Method and apparatus for controlling backlash in motor drive systems

A method for substantially eliminating backlash from a gear train having first and second drive gears which engage a driven gear, each of said first and second drive gears and said driven gear having a plurality of gear teeth, said method comprising the steps of:

• calculating a first motor torque, responsive to an input voltage X and providing a first electrical signal representative thereof, said first motor torque having a first constant slope torque curve with respect to said input voltage X;
• said first motor torque being calculated in accordance with the following expression:
• First Motor Torque=2.4›(X-2)-(X-2)e.sup.-(X-2).spsp.2 !+2.4(X+2)e.sup.-(X+2).spsp.2
• calculating a second motor torque, responsive to said input voltage X, and providing a second electrical signal representative thereof, said second motor torque having a second constant slope torque curve with respect to said input voltage X, said first constant voltage torque curve being offset from said second constant slope torque curve by an offset voltage .delta.;
• said second motor torque being calculated in accordance with the following expression:
• Second Motor Torque=2.4›(X+2)-(X+2)e.sup.-(X+2).spsp.2 !+2.4(X-2)e.sup.-(X-2).spsp.2
• actuating a first motor, responsive to said first electrical signal, said first motor being coupled to said first drive gear to transmit said first motor torque through said first drive gear to said driven gear;
• actuating a second motor, responsive to said second electrical signal, said second motor being coupled to said second drive gear to transmit said second motor torque through said second drive gear to said driven gear;
• reshaping said first and second constant slope torque curves whenever one of said first and second constant slope torque curves changes a sign by increasing and then decreasing the slope of one of said first and second constant slope torque curves while simultaneously decreasing and then increasing the slope of the other of said first and second constant slope torque curves to minimize impact loading on the gear teeth of said first and second drive gears and the gear teeth of said driven gear.

An anti-backlash gearing system comprising:

• a first drive gear having a plurality of gear teeth;
• a first motor having a drive shaft coupled to said first drive gear;
• a second drive gear having a plurality of gear teeth;
• a second motor having a drive shaft coupled to said second drive gear;
• a driven gear having a plurality of gear teeth, the gear teeth of said first and second drive gears engaging the gear teeth of said driven gear;
• said first motor transmitting a first motor torque to said driven gear through said first drive gear, said second motor transmitting a second motor torque to said driven gear through said second drive gear, said first motor torque and said second motor torque causing a rotational movement of said driven gear;
• said first motor torque and said second motor torque substantially eliminating backlash between said driven gear and said first and second drive gears whenever a sign change occurs in one of said first and second motor torques;
• and
• computing means for calculating said first motor torque and said second motor torque and for generating electrical signals representative thereof, said computing means calculating said first motor torque and said second motor torque from an input voltage X in accordance with the expressions:
• First Motor Torque=2.4›(X-2)-(X-2)e.sup.-(X-2).spsp.2 !+2.4(X+2)e.sup.-(X+2).spsp.2
• and
• Second Motor Torque=2.4›(X+2)-(X+2)e.sup.-(X+2).spsp.2 !+2.4(X-2)e.sup.-(X-2).spsp.2
• said computing means supplying said electrical signals to said first motor and said second motor, said first motor, responsive to said electrical signals, transmitting said first motor torque to said driven gear through said first drive gear and said second motor, responsive to said electrical signals, transmitting said second motor torque to said driven gear through said second drive gear.