Reducer Backclearance Concept for Servo Applications

1. backlash

There is no relative sliding friction wheel only in ideal, in fact, in order to ensure that no relative sliding, people use the gear and evenly arranged on the circumference of a circle with a certain number of tooth profile to make sure that no relative sliding, at the same time in order to avoid the rotation of meshing tooth interference to each other, and set up a certain amount of tolerance, this is the origin of back clearance.

P-B-19

A good gear transmission system requires a certain "clearance" between the transmission parts. Clearance prevents interference, wear, overheating, ensures certain lubrication, compensates for manufacturing tolerances, etc. Gear meshing clearance means that the gap between the teeth of a gear should be slightly larger than the width of the teeth. Similarly, we will also find a certain gap on the rolling bearing, that is, the small gap between the inner ring of the bearing, the rolling body (ball, roller) and the outer ring. Usually, there will be gaps in the keys and keyways of the shaft or hole. The clearance of the main parts of the gearbox (mainly from the toothside clearance) causes the output shaft to rotate at a small Angle during load reversal even though the input shaft is locked (not rotating). The "no-load Angle" of the shaft is called the rotational backclearance of the backlash.

P-B-20 show。 P-B-20

In theory, no torque is needed to generate backgap, but in practice, a certain amount of torque is needed to overcome the friction of the parts. When the clearance is eliminated, the part deforms elastically as the torque increases. From the point of view of the output shaft, it seems that the Angle of rotation depends on the torque and its size is the stiffness of the gearbox. The torque characteristic curve in practical application is shown in Figure B-21. The higher the slope of the curve, the worse the rigidity of the reducer.

In applications where there is no load reversal or where the post-reversal position is not critical, gearbox backlash is not a significant issue. P-B-21

In the precise positioning applications (such as robots, some automatic control equipment, etc.) where the load frequently reverses, the backgap directly affects the positioning accuracy. As a result, servo gearboxes designed for these applications are designed to have very low, tightly controlled clearances and high stiffness.

2.backlash Definition And Measurement

How to define and measure backlash

It is an unwritten industry standard to define backgaps in terms of output. The effect of the backgap measured at the output end on the input end basically depends on the deceleration ratio.

Output Back Clearance = i × The Input End Is Idle

Attention！The above formula is theoretical. There are deviations in actual measurements, especially in multi-stage gearboxes, because the effect of each stage clearance depends on the position of the clearance in the whole gear chain, and the clearance is not exactly the same in each engagement link.

Backclearance of servo gearbox is usually divided into units of Angle, 1 Angle minute =1 degree /60. Unfortunately, the backgap is often referred to as an "arc minute", which is a mathematical or physical fable, because the definition of an Angle in radians does not have the concept of minutes.

For example, if the gap between gears with a diameter of 500 mm is 0.4 mm, then the backclearance is：

[0.4mm/ ( 2 * 3.14 *500mm)] x 360limit x 60points = 2.75 Corner points

All the values indicated in the backclearance of the gearbox sample are actually "angular minutes". The backclearance of the low backclearance precision reducer should be less than 5 Angle, and the backclearance value of the standard backclearance precision reducer ranges from 5 Angle to 30 Angle.

3.Method of Measurement Of Backlash：

Although it may seem trivial, proper measurement of the backlash of a gearbox requires proper testing tools and instruments. Fixtures holding the gearbox and input shaft should be as stiff as possible. The rotation Angle of the output shaft can be measured directly by a high-precision encoder or by an indirect method. The indirect method refers to the installation of a relatively long rigid moment arm on the output shaft, the dial gauge is used to measure the displacement of a certain distance and calculate the corresponding rotation Angle.

Since a certain amount of torque is required to overcome all gaps in the system, the most accurate method is to measure a complete load reciprocation cycle of the gearbox (from zero to the clockwise rated load torque value, then unload and reverse to the counterclockwise rated torque value), as shown in Figure B-21 on the right. Through this method, the complete hysteresis curve of the gearbox can be obtained, which can not only determine the actual recoil, but also determine the torsional stiffness of the gearbox and the loss motion under any load. (We'll explain what that means later.)

A simple approximation is also possible: make sure the output shaft is preloaded clockwise and unloaded, and apply 2% of the rated load torque in the opposite direction. A dial gauge is used to measure the displacement of the rigid arm mounted on the output shaft at a certain distance from the center of rotation, and the corresponding rotation Angle is calculated.

3.stiffness

Rigidity (the reciprocal of the elastic value) describes the distortion of the output shaft with load due to the elastic deformation of the gear component. Rigidity and elasticity are determined by the ratio of the measured torsion deviation of the gearbox to the load. As shown in Figures B-20 and B-21. The unit of stiffness is the torque required to produce a unit torsion deviation. The units commonly used are：Nm/rad。

4.lost motion，Hysteresis loss

P-B-20，At the output end, after gradually applying the torque to the rated torque, the torque is gradually released to 0. At this time, the transmission Angle does not return to 0 as well, but there is a small lag value, which is called the lag loss.

Gearboxes such as harmonic, sejin, and RV have no backgap but have such errors due to elastic deformation.

The concept of loss motion is not used in planetary reducers, but as you can see in Figure B-21, it is only in these relatively low precision gearboxes that the backgap is a major factor, so manufacturers usually do not mention this error, but attribute it to torsional rigidity. P-B-22

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