Self Locking in Worm Drive with lead angle of about 8

[Yasir Zahoor]

Hi
I have built a gear drive for robotic arm that uses a worm set (worm gear +worm) at stage one. Worm (wheel) is of bronze and worm gear is steel haing a lead angle of appx 8 deg. This set is further coupled to a spur gear set that further increases the torque such that the over all gear ratio is 1: 320. Now ideally the gear drive can be rotated from the output shaft as the lead angle is greater than 4 deg. However for some reason this mechanism is exhibitoing self locking in a way that even applying 40 kgs of load at the output shaft, the input does not rotate. can anyone explain this? The literature suggests these lead angles should not indicate self locking.

 

[Baluncore]

Welcome to PF.
What are your units? torque? 40kg*metre ?
The locking is probably due to the ratio of 320. Driven backwards, 40kg/320 = 125g.
Too much interference between the worm and wheel will help self locking.

What lubrication do you use?
The critical lead angle is the arctangent of the friction coefficient.
Is static friction in the worm/gear significant? Once it starts to turn does it continue?

 

[Yasir Zahoor]

Hi,
Thanks a lot for replying. Please have a look at the image. The load (40 kg) is applied at the end of the lever which is 300 mm in length but the input worm gear does not rotate even then. The theory suggests that the back drive is more linked to the lead angle and as such not related to the torque. For my design, I want this self locking feature but i don't know at the moment why its exhibiting this self locking when lead angle is on higher side, so want to be sure. for lubrication i am using grease and the gear materials are bronze for worm and Stainless steel for worm gear and spur gears.

 

[Baluncore]

Your worm appears to be at 90 degrees to the plane of the worm wheel. Where is the axis of the worm ?
This makes the 8° lead angle specification confusing. Are you sure your angle is not (90° - 8°) = 82°

 

[Yasir Zahoor]

Apologise for not correctly indicating the worm mesh. Both planes are parallel (worm and worm gear) as they should be, which means that the axis of the wheel is perpendicular to the axxis of the worm gear. I tried to resketch the case.

 

[Baluncore]

So, when you rotate the worm, the 8° lead angle advances the worm wheel by one tooth per turn of the worm.
But when you turn the wheel it is driving the worm with an 82° contact angle. That is why it locks.

 

[Yasir Zahoor]

As i mentioned the theory suggests other wise. As per the literature, if the friction angle is greater than the lead angle the system is self locking which normally occurs with a lead angle of 5 degree. Can you explain your comment a bit in the ligh tof this theory?

 

[Yasir Zahoor]

worm gear is 2 start by the way

 

[Baluncore]

As i mentioned the theory suggests other wise. As per the literature, if the friction angle is greater than the lead angle the system is self locking which normally occurs with a lead angle of 5 degree. Can you explain your comment a bit in the ligh tof this theory?

As per what literature? You have given no references.
How do you define "friction angle" ?

I use the following to calculate required coefficient of friction from locking angles.
Tan( 3°) = 0.0524
Tan( 5°) = 0.0875
Tan( 8°) = 0.1405
Tan(10.75°) = 0.19 Static friction of lubricated brass on steel.
Tan(12°) = 0.2125
Tan(15°) = 0.2680
What is the coefficient for bronze on steel with different forms of lubrication ?
The viscosity of grease may be a problem. Use light machine oil.

Is static friction in the worm/gear significant? Once it starts to turn does it continue?

You have not answered: Does it continue to run once it starts to turn, or does it stop and lock again ?

I assume there is no motor connected to the worm for your tests. The worm must therefore have end thrust bearings. When the wheel drives the worm there is maximum thrust on those bearings so also maximum friction.

 

[Yasir Zahoor]

Here is a reference http://machinedesign.com/mechanical-drives/self-locking-worm-gears-fact-or-fiction(and more or less the same thing is found else where),
"All theoretical analyses of self-locking worm gears deal with static conditions. In such an analysis, the load on the worm gear can’t drive the worm if the coefficient of friction between worm gear and worm is larger than the tangent of the worm’s lead angle. In other words, the friction angle must be larger than the lead angle to prevent backdriving.

Consider a worm gear speed reducer with a lead angle of 5 deg and a static coefficient of friction of 0.13. The arctan of the coefficient of friction is 7.4 deg, and is the friction angle. Because the friction angle is larger than the lead angle, a worm gear with a 5-deg lead angle is considered statically self-locking. If, however, this self-locking reducer is subjected to shock and vibration, the friction coefficient between worm and gear may suddenly drop. If it drops to 0.08, then the friction angle (arctan of 0.08) drops to 4.6 deg, which is now less than the lead angle of 5 deg. During the time that the friction coefficient is 0.08, the gears are no longer self-locking and back-driving can occur. Once started, backdriving usually continues because the friction coefficient decreases with increasing speed."

The coefficent of friction is some where between 0.12 and 0.16, http://www.engineershandbook.com/Tables/frictioncoefficients.htm.

There is actually a motor driving the steel worm gear so its operated that way.
Thanks for your help.

 

[Baluncore]

According to the table you reference, bronze against steel has a "greasy" static coefficient of 0.16
That gives a friction angle of Atan(0.16) = 9.09°
It would be close but, I would expect an 8° steel worm to lock when driven by the bronze wheel.

There is actually a motor driving the steel worm gear so its operated that way.

What type of motor is used ? If that motor has poles and permanent magnets, it may provide a torque that makes rotation more difficult to start. If you turn the worm and motor by hand, can you feel torque variation as the poles in the motor pass ?