Program Pin Measurement for External Involute Worms Introduction

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1 Program Pin Measurement for External Involute Worms Introduction This model calculates the measurement over pins for an involute helicoid worm. Measurement over pins is used extensively in the industry and is a very accurate method for control of thread thickness. If the number of threads in the worm is even two pins are used and if the number of threads is odd three pins are used. For cylindrical involute helicoid worms the measuring pins will have their centers on the ball helix of the worm. The ball helix is the location of the center of a ball that is free to roll in the thread space of the worm. The problem of finding the measurement over pins for a given thread thickness and pin diameter then becomes a problem of finding the distance from the center of the worm to the ball helix. The model also calculates a recommended pin diameter that should contact the thread flanks near the diameter where the thread thickness is equal to the space width. The closest standard pin is then found and given in the Power User form or in the TK Solver Variable Sheet. The model may be used when the thread thickness is known and the measurement over pins is needed or when the measurement is known and the thread thickness is needed. In the first case we enter the thread thickness and solve for the measurement. In the second case we enter the pin measurement and solve for the thread thickness.

2 UTS Integrated Gear Software Examples Example 1 This example was selected to demonstrate the procedure to be followed for a solution for the size over pins given the thread thickness and also to solve for the thread thickness given the measured size over pins. The example is a two start worm with a standard axial pitch of 0.25 inch. The normal pressure angle is 25 degrees and the lead angle is 5.87 degrees. First we will find the measurement over pins when we know the axial thread thickness at the reference pitch diameter. We have the following data available: Number of threads = 2 Axial Pitch = 0.25 Normal Pressure Angle = 25 deg Lead Angle = 5.87 deg Axial Thread Thickness = Enter the known data, following the sequence of the data entry form and entering the data as shown in Figure 1-1. The measuring pin diameter will come into the form as a calculated default. Click the mouse pointer on this value to make it an input, then click the toolbar Solve button. The fully solved model should look like Report 1-1 2

3 Pin Measurement for External Involute Worms Fig. 1-1 Report 1-1 Unit System: US Number of Threads 2 Lead of Thread Lead Angle Axial Diametral Pitch Axial Module Axial Pitch Axial Pressure Angle in deg /in mm ` in deg 3

4 UTS Integrated Gear Software Unit System: US Normal Diametral Pitch Normal Module Normal Pitch Normal Pressure Angle Transverse Pressure Angle Reference pitch diameter Normal Thread Thickness Transverse Thread Thickness Axial Thread Thickness Base Diameter (Involute Helicoid) Lead Angle on Base Cylinder Recommended Pin Diameter Closest Standard Inch Series Pin Closest Standard Metric Series Pin Measuring Pin Diameter Radius Through Center of Pin Diameter Through Center of Pin Pin Contact Diameter Measurement Over Pins /in mm ` in deg deg in in in in in deg in in ` mm ` in in in in in Number of Pins 2 Minimum Length for 3 Pin Measurement --- in 4

5 Pin Measurement for External Involute Worms Notice that the thread=space pin is output along with the closest standard pin in this case, inch. Tables of standard inch series pins and metric pins are available in the TK Solver model. Select them from the TK Solver Table Sheet or from the Object Bar list. They are shown in Tables 1 and 2, below. 5

6 UTS Integrated Gear Software Table 1 6

7 Pin Measurement for External Involute Worms The model has solved for the measurement over two pins and the pin contact diameter. The pin contact diameter must be less than the worm outside diameter and greater than the required true involute form (TIF) diameter. The radius to one pin less the pin radius must be greater than the worm root radius to avoid contact on the worm root instead of on the thread flanks. Table 2 The next example illustrates how to use the model if you have measured a worm and wish to find the thread thickness. In this case it is only necessary to enter the measurement over pins along with the pin diameter used. Figure 1-2 shows the completed data input form. The solution is shown in Report

8 UTS Integrated Gear Software Fig. 1-2 Report 1-2 Unit System: US Number of Threads 2 Lead of Thread Lead Angle Axial Diametral Pitch Axial Module Axial Pitch in deg /in mm ` in 8

