Program 60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Introduction The purpose of this model is to obtain index and lead gear ratios for gears cut on hobbing machines without the use of a differential. The index and feed change gears on this type of hobbing machine must insure that all machine motions are properly related to each other. There are three constants with which we must concern ourselves in the use of this model. The first of these is the machine index constant (K). This constant is equal to the number of revolutions made by the hob while the work turns one revolution when the index gear ratio is 1 to 1. The next constant is the machine feed constant (M). This is the distance in inches that the hob advances for one revolution of the work when the feed gear ratio is 1 to 1. The value of these constants varies with the different models of this series of hobbing machine and with the number of threads on the index worm. The last constant is the C constant and is not set by the configuration of the machine. It is the number of revolutions turned by the work while the hob is fed one axial pitch and is used only for helical gears. The C constant establishes the relationship between the index and feed ratios so that the proper helix angle will be cut. We have some freedom of choice in selecting the C constant as a departure from the theoretical value will affect the only the feed per revolution of the work. (Of course, the feed gear ratio must still be determined to cut the correct helix angle.) We also will be concerned with the number of intermediate studs in the index and feed change gear boxes. The number of studs will affect the direction of rotation of the hob and work piece and is determined by the hand of the hob along with the type of cut (climb or conventional). Either one or two gears may be mounted on the studs. (If only one gear is mounted the number of gear teeth may be chosen for convenience as it will affect only the direction of rotation and not the ratio.) The number of studs calculated by the model is for COUNTER-CLOCKWISE rotation of the hob. The TK Solver model contains a table that lists the index and feed constants for the various models of #6-10 and #16-16 hobbing machines. (See the table named constants on the TK Table Sheet or in the dropdown list on the TK Object Bar) Figure 1 shows this table.
UTS Integrated Gear Software Fig. 1 2
60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Examples We will run some examples with the model assuming a standard #16-16 machine. This means that our index constant will be 30 and our feed constant will be.075. We will use a 2 thread, right hand hob and will conventional cut. The minimum number of teeth we will use for the change gears will be 21 and the maximum will be 96. The number of teeth in our work gear will be 30 and the normal diametral pitch will be 10. First we will use a helix angle of 10.5 degrees left hand. Figure 2 shows the input data. Fig. 2 We want the feed at about.03 inch per revolution and will accept a lead error of up to.0001 inch per inch of gear face. Notice that we have elected to calculate the ratios only and not the actual change gears by setting Calculate change gear sets? to No. The model has a large amount of work to do in calculating the ratios and the change gears and it is often best to solve for the ratios only to speed things up. Depending on the problem at hand and the speed of the computer you are using, the solution could take several minutes. Once a set of ratios has been found with acceptable ratio factors and acceptable feed the model only has to be solved again with Calculate change gear sets? set to Yes to obtain the number of teeth in the change gears. Report 1 shows the solved model. 3
UTS Integrated Gear Software Report 1 Model Title : Program 60-1963 Unit System: US Description Value Unit Comment Index Constant 30.0000 Feed Constant 0.0750 Hand, Hob? 'l=left 'r=right Hand, Gear? 'l=left 'r=right 's=spur Conventional or Climb Cut? 'co or 'cl Calculate Change Gear Sets? 'y or 'n Minimum No. of Teeth in Change Gears 21 Maximum No. of Teeth in Change Gears 96 Number of Teeth 30 Normal pitch Transverse pitch Normal module Transverse module Helix angle r l co y 10.000000 1/in 9.8325 1/in 0.100000 in 0.1017 in 10.500000 deg Number of Threads on Hob 2 Approximate Feed (if C not input) Actual Feed Allowable Lead Error per Unit Length Hobbed Lead Error per Unit Length 0.0300 in/rev 0.0292 in/rev 0.000 in/in 0.000 in/in C Constant 59.0000 4
