COMPUTER NUMERICAL CONTROL SIMPLIFIED EBOOK
Takes the mystery out of CNC-puts it into a logical sequence and expresses it in simple language that everyone can understand. Includes a CD-ROM with. Includes CNC Lathe and Mill programming in tests wherever appropriate. Presents 20 CNC Milling Projects (basic to intermediate) that include programming exercises suited to various stages in a CNC course. Offers 14 CNC Turning Projects (basic to intermediate) that include. Written by the authors of CNC Programming Basics: A Primer for the Skills USA/ VICA Championships, CNC Simplified covers everything from programming.
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Get this from a library! Computer Numerical Control Simplified.. [Steve Krar; Arthur Gill] -- Annotation This textbook is designed to take the mystery out of CNC by. Computer Numerical Control Simplified [Mike Fitzpatrick] on dovolena-na-lodi.info *FREE * shipping on qualifying offers. This easy-to-read numerical control text is. Computer numerical control simplified / Steve Krar, Arthur Gill, Peter Smid. Bookmark: Industrial Press eBooks. Connect to E-book on Industrial Press at .
The velocity loop is monitored by tach feedback between the servoamplifier and the servomotor. The result can be slow response times in telling the servomotor to speed up or slow down. Manolis reports response is faster and resolution finer, especially in contouring.
Heidenhain's TNC , for example, can maintain resolution of 0. When specifying a control for a new machine tool or for a retrofit, you should understand the two types of acceleration and deceleration provided by controls.
According to Griffith, high-speed and high-precision machining applications require a combination of the two. Preprocessing this data is necessary to look ahead to detect a part's comers and curvatures.
Think of turning a corner. At the transition point, you need acceleration and deceleration to smooth the comer. Older machine tools require more of this acceleration and deceleration because they really. CNCInformationSiteeBook aren't designed to accelerate at the rates required for high-speed machining. On Fanuc's Series 15 MB, most control functions, such as graphics, communications, individual axis control, and PLC functions, have their own processor.
These work in parallel with the bit main processor and communicate over a common bit bus. The reason is simple. Too many serial functions on a processor would slow it down. The bit processor is a requirement when you need block processing rates of 2 msec or faster and more precision than a bit processor can provide.
LeBlond Makino promotes use of high-speed, high power machining centers, fast controls and data communications, as well as Geometric Intelligence software, which can predict and compensate for machine dynamics on the fly.
By zeroing out the effects of axis reversals, geometric control capability on LeBlond production machines allows end users to interpolate holes with a small-diameter end mill.
They can form holes to different diameters and. User-friendly macros provided by the company allow end users to generate entire interpolation routines for holemaking, as well as threading with a special tool , from a few input parameters.
According to LeBlond engineers, interpolation can achieve higher removal rates and faster cycle times than conventional drilling.
Other benefits include the following: Interpolating the end mill also addresses the problem that speed at the center of a drill is always 0 sfm. By generating cutting action at every point on the tool, helical interpolation removes much of the cutting resistance. You may then be able to create holes in difficult work materials that conventional drills have trouble penetrating.
First, mold machining programs are often too long for the memory of the CNC, requiring an outside file server and communications processor. Second, communication speed must keep pace with the machine control. If data flow to the machine is too. CNCInformationSiteeBook slow, the control will suffer from data starvation, which will show up as dwell marks on the finished core or cavity surface.
Complex NC programs for moldmaking can require instantaneous communication rates beyond , baud. Some controls require a special interface card consisting of a large, volatile buffer memory and control logic. Executing long moves allows the system to supply data faster than required. As long as the average rate of data execution is less than the communications rate, the CNC will never starve for data. The size of the buffer determine the period over which the difference between communication input and execution output can be averaged.
The larger the buffer, the less likely the control will be starved. Starvation is more likely because of the very limited buffer between input and the point of http: For this reason, he recommends avoiding direct tape mode processing without an extended buffer when programs have a lot of short increments that must be processed at high feed rates. With simple software interfaces, Billhardt says that communications stop when a parity error is detected.
High-level DNC interfaces can request that the sender retransmit the bad packet. If the same packet has data transfer errors after several tries, the system will signal an alarm. Block search, restart, or program execution? A second control may require a special hardware option for drip-feeding in addition to providing a high-level software interface with error detection and correction. Often this isn't the case, yet these data are just as important as recommended cutting speeds and feeds in maximizing metal removal rates in high-speed machining.
