Machine Design

# Constant velocity in positioning systems

Smooth motion is key to precision; Here are some tips on how to get it.

Boaz Eidelberg
Charlie Falco
Bayside Motion Group
Port Washington, N.Y.

 An automatic optical inspection rig uses a Bayside custom XYZ gantry on a composite base with caged, recirculating bearings. Specs: 0.1-m m resolution; 60-kg moving mass; straightness = ±5 `m ` m/400 mm; flatness = 1.27 `m ` m/25 mm; 20-kHz controller/drive module. Constant velocity, Cv = ±1%, while position jitter, Xa = ±0.120 `m ` m. Note at a 10-kHz sampling rate, jitter frequency = 5 kHz in this case.

Precision-positioning systems used for metrology, inspection, printing, DNA assaying, and laser machining are typified by a need for smooth motion and constant velocity. For example, a camera uses edge contrast to measure line width on a silicon wafer. Precision of the line-width measurement equals axis velocity assumed to be constant multiplied by time. Constant velocity, in this context, is the difference between actual velocity deviation and a theoretical, desired value at a particular sampling rate as quantified by a power spectrum. Not specifying a sampling rate implies constantvelocity operation at all frequencies, which may not be possible because of the presence of high-frequency disturbance forces. High-harmonic vibrations introduce force ripple that disturbs constant velocity. Adequate system bandwidth (position, velocity, and acceleration) helps reject these disturbances. Bandwidth is defined as the capability of a system to follow a command signal with under 3 dB of error.

COMPENSATED AND UNCOMPENSATED MOTION
A related parameter called compensated motion refers to motion of a servopositioning stage subjected to disturbance forces that are within a system's frequency response or bandwidth. In other words, motor forces are able to counteract the negative effects of disturbance forces on constant velocity.

Consider a motion-control system that moves a 10-kg load at a constant velocity, v = 100 mm/sec. It must maintain a smoothness of motion, Cv = 0.1% at a sampling rate, s = 100 Hz, as a motor-cogging force disturbs the motion every 15 mm. Assume a stage stiffness, K = 1 N /m m. Typical design parameters include maximum velocity for compensated motion and encoder resolution, r.

Going through the numbers, system natural frequency, n and position bandwidth, bw are estimated at 50.4 and 16.8 Hz, respectively. Bandwidth is typically about 0.5 to 0.2 of natural frequency, depending on system robustness and tuning. A factor of 0.33 was used in this case. A cogging frequency, d = 6.6 Hz is lower than 16.8 Hz, the threshold for maintaining compensated motion. The system can attain a maximum compensated velocity of 252 mm/sec so requires an encoder resolution of 0.2`m ` m. Constant-velocity systems should use high-resolution encoders to hold velocity deviation to a few counts when operating within a system's bandwidth.

Uncompensated motion, in contrast, is that of a positioning stage under disturbance forces of a frequency higher than the bandwidth of the servosystem. For example, a lasercutting system with 20-Hz position bandwidth moves a 100-kg load at a constant velocity of 10 mm/sec and maintains a smoothness of 1% at sampling rates greater than 50 Hz. A vacuum-pump motor running at 6,000 rpm introduces a 20-N unbalance force. Design metrics, in this case, include uncompensated constant velocity and position jitter.

First, acceleration, Aa due to the force disturbance is 0.2 m/sec2. The disturbance frequency, d of 100 Hz exceeds the position bandwidth of 20 Hz so the system is considered to be operating uncompensated. To determine by how much, divide disturbance velocity, va = 0.32 mm/sec, by the desired constant velocity (10 mm/sec), which gives 0.32 or 3.2%, well beyond the required smoothness of 1%. Boost movable mass, raise disturbance frequency (pump rpm), or lower the unbalance force to improve motion smoothness. Finally, a jitter amplitude, Xa = 0.5`m ` m at a sampling interval of 0.2 mm, gives a position jitter of 0.25%.

JITTER AND vIBRATION: SOURCES AND FIXES
Jitter and vibration are two of the biggest enemies of constantvelocity motion. Ball screws, for example, can cause jitter when balls move in and out of grooves. For this reason, leadscrews generally work better for constantvelocity applications.