Model Title : Program 60-1963 Unit System: US 60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Description Value Unit Comment Axial Pitch Gear Lead Hobbed Lead Lead Length Error 1.7239 in 51.718 in 51.717 in 0.000 in We now have a solution for the change gears with an extremely small error. The hobbed lead error per inch is listed as 0 but is actually about.00000025. (To see any variable to 16 significant digits, just place the cursor on the value in the TK Solver Variable Sheet: the actual value will appear in the Status Bar at the bottom of the screen.) The feed is about.029 inches/rev. Next we need to look at the numerators and denominators of the index and feed ratios to see if we have a reasonable combination of factors for change gears. The table named gears (see the TK Table Sheet or the dropdown list on the TK Object Bar) contains this data. Figure 3 is the table. 5
UTS Integrated Gear Software Fig. 3 The factors of the drivers and drivens look pretty good. There are no factors larger than the largest change gear on hand (96 teeth) so we will set Calculate change gear sets? to Yes. This time the model will find change gears to meet the ratios if possible. Figures 4A and 4B show the tables Index and Feed (see the TK Table Sheet or the TK Object Bar table list). Fig. 4A 6
60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Fig. 4B These gears might be set up in the index change gear box as follows: 59 tooth on driving shaft 60 tooth and 23 tooth on intermediate stud 77 tooth on driven shaft The model will not necessarily find all gear combinations possible, since a list of ascending prime factors for the numerator and denominator is processed from both ends toward the middle. This is done to keep the computer running time within reason. If at least one gear combination is found within the prescribed max and min change gear teeth the processing stops. The model will tend to (but not always) find the largest gears usable for the set up. This may be a slight advantage because of lower tooth loads on the change gears. Also the effects of change gear backlash will be less. If you wish to check other possible combinations, all the prime factors (along with their exponents) are listed on the gears table. Since the C constant is not fixed by the machine configuration and affects only the amount of feed we can easily input another C and look at other change gear ratios. The C constant for the ratios just found is 59 and produced a feed of.02922 inches/rev. Let s check a C of 58. (The feed will increase with a decrease in C.) Blank the Approximate Feed and enter 58 for the C Constant. ( Calculate change gear sets? will be left set to Yes to illustrate the table output as we proceed.) Report 2 shows the solved model for these conditions. 7
UTS Integrated Gear Software Report 2 Model Title : Program 60-1963 Unit System: US Description Value Unit Comment Index Constant 30.0000 Feed Constant 0.0750 Hand, Hob? 'l=left 'r=right Hand, Gear? 'l=left 'r=right 's=spur Conventional or Climb Cut? 'co or 'cl Calculate Change Gear Sets? 'y or 'n Minimum No. of Teeth in Change Gears 21 Maximum No. of Teeth in Change Gears 96 Number of Teeth 30 Normal pitch Transverse pitch Normal module Transverse module Helix angle r l co y 10.000000 1/in 9.8325 1/in 0.100000 in 0.1017 in 10.500000 deg Number of Threads on Hob 2 Approximate Feed (if C not input) Actual Feed Allowable Lead Error per Unit Length Hobbed Lead Error per Unit Length 0.0000 in/rev 0.0297 in/rev 0.000 in/in 0.000 in/in C Constant 58.0000 8
Model Title : Program 60-1963 Unit System: US 60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Description Value Unit Comment Axial Pitch Gear Lead Hobbed Lead Lead Length Error Figures 5, 6A and 6B show the tables for this solution. Fig. 5 1.7239 in 51.718 in 51.718 in 0.000 in 9
UTS Integrated Gear Software Fig. 6A Fig. 6B We can see that a C constant of 58 provides us with no usable gear combination for the index or the feed. The Index Driven denominator is a prime number and, of course, cannot be factored into usable gears. The Feed Driven denominator produces gears larger than the maximum gear on hand no matter how the prime factors are combined. The Index Gear Sets and Feed Gear Sets tables indicate that no gear sets can be found. (Note that the feed increased to.02972 inches/rev.) Let s try a C of 57. Report 3 and Figures 7, 8A and 8B show the solved model. 10