With spindles providing 20, or 40, rpm, for example, chatter is a major detriment. Manufacturing Laboratories Inc. Gainesville, FL , which is conducting high-speed, high-power spindle research with Manufacturing Laboratories Inc. Gainesville, FL. Using the CRAC system, engineers start cutting at the maximum spindle speed and a stable depth of cut, then increase depth of cut incrementally until chatter occurs.
The CRAC system then commands a spindle-speed change to another stable cut, and automatically increases axial depth of cut until the cut is again unstable. The process repeats until the system can no longer find a stable cut. The metal removal rate that results for the last stable cut is often higher than that for initial cutting conditions.
Computer Numerical Control Simplified.
A test of a milling cutter machining aluminum illustrates CRAC results. The two-fluted, Tlusty reports chatter-recognition and control also can produce results in high-speed, high-power machining of cast iron. In both work materials, the search for optimum cutting conditions can be done on the work material before making the required cuts to produce a part shape.
Since cutting conditions are then optimized before part machining begins, less adverse forces act on fixturing and tooling. All rights Reserved. Control vendors can't seem to agree on the answer.
Material Properties and Cosmetics
Some believe its place is as a front-end interface for a conventional CNC. Others say the control of preference in coming years will be a PC with a CNC motion control board inside. Both groups, though, agree that most future controls will probably be one or the other. CNCInformationSiteeBook Fueling the growth of PC-based control software is a recent, major initiative by the Big 3 automakers to develop an open, modular architecture controller.
The automakers are working with control manufacturers to promote development of economical control technology that is: At this level of openness, the control will be hardware-platform independent. Along the way, though, we are targeting use of PC-based controls to provide a more open control environment--using the current PC platform and operating system standards and trying to integrate off-the-shelf components.
Controls will use PCs with the Microsoft Windows operating environment, which has become an off-the-shelf de facto standard.
Moreover, a control will be open in the sense that you can pick and choose the application components that you need. The problem is that you need a lot of engineering time to integrate all these components, which http: They may all run within the Windows environment, but that doesn't mean they will automatically interact as needed to control the process when I load the software into a system.
This frees the PC's CPU for other uses, such as tool management, programming, and statistical process control. Because of this, if the PC Windows environment were to lock up, the motion control board would shut the system down in an orderly fashion.
Mount Prospect, IL adds that PC-based CNC users no longer need worry about sacrificing servo update times for position feedback that could limit the speeds demanded by some precision machining applications. An obvious benefit of PC-based controls is their cost. Consider Wizdom Controls Inc. Prices don't include the controller board.
Controls also benefit from the rapid and inexpensive upgrading of today's PC technology. Still, the key benefit of PC-based controls is their flexibility to run a variety of user-specified software programs, in addition to providing machine control. For example, with FlexMate Inc. It also accommodates using touch probes for part inspection and location, automatic tool offsets, and SPC data collection; as well as tool changers, video cameras, coolant control, and systems for part handling or inspection.
PC-based software's customizable interface also is more user-friendly than a standard CNC. Ease of networking PC-based controls via the Novell network, another de facto standard, is a further benefit.
PC-based controls also can eliminate G-code programming, adds Bill Gibbs, president of shop-floor programming software manufacturer Gibbs Q.
Programs can be built graphically, reducing the programming learning curve dramatically. Pros and Cons Don't expect all control vendors to replace their conventional CNC technology soon, though. PC-based controls still face hurdles. For instance, while some reportedly can control up to 10 axes, applications requiring complex five-axis machining still will demand some conventional CNC technology. Moreover, most end users will probably not be running heavyduty CAM work with the PC-based control while the machine tool is cutting metal.
In addition, retrofitting the PC-based controls can take time. One retrofit of a PC-based control required four to six weeks. The end user reports three weeks of this required machine tool downtime. For companies that want PC processing flexibility, but don't want to or can't give up conventional CNC technology, several control manufacturers offer a PC front end.
Turner says this combines the functionality of the first option with a high-speed serial bus for high-speed data transfer. This contains the serial cable, and two interface cards, as well as all interface libraries and screen generation software needed. Its Sinumerik D machine tool control allows you to plug-in power as needed. For example, if you need a fifth axis, you http: NC control units include the following: Future Facts Least you attempt to downplay the impact PCs will have on machine tool control in the future, consider this.
