Machining is More Than Geometry Tony Schmitz, Professor and ORNL - PowerPoint PPT Presentation

Logo Machining is More Than Geometry Tony Schmitz, Professor and ORNL Joint Faculty University of Tennessee, Knoxville

We live in a digital world What was once blueprints and pencils is now… solid models and software applications. 2

We live in a digital world For discrete part manufacturing by machining, the digital world steps are: ▪ Design the part using computer-aided design (CAD) software ▪ Select the cutting tools that will be used to remove material from the pre-form (bar stock, forging, casting, additively CAD Tool selection manufactured near-net shape part) ▪ Generate the tool path using computer- aided manufacturing (CAM) software to produce the final design from the pre- form ▪ Remove material by following the tool path ▪ Inspect the part for conformance to Geometry CAM design specifications (geometry, surface finish, microstructure, …) 3

What can go wrong? These steps suggest that a digital world treatment is sufficient, but we live in a physical world. What can go wrong? The tool may not follow the commanded path ▪ machine tool positioning errors ▪ quasi-static – kinematics/thermal state ▪ dynamic – high-speed contouring The tool may wear out ▪ Machining is a competition between the sharp cutting edge and workpiece ▪ Higher speeds lead to higher temperature and accelerated wear ▪ Empirical – tool material/geometry, work material, coolant, parameters (sub-optimal) Vibration may be excessive ▪ The cutting force causes tool/workpiece displacement ▪ Can result in chatter, a self-excited vibration ▪ Behavior depends on setup (sub-optimal) Machine tool may fail ▪ Preventative maintenance ▪ Predictive maintenance 4

Machining is more than geometry Tap test Let’s consider CAD Tool selection vibration implications Structural dynamics Stability map Chatter Geometry CAM Stable Chatter Stable Process behavior Machining parameters 5

Machining is more than geometry Tap test Let’s consider CAD Tool selection vibration implications Structural dynamics Stability map Chatter Geometry CAM Stable Chatter Stable Process behavior Machining parameters 6

Mechanical vibrations All structures vibrate 7

Mechanical vibrations Natural frequency : vibrating frequency that is inherent to the structure X 1 X 1 Time to repeat, Δt 1 f n,1 = 1 Cantilever beam: t F ruler clamped to a Δt 1 table Motion stops after some time: damping X 2 X 2 Less time to repeat, Δt 2 f n,2 = 1 > f n,1 t Δt 2 F Shorter beam ▪ higher natural frequency ▪ smaller amplitude for same excitation; it has higher stiffness 8

Mechanical vibrations ▪ Mode shape : deformation profile while vibrating at a natural frequency Cantilever beam 1 st , 2 nd , and 3 rd mode shapes ▪ ▪ Each mode shape has an associated natural frequency f n,1 f n,2 … f n,3 Multiple natural frequencies and associated mode shapes are present in every structure. 9

Mechanical vibrations Frequency response function (FRF) X 2 ▪ contains information about natural frequency, stiffness, and damping ▪ specific to the structure and location: dynamic fingerprint X 1 F Real (X 1 /F) Real (X 2 /F) F w n f n,1 f n,2 Higher natural Lower natural w f f frequency, smaller frequency, larger w n amplitude amplitude Imag (X 2 /F) Imag (X 1 /F) f n,2 f n,1 w 10 f f

Mechanical vibrations Larger amplitude Frequency response function (FRF) ▪ with smaller stiffness can be expressed mathematically Excitation ▪ and damping complex-valued function (real and imaginary parts) frequency 2 𝑔 Real (X/F) 1 − Re 𝑌 = 1 𝑔 𝑜 𝐺 𝑔 w n 2 2 𝑙 2 f n 𝑔 𝑔 1 − + 2𝜂 𝑔 𝑔 𝑜 𝑜 Stiffness w f Damping ratio Natural frequency w n −2𝜂 𝑔 Imag (X/F) Im 𝑌 = 1 𝑔 𝑜 𝐺 𝑔 2 2 𝑙 2 𝑔 𝑔 1 − + 2𝜂 𝑔 𝑔 𝑜 𝑜 f n w f 11

Mechanical vibrations Tap test Tap test ▪ Instrumented hammer excites the structure ▪ Accelerometer measures the response ▪ Ratio is the FRF ▪ Provides the information required to predict machining performance 12

Machining dynamics Tap test Let’s consider CAD Tool selection vibration implications Structural dynamics Stability map Chatter Geometry CAM Stable Chatter Stable Process behavior Machining parameters 13