9 Pin Measurement for External Involute Worms Unit System: US Axial Pressure Angle deg Normal Diametral Pitch /in Normal Module mm ` Normal Pitch in Normal Pressure Angle deg Transverse Pressure Angle deg Reference pitch diameter in Normal Thread Thickness in Transverse Thread Thickness in Axial Thread Thickness in Base Diameter (Involute Helicoid) in Lead Angle on Base Cylinder deg Recommended Pin Diameter in Closest Standard Inch Series Pin in ` Closest Standard Metric Series Pin mm ` Measuring Pin Diameter in Radius Through Center of Pin in Diameter Through Center of Pin in Pin Contact Diameter in Measurement Over Pins in Number of Pins 2 Minimum Length for 3 Pin Measurement --- in Trigger for iterative solution for TT

10 UTS Integrated Gear Software Example 2 This example is a single start 20 degree pressure angle worm made to a standard module of 4 millimeters. Before beginning data entry in the data input form, make certain to click the radio button for metric units. Enter the known data as shown in Figure 2-1. The solved model should look like Report 2. Fig

11 Pin Measurement for External Involute Worms Report 2 Unit System: Metric Number of Threads 1 Lead of Thread mm Lead Angle deg Axial Diametral Pitch /in Axial Module mm ` Axial Pitch mm Axial Pressure Angle deg Normal Diametral Pitch /in Normal Module mm ` Normal Pitch mm Normal Pressure Angle deg Transverse Pressure Angle deg Reference pitch diameter mm Normal Thread Thickness mm Transverse Thread Thickness mm Axial Thread Thickness mm Base Diameter (Involute Helicoid) mm Lead Angle on Base Cylinder deg Recommended Pin Diameter mm Closest Standard Inch Series Pin in ` Closest Standard Metric Series Pin mm ` Measuring Pin Diameter mm Radius Through Center of Pin mm 11

12 UTS Integrated Gear Software Unit System: Metric Diameter Through Center of Pin mm Pin Contact Diameter mm Measurement Over Pins mm Number of Pins 3 Minimum Length for 3 Pin Measurement mm Trigger for iterative solution for TT Since we have an odd number of threads we now get the measurement over three pins. When three pins are used the two pins on one side should be placed in adjacent axial spaces. The required worm length to use three pins is one axial pitch plus and is calculated. (If the length of the worm is close to the minimum the use of 3 pins may be difficult and the measurement from the worm axis over one pin may have to be used.) 12

13 Pin Measurement for External Involute Worms Example 3 Example 3 is a 27 start 14.5 degree pressure angle worm. The normal diametral pitch is 10 and the lead angle is 27 degrees. Fig

14 UTS Integrated Gear Software Report 3 Unit System: US Number of Threads 27 Lead of Thread Lead Angle Axial Diametral Pitch Axial Module Axial Pitch Axial Pressure Angle Normal Diametral Pitch Normal Module Normal Pitch Normal Pressure Angle Transverse Pressure Angle Reference pitch diameter Normal Thread Thickness Transverse Thread Thickness Axial Thread Thickness Base Diameter (Involute Helicoid) Lead Angle on Base Cylinder Recommended Pin Diameter Closest Standard Inch Series Pin in deg /in mm ` in deg /in mm ` in deg deg in in in in in deg in in ` 14

15 Pin Measurement for External Involute Worms Unit System: US Closest Standard Metric Series Pin Measuring Pin Diameter Radius Through Center of Pin Diameter Through Center of Pin Pin Contact Diameter Measurement Over Pins mm ` in in in in in Number of Pins 3 Minimum Length for 3 Pin Measurement in This involute helicoid worm is, of course, exactly the same as a 10 normal diametral pitch, 14.5 degree pressure angle helical gear with a helix angle of 63 degrees. UTS Gear Model could have been used instead of this model. The only difference in this worm and the corresponding helical gear is the terminology used to describe them. However, as the helix angle gets closer to 90 degrees a different set of equations must be used and this model contains the proper equations for a low lead angle or high helix angle. 15

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