1、02FTM8Compliant Spindles in Lapping andTesting Machinesby: B. McGlasson, Gleason Works - RochesterTECHNICAL PAPERAmerican Gear Manufacturers AssociationCompliant Spindles in Lapping and Testing MachinesB. McGlasson, Gleason Works - RochesterThestatementsandopinionscontainedhereinarethoseoftheauthora
2、ndshouldnotbeconstruedasanofficialactionoropinion of the American Gear Manufacturers Association.AbstractThispaperpresentstheory,analysis,andresultsofanovelspindledesignwithapplicationtobevelgearlappingandtest-ingmachines. Thisspindledesignincludes arotationally compliantelement thatcan substantiall
3、yreduce thedynamicforces induced between the gear members while rolling under load. Together with a position-based servo controlscheme, this technology adds stability to the gear-rolling process and in lapping machines raises maximum speeds by50% as compared with conventional spindles.Copyright2002A
4、merican Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 2002ISBN: 1-55589-808-41 Compliant Spindles in Lapping and Testing Machines Bill McGlasson, Gleason Works Rochester 1 INTRODUCTION This paper presents theory, analysis, and results of a novel spindle
5、 design (patent pending) with application to bevel gear lapping and testing machines. This spindle design includes a rotationally compliant element that can substantially reduce the dynamic forces induced between the gear members while rolling under load. In lapping machines, this technology has add
6、ed stability to the process and raised maximum speeds by 50% as compared with conventional spindles. In testing machines, it has reduced the influence of the machine on the quality of the test results and allowed them to retain their integrity at higher speeds. Although, particularly advantageous in
7、 direct-drive spindle designs, the compliant concept can benefit belt-driven or geared spindles as well. The rotationally compliant element, found in at least one spindle in such machines, breaks the total spindle inertia into two parts: a relatively free forward part into which the workholding equi
8、pment and gear is mounted, and a servo-controlled rearward portion that contains the motor (or is driven by a motor), motion transducer, and chuck/dechuck mechanism. The inertia of the forward portion is minimized, whereas the inertia of the rearward portion can remain or be made large. When reduced
9、 inertia lowers the dynamic forces between the gear teeth at their point of generation, the motion transmission error (MTE) becomes truer to the gearset geometry and the excitation of the machine structure is reduced. The presence of a highly compliant rotational element with spring-like properties
10、also allows a novel torque control technique to be applied in a CNC machine. This technique reduces the burden on the electronic servo system to actively maintain torque in an environment of dynamic disturbances, relying instead on the laws of physics on a simple mechanism to reject these disturbanc
11、es. The theory of this highly compliant (HC) spindle concept is presented using simplified models, providing the explanation for the process benefits it brings. Analysis and simulations give additional insight into the dynamics of the system. Finally, some examples of actual lapping results are pres
12、ented. 2 BASIC BEVEL LAPPING AND TESTING MACHINES A 90-degree bevel lapping or testing machine is fundamentally simple. It is a machine tool with three independent linear axes that position two orthogonal spindles relative to each other in space. A gear and pinion are each mounted into a spindle, an
13、d the linear axes are brought to positions such that the gear-set is held in mesh (with backlash) at its designed relative position or other nearby position of interest. Figure 2.1 Example of lapping/testing machine configuration Figure 2.2 Another example of lapping/testing machine configuration Tr
14、aditionally, the pinion spindle is under velocity control and the gear spindle is under load, or torque, control. 2 In a testing machine, several gear quality measurements can be made. The size and position of the contact pattern between mating gear teeth can be discerned by rolling the set under lo
15、ad with a thin layer of grease-like colored marking compound pre-applied to the flanks. The rotational quality of the gear-set can be measured if high-resolution rotational sensors mounted to each spindle measure the relative rolling smoothness, or motion transmission error of the gear-set. And a me
16、asure of the gear-sets tendency to excite vibrations in the structure that holds it (structure-borne noise) can be made if machine-mounted accelerometers are monitored during rolling. The three linear axes can make small moves to allow investigation of gear-set behavior away from its ideal position.
