Using Precitech Servo Tool Options for Freeform Machining

Several optics manufacturers are studying servo tool machining technologies.

This article is targeted at providing the following:

  • A practical understanding of the operating features of different Precitech servo tool options
  • Data to find out which servo tool suits an application the best
  • A technique to determine servo tool machining cycle time

Benefits of Servo Tool Machining

It is possible to economically produce non-rotational symmetric surfaces including freeform surfaces on Precitech’s two-axis diamond turning lathes, the Precitech Nanoform 200, 350 and 700 systems using the company’s servo tool options.

The benefits of servo tool machining are:

  • Increasing the component range that can be made on existing Nanoform lathes
  • Minimizing cost and lead time for work piece holding fixtures

Servo Tool Machining - Typical System Configuration

A normal machine configuration for servo tool machining is shown in Figure 1. The work piece is mounted on the C axis, which is in turn mounted to the X-axis carriage. On the Z-axis carriage the servo tool is mounted. Machining with this machine configuration is called "XZC machining'.

X,Z and C axis motion

Figure 1. X,Z and C axis motion

Three Servo Tool Options

Precitech provides three servo tool options to cover broad range of application requirements. Table 1 shows the general characteristics of the Slow Tool Servo (STS) and two fast tool servo (FTS) options: the FTS500 and FTS70.

Table 1. General Characteristics Precitech STS, FTS500 and FTS70 servo tools

STS FTS 500 FTS 70
Drive & "bearing" technology Linear motor / Hydrostatic Oil bearing Voice coil / Air bearing and counter mass Piezoelectric stack / Flexure element
Characteristic Travel* 10 mm (@ 2 Hz) 500 um 70 um
Characteristic Bandwidth** 70 Hz 1000 Hz 700 Hz
Characteristic Surface finish^ 5 nm Ra 8 nm Ra 5 nm Ra
Characteristic form accuracy^ 250 nm PV 300 nm PV 600 nm PV
Position sensor Scale Analog Analog
Programming Software Diffsys SOP SOP

* See Figure 1 for a more complete description
** Related to servo control design and performance
^ Typical performance for test specimens (also typical real world results for many applications)

The STS option (lower acceleration, long excursion) is used normally for producing high amplitude non-rotationally-symmetric continuous surfaces. Instantaneous changes or inflection points are not features on a continuous surface.

The FTS70 and FTS500 options (high acceleration, short excursion) are normally used for producing higher frequency (higher spatial density), lower amplitude and surface structures, which may have surface discontinuities.

Best Suited Servo Tool Option

Choosing the right servo tool is a function of the following:

  • Surface finish requirements
  • Cycle time (productivity) goals
  • Form accuracy requirements
  • Transition area specifications (i.e. the area between clear apertures on discontinuous surfaces)

Each of the options has distinct operating features with regards to their physical design, drive technology and servo control algorithms. These very slight differences can be exploited to offer excellent performance in relation to a specific application.

In the area of form accuracy, both the STS and FTS500 (linear motor and voice coil drives) excel. Both these drives feature highly linear response curves that contribute to achieving high form accuracy.

In the area of surface finish, the FTSS70 (piezo stack) excels. The high characteristic, low mass bandwidth and very high positioning resolution of FTS70 is a suitable combination for generating high quality surface finishes.

The first step for choosing the best servo tool option is to find out if the tool path amplitude and the drive frequency needed by the application are within the operational limits of the servo tool.

Figure 2 shows the maximum amplitude of tool motion vs. drive frequency curves for each Precitech servo tool. The tool excitation frequency and the tool path amplitude needed to generate a surface can be plotted as an operation point with regard to these curves.

Operation limits for STS and FTS machining

Figure 2. Operation limits for STS and FTS machining

Drive Amplitude

One half of the complete Z-axis motion (the worst case) for a specific revolution of the work piece represents the amplitude. This motion is the non- rotationally symmetric component of the desired surface.

Tool Drive Frequency

The number of tool motion cycles per second is termed as the drive frequency. It is directly linked with the work piece’s rotational speed. Continuous surfaces feature simple arithmetic relationships between excitation frequency and rotational velocity (RPM). For each revolution of the part, a tilted flat surface completes one cycle of the tool motion.

For discontinuous surfaces, the following equation is used to approximate maximum tool excitation frequency:

Fd (Hz) = (2 Π Rmax)N(rpm)/60P


  • P = the pitch (spacing in mm) of the optical elements ' center lines (or chord distance across an element).
  • Rmax = the maximum turning radius in mm from the center of rotation to the most outlying optical element.
  • N = spindle speed

In cases where there are abrupt changes in the surface slope or there are steps in the surface height, it is important to consider the recovery time of the servo tool.