At present, though, those wanting complex five-axis control will still see an advantage in using the control. Pieper reports the Acramatic control differs from other PC-based units because it is a dual-PC platform. One PC motherboard controls workstation functions such as shop-floor programming and database work.
The other handles real-time servo control. Upgrading will be easier and less costly than with a specialized motion control board, says Pieper. The user also pays for no more capability than needed. For example, the two PC buses are http: Pieper sees an advantage to using Microsoft Windows NT for control. Pieper reports this operating environment offers more protection against crashes.
It also assigns different priority levels to various tasks, which ensures that CNC software has priority over other application software. Windows NT also is platform independent, allowing a company to move to other hardware as needs dictate. The 's three basic components include an operator CRT, the control box, and a hand-held pendant that provides all CNC push buttons and controls required for standard operation.
The pendant eliminates the need for the operator to stretch and strain to keep one hand on the feed hold button and one eye on the machine, notes Pieper.
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Also gone are the constant back and forth motions between part and CNC during setup and programming of a job. Moreover, the pendant's LCD readout allows the operator to observe the machining cycle from almost any angle without losing access to major CNC functions. Programming also is simplified using a resident assistant programmer. This allows programming a variety of cycles without G codes. Instead, operators touch an on screen icon of the desired machining function, then enter information when prompted by the system.
The control's Gibbs shop-floor programming system, for example, has an option that allows the user to verify the part during programming. Copyright Society of Manufacturing Engineers Aug In fact, this is one of their greatest benefits. But this important benefit can lead to a problem. If you are thoroughly satisfied with the productivity of your CNC machine tools, how can you tell when they are being under-utilized?
You can contrast your judgment of machine utilization against many factors, making the judgment of machine utilization level very subjective. Don't confuse utilization with application. A machine's application is simply what you are using the machine to do. A vertical machining center that is being used as little more than a glorified drill press is every bit as important to its owner as an identical machine being used to produce threedimensional shapes in molds. Also, don't confuse machine utilization with personnel utilization.
You may think you're making the best use of your CNC machine tools when in reality, you're making better use of your CNC people. For example, you may have one person running two or more CNC machines. These are common practices, but they lead to under-utilization of CNC machine tools. As human beings, we can't stand to see anyone sitting idle, waiting for a machine to complete its task. If your goal is to keep people busy, assign them tasks that are unrelated to the operation their CNC machines are performing.
But be sure they understand that the CNC machines are the top priority. Things have been changing in the CNC environment that are making companies take a closer look at machine utilization.
Among other things, lot sizes are getting smaller, quality expectations are higher and lead time are shorter. Sticking with current methods will lead to severe problems. Fortunately, most companies have built-in potential for improvement. Again, maybe you've been so satisfied with the performance of your CNC machines that you've never questioned utilization. It's likely that at least some of your machines have been under-utilized, allowing room for improvement.
My first suggestion for judging a CNC machine's utilization level is simple: If, for example, you find that during an 8 hour shift, the machine is in cycle 7 hours not in cycle for one hour , this machine's utilization level is Acceptable machine utilization levels will vary from company to company.
A product-producing company will have higher expectations than a contract shop. Unless your company has already implemented some kind of improvement program, there probably will be room for improvement. Fortunately, improvements in this area will be relatively easy. Just come up with ways to http: It may take rethinking your company's personnel utilization teaming up on jobs as opposed to having one person do everything.
It may require better organization why does the operator have to go all the way to the tool crib to get more inserts? It may require more work in preparation, getting managers and lead people more involved with scheduling.
My second suggestion for judging CNC machine utilization level is to consider bottlenecks. Is there one machine or department that's always behind? Is there a machine or department that has an unusually high scrap rate? Is there a machine or department that has unusually high turnover? Bottlenecks of any kind are an important symptom of under utilization.
Improvements will likely be more challenging, often requiring an overhaul in processing, workholding, and cutting tools, generally re-thinking how the job is done. My last suggestion for judging CNC machine utilization level is to examine the number of mistakes especially repeated mistakes being made.
If a mistake causes scrap, the time it takes to run the scrap workpiece cannot be counted as part of the machine utilization level calculation given above. But even if mistakes don't cause scrap, it's likely that they do cause a decrease in machine utilization level.