60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Report 3 Model Title : Program 60-1963 Unit System: US Description Value Unit Comment Index Constant 30.0000 Feed Constant 0.0750 Hand, Hob? 'l=left 'r=right Hand, Gear? 'l=left 'r=right 's=spur Conventional or Climb Cut? 'co or 'cl Calculate Change Gear Sets? 'y or 'n Minimum No. of Teeth in Change Gears 21 Maximum No. of Teeth in Change Gears 96 Number of Teeth 30 Normal pitch Transverse pitch Normal module Transverse module Helix angle r l co y 10.000000 1/in 9.8325 1/in 0.100000 in 0.1017 in 10.500000 deg Number of Threads on Hob 2 Approximate Feed (if C not input) Actual Feed Allowable Lead Error per Unit Length Hobbed Lead Error per Unit Length 0.0000 in/rev 0.0302 in/rev 0.000 in/in 0.000 in/in C Constant 57.0000 11
UTS Integrated Gear Software Model Title : Program 60-1963 Unit System: US Description Value Unit Comment Axial Pitch Gear Lead Hobbed Lead Lead Length Error Fig. 7 1.7239 in 51.718 in 51.718 in 0.000 in 12
60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Fig. 8A Fig. 8B We again have a usable setup. The feed is now.03024 inches/rev. Now let s try a spur gear. We will use the same number of gear teeth and pitch as before. The same number of hob threads will be used but we will change the hand of the hob to left. Figure 9 shows the data inputs; Report 4 and figures 10, 11A and 11B show the solved model. 13
UTS Integrated Gear Software Fig. 9 Report 4 Model Title : Program 60-1963 Unit System: US Description Value Unit Comment Index Constant 30.0000 Feed Constant 0.0750 Hand, Hob? 'l=left 'r=right Hand, Gear? 'l=left 'r=right 's=spur Conventional or Climb Cut? 'co or 'cl Calculate Change Gear Sets? 'y or 'n Minimum No. of Teeth in Change Gears 21 Maximum No. of Teeth in Change Gears 96 l s co y 14
Model Title : Program 60-1963 Unit System: US 60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Description Value Unit Comment Number of Teeth 30 Normal pitch Transverse pitch Normal module Transverse module Helix angle 10.000000 1/in 10.0000 1/in 0.100000 in 0.1000 in 0.000000 deg Number of Threads on Hob 2 Approximate Feed (if C not input) Actual Feed Allowable Lead Error per Unit Length Hobbed Lead Error per Unit Length C Constant Axial Pitch Gear Lead Hobbed Lead Lead Length Error 0.0300 in/rev 0.0300 in/rev 0.000 in/in in/in in in in in 15
UTS Integrated Gear Software Fig. 10 Fig. 11A 16
60-1963 Index and Lead Gear Ratios for Barber Colman #6-10 and #16-16 Hobbing Machines Fig. 11B For this spur gear we have an index ratio of 2/1 and a feed ratio of 2/5. The index change gears are listed as 42 driver and 21 driven with an idler. It is obvious that many other combinations could be used. The model, in this case, stopped looking after it found one gear set. In the case of the feed gears the model found all possible combinations. Note that with this setup two intermediate studs are listed for both the index and the feed gear sets and idler gears (of any convenient size) must be placed on the intermediate studs to keep the hob and work rotations correct. TK Solver Model Note Display Intermediate Values, in Settings under the TK Solver Options menu, has been set to No for this model. This was done to decrease processing time. If you wish to watch the processing of the various lists used in the tables you may reset this to Yes. Then go to the table you wish to observe. (Again, choose it from the TK Table Sheet or from the dropdown list in the TK Object Bar.) Now when the model is solving the lists will be displayed as they are being processed. This model is NOT a substitute for the hobbing machine manual. The manual contains information on possible limitations concerning torques and speeds of the various machine elements and should be consulted before using any set up. Cutting of long leads and spur gears with prime numbers of teeth greater than 100 requires the use of a differential. See the manual for further information. Other UTS Models are available for other hobbing machines. Contact UTS for more information. 17