Transition Areas in Discontinuous Surfaces

The clear aperture area of each optical element is clearly specified by components that show discontinuities in their surfaces or repetitive shapes combined together across the surface.

From the component specifications and the features of the servo tool, the following items are known:

  • The allowable form error in the clear aperture area,
  • The characteristic bandwidth of the servo tool
  • The physical dimensions of the clear aperture and transition areas,

Using this data and Figure 4, it is possible to determine the maximum surface velocity of the part relative to the tool bit. From this, it is possible to determine the part spindle speed and the part cutting cycle time.

Classic Control Loop

A classic control loop response to a tool path command, which alters the direction of motion is shown in Figure 3.

Traversing a +0.2 to -0.2 slope change at 150mm/s

Figure 3. Traversing a +0.2 to -0.2 slope change at 150mm/s

The difference between the actual motion and the ideal motion causes error in the part surface. The speed at which the tool path can correct for drastic slope or surface height changes is associated with the characteristic bandwidth of the control loop of the servo tool.

As seen in Figure 3, the period of the sinusoidal error motion is the inverse of the natural frequency of the servo tool control loop. Table 1 shows the characteristic bandwidth of the servo tools, which is the drive frequency where resulting (output) tool motion amplitude is 3dB (30%) down from the commanded (input) amplitude. The servo tool control loop’s natural frequency is 30% lesser than the characteristic bandwidth.

“Residual error” is the allowable form error in the clear aperture region. Normally the cutting speed is regulated such that the residual error on exiting the transition area (at the end of the recovery zone) is less than (just under) the allowable form error.

An Overall Insight

Figure 4 relates the following in a dimensionless presentation:

  • Error motion amplitude and tool path slope (S) , error = f(S)
  • Recovery zone width (RZ) and Servo tool bandwidth (Bw), RZ = f(1/BW)
  • Tool surface velocity (Vs) and Recovery Zone width RZ, Vs = RZ x BW / RZbar

Dimensionless Surface Error When Machining a Corner with Equal +/- Slopes at Surface Velocity Vs

Figure 4. Dimensionless Surface Error When Machining a Corner with Equal +/- Slopes at Surface Velocity Vs

The following example shows how to apply this data to determine the right servo tool for an application and determine the cycle time for a finish cut.

Application: Lenslet Array

The lenslet array specifications are:

  • Component size: 50mm diameter
  • Lens diameter (pitch) (P) 5mm
  • Lens form spherical R = 12.5mm (PV sag = 0.25mm)
  • Allowable form error within the clear aperture (also equal to the residual error(RE)) RE = 0.00031 mm = 0.31µm
  • Clear aperture diameter 4.61mm (clear aperture area is 85% of the overall lens area)
  • Recovery Zone width ( Transition area span / 2 ^^ ): RZ = 0.195mm
  • Tool path slope (rise/run) within transition area (S) S = 0.2

^^ Note: In this example the part is designed with the transition area placed symmetrically about the boundary between the lens features. Tool path error is not symmetric in relation to these boundaries. Following error predominates. This can be exploited to further reduce part manufacturing costs if the optical design allows for non-symmetric transition areas.

Servo Tool Amplitude

Based on the tool amplitude needed (125µm = 0.25mm/2) and referring to Figure 2 it is possible to cut this component using either the FTS 500 or the STS servo tool but not with FTS 70 servo tool.

Maximum Spindle Speed

Next, the maximum spindle speed is determined using Figure 4.

REbar = RE(µm) / RZ(µm) / S = 0.31 / 195 / 0.2 = 0.00795

Using the REbar value and the curve in Figure 4, the RZbar value was found to be ~ 1.3

Assuming the FTS 500 servo tool option (BW= 1000Hz) the maximum surface velocity Vs is:

Vs = BW (Hz) * RZ(mm) / RZbar = 1000 * 0.195mm / 1.3 = 150mm/sec = 9,000mm/min

Spindle speed, RPM = Vs / (circumferencemax) = 9000 / (Π * 50) = 57RPM

Servo Tool Drive Frequency

The tool drive frequency is next determined:

Fd = (2 *Π* N(RPM) / (60 * P)) = (2 *Π * 57 / (60 * 5) = 30Hz

Referring to figure 2 again, this drive frequency and amplitude combination exceeds the capabilities of the STS servo tool.