Repeated mistakes should be a signal that you need to increase skill levels through training or decrease the skill level required to perform the mistake-causing task through task simplification. CNC maintenance training - computer numerical control - column Golden E.
Some of the training is informal, some formal covering a wide variety of technologies such as: Each of these categories of training plays an important role in the successful installation of a new machine and each imposes a different set of discipline on instructors and students.
The following focuses on just one of these categories of training CNC maintenance. The training methods used in CNC maintenance classes have changed significantly from the class conducted in the early years of NC largely due to the developments of new diagnostic tools in the controls. During the early. CNCInformationSiteeBook years of hardwired NC, built-in diagnostic tools were almost non-existent and consequently maintenance training was based on teaching the theory of operation.
In fact, control builders provided either a "Theory of operation" manual or a very thick chapter in their maintenance manual on "theory. Today's CNCs have a high level of built-in diagnostic features and as such the maintenance training classes over the years have gradually been restructured to reflect their use. The amount of theory now taught in the classroom has been scaled down to just enough to provide the student with an overall understanding of the control's operation. Consequently a significant amount of the training time is devoted to understanding and using the diagnostic tools provided in the control.
The emphasis has changed from "how it works" to "how to fix it. Classes are normally held at the control builders plant where adequate facilities and equipment for hands on experience are available, but a certain percentage of users request that the control builder bring the class to their facility.
One control builder for example indicates that forty percent of their training based on number of students trained is done at the user's plant. The advantage of on-site training is obvious in that the user can send more employees since there are no travel expenses. The disadvantage is often inadequate training facilities and equipment for lab training.
In addition the students are subject to being called out of the class to perform a routine maintenance job, breaking the continuity of the class. Even though instructors would like to see a ratio of one student per control for lab exercises, this is seldom possible.
Generally instructors target the CNC maintenance classes for eight students with enough equipment to allow two students per control. Instructors all seem to agree that a class size of 12 with three students per control are numbers that should not be exceeded. The practice of control builders differs when it comes to testing students. Some control builders require students take written exams, others do not.
Cincinnati Milacron is one company that requires student testing and issues certification only when a student meets the requirements. The instructors evaluation of the student is based on both classroom work and lab exercises. The results are sent to the students supervisor since it is felt that companies are entitled to this information so they can properly assess their maintenance resources.
But, "what is good for the student is good for the instructor. This permits the training manager to assess the effectiveness of the training programs.
In the early years of CNC the most important prerequisite for a good control technician was a sound electronic background. Today a good understanding of electronics is still important but the ability to understand the control from a system standpoint interrelationship of hardware and software may have replaced electronic background as the most important factor. With today's diagnostic tools, faults are diagnosed to the module level.
The service technicians today replace an entire plug in module rather than replacing individual components within a module. This has led to less emphasis being placed on the function of each electronic component and more on the control as a system. CNCInformationSiteeBook One problem faced by all training departments is how to get a beginner student up the learning curve so that he does not slow down the class with elementary questions or even worse, not ask questions and stay confused.
General numeric addresses this problem by providing a book on request to students titled "Introduction to NC. It has been well established that training plays a major role in the success of any new NC machine installation and as such, control builders have devoted significant resources to this segment of their operations.
However, it is the end user's responsibility to take full advantage of this service. To what degree the postprocessor can take advantage of a CNC's capabilities, and vice versa, determines the number of available programming options and degree of programming difficulty.
There isn't a comprehensive, unifying solution that marries all CNCs and postprocessors in such a way. This dedicated postprocessor speeds and simplifies programming, while taking some of the mystery out of accessing the control's high end HSM features.
It supports D control features such as: It does this by providing an intuitive dialog box to choose parameters such as exact stop, acceleration pattern, feed forward control, and data compression, and then combines these into a single cycle command.
Is manual programming really important? Mike Lynch I am often questioned about the scope of this column. The most common question is: It is important not only for short term issues and specific applications, but for the long haul in every CNC environment--from a person's first acquaintance with CNC through their attainment of expert status. For entry-level CNC programmers, course related to manual programming pro.
Features such as program zero, coordinate systems, absolute versus incremental, motion types, the various compensation types and special. CNCInformationSiteeBook programming features are best presented during a discussion of manual programming. Trying to present these features to entry-level students while they're trying to learn a CAM system will confuse them and have limited success.