17、 A lapping machine is similar except that it has a pump and recovery system to deliver lapping compound (abrasive slurry) to the meshing zone during rolling. The lapping process refines the surfaces of the mating members to improve their running quietness and contact position. Small linear-axis moti
18、ons are made during rolling to bring the lapping action across the whole tooth surface and control where metal is removed. Achieving machine stability and good process results at high speeds has been historically more difficult on lappers than on testers. This is because lapping typically occurs at
19、lower torques and is a metal-removal process that can feed back on itself in unstable ways. The greatest machine dynamic problems occur when flanks are bouncing or chattering out of single-flank contact, and this occurs most readily during lightly-loaded high-speed rolling exactly the requirements o
20、f high-productivity lapping. (High-speed testing, on the other hand, can usually be stabilized by increasing torque above lapping limits.) And since lapping is continually modifying the gear geometry, a small dynamic problem can lap itself into a large dynamic problem, much like repeated traffic dow
21、n a gravel road can create an ever-worsening washboard surface. 3 OLD AND NEW COMPLIANT SPINDLE CONCEPTS Adding compliance to a lapping spindle is not a new concept. Elastomeric (i.e. “rubber“) couplings and other means have been known techniques for more than 20 years, but only a minority of machin
22、es in production has employed them. The concept of adding compliance to a tester spindle is even less common. In either application, the benefits of doing so may not be immediately obvious. In fact, it is initially counter-intuitive to many practitioners, since stiffening a system and adding inertia
23、 is often key to stabilizing a dynamic process. So what has guided machine designers and gear process experts to seek compliance over the last several decades? A desire to achieve higher process speeds. For instance, there has historically been a practical ceiling in lapping of about 2200 to 2400 pi
24、nion rpm for automotive gear-sets, with truck-size parts being slower still. Attempting to operate above these speeds, even with the older compliant mechanisms, has led to bad lapping results often accompanied by prominent machine vibration. Machines with this new HC spindle technology, however, rou
25、tinely and successfully lap automotive and even truck gear-sets at 3000 rpm and higher. If spindle compliance per se, then, is not a new concept, why has the system disclosed here been more successful than its predecessors? Four distinctives are: 1) the magnitude of the compliance, 2) the dynamic ch
26、aracteristics of the compliant element, 3) the novel CNC torque control scheme of which it becomes part, and 4) its application together with directly-driven spindles. How compliant is optimal? Prior art methods (e.g. “High Speed Lapping Machine and Method“, U.S. Patent 3,807,094, Ellwanger et al.,
27、1974; “Spindle Insert“, European Patent Application 82101990.B, Konersmann et al., 1982) of compliance disclosed in the literature allow at most plus or minus a degree or so of compliant motion at the gear spindle; the present method allows about plus or minus 10 degrees, and its compliance is an or
28、der of magnitude or more higher. (In physics, compliance is defined as the reciprocal of the more familiar term stiffness. The stiffness of a spring is given as force per unit displacement. The compliance of a spring, then, is displacement per unit force. In rotational systems, compliance can be giv
29、en as deg/N-m.) Prior art devices have utilized rubber or elastomeric elements that exhibit greatly non-linear torque over displacement behavior within the machines usable torque range. Additionally, these elements have significant dynamic damping characteristics. (Whereas true spring-like elements,
30、 however non-linear, are not velocity dependent and do not absorb energy, elements with damping characteristics are and do.) The present compliant method provides a relatively linear spring characteristic within the useful range with small physical damping. Historically, torque in a lapping or testi
31、ng machine has been achieved with a mechanical brake, or more recently with CNC servo motor torque control, applied at the gear spindle. Any compliant element, if present, was merely a passive mechanism that displaced according to the transmitted torque. Although its presence modified the nature of
32、the dynamic disturbances transmitted from the gear-set to the torque-controller, the design and application of the torque controller remained the same. In the present method, the gear spindle motor is operated 3 not in a torque-control, but in a position-control, mode; it makes its object not to con
33、trol torque directly, but to control the positional wind-up, or displacement, of the compliant spring. And finally, the application of this technology together with a direct-drive gear spindle motor is novel. Prior-art servo-controlled gear spindles have employed belts or gearing to transmit torque