Finish Cut Cycle Time

Assuming a constant spindle speed and 3µm feed / rev, the cycle time for the finish cut is:

Cycle time (min) = Part dia. / (2 * feed/rev * RPM) = 50/(2*0.003*57) = 146min.

Other Application Examples

In Table 2 there is a list of relevant operational parameters for a range of applications. All these are based on actual cutting experiments performed at Precitech. The results in Table 2 are consistent with practical production results as observed by customers.

Table 2. Cutting results using various servo tool options

Application Description Servo Tool Part Dia. (mm) Spindle (rpm) Feed/ Rev (μm) Cycle Time (min.) Z amplitude (mm) Drive Freq. (Hz) Tool Radius (mm) Measured Form Error PV (μm) Ideal Surface Finish Ra (nm) Measured Surface Finish Ra (nm)
2mm Tilted flat -- Cu STS 50 50 10 50.0 1 0.83 1.5 0.35 2.1 2.7- 4.7
2mm Tilted flat -- Cu STS 50 150 5 33.3 1 2.50 1.5 <0.25 0.53 2.9 - 4.5
2mm Tilted flat -- Cu STS 50 150 8 21 1 2.50 2.5 0.2 0.82 3.0-4.0
2mm Tilted flat -- Cu STS 50 225 10 11.1 1 3.75 1.5 <0.25 2.1 5.0 - 8.1
A12TF 200um Tilted flat - Cu FTS500 12 500 2 6.0 0.1 8.30 0.77 0.25 0.16 3.1 - 4.5
A13TF 200um Tilted Flat - Cu FTS500 12 1000 2 3.0 0.1 16.70 0.77 0.25 0.16 3.2 - 5.4
500um Tilted Flat - Cu FTS500 12 500 2 6.0 0.24 8.3 0.5 0.3 0.26 3.2 - 6.4
500um Tilted Flat - Cu FTS500 12 1000 2 3.0 0.24 16.7 0.5 0.3 0.26 3.2 -11.0
Toric surface in 303 SST (Aps Note 0303) (CBN tool) FTS70 9 2000 2.5 0.9 0.031 66.67 0.5 <.35, .42 0.40 N/A
Toric -- Cu (Aps Note 0301) FTS70 9 2000 2.5 0.9 0.032 66.67 0.5 < .25, .37 0.40 3.5 - 8.5
70um Tilted flat - Cu FTS70 12 500 4 3.0 0.035 8.30 2.16 0.35 0.24 2.8 - 3.7
2mm Lenslet Array -Nickel (Aps Note 03.11-1DT) FTS70 12 250 4 6.0 0.031 75.00 0.5 1.5 1.02 3.7 - 10
35um Tilted flat-- Cu (Aps note 0306) FTS70 20 1000 1 10.0 0.017 16.67 0.5 0.206 0.70 1.3
35um Tilted Flat --OFHC Cu (Aps Note A-0316) FTS70 50 1000 2.5 10.0 0.017 16.67 0.5 0.017 0.70 1.54
Corner Cube Lens Array -- OFHC Cu (Aps Note A-0214) FTS35 50 150 5.3 31.4 0.015 87.27 1.0 0.097 0.92 3.4


Precitech boasts an extensive range of servo tool options in the ultra-precise machining industry. A number of factors need to be considered while choosing the ideal servo tool for a specific customer application.

The Precitech application engineering team works on a regular basis with existing and new customers to help determine the right solutions to challenging applications. The XZC machining solutions from Precitech are also production ready and robust.

About Precitech

Precitech began operations in 1992, but continues the rich history of ultra-precision machine tool building dating back to 1962, when Pneumo Precision was founded. In October of 1997, the Pneumo ultra-precision machine tool division of Taylor Hobson (formerly Rank Taylor Hobson / Rank Pneumo) was merged with Precitech. The Precitech name was retained for this corporate entity and all offices and manufacturing facilities are now located at 44 Blackbrook Road in Keene, New Hampshire.

Our facility staffs approximately 100 talented individuals in a recently designed 60,000 Sq. Ft. building.

Precitech is a member of AMT (The Association of Manufacturing Technology) and has corporate affiliations with several professional societies and academic institutions such as Germany’s Research Community for Ultra Precision Technology at the Fraunhofer Institute, ASPE the American Society for Precision Engineering, and EUSPEN the European Society for Precision Engineering and Nanotechnology.

This information has been sourced, reviewed and adapted from materials provided by Precitech.

For more information on this source, please visit Precitech.


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