Bearings are another significant source of high-frequency position jitter that can hurt uncompensated constant —elocity. For instance, cam followers typically ha—e about 5-m m jitter, where air bearings ha—e just 0.1`m ` m. Crossroller stages produce jitter le—els of about 0.3`m ` m, caged-recirculating stages roughly 0.5`m ` m, and noncagedrecirculating bearings about 1`m ` m. The remo—al of damping rings from air bearings,or seals from caged and noncaged recirculating stages and bearings, can lower jitter le—els. Jitter can also be lessened by smoothing the surfaces on which cam followers roll or by the use of tight-tolerance hollow rollers in crossroller stages.

Stages should be mechanically stiff and have a high natural frequency to minimize relative displacement either between a sensor and target or a tool and work. Machine bases, on the other hand, are built massive to lower natural frequency to a few Hertz, which resists motion reaction and high-frequency vibration. High-damping base materials such as concrete epoxy composite or metal matrix excel at damping high-frequency structural vibrations and acoustic waves. vibration isolation mounts further isolate equipment from shock loads and floor vibrations.

Vibrations from adjacent equipment, nearby trains, or walking can introduce a wide spectrum of noise that may excite system resonance and disturb smooth motion if not filtered properly by vibration-isolation mounts. Floors where machines locate are typically surveyed for noise levels to help in the selection of suitable isolators. Isolators include resilient pads that isolate frequencies above 15 Hz. Air mounts work for vibration frequencies above 3 Hz, where active dampers (voice-coil control) provide isolation above 0.5 Hz.

Acoustic noise from manufacturing equipment and personnel can also hurt motion smoothness and constant velocity. Low-frequency acoustic vibrations less 300 Hz often coincide with structural resonance of positioning stages. Sound barriers or soundproof chambers help isolate equipment from acoustic noise.

Also consider the effects of electromagnetic and radio-frequency interference (EMI/RFI) on constant velocity. EMI/RFI from power lines, transformers, and amplifiers introduce parasitic noise that may trigger equipmentdamaging motor oscillations at high frequencies and high-pitch audible noise. The use of twisted-wire pairs, shielding, common grounding points, and separation of power from signal lines help lessen the effects of electrical noise.

Contacts within connectors and terminal boards must be robust to prevent intermittent connection, signal contamination,and electrical noise. Controllers that use low-pass and notch filters can suppress the amplification of resonance frequencies from external disturbances. The use of linear rather than PWM amplifiers also improves constant velocity performance because the latter generate high-frequency noise. Smooth-running brushless motors with sinusoidal commutation excel in constant-velocity applications. Ditto for linear motors. Their noncontact, frictionless design provides smooth motion, especially cogfree ironless types.

Encoders and constant velocity

A metrology tool maps glass surfaces with a linear camera. The stage scans at a rate of 50 mm/sec while a sensor samples the motion at 1 kHz. The resulting configuration acquires an image in 50-micron/sample slices. Required position accuracy is ±1`m ` m so position jitter should also be less than ±1`m ` m. The constant —elocity of the stage at 1 kHz is ±2 %.

An encoder with a precise pitch of 20`m ` m and an interpolated resolution of 0.1`m ` m should handle the job. However, accuracy within a pitch interval can be off by as much as 30% or 7`m ` m. This is because encoders typically generate 1 V peak-to-peak analog sine and cosine signals per encoder pitch 20`m ` m of linear travel in this case. In theory, a plot of the two encoder signals (at equal linear intervals on XY axes) gives equal angular intervals around a circle of radius 0.5 V (Lissajoure circle). In practice, a misaligned encoder read head, as well as variations in motion straightness and flatness, may distort the radius of the Lissajoure circle. In other words, the size of linear increments varies with corresponding, equal encoder angular increments. For this reason, it is important to use error mapping or rely on constant velocity when high-positioning accuracy is a must.

MAKE CONTACT
Bayside Motion Group,
(516) 484-5353, baysidemotion.com

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