied with the results of your calculations don’t hesitate to fill out the application data sheet and contact TranTek. Often, subtle changes can be made to a motion profile to add life or to allow for lower horsepower motors to be used. For instance, if the acceleration/deceleration profile were reduced from 25% to 20%, it might increase the calculated drive life and require less peak horsepower. However, during the acceleration and deceleration portion of the motion profile, it may cause enough of an increase in thread pressure to render the change impractical.

Our screw/nut sizing program takes all known variables into consideration to calculate life in terms of number of cycles, as well as years. When necessary, TranTek engineers are willing to work closely with customers on the specifics of an application, providing us with feedback to assist in product improvements, while developing a mutually beneficial customer/supplier relationship.