34、from separately mounted motors to the spindle. High reflected-load-inertias to these motors and the non-ideal characteristics of gearing and belts (backlash, resonances, motion errors, slipping, etc.) have interfered with achieving the quality of torque control and servo dynamics necessary for high
35、speed lapping. 4 A SPECIFIC COMPLIANT SPINDLE IMPLEMENTATION Figure 4.1 shows a simplified cross-section of one possible HC spindle implementation. Figure 4.1 An HC Spindle Concept The illustration shows a main spindle with an integrated direct drive motor. The forward (compliant) spindle, shown wit
36、h arbor and gear installed, is mounted within the rear (main) spindle, such that the forward spindle bearings do not see continuous rotation, but only accommodate the wind-up of the springs. The compliance itself is achieved by one or more deformable elements. These spring-steel pieces essentially f
37、unction as cantilever beams in bending. The circular cross-section diameter is varied along the length of the element for optimal spring properties. One end is fixed rigidly into the forward spindle. The other end, having a spherical portion, extends into a receiving bore in the main spindle. This i
38、mplementation can allow a high degree of compliant motion (for instance +/- 10 degrees) with very little backlash and friction. The spring elements can be installed and removed from the front of the spindle. 5 THEORY AND ANALYSIS 5.1 Dynamic Stiffness Concepts It will be useful to briefly review som
39、e basic concepts of dynamic stiffness (DS) as they apply to rotational springs, dampers, and inertias. Stiffness, defined as force per displacement, is usually thought of in a static (without motion) sense. For instance, a simple spring has static stiffness because if it is deflected and once all mo
40、tion stops, it still exerts a force resisting that displacement. But a pure inertia (for instance an ideal flywheel) exerts no force, once it comes to rest, as a result of a displacement. Therefore, the inertia has no static stiffness. But in a dynamic sense, even the frictionless ideal flywheel has
41、 stiffness. By virtue of its inertia and according to Newtons second law, the flywheel resists any kind of dynamic displacement with a force proportional to the imposed acceleration. Likewise a damper has no static stiffness, but resists any kind of dynamic displacement with a force proportional to
42、imposed velocity. Dynamic stiffness, therefore is a function of the frequency of the imposed displacement, and this behavior can be shown graphically in plots such as Fig. 5.1. Consider imposing a sinusoidal displacement of plus and minus one degree onto a simple rotational spring. It will take a si
43、nusoidal torque of, say, 1 N-m peak to achieve this displacement. No matter the frequency of application of this sinusoidal displacement, it is always requires 1 N-m. This ideal spring behavior, independent of frequency, is shown as a straight line in a) on the DS plot. 0 50 1000510a) SpringMagnitud
44、e (N-m/deg)0 50 10004590135180Phase (deg)0 50 1000510b) Damper0 50 1000 50 1000510c) Inertia0 50 100Frequency (Hz)Figure 5.1 Dynamic stiffness characteristics of some basic system elements. 4 Now consider imposing a sinusoidal displacement of plus and minus one degree on a rotational inertia. It wil
45、l take a sinusoidal torque of a peak magnitude that depends on the frequency of displacement imposed; a very slow oscillation requires little torque since accelerations are small. A very fast oscillation requires a large torque since accelerations are large. This inertial characteristic is shown on
46、the dynamic stiffness plot as parabolic curve c), where the peak torque required is proportional to the square of the frequency. Similarly, a pure damping element shows up on the DS plot as shown in b). Peak torque required to achieve sinusoidal displacements of a damper is linearly proportional to
47、the frequency. Also shown in the figure is the phase response of each element. It can be noted that a spring response has a phase change of zero (torque and displacement are directly in-phase), the damper response is 90 degrees out-of-phase, and the inertial, at 180 deg, is directly out-of-phase. Fi
48、g. 5.1 has shown dynamic stiffness plotted on linear axes. It is often preferable, however, to plot these data with logarithmic scales for both axes, as shown in Fig. 5.2. On this scale, all three behaviorsspring, damper, and inertiashow up as straight lines. Dynamic stiffness plots like this will b
49、e employed later in the analysis of the compliant spindle system. 10-2100102-4004080Dynamic Stiffness vs Frequencyfrequency (Hz)magnitude (dBN-m/deg)SpringDamperInertiaCombinedFigure 5.2 Dynamic stiffness curves plotted on logarithmic scales (dB vs. log scale frequency) Finally, if a system is composed of all three of these basic characteristics, as in the Combined curve, then different frequency ranges can often be identified where the primary source of dynamic stiffness is just one of the elements. For instance, in Fig. 5.2 there is a frequency above which the only