Starting at CAM system level without understanding the basics of manual programming is like learning to use an electronic calculator without understanding basic arithmetic. Entry level CNC setup people and operators must eventually understand at least some manual programming techniques if they will be expected to edit programs at the machine during a program's verification.
While not all companies expect this, the more setup people or operators understand about manual programming, the better they can perform. Consider what it takes to run the first workpiece using a new program. The setup people will place the machine in single block mode and step through the program. As they do so, they must be sure that each upcoming command is correct. Regardless of whether the program is originally created manually or with a CAM system, how can they safely do this without understanding manual programming?
An understanding of manual programming is important far beyond a person's introduction to CNC.
Some of the best machine utilization enhancements reducing setup and cycle time, for example can only be accomplished with manual programming techniques. Indeed, utilization enhancements--and the manual programming techniques that allow them--have been the topic of many past CNC Tech Talk columns.
CNCInformationSiteeBook examples of techniques that are best applied with manual programming techniques. Programming method is of utmost importance when it comes to cycle time reduction.
One factor that contributes to bare minimum cycle time is how the program is formatted. While CAM systems are getting more powerful in this regard, no other programming method beats the intimacy that can be achieved with manual programming. As production quantities grow, every second of program execution time becomes more critical. Again, CAM systems have come a long way, but it can be difficult, if not impossible, to cause some CAM systems to output CNC programs as efficiently as can be done with manual programming techniques.
Manual programming is also important if you have any interest in applying parametric programming techniques. All applications for parametric programming require a firm understanding of manual programming. Admittedly, there are people who rely exclusively on their CAM system to prepare programs and have little or no understanding of manual programming. Yet they successfully create programs, machine good parts and meet production schedules. Maybe they have extremely complicated work that can only be programmed with a CAM system.
Maybe lot sizes are so low that cycle time is of little importance. Maybe there is very little repeat business, so every program must be created before the job can be run. In these cases, cycle time may not be critical.
But if you don't know manual programming, how can you be sure your CAM system is outputting programs in the most efficient manner? The first step to making any improvement is knowing what's possible. CNC export regulations - computer numerical control equipment Golden E. Herrin There are not many things in life that get more complicated than export regulations, and any company that exports CNC controls or CNC controlled machines has had to deal with the difficult issue of interpreting and applying them.
In addition to machine related issues such as accuracy which can cause a machine shipment to be restricted, there are three CNC features that will also cause the CNC to be restricted - and, when the CNC is attached to a machine, the entire package machine and control becomes restricted.
This article discusses U. What Is Restricted? There are three machine control features, or capabilities as referenced in the export regulations, that will cause a control to be restricted. All deal with path control and therefore target the more capable CNCs.
Functions restricted are: The name Wassenaar comes from the city in Holland where the final agreement was signed. In the transition from COCOM to Wassenaar, the changes took emphasis off the control hardware and redirected it to the software. The result however is still the same, any CNC having one or more of the restricted capabilities is controlled and as such is subject to export licensing depending on the receiving country.
Why Are There Restrictions? In its 46 years of existence COCOM had become grossly out-ofdate as the landscape of our allies and enemies changed. Under the Wassenaar Arrangement, Russia has become a member country and the targeted countries, which are not explicitly defined, are essentially pariah countries or "countries of concern. Iran, Iraq, Libya, and North Korea. What Technology Are We Protecting? Obtaining a U. In some cases, foreign customers have even stopped soliciting quotations from U.
Instead they have gone to foreign manufacturers where the export rules are interpreted more liberally. Why is it that the U. It appears that the U. Department of Defense DOD is the motivating agency in this matter. DOD maintains that all three CNC restrictions are valuable capabilities when it comes to making small, very accurate parts associated with manufacturing nuclear weapons. DOD has been very consistent in their position that the machines with one or more of the three restricted capabilities would be of significant value to non-friendly countries for manufacturing weapon systems that are a threat to our national security.
It is up to the industries affected by export regulations to keep the pressure on government. One of the organizations involved in providing advice to government is the Department of Commerce's Materials Processing Equipment Technical Advisory Committee MPETAC which has been working for the past few years to educate government regulators about the changes and the availability of CNC controls.
The industry representatives serving on the TAC continue to work toward achieving a more realistic set of export regulations that will level the playing field with our allies when it comes to international trade.
Based on this broad definition, there are very few people in your company that are not part of your CNC environment. The most important role of your CNC coordinator is first to identify the elements of your own CNC environment, and then to facilitate smooth interaction among the people involved. Optimum CNC machine utilization is the most basic criteria upon which any decision is based. There are three basic element types in any CNC environment.
