Feeder Etc.
You seriously need to understand that the driven or drive shaft will shear itself from load due to the smaller stepped diameter and reduced surface areas. ■
Re: Feeder Shafts - Stepped Down
I've calculated the shaft sizes based on stress at the hub location (where the bending moment is the greatest). However, if we pick a spot closer to the bearing (say 1/3 of A), where the bending moment is also 1/3M, the required shaft size will be smaller. This will allow us to use less expensive bearings.
My question is regarding the deflection limitation closer to the bearing?
Any thoughts? ■
Re: Feeder Shafts - Stepped Down
I think the calculations I have completed (albeit limited in number) were initiated using a stress calculation (we typically use AS1403) and then checked the deflection using the "area method" or similar method. I haven’t as yet had revise a calculated diameter due to deflection, hence so far for me stress has been the more stringent requirement. The "area method" will enable you to confirm the total deflection at any point in the shaft as you can superimpose deflections of sections with varying dimensions. ■
Re: Feeder Shafts - Stepped Down
The deflection of the shaft is specified in radians or minutes of arc to control the rotation of the locking mechanism. In detail, it controls the rocking action and bolt tensile loading of taper bushings, and Ringfeder type locking devices.
It is specified to control the shaft arc of rotation at the center line of the hub.
8 minutes of arc is for small shafts up to 8 in. (200 mm) diameter under the locking device.
5 minutes of arc are normally specified for non-driven pulley shafts larger than 8 in. (200 mm).
3.5 minutes of arc are specified for drives, brakes and holdback shaft deflection criteria.
However, there are other shaft diameter criteria. One is the localized stress of the locking device edge. If the end disk is extremely stiff, then the shaft stiffness should match in order to control the local plastic deformation at the outer edge of the locking device. Some mfgrs. tend to make the end disk too stiff which leads to locking device failure or yielding of the shaft at the noted position.
The shaft turndown from hub to bearing is controlled by the combined axial bending, axial shear, and torsional shear fatigue stresses. As a rule some designers limit the turndown to 75% of the primary diameter. Others allow turndowns to 67% so long as all loading and fatigue criteria are met.
The secret to the turndown is how large a fillet radius to specify in combination with the above. "Peterson Stress Concentrations" has prudent fatigue criteria for turndown proportions for bending and torsion. If too big the bearing center to hub moment arm is too long. If too short then there is a stress concentration penalty.
Its all pretty pedantic. ■
Re: Feeder Shafts - Stepped Down
Thanks for the feedback.
I realize this issue may be getting into too much detail, but unfortunatley I'm still being asked to identify the design limits.
I'll try the 67% rule of thumb and check for stress and fatique.
My tentative plan is as follows:
1) shaft diam at hubs is max of: stress method vs. deflection method (8 minutes as our shafts are < 8" diam)
2a) brg shaft size = 67% of 1) and apply stress concentration factors for M (at 1/3*A approx) and T and calc diam using stress method
2b) at step location, calc diam req'd using 1/3*A with a deflection limit of 8 minutes also. I will not add a concentration factor to the resultant pulley load.
Answers for both 2a and 2b must be less than 67% of 1).
I'll use the largest fillet possible with a nice finish.
Question:
Regarding the 3.5 minutes for pulley drive shafts....do you think this is necessary for slow feeders (10-15rpm)? ■
Re: Feeder Shafts - Stepped Down
No. I just gave an answer to all the potential of the question.
However, I do not know your feeder. If the feeder width is large, say above 1500mm then I would vote for the 5 min. arc.
Feeders work on torque and subject the pulley to greater stress for a given horsepower.
If your doing 8 inch dia. and have 8 min., you might pick a more conservative 5 min. given that the feeder does have times when it needs to pull the load from under the bin or pile. In such a case, the demand low speed torque can get quite large. ■
Re: Feeder Shafts - Stepped Down
Lyle,
Thanks for the attached ref for the Moment Area Method. It confirmed the method I have found in my texts. It should work well for driven pulley shafts that are stepped down for the brgs. For drive pulley shafts with overhung gearboxes and steps for brgs, I'm looking at using Mohrs circle, moment area method and/or transmission shaft theory. Wish me luck. ■
Re: Feeder Shafts - Stepped Down
No problems. As long as you can calculate the moment and you know the length from a fixed point to the location in question, you can use the method. I like it as you dont have to remember any fancy equations (just the method), calculate the BM and you are away. ■
Feeder Shafts - Stepped Down
I think the question was, for pulley shafts, do we need to recalcuate the shaft deflection for the stepped shaft when the shaft is turned down at the hubs, bearings, drive? The answer is no we do not. The deflection is calculated at the hubs so that the step down right at the hubs and beyond does not affect the results.
The pulley shaft interaction is complicated. Pulley shaft analysis per CEMA "B105.1" is not. The shaft deflection calculations don't recognise the interaction, they assume a simple span between bearings and simple loads at the hubs. This approach tends to be conservative. Limiting the shaft deflection limits the rocking rotation at the hubs thus limiting flexural loading of the end discs. End disc failure or walking of the locking devices are the common consequences of excessive shaft deflections, no shaft failure. Shaft deflection is due to the shaft diameter between the hubs while stresss are due to the diameters outboard of the hubs.
Rules regarding maximum turn down are good safe rules of thumb but if you take the time to analize the turn downs including the stress concentrations then you don't have to be subject to those rules.
Similarly if you analize the the pulley and shaft composite, using a moment distribution at the shaft/end disc juncture then the shaft deflection criteria is negated.
Joseph A. Dos Santos, PE ■
Re: Feeder Shafts - Stepped Down
Things are looking up. Thanks for the great replies.
As pulley end disc design has not been done, I will adopt deflection criteria at hubs per 105.1. For stepped shafts, I will apply concentrations factors and consider stress limits only.
On a related issue, is HP vs shaft sizing. See this thread posted by me.
https://forum.bulk-online.com/showth...9873#post29873
Thanks again. ■
Re: Feeder Shafts - Stepped Down
Regarding step down at different places, you may consider the following guidelines :
1) Shaft size at bearing central plane would be based on only torque.
2) Shaft size at bearing edge would be subjected to torque plus certain magnitude of bending moment.
3) Shaft diameter at hub will have torque plus maximum value of bending moment.
4) Shaft diameter between hubs will be of constant magnitude. If we ignore the restoring deflection by the end disc then its magnitude is same as bending moment at hub
5) Shaft deflection is mainly governed by the shaft diameter between hubs unless you have got a pulley of small width, wherein either you have to take some mean average diameter for calculating deflection or look in to the engineering books to get the deflection value for differing size of the shafts (I will recommend to take mean size instead of going in to complexities).
6) Calculate the values at different points as above and then choose the values generally in conformity with the convention / practice and the information given by the earlier respondents.
Regards,
Ishwar G Mulani.
Author of Book : Engineering Science and Application Design for Belt Conveyors.
Author of Book : Belt Feeder Design and Hopper Bin Silo
Advisor / Consultant for Bulk Material Handling System & Issues.
Email : parimul@pn2.vsnl.net.in
Tel.: 0091 (0)20 25882916 ■
Feeder Shafts - Stepped Down
For belt feeders/conveyors, the allowable deflection of pulley shafts at the hub is 8 minutes according to ANSI / CEMA B105.1.
This standard does not include info about stepping the shafts down for smaller bearings.
- Do I need to worry about re-calculating the deflection at the location of the step?
- I think I should re-calculate diam. required by stress method and include load concentration factors for torque and moments.
Has anyone done this before??
Thanks!! ■