Machining dynamics Tool flexibility Cutting tools are designed to be stiff. The materials are selected to be hard and resist deformation. However, when the cutting force is applied to the tool it still deflects. You can think of a tool as a stiff spring. Workpiece flexibility Sometimes the workpiece is also flexible. In this case, the workpiece can deflect as much or more than the tool when the cutting force is applied. It can also be thought of as a spring. Damping is also important! 14

Machining dynamics Cutting force The cutting force is generated as the tool shears away material in the form of a chip. Chip thickness ▪ The cutting force depends on the chip thickness, chip width (into page), material properties, and tool geometry. ▪ Larger chip width/thickness and gives higher force. 15

Machining dynamics Why does vibration occur in milling? ▪ teeth constantly enter and exit the cut ▪ the cutting force varies with these entries and exits ▪ the variable cutting force acts on the flexible tool and/or workpiece and causes displacement ▪ this variable displacement is vibration ▪ the amplitude of vibration depends on the tool/workpiece stiffness and spindle rotating frequency y y F x t t 16

Machining dynamics There are two main types of vibration in milling. 1) Forced vibration F The variable force causes the tool or workpiece Real (X 1 /F) to vibrate at the same frequency. For a spindle w n speed of 12000 rpm and a cutter with two f n,1 t teeth, the tooth passing frequency is 12000/60*2 = 400 Hz. y w f The corresponding amplitude of vibration depends w n on the relationship between the tooth passing t frequency and the tool/workpiece dynamics. We describe the dynamics using the frequency response function , or FRF. f n,1 w f 17

Machining dynamics 2) Self-excited vibration Steady input force is modulated into vibration at the system natural frequency . x(t) Examples include: ▪ whistle - steady air flow produces acoustic vibration ▪ violin - bow across string produces vibration at frequency that depends on the string length ▪ airplane wing flutter t (sec) ▪ chatter in machining - steady excitation of teeth impacting work leads to large tool vibrations at system natural frequency Tacoma Narrows Bridge opened in July 1940, but collapsed due to aero-elastic flutter four months later. 18

Machining dynamics Why does chatter (self-excited vibration) occur in machining? Regeneration is a primary mechanism for chatter Chip thickness varies so ▪ force depends on chip thickness force varies → unstable ▪ chip thickness depends on current vibration feedback and previous pass Chip thickness is nearly constant – ▪ current vibration depends on force small force variation → stable 19

Machining dynamics Unstable Axial depth, b b Stable Spindle speed Stability map for milling ▪ separates unstable (chatter) from stable (forced vibration) zones ▪ select spindle speed and axial depth combination to obtain stable cutting conditions without trial cuts ▪ best spindle speeds depend on dynamics and probably do not correspond to handbook values. 20

Machining dynamics How can we construct a stability map for milling? Frequency Response Function (FRF) -6 x 10 1 Real (m/N) 0 -1 Signal analyzer 0 1000 2000 3000 4000 5000 6000 -6 x 10 0 Imag (m/N) -1 -2 -3 0 1000 2000 3000 4000 5000 6000 Frequency (Hz) Cutting force coefficients = F k h b Unstable Axial depth, b t t 0 F n = F k h b n n 0 F t Stable h 0 Spindle speed 21

Machining dynamics How do the two vibration types relate to the stability lobe diagram? Forced vibration y t Unstable Axial depth, b b y Stable t Spindle speed Chatter 22

Machining dynamics Tap test Let’s consider CAD Tool selection vibration implications Structural dynamics Stability map Chatter Geometry CAM Stable Chatter Stable Process behavior Machining parameters 23

Machining is more than geometry Test case description ▪ 25% radial immersion up milling (3 mm radial depth) ▪ 12 mm diameter endmill, 4 teeth, 30 deg helix ▪ 4 mm axial depth 6061-T6 aluminum ▪ 0.25 mm feed per tooth ▪ {5500, 6400, 7400} rpm spindle speed Tool path Original pocket 34 mm 40 mm 24

Machining is more than geometry Tool point dynamic response (frequency response function, FRF) ▪ 500 Hz, 8×10 6 m/N stiffness, 2% damping ▪ x (feed) and y directions assumed symmetric ▪ workpiece assumed rigid relative to tool Cutting force model: 6061-T6 aluminum 25

Machining is more than geometry Entry angle = 0 Entry angle = 0 3 mm Exit angle = 60 deg 11.2 mm ▪ FRF ▪ Force model Exit angle = 150 deg 75% radial immersion up milling 25% radial immersion up milling Chatter Chatter 5500 6400 7400 6400 5500 7400 rpm rpm rpm rpm rpm rpm Stable Stable 26

Machining is more than geometry a 5500 rpm: Unstable for 25% radial immersion, unstable for 75% radial immersion 25% radial immersion up milling 75% radial immersion up milling 27