Core elements are those easily identified people, machine tools, and accessories that form the heart of your CNC environment. People in this area include CNC programmers, operators, setup people, and instructors. They're the ones working with CNC on a daily basis. Since they are so easily identified, and since they have the largest impact on how well the CNC environment performs, most companies place a high emphasis on the core elements.
In fact, some companies concentrate so heavily on core elements that other important elements are completely overlooked. Satellite elements are those people, machinery, and accessories that affect the way CNC machine tools function, though to a less tangible degree. Yet they are still very important and, if overlooked, can have a devastating impact on the CNC environment. Among the people in this category are. CNCInformationSiteeBook design engineers, tool engineers, process engineers, quality control engineers, production control people and even the company's sales force.
Target elements are those people, machinery, and accessories that are in some way affected by what the CNC machine tools do. Some of the people in this category are assembly people and operators of machines performing secondary operations. Identifying CNC-related areas in need of improvement is actually very easy. Simply schedule a meeting and invite representatives from all three areas to attend.
You may be surprised at what the meeting renders. It is likely that you'll turn up a great deal of confusion, duplication of effort and waste. Even within one element type, you may locate problems caused by communication breakdowns. When it comes to core elements, for example, you may find that your setup people waste time searching for hand tools, cutting tools and gages needed during each setup due to poorly documented setup sheets.
You may find that your CNC operators are consistently having problems holding size due to poorly formatted CNC programs. You may find that your operators require more training in given areas. As you expand the discussion to include all three element types, you will surely turn up even more problems that can be improved. You may find that simple changes in the way design engineers dimension and tolerance workpieces will minimize the calculations required of programmers, operators and inspectors - saving time and minimizing mistakes.
You may find that your company's sales people have been unaware of your company's true capabilities and have not been offering all of the available products and services. You may find that if your production control people order workpieces in a more logical order for workpieces made of the same stock size, requiring the same tooling and run on similar machine tools , a great deal of setup time can be saved while still adhering to just-in-time principles.
CNCInformationSiteeBook You may learn that assembly people prefer that certain important tolerances be held on the high or low side in order to facilitate easy component assembly. As stated, finding areas within the CNC environment in need of improvement will be easy. However, determining the best methods for improvement and actually implementing them will be more challenging. You'll need help from the same people that helped identify problems.
In most cases, they will be the best people to make suggestions for improvement. However, you must make it clear that improving CNC machine utilization is the most important goal. In some cases, the improvements you implement will mean more or different work for the people involved. Be on the look-out for human nature-related problems like complacency we've always done it that way , pride of authorship my way is the only way and personality conflicts us versus them.
As long as your people have your company's best interest at heart, you should be able to motivate them to a high degree of cooperation. CNC data interfaces Golden E.
The many names by which CNC data interfaces are specified have been a contributing factor. Some of the more common terms are: These terms are often combined with vague definitions and written into equipment specifications.
For example, the following definitions are taken from actual specifications: A BTRI is acceptable. For example, an RS interface can include a very sophisticated protocol that provides error checking and status reporting capability, or it may not have any of these capabilities. Even though this architecture is a model for open systems interconnection OSI for LANs, it can also provide a common base of understanding for serial interfaces as well.
The seven layers consist of: When specifying a serial data interface there are three functions to be considered: The ISO seven-layer structure is used in the following description to explain these three functions: Connection--This is the most basic part of the specification. It is the way the data is to be transmitted.
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Preview Unable to display preview. Download preview PDF. References 1. SPUR, G. Machine Tool Con f. Google Scholar 2. Injection molded rubber silicone part. Instead, consider how your product will be manufactured and work backwards from there. If you have an assembly line going and have a supply chain emergency, we can cover you. If you come to us three months into your design and you need parts in a week, you might hit a roadblock and have to go back to square one.
The company has over CNC mills, more than 70 molding machines and more than 50 3D printers, so capacity is never an issue. All of our quoting is free of charge. Proto Labs has sponsored this post. It had no editorial input into this post. All opinions are mine.WorldCat is the world's largest library catalog, helping you find library materials online. We have included the programs in the book on the CD so the reader can watch them run. In order to improve the availability of interpreter, the design adopts the function pointer array and expression evaluation algorithm.
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